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BACHELOR’S DEGREE FINAL THESIS

Chemical Engineering Degree

Industrial Electronics and Automation Engineering Degree

TRAINING COURSE IN SIMULATION OF CHEMICAL PROCESS

CONTROL

Master thesis

Authors: Alex Nogué, Pasquale Orlo Director: Jordi Solà, Moisès Graells Announcement: June 2020

Training Course in Simulation of Chemical Process Control Alex Nogué, Pasquale Orlo

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Abstract

The course designed in this project allows engineers to find solutions to process control issues through

the hybrid simulation approach. The control system design relies on the use of a chemical process

simulator (Aspen HYSYS), where the process dynamics is studied, and on the use of another numerical

computing software (MATLAB-SIMULINK), where to apply the system identification method obtaining

the transfer function of the process and to obtain the performance indexes of the final responses.

Different control strategies are tested using the simulator software, which allows implementing the

Internal Model Control (IMC) method to tune the controllers. Feedback, cascade and feedforward

control schemes are simulated, starting from controlling one variable (tank liquid level, temperature in

a heat exchanger), passing through an introductory multivariable process as the heated tank (liquid

level and temperature simultaneously), and ending with a binary distillation column where 5 variables

must be controlled.

The course is organized in 8 modules with a total duration of three days. It is intended for chemical and

control engineering students willing to obtain a deeper education in process control before getting to

work or for any engineer who wishes to get started with this theme. Simulation manuals, simulation

files and other documentation were designed and produced to enhance a better course experience for

both the attendee and professor.

The project viability has been confirmed through an economic analysis, which proves that the

investment for designing this course is recovered after one year. A pilot test in the Master’s degree in

Chemical Engineering – Smart Chemical Factories (EEBE-UPC) was also carried out. The results show a

great interest and satisfaction from the attendees, who showed attraction for an advanced part,

validating the course design.

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Resumen

El curso diseñado en este proyecto forma a los ingenieros para encontrar soluciones a problemas de

control de procesos mediante la simulación híbrida. El diseño del sistema de control se basa en el uso

de un simulador de procesos químicos (Aspen HYSYS), donde se estudia la dinámica del proceso,

asimismo en el uso de otro software de computación numérica (MATLAB-SIMULINK), donde se aplica

la identificación de sistemas para obtener la función de transferencia del proceso, así como los índices

de rendimiento de las respuestas. Se han examinado diferentes estrategias de control usando el

programa de simulación, el cual permite la implementación del método del Internal Model Control

(IMC) para encontrar los parámetros de los controladores. Se han simulado esquemas de control en

feedback, cascada y feedforward, empezando desde el control de una variable (nivel de líquido en un

tanque, temperatura en un intercambiador de calor), pasando a un sistema multivariable introductorio

como el tanque con serpentín (control del nivel y temperatura simultáneo), finalizando con una

columna de destilación binaria donde se deben controlar cinco variables.

El curso se ha dividido en 8 módulos con una duración total de tres días. Está enfocado a estudiantes

de ingeniería química y de control que quieran formarse en control de procesos antes de trabajar o a

cualquier ingeniero que desee empezar con esta temática. Se han elaborado manuales y ficheros de

simulación, y otra documentación para mejorar el aprendizaje del asistente al curso y como soporte al

profesor.

La viabilidad del proyecto ha sido confirmada mediante un análisis económico, el cual demuestra que

la inversión realizada para diseñar el curso se recuperaría al cabo de un año. Además, se llevó a cabo

una prueba piloto en el máster de Chemical Engineering – Smart Chemical Factories (EEBE-UPC). Los

resultados muestran un gran interés y satisfacción por parte de los estudiantes, los cuales han

mostrado su disposición a realizar una parte avanzada, validando así el diseño del curso.


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Resum

El curs dissenyat en aquest projecte forma els enginyers per trobar solucions respecte a problemes de

control de processos mitjançant la simulació híbrida. El disseny del sistema de control es basa en l’ús

d’un simulador de processos químics (Aspen HYSYS), on s’estudia la dinàmica del procés, i en l’ús d’un

altre software de computació numèrica (MATLAB-SIMULINK), on s’aplica la identificació de sistemes

per a la obtenció de la funció de transferència del process així com per als indicadors de rendiment de

les respostes. S’han testejat diferents estratègies de control utilitzant el simulador, cosa que permet la

implementació del mètode de l’Internal Model Control (IMC) per a trobar els paràmetres dels

controladors. S’han simulat esquemes de control en feedback, cascada i feedforward, començant des

del control d’una variable (el nivell de líquid en un tanc, la temperatura en un intercanviador de calor),

passant per un sistema multivariable introductori com n’és el tanc amb serpentí (control de nivell i

temperatura simultani), finalitzant amb una columna de destil·lació binària on s’han de controlar cinc

variables.

El curs s’ha dividit en 8 mòduls amb una duració total de tres dies. Està enfocat a estudiants de

enginyeria química i de control que vulguin formar-se en control de processos abans de començar a

treballar o a qualsevol enginyer que desitgi començar amb aquesta temàtica. S’han elaborat manuals

i fitxers de simulació, i altra documentació per tal de millorar l’aprenentatge del participant i com a

suport pel professor.

La viabilitat del projecte ha estat confirmada mitjançant una anàlisi econòmica, la qual demostra que

la inversió realitzada per a dissenyar el curs es recuperaria al cap d’un any. A més a més, s’ha dut a

terme una prova pilot en el màster Chemical Engineering – Smart Chemical Factories (EEBE-UPC). Els

resultats obtinguts mostren un gran interès i satisfacció per part dels estudiants, els quals van mostrar

la seva disposició en realitzar una part avançada, validant així el disseny del curs.

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Acknowledgements We would like to sincerely show our gratitude to Marc Caballero, chemical engineer and professor in Process Control at EEBE, who helped us in the dynamic modelling and the control simulation, and at the same time, embraced us with his positivity and motivation.

Alex Nogué, Pasquale Orlo

I would like to thank Marta, my love, for giving me strength and security when I needed it.

Finally, I would like to thank my parents who taught me never to give up, and my sister Elena who has always believed in me.

Pasquale Orlo

I would like to thank my parents, my sisters, my uncles and aunts and my grandparents who helped and encouraged me throughout all of the degree.

Alex Nogué

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Contents

ABSTRACT ___________________________________________________________ I

RESUMEN __________________________________________________________ II

RESUM _____________________________________________________________ III

ACKNOWLEDGEMENTS________________________________________________ V

1. INTRODUCTION _________________________________________________ 3

1.1. Objectives ................................................................................................................ 4

1.2. Project scope ........................................................................................................... 4

2. METHODOLOGY _________________________________________________ 5

2.1. Approaches to process control ................................................................................ 5

2.2. Hybrid simulation..................................................................................................... 6

2.2.1. Communication ....................................................................................................... 6

2.2.2. External use ............................................................................................................. 7

2.3. Resolution method .................................................................................................. 8

2.3.1. Identifying the process ............................................................................................ 8

2.3.2. Chemical process simulation .................................................................................. 9

2.3.3. Open loop response and process dynamic analysis ............................................. 18

2.3.4. Transfer function fitting ........................................................................................ 18

2.3.5. Variable pairing ..................................................................................................... 21

2.3.6. Selecting the control scheme and tuning the controller ...................................... 26

2.3.7. Control system test ............................................................................................... 34

3. COURSE DESIGN ________________________________________________ 36

3.1. Potential attendee and educational objectives .................................................... 36

3.2. Selected cases and course schedule ..................................................................... 37

3.3. Didactic material .................................................................................................... 40

4. CASES AND RESULTS ____________________________________________ 41

4.1. Tank liquid level ..................................................................................................... 41

4.1.1. Mathematical modelling of the atmospheric tank ............................................... 41

4.1.2. Atmospheric tank using Aspen HYSYS .................................................................. 44

4.1.3. Comparison between MATLAB and HYSYS .......................................................... 54

4.1.4. Liquid level control ................................................................................................ 56

4.2. Heat exchanger ...................................................................................................... 73


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4.2.1. Dynamic simulation of a heat exchanger ............................................................. 74

4.2.2. Disturbances and open loop responses ............................................................... 83

4.2.3. Feedback control loop .......................................................................................... 85

4.2.4. Cascade control loop ............................................................................................ 89

4.2.6. Feedforward control loop .................................................................................... 93

4.2.7. Comparison of the different control schemes ..................................................... 97

4.3. Heated tank .......................................................................................................... 101

4.3.1. Dynamic simulation of a heated tank ................................................................ 102

4.3.2. Disturbances and open loop responses ............................................................. 106

4.3.3. Multiloop control ................................................................................................ 110

4.4. Distillation column ............................................................................................... 120

4.4.1. Distillation column theory .................................................................................. 120

4.4.2. Steady state simulation of a distillation column ................................................ 123

4.4.3. Dynamic simulation of a distillation column ...................................................... 126

4.4.4. Tray Selection for Temperature Measurements ............................................... 140

4.4.5. Distillation column control ................................................................................. 142

4.4.6. Multivariable control of a distillation column .................................................... 142

4.4.7. Tuning the controllers of the distillation column .............................................. 149

4.4.8. Testing the system .............................................................................................. 152

5. ECONOMIC ANALYSIS __________________________________________ 161

5.1. Investment ........................................................................................................... 161

5.2. Variable cost ......................................................................................................... 162

5.3. Market study ........................................................................................................ 164

5.4. Project viability ..................................................................................................... 164

5.5. Pilot test ............................................................................................................... 165

CONCLUSIONS _____________________________________________________ 173

ENVIRONMENTAL IMPACT ANALYSIS __________________________________ 175

BIBLIOGRAPHY ____________________________________________________ 177


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1. Introduction

Since the 1950s, automatic control has become essential for chemical processing plants due to safety

and economic reasons. Without it, the plant should be controlled manually by many operators keeping

under observation many process variables, as it was done prior to 1940s [1]. Large tanks were used as

buffers, to mitigate the dynamic disturbance effects, increasing the equipment cost. Therefore, it is

crucial for process engineers to have the proper process control training.

When designing a plant, chemical and control engineers commonly work in the same team. In order to

design the right control system, it is required collaboration and knowledge sharing. However, this can

be a very hard task since their objectives and, above all, their vocabulary may be very different.

Therefore, this project intends to design a course that allows mixing both vocabularies and both

knowledge all in one figure. The course is based on the Svrcek’s approach to chemical process control,

which relies not only on the classical techniques but also on the use of professional process simulators

[2]. Svrcek (A real time-approach to process control, 2006, Preface) states:

For decades, the subject of control theory has been taught using transfer functions, frequency-domain

analysis, and Laplace transform mathematics. For linear systems (like those from the electromechanical

areas from which these classical control techniques emerged) this approach is well suited. As an approach

to the control of chemical processes, which are often characterized by nonlinearity and large doses of

dead time, classical control techniques have some limitations.

In today’s simulation-rich environment, the right combination of hardware and software is available to

implement a ‘hands-on’ approach to process control system design. Engineers and students alike are now

able to experiment on virtual plants that capture the important non-idealities of the real world, and readily

test even the most outlandish of control structures without resorting to non-intuitive mathematics or to

placing real plants at risk.

Thus, the basis of this text is to provide a practical, hands-on introduction to the topic of process control

by using only time-based representations of the process and the associated instrumentation and control.

We believe this book is the first to treat the topic without relying at all upon Laplace transforms and the

classical, frequency-domain techniques. For those students wishing to advance their knowledge of process

control beyond this first, introductory exposure, we highly recommend understanding, even mastering,

the classical techniques. However, as an introductory treatment of the topic, and for those chemical

engineers not wishing to specialize in process control, but rather to extract something practical and

applicable, we believe our approach hits the mark.

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1.1. Objectives

The main objective of this master thesis is to design a viable course to train engineers in the field of chemical process control. In order to achieve this goal, these are the sub-objectives to be accomplished:

Bases of the course and configuration

To determine the opportunities, such as the demand of this type of courses and the market competitiveness.

To determine the profile of the attendees. To settle the range and the scope of the course. To establish the educational objectives. To determine the tools to be used. To select and design the cases to be addressed. To state the course schedule.

Materials

To simulate the cases and provide intermediate simulations for the attendee to better follow the course.

To draft the simulation manuals. To draft additional documentation.

Market study

To carry out a pilot experiment. To perform an initial and final survey. To determine the viability of the course.

1.2. Project scope

The scope of this project consists on designing a simulation course on chemical process control, elaborating the configuration and basis of the course, including the course materials, and simulating and controlling the studied cases. Furthermore, a pilot test has to be done in order to obtain feedback from potential attendees, complete the economic analysis, and check the viability of the course.

The cases addressed in the training course, and so in this master thesis, are continuous systems where a rigorous design of the equipment was avoided to better concentrate on the dynamic study and control strategy. Most of the cases were simulated without dead-time as a mean of simplification, and because they should have been selected arbitrarily, since the process simulator does not intrinsically have time delays.


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2. Methodology

2.1. Approaches to process control

The classical approach to process control problems is by mathematically modelling the process through

the application of the laws of conservation of mass, energy and momentum [1]. As a dynamic study is

needed, the mathematical model is in the time derivatives form. When doing so, partial differential

equations or ordinary differential equations can either be used:

A partial differential equation (PDE) is an equation that describes the evolution of a physical

quantity, not only with time, but also according to other variables, such as space. They are applied

in the distributed systems, where differential operators like the gradient, divergence curl and

Laplacian are commonly used [3].

An ordinary differential equation (ODE) is an equation that contains one or more functions of an

independent variable (time) and its derivatives [4]. Two types of ODEs can be differentiated: linear

and non-linear. If the equation contains variables only to the first power it is a linear ODE,

otherwise, it is non-linear.

Most chemical engineering systems are non-linear and can have thermal or concentration gradients in

three dimensions [5]. However, when mathematically modelling the system, some simplifications can

be carried out. The hypothesis of perfect mixing in each phase eliminates the spatial gradients, turning

the system from distributed to lumped, so only time-dependent. Moreover, there are mathematical

techniques, like the Taylor series, that allows simplifying the non-linear equations to linear ODEs.

Indeed, it must be taken into account that the simplified model provides an accurate dynamic response

of the system in some region around the steady state conditions, and the size of this region depends

on the degree of non-linearity of the process [1].

Once the process has been modelled, the set of equations must be solved. One way is by direct solution

of the differential equations working in the time-domain, obtaining as a result functions of time.

Sometimes, instead, the Laplace transforms can also be used to describe the dynamics of the system,

working in the Laplace-domain. Another option is working in the frequency-domain when the system

becomes more complex and higher in order [1].

The advances in computational power allowed computer simulation to have a vital role in the

resolution of the systems of equations obtained. This requires programming the code to solve the

equations, either by numerical integration or iterative methods [1]. It could be done using any

programming language, such as FORTRAN, VBA, Python etc... However, the MATLAB-SIMULINK

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software is the most commonly used, as its interface includes different types of tools and add-ins, such

as the Partial Differential Equation Toolbox, that can help in the modelling of the process.

Furthermore, there are professional chemical process simulators, such as Aspen HYSYS, Aspen PLUS,

ChemCAD, gPROMS, ProSim and many others, which can be very time-saving since they already include

the libraries for each process unit and chemical and thermodynamics properties. In particular, the

dynamic simulation aided by these software provides a deeper understanding of the process, which

helps in the control system design. In addition, they also include controller modules through which is

possible to test different control strategies with no effects on the real plants, making the control design

safer.

The combination of a chemical process simulator with another software can lead to a satisfactory

control design. This is the so called hybrid simulation, and it is the chosen method for this project. The

tools required have been decided to be Aspen HYSYS, since it is one of the most used process

simulators software and many literature can be found about it, and MATLAB, since it has additional

toolboxes and add-ins, such as the system identification toolbox and SIMULINK, which can assist the

user in the control design process.

2.2. Hybrid simulation

The hybrid simulation takes into account two software, MATLAB and HYSYS in this case, in order to

favour the strengths of both and solve a process control problem. Some examples can be [6], [7]. The

implementation of this type of simulation can be done in two main ways: by means of communication

and external use.

2.2.1. Communication

The first approach consists on considering Aspen HYSYS as the chemical plant and MATLAB as the

control station. In this case, while HYSYS simulates the process through all the core mathematical

relations, MATLAB allows for a lot of flexibility in order to choose the type of controller that is desired.

This could also provide helpful insight on what a field test looks like where control operators are

trained. Nowadays, there are two main options in order to communicate both software. These are the

DCS and the ActiveX servers.

With the communication via DCS (Distributed Control System), both Drivers are DDE Clients that

initiate communications with DDE Servers. The DCS option in HYSYS is admitted for EXCEL and MATLAB,

allowing to build multiple controllers and export different types of variables and arrays to the selected

program.


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Figure 2.1. First Hybrid approach considered.

About the ActiveX communication, the commands are used in the MATLAB command window or

scripts, which allows controlling almost every parameter from the HYSYS simulation. In order to

transfer the values, HYSYS’ spreadsheets are used. MATLAB connects to the spreadsheet cell where

the value is stored, being able to obtain it and modify it. For the communication of both software,

special libraries already created were used [8].

In this project, the chosen communication method to test is ActiveX. This is mainly due to the DCS

protocol being not compatible with the latest versions of MATLAB, so in case it was to be used, the

MATLAB version would have to be downgraded to a much older version with less capabilities, which

would restrict the MATLAB part.

The run tests with the ActiveX communication protocol proved successful, as variables could be

exchanged between both MATLAB and HYSYS. Furthermore, the controller built in MATLAB proved to

work well enough with the HYSYS simulation. However, due to Covid-19 outbreak, the communication

tests had to be stopped as the communication could only be made with both software on local. The

documentation about the ActiveX communication can be found in Annex C7.

2.2.2. External use

The second approach, and the one that was finally used, consists on using HYSYS for both the plant and

controller, even though, when it comes to the process control and the final tests, MATLAB-SIMULINK

is used.

In this case, MATLAB is used to perform the system identification of the process and to check that the

transfer function obtained provides a good fitting. It is also used when it comes to comparing different

tuning parameters as well as to calculate the performance criteria values.

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Figure 2.2. Second hybrid approach considered.

2.3. Resolution method

In order to define a pattern to solve the process control cases, there are a few steps that need to be

followed. These are:

1. Identifying the basics of the process.

2. Simulating the process.

3. Obtaining the open loop response and make a process dynamics analysis.

4. Transfer function fitting.

5. Variable pairing.

6. Selecting the control scheme and tuning the controller.

7. Testing the control system.

2.3.1. Identifying the process

When facing a process control problem, there is a need to determine if the system is a SISO (single

input, single output) or a MIMO (multiple input, multiple output). This is essential in order to define

the process variables and the manipulated variables of the system. From a control and chemical stand

point, MIMO systems are much more complex than SISO systems because they include process

interactions that can occasionally make the system unstable.


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Figure 2.3. SISO and MIMO system block diagram.

Once the system has been defined, the next step is to identify the variables of interest (the process

variables and the manipulated variables) and to define the principal disturbances that can affect the

system. Depending on the nature of the disturbance and the place of the system where the

disturbances affect, different control schemes could prove to be more effective than others on

rejecting them. The decision about which alternative suits the problem best is better provided by

dynamic simulation.

2.3.2. Chemical process simulation

Process simulators software have become a fundamental tool for the process engineer since they save

a lot of time in the design calculations [9] and manpower or money avoiding the physical testing of the

design idea [10]. In addition, modern versions of such software provide a very interactive experience

and intuitive environment by the modular approach simulation.

When modelling a process with a professional process simulator, there are two main types of

simulations: steady state simulation and dynamic simulation. The steady state simulation is very useful

to solve material and energy balances, obtain a first flowsheet design, and evaluate different options

for the same process. This allows a first optimization of the process through an objective function that

reduces waste and maximize production and thus benefits [5]. Nevertheless, the steady state is an

ideal situation that real plants try to reach and keep. A sudden change in feed, a failure in the supply

stream, malfunction of a valve or even a change in environmental conditions are some of the possible

causes of disturbances that can be induced in the process. Such disturbances will move some process

variables from their steady state value. In addition, start-up and shut-down can be very frequent

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operations. When in some of these scenarios, there is no steady state and knowledge on the transient

behaviour of the system is essential to carry out the operations in a safe and controlled way. Therefore,

dynamic simulation is also needed to perform a correct design of the process.

The difference between steady state and dynamic simulation is that the second one is time-based,

which gives a more realistic level to the simulation. Therefore, dynamic simulation enhances a better

study of the transient behaviour of the process and the effect of each disturbance. This can lead not

only to a deeper understanding of the system but also further applications than steady state

simulation. For instance, dynamic simulation is used to design the control system and test it before

even building the plant. In this field, operator training finds a good opportunity, avoiding inducing any

disturbance in the real plant. In fact, there are several OTS (operator training simulators) courses

focused on preparing the control operators for different possible plant scenarios using a dynamic

simulation [11]. Furthermore, a safety evaluation is possible by making the HAZOP analysis more

accurate [9]. Finally, it can be used to perform a more detailed optimization of the process, including

the control scheme.

In this project, the steady state simulation has been generally used to create the flowsheet and size all

the equipment, but it has been then converted to dynamics mode where the controller has been

tested. You can easily switch from steady state to dynamics mode, after making the appropriate

modifications. The Dynamic Assistant tool helps in this task providing suggestions to adapt the model

to the dynamic mode [5].

Before running a dynamic simulation in Aspen HYSYS, some dynamic features must be revised:

Pressure Flow Solver: in real life there is no flow if there is no pressure difference. In steady state

mode this relation is not taken into account, while in dynamic mode a pressure drop through the

units is necessary to have a flow. This also means that if the pressure in the output gets higher

than the input pressure, the flow is reversed. That’s why the process happens to be pressure-

driven and not flow-driven. Pressure specifications are needed to solve the balances and

hydrostatic pressure is well simulated by properly modifying the height of each equipment [5].

Resistance Equations: valves turn to be essential to provide a pressure drop through which

regulate the flow of the process streams. The flow across a valve is calculated through a resistance

equation which has the following general form:

𝐹𝑙𝑜𝑤 = 𝑘 · √∆𝑃 (Eq. 2.1)


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Others equipment can also be modelled with the Eq. 2.1, such as the Heat Exchangers or even

each stage of a distillation column [5]. The effect and role of the k parameter will be explained in

further chapter.

Hold-up: if there is no steady state, and variables depend on time, the term of accumulation of

the balance equations turns different from zero. Information about the retained material in the

equipment is given, such as composition, temperature and rate of change. That’s why a proper

sizing of each equipment in the simulation is needed. For example, specifying the volume of a tank

is essential yet it determines the capacitance of the equipment (Volume balance equations [5]).

Capacitance: Svrcek et al. define capacitance as “the system’s ability to absorb or store mass or

energy”. They also define it as “the resistance of a system to the change of mass or energy stored

in it, i.e. inertia” [2]. This means that if there is a disturbance, a new steady state will not be

reached instantaneously, being slower as much as there is more capacitance. A big capacitance

can be a choice to improve the control strategy. Some tanks, called surge tanks, due to the volume

they hold, are sometimes used to smooth a flow disturbance coming from the previous operation,

as a kind of protection for the next one.

Dead-time: it is the delay time since a disturbance is induced in the system until the process

variable gets affected. Unlike capacitance, dead-time can be very bad for the process control,

since the disturbance is detected later and the controller will act with delay too. Anyway, the

impact of this delay depends on the relation between dead-time and process time. If dead-time

is quite smaller than the process time it won’t be difficult to control the process, but if it is similar

or even bigger than the process time, then the system can become unstable. An example could

be the flow through a long pipe. It will take some time for the material to move from the beginning

to the end of the pipe, depending on its velocity. If there is any disturbance at the beginning of

the pipe, it will arrive at the end with some delay [12]. Generally, dead-time can be minimized

with large capacitance in the process [2].

Aspen HYSYS uses the Implicit Euler method to solve both linear and non-linear ODEs, and does not

take into account PDEs [5]. The resolution method approximates the exact areas obtained through the

integrals to rectangular areas:

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Figure 2.4. Implicit Euler method [5].

This is an implicit method because information is required at time tn+1.

Furthermore, to reduce computational demand, Aspen HYSYS solves volume (pressure-flow), energy

and composition calculations at different frequencies [5]. However, if the system is unstable or more

precision is required, the integration step and the execution rates of the calculations can be adjusted

in the integrator tab.

When simulating, the speed can also be regulated by the Desired RealTime Factor. For example, if the

Desired RealTime Factor is set to 200, the simulation occurs 200 times faster than reality (it takes 1 min

to simulate 200 real minutes). In the same way, if it is set to 1, the simulation will occur at real time.

2.3.2.1. Control Valves

Valves are mechanical devices used to regulate flow and pressure within a process and are the most

common final control element in a control system [2].

The presence of a valve in a pipeline represents an obstacle that modifies the flow configuration,

causing turbulences and energy loss, from kinetic to friction and noise. This translates into pressure

loss between the input and output of the valve [14], [15]. Figure 2.5 shows how the stem of the valve

reduces the pass area and the vena contracta when the control valve is approximated to an orifice.

Figure 2.5. Control valve and vena contracta [16].


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The pressure drop depends on the parameters of flow and the geometry of the valve (type, size,

manufacturer, opening). That’s why losses are known from experimental measurements. Generally,

losses are given as a quotient between the pressure drop through the element or static height (hm) and

the kinetic height of the pipeline (hL):

ℎ = ∆𝑝

𝜌𝑔 (Eq. 2.2)

ℎ = 𝑉

2𝑔

(Eq. 2.3)

𝐾 = ℎ

ℎ=

2∆𝑝

𝜌𝑉 (Eq. 2.4)

Where K is the dimensionless coefficient of losses [17].

Table 2.1. Coefficients of losses K for open valves, elbows and tee [17].

In most valves the friction losses are minimum respect to losses due to changes in direction of the flow,

so the coefficient K can be considered independent of the Reynolds number. However, it still depends

on the opening of the valve, as Figure 2.6 shows. When the valve is wide open, the minimum losses

are observed. They increase when the opening is reduced.

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Figure 2.6. Coefficient of losses for different types of valve and openings [17].

As the pressure drop increases, the flow increases too but not linearly. To describe this dependence,

the flow factor Cv is used in the following equation, which derives from Bernoulli’s equation [2]:

𝑄 = 𝐶∆𝑃

𝑆𝐺

(Eq. 2.5)

Where:

Q = volumetric flow rate

ΔP = pressure drop across the valve

SG = relative density compared with water at 60 F and 14.7 psia [18]

So the Cv factor relates the capacity of the valve and the valve flow characteristics. It depends on the

type and geometry of valve, and so, as the coefficient of losses K, it is determined experimentally.

Generally, it can be defined as the number of US gallons of water at 60 F (15.5 ºC) that flow through a

control valve in 1 minute, when the pressure differential across the valve is 1 psi [2], [14], [15].

It is important not to confuse the Cv factor with the coefficient of losses K. The first has units of

gpm/√psi, while the second is dimensionless and relates the pressure drop in meters of water column

with the velocity of the fluid according to equation 2.4. In fact, by changing units, it can be derived a

formula that relates Cv and K [18]:

𝐶 = 29.84 ·𝑑

√𝐾

(Eq. 2.6)


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There is an equivalent to metric units named Kv, obtained as [14]:

𝐶 = 0.15 · 𝐾 𝑚

ℎ𝑏𝑎𝑟

(Eq. 2.7)

Due to the high value of the Reynolds number inside a valve, the dependence of Cv on it cannot be

appreciated. The value of Cv is a function of the valve opening. The curve giving the variation of Cv with

valve opening at high Reynolds number and at constant pressure drop is named the inherent

characteristic of the valve. The maximum value of Cv occurs when the valve is wide open and depends

on the design and size of the valve, as said before [2]. In Figure 2.7 are shown three common examples

of inherent valve characteristics: quick opening, linear and equal percentage. The Cv is represented as

percentage of the maximum flow because like this it will apply to a set of geometrically similar valves,

independent of size.

Figure 2.7. Inherent valve characteristic curves [2].

However, the pressure drop across the valve is not constant (when closing the valve it will increase),

and the variation of Cv will not follow the inherent characteristic (given by the manufacturer) but the

operating characteristic. Equal percentage will deform to a curve closest to the linear one, and the

linear to the quick opening [14].

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Figure 2.7 shows the differences between the three inherent characteristics, but to better appreciate

them, a gain plot versus the percentage of lift of the valve is shown:

Figure 2.8. Gain curves for the three inherent valve characteristic [2].

Comparing the slope of these curves, it can be seen how fast the Cv changes for a very small lift change

for the quick opening type, while this change decreases rapidly at opening less than 50%. The linear

has slope 0 and the variation of Cv with lift is constant, while for the equal percentage an exponential

behaviour can be observed. The Cv increases relatively slow at low lift, but increases relatively high at

higher lift.

Choosing the type of control valve depends on the specific process, but normally the following

indications can be applied [19]:

Linear: Liquid level and flow control

Equal Percentage: Temperature [20] and Pressure control

Quick opening: Pressure-relief applications

2.3.2.2. Valves in HYSYS

Sizing the valve [13] is a fundamental step to properly design the process and very important for the

control purpose. Aspen HYSYS allows sizing the valve in three different ways:

ANSI/ISA: It uses the industry-standard ANSI/ISA S75.01, considered the state-of-the-art in

valve sizing.

Manufacturer specific methods: It is possible to select a manufacturer specific method from

the Valve Vapor Flow Models list. It includes, for example, the Masoneilan, Introl, Valtek, Fisher


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methods etc… and some of these models give the possibility to choose a specific type of valve

(globe, control ball, split body, butterfly etc…)

Simple resistance equation: It uses an equation very similar to Eq. 2.1 treating the flow as

always being proportional to the square root of the pressure drop. It is not possible to select

any inherent characteristic.

The main difference between the three sizing methods are the constants and equations that model

the valve. Details about these equations and parameters can be found in the Valve section of the Aspen

HYSYS Help.

Since a detailed design of the equipment is out of scope, the sizing method used in this work is the

ANSI/ISA yet it can be applied for any valve types, style and trim once the three parameters required

are specified (Xt, FI, Fp). In all the studied cases the default values for each one of these parameters

have been used. For this method, the Cv or Cg value, depending if the stream is in the liquid or vapour

phase, must be set or can be even auto-calculated by the process simulator. The value specified or

obtained is the maximum possible conductance value, and it will decrease depending on the pressure

drop and valve opening according to the inherent characteristic chosen.

When a valve is used as an OP (controller output), another component must be considered: the

actuator. It is a device that causes the valve to move when a signal from the controller is received.

Since both valve and actuator are physical elements, it will take time to move to their specified

positions. However, Aspen HYSYS lets you decide between four actuator modes:

Instantaneous Mode: the change in the position of the actuator occurs instantaneously.

First Order Mode: The lag is modelled as a first order behaviour specifying the actuator time

constant, τ, in the following differential equation:

𝜏𝑑(𝐴𝑐𝑡%)

𝑑𝑡+ 𝐴𝑐𝑡% = 𝐴𝑐𝑡 % (Eq. 2.8)

Second Order Mode: The lag is modelled as a second order behaviour.

Linear Mode: The movement of the actuator occurs at constant rate. The Actuator Linear

Rate parameter must be specified to solve the following equation:

𝐴𝑐𝑡% = (𝐴𝑐𝑡. 𝐿𝑖𝑛𝑒𝑎𝑟 𝑅𝑎𝑡𝑒)∆𝑡 + 𝐴𝑐𝑡 % 𝑢𝑛𝑡𝑖𝑙 𝐴𝑐𝑡 = 𝐴𝑐𝑡 % (Eq. 2.9)

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Furthermore, it is possible to model the valve delay by specifying the time constant τsticky in the

following equation that relates it to the actuator position:

𝜏𝑑(𝑉𝑎𝑙𝑣𝑒%)

𝑑𝑡+ 𝑉𝑎𝑙𝑣𝑒% = 𝐴𝑐𝑡% + 𝑂𝑓𝑓𝑠𝑒𝑡 (Eq. 2.10)

The offset must be also specified.

However, as a mean of simplification, in this project the majority of the control valves have been

simulated with an instantaneous actuator and with no delay on the valve response. The details about

each control valve can be found in each case chapter.

2.3.3. Open loop response and process dynamic analysis

Once the dynamic simulation is ready, different disturbances can be simulated in order to study the

dynamic behaviour of the process. This can aid a better understanding of the relation between the

process variables.

When knowledge on the process has been acquired, it is time to start the control simulations. In order

to do so, the first thing needed is to place a controller and select the manual mode in the HYSYS

flowsheet case. Once the connections have been configured, a step input must be applied in the

controller output. This will provide the open loop transfer function of the plant and the control valve

of the system. This function will later be used to find the control parameters.

Note that this would be the same as obtaining both valve and plant open loop responses separately: if

a step was applied in the controller output and the mass flow of the stream was measured, then the

open loop response of the valve would be obtained; if a step was applied in the stream that is used to

control the process variable and the process variable itself was measured, then the transfer function

of the plant would be obtained.

Once the response has been obtained, it is exported to MATLAB. The export method used is via .csv

spreadsheet, explained in the Exporting Data appendix.

2.3.4. Transfer function fitting

The next step is to obtain the transfer function of the system. In order to do so, the open loop response

obtained via HYSYS is plotted in MATLAB and approximated to a certain model. This can be done

following two different approaches: using the System Identification Toolbox in MATLAB or doing it

manually with many different existent methods. The chosen method is to do it manually, as for the

course it is expected that the attendees do not know the basics of system identification. In addition,

the results obtained have been checked by using SIMULINK. Indeed, the System Identification Toolbox


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would probably be the preferred method in an advanced course, as it is able to obtain models of

dynamic systems not easily modelled from first principles or specifications.

The three methods used in this project are fittings for first [21] and second order systems as well as an

approximation for higher order systems. Note that the result of this process is a function in the Laplace

Domain.

One of the most basic responses that can be obtained after a step input is applied is a first order system,

in which the function obtained resembles Figure 2.9. This type of function has the form shown in Eq.

2.11.

𝐺(𝑠) = 𝐾

𝜏𝑠 + 1 (Eq. 2.11)

In order to calculate the parameters for this transfer function, the first thing to do is to calculate the

gain. The gain of the system is going to be the final value of the process variable minus its initial value

divided by the step input applied.

𝐾 = 𝑌 − 𝑌

𝑈 − 𝑈 (Eq. 2.12)

Finally, in order to obtain the time constant, it will be estimated as the time where the process variable

reaches the 63.2% of its final value. This value corresponds to point A in Figure 2.9.

𝑌(𝜏) = 𝑌 − 𝑌 · 0.632 + 𝑌 (Eq. 2.13)

Figure 2.9. First order transfer function and its characteristics [22] .

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Another type of fairly common response in chemical processes is the second order:

𝐺(𝑠) = 𝐾

(𝜏 𝑠 + 1)(𝜏 𝑠 + 1) (Eq. 2.14)

According to [21] the use of Eq. 2.14 as a transfer function does not cover all the possible second order

behaviour. The two limiting cases are τ2/τ1=0 where the system becomes critically damped and τ1/τ2=1,

where the system becomes a first order model.

For second order transfer functions that include time delays or that are underdamped, the transfer

function that should be used is the following:

𝐺(𝑠) = 𝐾 𝑒

𝜏 𝑠 + 2𝜉𝜏𝑠 + 1

(Eq. 2.15)

The technique used to obtain the unknowns of Eq. 2.15 is called the Smith’s method [21] and it requires

the times at which the normalized response reaches the 20% and the 60% of its value. With these time

parameters, then the t20/t60 ratio is calculated. With the ratio, the parameters of τ and ξ can be obtained

from the Smith’s plot, shown in Figure 2.10.

Figure 2.10. Smith’s method plot [23].

Nevertheless, in some occasions, fitting a second order or higher order responses into a first order plus

time delay could prove useful. If this was the case, Skogestad’s half rule can be used [23], [24]. To apply

this rule, the transfer function must fulfil two requirements:

1. It has to be overdamped.

2. The largest time constant has to be 1.5 times larger than the second largest one.


21

If this was the case, the function can be approximated into a first order plus time delay (FOPDT) transfer

function, as shown in Eq. 2.16.

𝐺(𝑠) = 𝐾 𝑒

𝜏𝑠 + 1

(Eq. 2.16)

An example could be done considering the transfer function shown in Eq. 2.17.

𝐺(𝑠) = 𝐾

(𝜏 𝑠 + 1)(𝜏 𝑠 + 1)(𝜏 𝑠 + 1) (Eq. 2.17)

With 𝜏 > 𝜏 > 𝜏 in order to fit it into a FOPTD, the time constant of the resulting function is going to

be the largest time constant plus half of the second largest one.

𝜏 = 𝜏 + 𝜏

2 (Eq. 2.18)

And the time delay is going to be half of the second largest one plus all the other time constants

remaining in the transfer function.

𝛳 = 𝜏

2+ 𝜏 (Eq. 2.19)

All the results provided by the system identification method can be found in Appendix B.

2.3.5. Variable pairing

This step is only made in those cases where there are multiple process variables and multiple

manipulated variables, the MIMO systems. So, the cases where variable pairing is needed are cases 3

and 4, the Heated Tank and the Distillation Column.

In MIMO systems, there are 2 or more variables that need to be controlled, and to achieve this task

the same number of manipulated variables has to be selected for the control. Moreover, it is essential

to select the right configuration for each system as a wrong pairing could potentially turn the process

unstable because of the interactions between the process variables.

To illustrate the methods, the assumption that the system has two process variables and two

manipulated variables is made. In that case, the control strategy would be to pair each manipulated

variable with one process variable using a feedback controller [21].

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Figure 2.11. Heated tank MIMO system.

In the process shown in Figure 2.11, there are two control variables and two process variables, making

it a 2x2 system, where four transfer functions can be found.

𝐺 (𝑠) = 𝑌 (𝑠)

𝑈 (𝑠)

(Eq. 2.20)

𝐺 (𝑠) = 𝑌 (𝑠)

𝑈 (𝑠)

(Eq. 2.21)

𝐺 (𝑠) = 𝑌 (𝑠)

𝑈 (𝑠)

(Eq. 2.22)

𝐺 (𝑠) = 𝑌 (𝑠)

𝑈 (𝑠)

(Eq. 2.23)

The last four transfer functions can be rewritten in terms of the output values, as shown in Eq. 2.24

and Eq. 2.25.

𝑌 (𝑠) = 𝐺 (𝑠)𝑈 (𝑠) + 𝐺 (𝑠)𝑈 (𝑠) (Eq. 2.24)

𝑌 (𝑠) = 𝐺 (𝑠)𝑈 (𝑠) + 𝐺 (𝑠)𝑈 (𝑠) (Eq. 2.25)

If two feedback loops are used to control both multiple variables, there are two possible process

configurations: a scenario where y1 is controlled by u1 and y2 is controlled by u2, but there is another

possible scenario where y1 is controlled by u2 and y2 is controlled by u1. The first configuration is called

1-1, 2-2, while the second is called 1-2, 2-1 [21].


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Figure 2.12. Block diagram for the u1-y1, u2-y2 systems.

Figure 2.13. Block diagram for the u1-y2, u2-y1 systems.

For instance, considering 1-1, 2-2 schemes, if there was an error in one of the two controllers caused

by a set-point change in Ysp1, the controller Gc1 would adapt to that set-point change and force Y1 to

reach that value. Meanwhile, Y2 would also change due to the process interactions, and then the

controller Gc2 would have to adjust Y2 to bring it to its set-point Ysp2, but that would also affect Y1. This

process would go on until a steady-state between the two variables is reached.

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In order to pair the controlled variables and the manipulated variables the Relative Gain Array (RGA)

Method will be discussed [21], [25]. Bristol’s RGA Method calculates the relative gain λij, which can be

defined as the division between open-loop and the closed loop gain, intending the open-loop gain as

the one obtained when no interactions between the input variables is considered:

𝜆 =

𝜕𝑦𝜕𝑢

𝜕𝑦𝜕𝑢

(Eq. 2.26)

Here is the gain between the input i and the output j when all the other inputs are held constant,

and is the gain between input i and output j when all the other outputs are held constant. If the

relative gain for every input and every output is calculated, then the RGA can be constructed.

𝛬 =

𝑦𝑦⋯𝑦

𝜆 𝜆 ⋯ 𝜆𝜆 𝜆 ⋯ 𝜆⋯ ⋯ ⋯ ⋯

𝜆 𝜆 ⋯ 𝜆

(Eq. 2.27)

The relative gains can be calculated from the steady-state data of the system or from simulated process

model. For a 2x2 systems, linearizing the model provides the following equations [21]:

𝑦 = 𝐾 𝑢 + 𝐾 𝑢 (Eq. 2.28)

𝑦 = 𝐾 𝑢 + 𝐾 𝑢 (Eq. 2.29)

In order to calculate the open-loop gain, the u2 is set to zero, so the gain equals K11 .

𝜕𝑦

𝜕𝑢= 𝐾 (Eq. 2.30)

About the closed loop gain, the first thing to do is to obtain the equation of u2 when y2 equals to zero.

𝑢 = − 𝐾

𝐾𝑢 (Eq. 2.31)

If then it is substituted in equation 2.28, the following closed-form is achieved.

𝑦 = 𝐾 −𝐾 𝐾

𝐾 𝑢

(Eq. 2.32)


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If now equation 2.32 is substituted into equation 2.26, where the open loop gain is divided by the

closed loop gain, the relations obtained for parameter λ are shown in Eq. 2.33 [25].

𝜆 = 1

1 −𝐾 𝐾𝐾 𝐾

(Eq. 2.33)

The RGA has some important properties for steady state models [21], which are:

1. The matrix is normalized and the sum of the columns and rows equals to one. 2. The relative gains are dimensionless.

Taking into account these properties, the RGA can be constructed by values that are a function of λ11.

𝛬 = 𝜆 1 − 𝜆

1 − 𝜆 𝜆 (Eq. 2.34)

In order to obtain the steady-state gains, it can be done with the HYSYS process model. For example,

to calculate the output gain for one variable, the input can be changed in a stepwise form while all the

other inputs are held constant.

There are five different scenarios depending on the value of λ [21]:

1. λ=1. It means that closing the loop 2 has no influence in loop 1. In this situation, y1 should be paired with u1 and y2 with u2.

2. λ=0. In this case, it is the opposite of the first one, and means that closing loop 2 has no influence in loop 2. Therefore, y1 will be paired with u2 and y2 will be paired with u1.

3. 0 < λ < 1. In this case, there is interaction between both loops, and depending on the degree of interaction one situation or the other will be chosen.

4. λ>1. For this case, closing the second loop reduces the gain between y1 and u1, meaning that both loops interact. This interaction is greater when λ is closer to infinite.

5. λ<0. When the value is negative, closing the second loop has an adverse effect in loop 1.

The conclusion is that y1 should be paired with u1 if λ >= 0.5. Otherwise, it should be paired with u2.

According to [21], the disadvantage of the RGA analysis is that dynamic considerations are not taken

into account. This is especially problematic when there is a process function with time delay or with a

very large time constant, and in some cases, if there is a really slow response of y1 to a change in u1, an

y1-u2 pairing might be more desirable.

The Singular Value Analysis (SVA) method [21], [26] is another technique that helps with the selection

of the variables, evaluates the robustness of the control strategy and determines the best multiloop

control configuration ([21], [26]).

In this project, the singular value analysis will be done with the steady-state gains. In order to do so,

the steady-state gain matrix (Eq. 2.35) is needed. It is desirable that the vectors of this matrix are

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linearly independent, which means that the determinant of the matrix cannot be null. The parameters

that need to be obtained are the singular values, obtained by calculating α’, and obtaining its roots.

𝐾 =

𝐾 𝐾 ⋯ 𝐾𝐾 𝐾 ⋯ 𝐾⋯ ⋯ ⋯ ⋯

𝐾 𝐾 ⋯ 𝐾

(Eq. 2.35)

|𝐾 𝐾 − 𝛼′𝐼| = 0 (Eq. 2.36)

𝜎 = 𝛼 ; 𝜎 = 𝛼 (Eq. 2.37)

With the eigenvalues, the final value that needs to be calculated is the condition number (CN):

𝐶𝑁 =𝜎

𝜎 (Eq. 2.38)

Where the condition number is calculated by dividing the largest and the smallest singular values. If

the CN value is large, it will indicate poor conditioning, as it will mean that the large manipulated

variable will have CN times more effect on the system than the other one. The SVA is really helpful for

some cases where the RGA doesn’t indicate the poor conditioning of the system [21].

Another tool to analyse the stability of control loop pairings is the Niederlinski index [2]. This method

is used to prove that a 2x2 matrix is stable, even though, if the matrix is larger than a 2x2, it can only

be used to determine that the control loop is definitely not stable. If the NI is negative the system will

be unstable.

𝑁𝐼 = |𝐾|

∏ 𝑘

(Eq. 2.39)

2.3.6. Selecting the control scheme and tuning the controller

The process can be controlled using different control strategies. The control schemes used in this

project are feedback, cascade and feedforward control (this last explained in chapter 4.2.6). Each

scheme provides a different response and a comparison allows picking the best one. The tuning

method depends on the control scheme and on the type of system. For example, different tuning

strategies are applied for a SISO or a MIMO system.

2.3.6.1. Feedback control

Nowadays, there are multiple control loops that can be used, but the most common and the most used

one is the feedback control. In a feedback control loop, the controller compares the measured variable


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to the set point and takes the corrective action by calculating the controller output and transmitting

the signal to the control valve. There are many feedback controllers, and some examples are P, PI, PD

or PID. P (proportional), I (integral) and D (derivative) are the corrective actions that modify the error

to produce the controller output.

About the proportional action, the controller gain can be adjusted in order to make the changes more

or less aggressive, and the sign of the proportional gain can be adjusted to make the controller output

increase or decrease as the error signal increases. In P controllers there needs to be a bias value,

because when the controller output equals the desired value, the error is zero, thus making the

controller output also zero [27]. In this kind of controllers, the controller output is proportional to the

error signal:

𝑜𝑝(𝑡) = 𝑏𝑖𝑎𝑠 + 𝐾 · 𝑒(𝑡) (Eq. 2.40)

The main drawback of proportional-only controllers is that an offset occurs after a setpoint change or

a disturbance, meaning that it will not reach the desired value.

Integral action provides the elimination of the offset, thus achieving to make the error value equal to

zero. When integral action is used, the output of the controller changes until it attains the value

required to make the steady-state error zero.

𝑜𝑝(𝑡) = 𝑏𝑖𝑎𝑠 + 1

𝜏𝑒(𝑡)𝑑𝑡

(Eq. 2.41)

The basic function of the derivative action is to anticipate the future behaviour of the error signal. In

other words, the derivative action seeks to not allow rapid movements of the process variable.

𝑜𝑝(𝑡) = 𝑏𝑖𝑎𝑠 + 𝜏𝑑𝑒(𝑡)

𝑑𝑡

(Eq. 2.42)

From the derivative action equation, it can be seen that the value of the output is equal to the bias as

long as the error is constant, which is the main reason why the derivative action is never used alone.

The PID is the combination of the three corrective actions, and it is one of the most used controllers

nowadays. The most common form of PID is the following, which is called the parallel form. The PID

controller continuously calculates the error value and applies a correction action based on the three

tuning parameters.

𝑜𝑝(𝑡) = 𝑏𝑖𝑎𝑠 + 𝐾 𝑒(𝑡) + 1

𝜏𝑒(𝑡)𝑑𝑡 + 𝜏

𝑑𝑒(𝑡)

𝑑𝑡

(Eq. 2.43)

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Even though the parallel PID is among the most common forms, there are other digital versions of the

PID. These two alternatives are the position and velocity form [21]. What these two forms do is to

replace the integral and derivative terms by finite difference approximations.

𝑜𝑝 = 𝑜𝑝 + 𝐾 𝑒 + 𝛥𝑡

𝜏𝑒 +

𝜏

𝛥𝑡 (𝑒 − 𝑒 )

(Eq. 2.44)

Where:

Δt is the sampling period or the time between two measurements.

ek is the error at the sampling instant k.

In the velocity form, the result of the equation is the change of the controller output:

𝑜𝑝 = 𝑜𝑝 + 𝐾 𝑒 − 𝑒 + 𝛥𝑡

𝜏𝑒 +

𝜏

𝛥𝑡 (𝑒 − 2𝑒 + 𝑒 )

(Eq. 2.45)

According to [21], the velocity form has three advantages over the position form:

1. It contains an anti-reset windup. 2. The output can be expressed in the increment form, which is useful for some final control

elements. 3. It does not require initialization of the output when transferring the controller from manual to

automatic.

2.3.6.2. Stability margins

For simplicity reasons, the margins of stability have only been calculated for simple feedback loops.

Using the block diagram of the system, the margins of stability of the controller can be calculated via

the Routh-Hurwitz criterion [28]. This will allow the engineer to know between which margins the

controller parameters values are. The block diagram a feedback control system is shown in Figure 2.14.

Figure 2.14. Feedback system block diagram.


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Two transfer functions can be obtained, one relating the output to the set-point and the other relating

the output to the disturbance. For a set-point change, the closed loop transfer function of the system

is shown in Eq. 2.46 obtained when Yd equals to 0.

𝑌(𝑠)

𝑌 (𝑠)=

𝐺 𝐺 𝐺

1 + 𝐺 𝐺 𝐺 (Eq. 2.46)

For a disturbance change, the closed loop transfer function is shown in Eq. 2.47 obtained when Ysp

equals to 0.

𝑌(𝑠)

𝐷(𝑠)=

𝐺

1 + 𝐺 𝐺 𝐺 (Eq. 2.47)

As it can be seen, both transfer functions share the same denominator (1 + 𝐺 𝐺 𝐺 ), which means that

both functions share the same characteristic equation [21].

The Routh-Hurwitz stability criterion is an analytical technique to determine if any roots of a polynomial

have positive real parts, which would mean that the polynomial has right plane poles, making the

system unstable. The method can only be applied to systems whose characteristic equations are

polynomials in s, making it not valid for time delay transfer functions [21]. In the case of time delay

systems, either the First Order Taylor Approximation or the Padé Approximation should be used for the

time delay part.

The characteristic equation has the following form:

𝑎 𝑠 + 𝑎 𝑠 + ⋯ + 𝑎 𝑠 + 𝑎 = 0 (Eq. 2.48)

One of the conditions in order to determine if the system is stable is that all the coefficients of the

polynomial are positive. This condition is necessary but not sufficient to determine the stability of the

function. The next thing to do is to create the Routh array:

1234⋮

𝑛 + 1

𝑎𝑎

𝑏𝑐⋮

𝑧

𝑎𝑎

𝑏𝑐00

𝑎 𝑎

𝑏…00

⋯⋯⋯000

(Eq. 2.49)

In the last matrix, n is the order of the characteristic equation. Finally, the values of b and c are

calculated as it follows:

𝑏 = 𝑎 𝑎 − 𝑎 𝑎

𝑎 (Eq. 2.50)

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𝑏 = 𝑎 𝑎 − 𝑎 𝑎

𝑎 (Eq. 2.51)

𝑐 = 𝑏 𝑎 − 𝑏 𝑎

𝑏

(Eq. 2.52)

𝑐 = 𝑏 𝑎 − 𝑏 𝑎

𝑏

(Eq. 2.53)

Nevertheless, there are some cases where the Routh array criterion might be difficulty to apply,

especially notable in MIMO systems, as in those kinds of processes, the denominator of the closed loop

transfer function includes all the transfer functions of the system, making it much more difficult to

obtain.

2.3.6.3. Cascade control

About the cascade controller, the main difference with the feedback one is that it involves two

controllers, where the output of the first one provides the set-point for the second, having one loop

nested inside the other:

Figure 2.15. Block diagram of the cascade control system.

When it comes to improving the feedback controller, the cascade scheme will outperform the feedback

one when the disturbances are associated with the manipulated variable [21].

In order to tune the cascade controller, there are few steps that need to be followed [2]:

1) Place the primary controller in manual and the second controller on the local set point. It will break the cascade system and allow the inner controller to be tuned.

2) Tune the secondary controller. 3) Return the secondary controller to remote set point. 4) Tune the primary controller.


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Once both controllers have been tuned there shouldn’t be any interaction between them. In case there

was, it means that the primary loop is not slow enough and it overlaps with the inner loop. About

cascade controllers, there is a rule of thumb that says that in order to avoid overlapping both

controllers, the inner loop has to be at least four times faster than the primary loop [2].

2.3.6.4. IMC tuning method

When it comes to the tuning of a PID controller, there are multiple tuning rules that could be followed.

These rules can be divided in two categories: on-line and offline. The main difference between them

is that online methods are based on experimental tests to calculate a set of initial controller

parameters, whereas in offline tuning, the parameters obtained are normally reached through block

diagram algebra or via the transfer function of the process. Some examples of on-line tuning methods

could be the Ziegler-Nichols or the Tyreus-Luyben, and for off-line methods, the Direct Synthesis and

the IMC method.

In this project, it was decided to use the IMC method [7], [21], as it provides good results and has a

degree of freedom that allows the operator to achieve a faster or slower response depending on the

characteristics of the system. The IMC method [21] is based on an assumed process model that leads

to analytical expressions for the tuning of the controller. One of the main advantages of the IMC

method is that it allows trade-offs between performance and robustness (where robustness means

that the control system can provide a satisfactory performance for a wide range of process conditions

and [21]) to be considered.

Consider the block diagram shown in Figure 2.16, where 𝐺 represents the internal model that is perfect

for the system and G is the physical model of the process.

Figure 2.16. Initial block diagram of the IMC model.

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If the block diagram is transformed into the one shown in Figure 2.17, via block diagram algebra, the

transfer function of the controller can be obtained (Eq. 2.54).

Figure 2.17. Initial block diagram modified with block diagram algebra.

To find Q, the IMC method states that it is equal to the inverse of the stable part of the given function

multiplied by a filter (Eq. 2.54). The filter part is multiplied in order to make sure that the function

obtained is a semi-proper system, where the degree of the numerator does not exceed the one of the

denominator.

𝑄 = 𝐺 · 𝐹 𝑤ℎ𝑒𝑟𝑒 𝐹 = 1

𝜆𝑠 + 1 (Eq. 2.54)

Once the Q has been obtained, it can be substituted into Eq. 2.55, and matched with the transfer

function of the desired controller in order to obtain the parameters.

𝐺 = 𝑄

1 − 𝑄 · 𝐺 (Eq. 2.55)

For the three main transfer function shown in chapter 2.3.4 (first order, second order, first order plus

time delay), the tuning parameters are shown hereafter. For a detailed explanation on how to obtain

them, refer to the IMC Manual in Appendix C5.

First order

𝐾 = 𝜏

𝐾 · 𝜆

(Eq. 2.56)

𝜏 = 𝜏 (Eq. 2.57)


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Where Eq. 2.56 and Eq. 2.57 can be substituted into Eq. 2.58.

𝐺 (𝑠) = 𝐾 1 +1

𝜏 𝑠 (Eq. 2.58)

Second order

𝐾 =2𝜉𝜏

𝐾 · 𝜆

(Eq. 2.59)

𝜏 = 2𝜉𝜏 (Eq. 2.60)

𝜏 =𝜏

2𝜉 (Eq. 2.61)

Where Eq. 2.59, Eq. 2.60 and Eq. 2.61 can be substituted into Eq. 2.62.

𝐺 (𝑠) = 𝐾 1 +1

𝜏 𝑠(𝜏 𝑠 + 1)

(Eq. 2.62)

First order plus time delay

𝐾 = 𝜏

𝐾 · (𝜆 + 𝛳)

(Eq. 2.63)

𝜏 = 𝜏 (Eq. 2.64)

Where Eq. 2.63 and Eq. 2.64 can be substituted into Eq. 2.65.

𝐺 (𝑠) = 𝐾 1 +1

𝜏 𝑠 (Eq. 2.65)

If the parameters for different transfer functions such as first order or first order plus time delay are

obtained, one of the main disadvantages that can be seen is that the integral part of the controller

doesn’t change with the tuning parameter. This makes it easier to tune but can be a problem if the

system has slow dynamics or a large dead-time. In this case the integral time will have a disproportional

value. Nevertheless, in order to mitigate this effect, the Skogestad’s theorem [23] that allows obtaining

smaller integral parts. It states that for large values of the time constants or systems with large dead-

times, the value of τI, will be the minimum of either the process time constant or 4 times the tuning

value plus the time delay.

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𝜏 = min{𝜏, 4(𝜆 + 𝛳)} (Eq. 2.66)

2.3.6.5. Multivariable systems

When the system to control is a multivariable one the approach is quite different. There are two

options: a multivariable controller and a multiloop controller. In this project, multiloop controllers have

been used for cases 3 and 4, as they are easier to understand and require less parameters to tune.

About the tuning, there are multiple methods that can be used [21]:

Detuning method: each controller is designed ignoring process dynamics. Then, the process

interactions are taken into account by detuning the controllers until the result achieved is

satisfactory.

Sequential loop method: the controller for a selected process variable and manipulated variable

is tuned and that loop is closed, then the second controller is tuned and its loop is closed too, and

so on for every controller in the process. The main advantage is that it is a simple method, while

the main disadvantage is that it is heavily reliant on the first controller tuned.

Independent loop method: each controller is designed based on the open-loop transfer functions

of each process.

2.3.7. Control system test

Once the control system has been designed and tuned, it must be tested in order to prove its efficiency.

It can be done by simulating a wide variety of set-point changes and disturbances. For the same case,

different control schemes were tested. To better compare them, the Event Scheduler tool provided by

HYSYS has been used. This tool allows programming the disturbances and makes it easier and faster to

reproduce them at the same specific simulation time. The set-point changes and the disturbances are

equal for all the parameters tested.

In order to objectively verify which response is better, some indicators can be used [29]. These are the

IAE (Integral of the absolute value), ISE (Integral of the squared error) and ITAE (Integral of the time-

weighted absolute error).

𝐼𝐴𝐸 = |𝑒(𝑡)|𝑑𝑡 (Eq. 2.67)

𝐼𝑆𝐸 = 𝑒(𝑡) 𝑑𝑡 (Eq. 2.68)


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𝐼𝑇𝐴𝐸 = 𝑡|𝑒(𝑡)|𝑑𝑡 (Eq. 2.69)

The IAE integrates the error over time without adding weight to the errors. ISE integrates the square

of the error over time, which penalizes large errors. While the ITAE integrates the absolute error

multiplied by the time, which weights errors that exist after a long time more heavily than those at the

start of the response [30].

It is desired that these indicators have a value as small as possible, which would mean that the errors

obtained are really small. In some cases, it could happen that different responses obtain better results

on different indicators, this would mean that the response performs better on what that indicator

values the most.

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3. Course design

The aim of this course is to train engineers in facing the process control issue by the use of a

professional process simulator, taking advantage of the big computational power nowadays available.

Once attended the course, knowledge about both process control and dynamic simulation will be

acquired. Through this, the engineer can afford solving control design tasks in a relatively quick way,

with no need of performing experimental disturbances in the real plant, making it safer. Furthermore,

the engineer will be able to compare different control schemes and choose the one which best suits

the problem.

There are many other similar training courses on this topic. Inprocess, Chemstations and PSE, are some

examples of companies that offer these services. Each one uses a process simulator (Aspen Hysys,

ChemCad, gPROMS) to accomplish different educational objectives, which include initiation to process

simulation, modelling advanced reactor or designing control systems among others. Many kinds of

training courses are given frequently, which means that there is a good demand for this product.

The current course may differ from the others in the difficulty level, since it pretends to be a basic

course. The idea is to design a course not only for chemical engineers, but for whoever may want to

approach process control and, above all, for non-experienced engineers. In order to do so, the course

has been organized in cases of increasing difficulty, where the knowledge acquired through one case

is then integrated in the next one to make a further step. Like all the courses, the teaching language is

English, since it allows further market opportunities.

3.1. Potential attendee and educational objectives

Any engineer whose role includes process control tasks could be interested in this course. The following

potential attendee profiles can be considered:

Chemical or control engineering student wishing to educate deeply in process control before getting to work.

Any engineer wishing to get started with chemical process control or interested in this kind of approach.

The knowledge and skills provided by this course are summarized through the following educational

objectives:

To identify the process variables, the input variable, the set-point and the control element given

a certain process to be controlled.

To learn the basic control theory.

To learn the basic process dynamic concepts.


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To understand the effect of different disturbances in a process and how to reduce them.

To learn to perform dynamic simulations and control them in Aspen HYSYS.

To apply the system identification method, obtaining the transfer function of the process.

To analyse and tune control alternatives for the same process.

To perform a multivariable control.

Anyway, in order to make sure that the attendee will be able to accomplish all these objectives, some

few requirements are needed. Familiarity with the steady state simulation and MATLAB environment

is recommended. In addition, a basic knowledge about the classical techniques and mathematical

modelling could provide a richer experience for the attendee.

3.2. Selected cases and course schedule

The intention is to facilitate everyone’s approach to the course by starting with an easy case where no

specific process knowledge or experience is needed. The control of the tank liquid level is a good

starting point since it only needs the conservative principle of matter to be applied. In addition, it only

has one variable to be controlled and the process dynamic is very intuitive. The simplicity of this case

allows an easier introduction on control theory, process dynamics and types of control valves, and

alternative control strategies (feedback with different MV and cascade control loop). Furthermore, it

is used to compare the mathematical modelling with the professional chemical process simulators

approach, highlighting the benefits provided by the last one.

Then, another process with only one variable to be controlled is faced. The heat exchanger is a very

common unit in chemical plants and allows introducing the temperature control, which is directly

linked to plant safety and production objective. In this case, the system requires knowledge about the

heat transfer phenomena and the design parameters of the equipment. However, through a brief

introduction on the heat exchangers and the dynamic analysis of the process, even the attendee who

does not have a chemical engineering education will be able to accomplish all the course objectives

planned for this case. Furthermore, as the attendee has already used more than one control strategy

in the first case, the heat exchanger case is used to introduce the feedforward control loop. Once again,

a comparison between the possible control schemes helps the attendee to decide which one is the

best option for the proposed problem.

The third case serves as an introduction to multivariable control, taking advantage of the tools acquired

through the previous two cases. The heated tank is a process with two variables to be controlled: the

liquid level and the temperature. Moreover, the two variables are not independent. For instance, if the

temperature increases the water density increases too and the liquid level rises. On the other hand, if

the liquid level decreases, the heat is absorbed by a smaller amount of liquid, so the temperature

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increases. The principles behind this process have already been analysed in the first two cases, which

makes it easier to introduce the RGA and SVA methods and the multiloop tuning.

By the moment, the cases have been selected in order to have a smart increasing difficulty level. The

last case reunites the knowledge acquired through all the other cases all in one, but still adding some

more difficulty due to a higher process dynamic complexity and number of variables. The distillation

column is a very common separation unit in chemical plants. Since the separation strategy involves

thermodynamic concepts, a brief theoretical introduction about distillation process is included. The

dynamic analysis helps understanding the relation between the many process variables, stating clearly

that the dynamic simulation, and so the course approach, is very useful to get a deeper view in process

control.

The course has been organized in three days. Here is the schedule and timing:

Module Content Description Time Day

1

Introduction to the control problem

Tank Liquid Level open loop example using mathematical modelling approach (MATLAB and SIMULINK). Introduction to control terminology (set point, process variable, disturbance etc…).

2 h

DAY 1 2

Initiation to Dynamic Simulation

Tank Liquid Level open loop example by simulation using Aspen HYSYS. Steady state simulation and transition to dynamics mode. Dynamics concepts (pressure driven process, control valves, resistance equation, capacitance, hydrostatic pressure etc…). Stripcharts. Benefits of the capacitance on controllability. Comparison between the two approaches and difference analysis.

2 h

3

Liquid Level Control

Tank Liquid Level closed loop. Exporting Data from HYSYS and application of the system identification method. PID in HYSYS. Feedback and cascade control loop. IMC tuning of PID. Controller test using the Event Scheduler tool.

3 h


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4

Dynamic Simulation of a Heat Exchanger

Heat transfer concepts and dynamic simulation of a heat exchanger. Analysis of the effect of the volume on the heat transfer. Dynamic analysis of the open loop responses to temperature and flow disturbances.

2 h

DAY 2 5

Temperature Control Loops

Feedback, Cascade and feedforward + feedback control loop for temperature control in a heat exchanger. Comparison using the Event Scheduler and evaluation of the best control strategy.

2 h

6

Initiation to Multivariable Control

Dynamic simulation of a tank constantly heated using steam passing through the tube bundle. Dynamic analysis to study the dependent variables and their relations. Simultaneous temperature and level control. Introduction to RGA and SVA for the variable pairing. Introduction to multiloop tuning.

3 h

7

Distillation Column Simulation

Distillation theory and VLE concept introduction. Shortcut and steady state simulation for a binary distillation column of n-butane and n-pentane. Dynamic simulation of a distillation column adding equipment by equipment. Dynamic analysis to better understand the relation between all the variables.

2.5 h

DAY 3

8

Distillation Column Control

Degrees of freedom and possible control schemes. RGA analysis. Tuning of the controllers. Comparison between the proposed control strategies selecting the one which best suits the process requirements.

3.5 h

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3.3. Didactic material

The professor will guide the attendees in the cases resolution, solving the case himself/herself. In

addition, the attendee can rely on simulation manuals for each case, where the resolution is guided

step by step. Furthermore, intermediate simulation files are provided for the attendee to have many

starting points and maintain the class rhythm in case of necessity. This is also useful in case the

attendee wanted to repeat the cases once the course is over. Further documentation available for this

course is:

IMC tuning method document: an introduction to the IMC method and a demonstration of how

to obtain the controller parameters.

Event scheduler manual: a step by step guide to the use of Event Scheduler tool applied to a

general case.

Data export by .csv: a brief explanation on how to export data from HYSYS to use it elsewhere.

Piping and instrumentation diagram (P&ID) document: an introduction to the drawing of P&ID,

explaining the basic standards for the representation of each control system element.


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4. Cases and results

This chapter shows all the selected cases that are going to be addressed to the course. For each one of

them, the most relevant aspects of the dynamic simulation have been explained and, in order to

concern the attendee with the process dynamics, the open loop behaviour of each system has been

analysed under the effect of many disturbances. Finally, each chapter reports the results for different

control strategies, each one tested under the same conditions.

4.1. Tank liquid level

The first case regards the control of the liquid level in an atmospheric tank. It was decided to simulate

the system in both MATLAB-SIMULINK, using the mathematical model, and HYSYS. Finally, the open

loop responses have been compared in order to state the differences between the two results and the

benefits or disadvantages of each approach.

4.1.1. Mathematical modelling of the atmospheric tank

The proposed system is a tank open to the atmosphere with only two streams, as shown in Figure 4.1.

When in steady state, the inlet flow (Fi) equals the outlet flow (Fo) and the liquid level is fixed to a value.

Figure 4.1. Flow diagram of the tank.

By applying the material balance to this process, the transient behaviour can be modelled. This

equation [31] states that the inlet flow minus the outlet flow equals the rate of accumulation in the

tank.

𝐹 − 𝐹 = 𝑑𝑉

𝑑𝑡

(Eq. 4.1)

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So, if the inlet flow is higher than the outlet flow, the rate of accumulation will be positive and the

liquid level rise, while if it is lower, the rate of accumulation will be negative causing the level to drop.

Considering a vertical cylindrical tank, the hold-up volume is the base area of the tank multiplied by

the height of liquid (F is the volumetric flow):

𝐹 − 𝐹 = 𝐴 ·𝑑ℎ

𝑑𝑡

(Eq. 4.2)

The outlet flow depends on the valve opening, the valve unknown constant and on the hydrostatic

pressure. The latter causes the height of the liquid inside the tank to be proportional to the square root

of the height of liquid inside the tank. So, the material balance turns to be:

𝐹 − 𝑘 · 𝑉𝑎𝑙𝑣𝑒𝑂𝑝𝑒𝑛𝑖𝑛𝑔 · √ℎ = 𝐴 ·𝑑ℎ

𝑑𝑡

(Eq. 4.3)

If the terms of the equation are rearranged, Eq. 4.4 is obtained:

𝑑ℎ

𝑑𝑡=

𝐹 − 𝑘 · 𝑉𝑎𝑙𝑣𝑒𝑂𝑝𝑒𝑛𝑖𝑛𝑔 · √ℎ

𝐴

(Eq. 4.4)

In order to calculate the unknown constant of the valve (k), the equation has to be considered in

steady-state, in which the derivative term is equal to zero. The initial value of the height is 1.024 m

(50% of total height) and the valve opening is 50%:

𝑘 = 𝐹𝑖

√ℎ · 𝑉𝑎𝑙𝑣𝑒𝑂𝑝𝑒𝑛𝑖𝑛𝑔=

0.002495

√1.024 · 0.5= 4.93𝑒 − 3

(Eq. 4.5)

Simulating this system in SIMULINK with the calculated k value demonstrates that the system is at

steady state. Figure 4.2 shows that the graphic of the liquid height over time is flat, hence the liquid

level has remained constant at 1.024 m.

In order to observe a change in the height value, a positive disturbance has been introduced in the

input flow. The liquid level rises until a new equilibrium is reached at a higher height value. The

response obtained is a first order type, which demonstrates that the model could be approximated to

a linear ODE.


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Figure 4.2. Steady state simulation.

Figure 4.3. Open loop response of the system to a flow disturbance.

Hei

ght

(m)

0 50 100 150 200 250 300

Time (minutes)

1

1.1

1.2

1.3

1.4

1.5

1.6

Hei

ght

(m)

Open Loop Response to a Step Disturbance

Height Value

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4.1.2. Atmospheric tank using Aspen HYSYS

In order to simulate an atmospheric tank in HYSYS, a steady state simulation has been performed first.

It has then been converted to a dynamic simulation making the proper modifications explained here.

For more details about the simulation see Simulation Manual – Tank Liquid Level in Appendix C1, where

you will find a step by step simulation guide for this case.

The tank feed has the following specifications:

Table 4.1. Tank feed specifications.

FEED Temperature 25 ºC Pressure 140 kPa Std. ideal Liquid Vol. Flow 9 m3/h Molar fraction H2O 1.00 Molar fraction N2 0.00 Molar fraction O2 0.00

The need of nitrogen and oxygen will be discussed later. The fluid package used for the system H2O-

N2-O2 is Peng-Robinson.

The steady state simulation only requires 3 material streams and a vessel, which only needs connection

information.

Figure 4.4. Tank Liquid Level: Steady state flowsheet.

The results are resumed in Figure 4.5. As expected, all the water that enters the system exits from the

bottom of the tank and there is no flow through Vapour stream. As it can be seen, the simulation can

be done without knowledge of the liquid level.


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Figure 4.5. Tank Liquid Level: Steady state worksheet.

Even if the material balance is correct, this simulation does not provide a faithful reproduction of

reality. If you observe the pressure values, there is no pressure drop along the system. This is wrong

for two reasons:

No pressure drop means that there is no flow through the tank.

In a half-filled tank, there is a column of liquid that contributes to the pressure, so the pressure

at the bottom of the tank should be higher than the one at the liquid surface.

Furthermore, considering that every vessel in HYSYS is closed, there is no information about the 50%

tank volume left. To simulate an open tank there should be air at atmospheric conditions entering or

exiting depending on whether the liquid level drops or rises respectively.

4.1.2.1. Dynamic simulation

In order to convert the simulation to a dynamic one, many modifications must be made. First of all, the

vessel must be sized. This allows having information about the liquid height and the residence time of

the hold-up liquid. A flat vertical cylinder tank is chosen with a 3 m3 volume. Aspen HYSYS automatically

calculates a diameter and a height:

Figure 4.6. Tank Liquid Level: Tank sizing.

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Then, to better model this system, a valve is added to each stream obtaining the following flowsheet:

Figure 4.7. Tank Liquid Level: Steady state flowsheet with valves.

Each valve has a linear inherent characteristic (liquid level control) but they have been sized differently:

Feed valve (VLV-100): It has a 50% opening and the pressure drop equals the difference

between FEED pressure (140 kPa) and the inlet pressure to the tank (101.3 kPa = 1 atm). With

these data and the flow passing through the valve, the Cv can be obtained by auto-sizing with

the ANSI/ISA method.

Liquid valve (VLV-102): It also has a 50% opening but the pressure drop is calculated differently.

As the steady state simulation does not take into account hydrostatic pressure, the pressure

at the bottom is not real. The pressure due to the liquid height can be calculated through the

following equation:

∆𝑝 = 𝜌𝑔∆ℎ (Eq. 4.6)

The density can be obtained by the Liquid stream properties, while the height of liquid depends

on the liquid level desired. In this case, the height of the tank is 2.048 m and, as the liquid level

wanted is 50%, Δh will be 1.024 m. Considering that the outlet pressure is the atmospheric

one, this pressure differential will be equal to the pressure drop in the Liquid valve:

∆𝑝 = 1007𝑘𝑔

𝑚· 9.81

𝑚

𝑠· 1.024 𝑚 ·

1 𝑘𝑃𝑎

1000 𝑃𝑎= 10.12 𝑘𝑃𝑎

(Eq. 4.7)

Once again, with this data and the flow through the valve, the Cv value is obtained by auto-

sizing.

Vapour valve (VLV-101): This valve does not exist in the real process, but here it has been

included for integration purposes. So, there should be no resistance through this valve, that’s

why the opening is set to 100% and the Cv to 1E+05, a very high conductance value.


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Unlike the steady state mode, the dynamics mode allows simulating reversal flows with components

that are not entering the system. This feature has been employed to simulate the air dynamics. In the

Vapour 2 stream, in the Product Block section, it has been specified that for reversal flows, a stream

containing 0.79 N2 and 0.21 O2 at 25ºC should enter the system.

In order to reproduce the reality properly, one last feature must be considered: the height of the

equipment. As hydrostatic pressure is taken into account, the height difference between a valve and

the connection to the tank could lead to pressure loss. That’s why it is very important to select the

vessel nozzles heights first:

Figure 4.8. Tank Liquid Level: Nozzles height.

The Feed inlet is set to 100% of the total tank height because, in this way, the water always enters the

tank at atmospheric pressure, even if the liquid level exceeds the 50%. If the feed nozzle would be at

40%, the pressure would be higher due to hydrostatic pressure. For similar reasons, the liquid nozzle is

maintained to 0% of tank height in order to have the maximum possible pressure at the bottom in

every scenario. The Vapour nozzle is maintained to 100% because, for lower heights, there could be

liquid loss. Finally, to avoid additional pressure loss, the valves heights are set equal to the tank nozzles

ones.

Through these modifications, the process modelling has been improved and made much more realistic.

However, before performing a dynamic simulation, other features must be revised. As explained in

chapter 2.3.2, in dynamics mode the solver is a pressure-flow solver. This means that it needs pressure

specifications in order to determine the stream flows. The Dynamics Assistant is a very useful tool that

can help in setting these specifications. Figure 4.9 shows the suggestions for the steady state

simulation:

Figure 4.9. Tank Liquid Level: Dynamics Assistant suggestions.

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The HYSYS manual suggests setting the pressure specifications in every boundary stream and avoiding

the flow specifications. In Figure 4.7, these specifications are better visualized through the colour code:

green streams have pressure specification only, yellow streams have flow specification only, blue

streams have no specification, while red streams have both pressure and flow specification.

All the dynamics specifications can be modified in the Dynamics tab of each equipment. To correctly

solve the integration, the valves should also have the pressure-flow relation activated (default option).

If this option is not selected, the pressure drop, and so the Cv, are not allowed to change losing realism

in the simulation.

Figure 4.10. Tank Liquid Level: Valves dynamics specifications.

The starting point can also affect the dynamics behaviour. As a continuous process is to be simulated,

the initial liquid level must be 50%:

Figure 4.11. Tank Liquid Level: Tank starting point.

Note that the static head contribution must be enabled in the integrator tab. The progress of the

dynamic simulation can be monitored through the Strip Chart, which are graphics where the chosen

variables actualize their value as time passes by. Running the simulation during 200 minutes provides

the following results:


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Figure 4.12. Tank Liquid Level: Dynamic simulation results (200 min).

Figure 4.12, at the beginning, shows an incoherent behaviour which has to be ignored: Liquid

volumetric flow decreases and then increases in a short period of time, which leads to a liquid level

rise. This is due to an initial phase where pressures need to stabilize, yet at time 0 static head

contribution is taken into account and there is a rapid change in the pressure at the bottom of the tank.

Finally, the output flow equals the input flow (FEED volumetric flow) and the liquid level stabilizes at

50%. No more change is observed, which means that a steady state has been reached.

Figure 4.13. Process pressures in dynamic simulation (200 min).

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Observing the process pressures in the flowsheet, it can be seen how the bottom pressure raised due

to the hydrostatic pressure.

Figure 4.14. Process mass flows in dynamic simulation (200 min).

Observing the process mass flows in the flowsheet, it can be seen that a negative flow is in the head of

the tank, which means that air is entering. However, it is negligible respect to the inlet and outlet flows.

4.1.2.2. Open loop response in HYSYS

In order to obtain the system open loop response, a feed flow disturbance is induced in the process.

To do so, a pressure change in FEED stream is done: from 140 kPa to 160 kPa, and then from 160 kPa

to 120 kPa. Changing the inlet pressure will affect the pressure drop and so the flow passing through

the system. It also could be done by forcing a flow specification; however, the pressure change method

is more realistic.

The first disturbance causes a FEED flow increase. The FEED flow changes instantaneously from 9 m3/h

to 11.08 m3/h, being a step disturbance. The tank begins to accumulate water and liquid level rises.

Consequently, hydrostatic pressure increases and so does the Liquid flow. A new steady state is

reached when Liquid flow equals FEED flow.

The second disturbance causes a FEED flow decrease. Again, it is a step disturbance, but as the outlet

flow is higher than the inlet flow, the liquid level drops until the flows are equals and equilibrium is

reached again at a difference liquid level.


51

Figure 4.15. System response to FEED flow disturbances.

A mass flow Stripchart has been created to see what happens to Vapour Flow:

Figure 4.16. Vapour flow response to disturbance.

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At the beginning there is a relatively great increase in the flow outside of the tank. This is due to the

liquid level rise. By rising, water displaces the air above it. As the rising rate decreases with time, the

Vapour flow starts to decrease until becoming approximately null. The opposite happens with the

second disturbance. As Liquid Level drops, more air enters the tank. When the dropping rate begins to

decrease, the vapour flow returns to an approximately null value.

Figure 4.17. Pressure response to disturbance.

The same behaviour observed in Figure 4.15 is in Figure 4.17, yet flows depend on pressure. Only

Vapour pressure does not change because the tank is open to the atmosphere. The flow is only due to

the liquid displacement.

4.1.2.3. Capacitance effect

In order to better study the capacitance effect on the system response, the same process was

reproduced but a tank volume of 9 m3 was used this time. The feed stream is exactly the same, the only

difference is in the diameter of the tank, yet the height was fixed at 2.048 m as the first tank, to avoid

hydrostatic pressure differences. Both systems were studied for disturbances in the feed flow (dashed

lines represent the bigger, B, tank variables):


53

Figure 4.18. Capacitance study: Stripchart legend.

Figure 4.19. Capacitance study: Open loop response (160kPa and 120kPa).

The system behaviour is the same as explained before. It can be seen how the bigger tank reaches the

same final value but in much more time being the liquid level change smoother. For example, for the

first disturbance, the stabilization time was 150 minutes for the smaller tank against the 400 minutes

for the bigger tank. A further analysis can be done inducing a flow disturbance with consecutives

positive and negative steps:

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Figure 4.20. Capacitance study: Open loop response (Consecutive disturbances).

Pressure changes from 160 kPa to 120 kPa were performed each 5 minutes. It can be seen how the

bigger tank response is smoother all the time. The liquid level is maintained to low values and the outlet

liquid flow oscillates less. This proves why capacitance improves the process controllability. The reason

is that “the same force” is trying to move a bigger mass of water. As the inertia is higher, the

acceleration is lower and the system behaves smoother.

4.1.3. Comparison between MATLAB and HYSYS

Once the system has been simulated in both MATLAB and HYSYS, the open loop responses are

compared. In order to do so, the same feed flow disturbance has been induced. In HYSYS a pressure

change from 140 kPa to 160 kPa leads to a flow increase of 2.09 m3/h, which is the step input

introduced in MATLAB. Exporting the HYSYS experimental results into MATLAB, it can be seen that

both responses are identical:


55

Figure 4.21. Comparison of the HYSYS and MATLAB open loop response to a pressure disturbance.

To further test the system, a set-point disturbance was induced to see how both systems behave and

to see if when facing another type of change they would still be similar.

Figure 4.22. Comparison of HYSYS and MATLAB open loop response to a set-point change.

0 50 100 150 200 250 300

Time (minutes)

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

He

igh

t (m

)

Comparison of Open Loop Responses

SIMULINK ValuesHYSYS Values

0 50 100 150 200 250 300

Time (minutes)

1

1.05

1.1

1.15

1.2

1.25

1.3

1.35

1.4

He

igh

t (m

)

Comparison of Open Loop Responses

SIMULINK ValuesHYSYS Values

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In Figure 4.22, it can be seen again that both curves are almost identical, which demonstrates that the

MATLAB and HYSYS models are able to achieve the same responses.

If one compares the simulation requirement for each program, the MATLAB model can be the best

option if the liquid level response is the only objective, since it’s time-saving and only needs an

equation, which is the material balance. In contrast, HYSYS requires simulating the air dynamics, the

selection of a fluid package, the proper sizing of the valves and the selection of the equipment height.

It takes into account the air-water interaction, water vaporization, frictional temperature changes, and

pressure-flow relations making the simulation much more complex than in MATLAB.

For this specific case, all these aspects were negligible and maybe HYSYS is not necessary. Nevertheless,

if the system changes, this statement can turn to be false. For instance, if the liquid was not water but

acetone instead, its volatility is not negligible and air interaction is very important. The same would

happen if a phase mixture feed entered the tank or if the temperature is much higher than the ambient

one. Moreover, the nozzles location makes the simulation more realistic, yet if the feed nozzle is below

the liquid level, the water would enter the tank at a different pressure due to the static head

contribution, which could affect the inlet and outlet flow. In addition, HYSYS allows a holdup analysis

that for more complex systems, with different composition, could be very useful.

It is possible to reproduce in MATLAB the same response as in HYSYS for any process. However, this

means adding many and many equations such as Peng-Robinson state equation, resistance equations

for valves or heat exchangers, material and energy balances for all the equipment, sizing relations, etc…

For all these reasons, the next cases will be simulated in Aspen HYSYS, yet all the equations are already

integrated and is much more interactive thanks to the software design.

4.1.4. Liquid level control

By the moment, the tank has been simulated as an open loop system. As there is no feedback action,

the loop is very sensitive to noise and disturbances.

Figure 4.23. Open loop system.


57

If a controller and a sensor were introduced and the control loop was closed, the process variable

would be used to differentiate the set-point with the output, comparing both values to achieve a better

control of the system.

Figure 4.24. Closed loop system.

From a control stand point, the objective is to maintain a constant liquid percent level inside the tank,

which is the desired value or set-point (SP). To perform this task, a controller must be added to the

system in order to regulate the opening of one of the valves depending on the current level value and

the set-point introduced. In that case, the valve opening would be the OP of the process.

There are multiple options when choosing the type of control to be used because, for most tanks, the

precision might not be the most important feature. In some cases, it might be a good option to trade-

off some precision for an easier control. If that is the case, an option could be using a proportional-only

controller. By doing so, the cancellation of the error might never be achieved, but the error would be

between the margins specified.

Another option would be using a PI controller, which is among the most popular for tanks level control

and all control systems in general. By using this type of controller, the cancelation of the error would

be achieved, as the proportional control would obtain a good result in decreasing the error and the

integral part would take it to the set-point.

The last option argued in this document is shown in [6], where two proportional controls and one PI

control have been used. High gain proportional controls are used when the level reaches its 90% and

10%, while in between this margin the Proportional-Integral is used.

In this case, it was decided to use the proportional and integral controller, since its implementation is

not the most complicated between the options mentioned, and because no off-set provided by a P-

only controller is desired.

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For the tank considered, there are two possible options to achieve the control objective: output and

input streams as manipulated variables. Both are acceptable and can provide good results. The only

difference between both control schemes is the transfer function of the process and the action of the

controller.

About the first scheme, the transfer function of the process is going to have a negative gain. This

happens because if the valve opens, the level is going to drop, meaning that one of the variables

involved in the gain calculation must be negative. The controller action must be direct because if the

level rises and it is greater than the set-point, the output valve must open for the level to reach the

desired value again.

Figure 4.25. Liquid tank control scheme using the output flow valve.

About the second scheme, shown in Figure 4.26, the transfer function of the process is going to have

a positive gain instead. This happens because if the valve opens, the level rises, and both parameters

involved in the gain calculation are positive. In terms of the control action taken by the controller, it

must be a reverse action. If the level rises and it is greater than the set-point, the valve must close.

In order to demonstrate the differences between both system and that both schemes can be

implemented obtaining good results in both set-point tracking and disturbance rejection, both cases

have been simulated.


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Figure 4.26. Liquid tank control scheme using the input flow valve.

4.1.4.1. PID Controller in HYSYS

The controlled in HYSYS can be added from the model palette together with all the other modules. It

first requires 2 connections: the PV, the variable that is going to control, and the OP that is the variable

that is changed to reach the SP. In each case of this project, the OP is the valve opening of the control

valve.

Figure 4.27. HYSYS controller “Connections” tab.

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Once these variables have been selected, the next step is to configure the parameters tab:

Figure 4.28. HYSYS controller “Parameters” tab.

As Figure 4.28 shows, it can be set if the controller has a Direct or Reverse action. Then, the set-point

mode can be chosen to be on Local, if the set-point is given by the user, or on Remote, if it is given by

another controller. In the Mode specification, several can be chosen:

Off: The controller doesn’t track the PV. Manual: The controller is not running but the OP can be changed from the controller tab. Automatic: The OP is set by the PID algorithm selected. Casc: For the cascade mode. It is only available when another controller is attached. Indicator: PV tracking is enabled, but the OP is static.

In the PV range, both maximum and minimum values must be specified. In order to determine the

range, general rules have to be followed. For example, for liquid levels, the percentage will go from 0

to 100 %, but in flow controllers the minimum will be the flow passing through the valve when it is

completely closed (0 kg/h) and the maximum will be the flow when the valve opening is 100%. It is

encouraged for these tests to be performed when the system is operating in nominal conditions.

Several PID algorithm types can be chosen, such as HYSYS, Honeywell, Foxboro, Yokogawa, but for all

the cases in this project, the default option has been used (HYSYS algorithm) [5]. The algorithm subtype

indicates the form of the PID controller. Different types can be chosen but for each case the Velocity

form has been selected as it contains some advantages that other forms don’t, as it was already argued

in chapter 2.3.6.1.


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4.1.4.2. Feedback control: Output flow

If the outlet flow is selected as MV, the OP is the valve opening of the output valve while the PV is the

liquid level inside the tank. Figure 4.29 shows the block diagram of the process, where two transfer

functions are obtained. These functions are the relation between the height of the system and the set-

point, and between the same process variable and the main disturbance of the system.

Figure 4.29. Staring block diagram of the liquid tank control scheme.

Following the methodology explained in chapter 2.3.4, from the open loop response of the tank, a first

order model has been obtained.

𝑌 (𝑠)

𝑈(𝑠)=

−2.35

25.12𝑠 + 1 [𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠]

(Eq. 4.8)

About the disturbance, if a step input is applied in the pressure, the transfer function in Eq. 4.9 is

obtained:

𝑌 (𝑠)

𝐷(𝑠)=

1.23

23.44𝑠 + 1

%

𝑘𝑃𝑎

(Eq. 4.9)

With both transfer functions calculated, the final block diagram is shown in Figure 4.30.

Figure 4.30. Block diagram of the tank.

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As already stated in Chapter 2.3.6, the characteristic equation obtained for the system, is the same one

for the set-point and disturbance closed loop transfer functions, and because of this the Routh-Hurwitz

criterion can be applied in order to obtain the margins of stability for the controller.

1 + 𝐺 𝐺 𝐺 = 25.12𝑠 + 𝑠(1 − 2.35𝐾 ) − 2.35𝐾 = 0 (Eq. 4.10)

If the Routh array is constructed, the following matrix is obtained:

𝑠𝑠𝑠

25.12

1 − 2.35𝐾−2.35𝐾

−2.35𝐾00

(Eq. 4.11)

Since all the parameters must be positive, the limit parameters for the controller are going to be:

𝐾 < 0.43 (Eq. 4.12)

𝐾 < 0 (Eq. 4.13)

Where KI = KC/τI. So, the Routh criterion states that the proportional gain should be smaller than 0.43,

which means that it will more likely be negative in this system. The integral gain needs to be negative,

which means that the proportional gain and the τI have opposite signs in order for the system to be

stable.

When applying the IMC tuning method, different values of λ will be tested in order to show the

difference between a faster and a lower response. The Skogestad’s theorem has also been applied to

work with a different value of τI.

Table 4.2. Controller parameters obtained for the different tuning parameters.

Kc τI

IMC (λ = 3) -3.56 25.12

IMC (λ = 20) -0.53 25.12

SKO (λ = 3) -3.56 12

In order to test the system, different SP changes and disturbances have been applied and the responses

obtained have been compared to appreciate the differences. The introduced disturbances are:

1. Pressure change from 140 kPa to 160 kPa in minute 100. 2. Set Point change from 50% 30% in minute 500. 3. Pressure change from 160 kPa to 140 kPa in minute 900. 4. Set Point change from 30 %to 80% in minute 1300. 5. Set Point change from 80 % to 50% in minute 1700.


63

Figure 4.31. Test disturbances applied in the system.

The level and controller output responses to those disturbances are shown in figures 4.32 and 4.33

respectively.

Figure 4.32. Response obtained for the different tuning parameters.

0 200 400 600 800 1000 1200 1400 1600 1800 2000100

110

120

130

140

150

160

170

180

190

200

0

10

20

30

40

50

60

70

80

90

100Tank level case disturbances

Pressure disturbanceSet-point disturbance

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Figure 4.33. Valve response to the different disturbances tested.

From Figures 4.33 and 4.34, it can be seen that the values obtained with the Skogestad limit value are

the best in both set-point tracking and disturbance rejection, however, they produce really high

changes in the control valve in a very short time, which in some systems might be a problem.

In order to objectively define which system obtains the best responses, the IAE, ISE and ITEA

performance criteria have been applied. The results are shown in Table 4.3.

Table 4.3. IAE, ISE and ITAE indexes obtained for the responses simulated.

IAE ISE ITAE

IMC (λ = 3) 1928.10 27257.70 16.10

IMC (λ = 20) 3746.40 49608.80 31.20

SKO (λ = 3) 920.30 15544.00 7.70

Where the units used for level are the percentage (%) and for time are minutes (min).

From the last table, it can be seen that the tuning parameters that provide a better response are the

ones obtained with the Skogestad method, which outclasses both other sets of parameters in all three

performance indexes. However, these parameters produce really aggressive changes to the control

element, which might put a lot of stress in the valve. So, the tuning that would be chosen for the tank

level case, depends on what it is pretended to achieve. For example, if a fast response and minimum


65

error are needed, the parameters obtained with the limit of value would fit best. However, if a fast

response is not needed, it might be useful to considerate the IMC with a constant of 20.

4.1.4.3. Feedback control: Input Flow

If the manipulated variable is the input flow, the OP is the inlet valve this time. If the open loop

response is simulated, the transfer function of the system is the one shown in Eq. 4.14. As it can be

seen, it has a positive gain, unlike the one shown in the output flow control.

𝑌 (𝑠)

𝑈(𝑠)=

2.2


(Eq. 4.14)

The block diagram of the system is the following.

Figure 4.34. Block diagram of the level tank.

With the block diagram, the closed loop transfer function can be obtained:

1 + 𝐺 𝐺 𝐺 = = 23.44𝑠 + 𝑠(1 + 2.2𝐾 ) + 2.2𝐾 = 0 (Eq. 4.15)

If the Routh array is constructed, matrix xx is obtained, and the limit parameters for the controller are

Eq. 4.17 and Eq. 4.18.

𝑠𝑠𝑠

23.44

1 + 2.2𝐾+2.2𝐾

+2.2𝐾00

(Eq. 4.16)

𝐾 > −0.45 (Eq. 4.17)

𝐾 > 0 (Eq. 4.18)

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In this case, it can be seen that the value of the proportional gain will be positive, as well as the integral

part of the controller.

Again, if the IMC rules are applied into the calculation of the proportional and integral terms, the

following parameters are obtained:

Table 4.4. Controller parameters obtained for the different constant values.

λ Kc τI (w/limit of value)

4 2.64 16

5 2.12 20

6 1.77 23.44

In this case, as the difference between faster and slower parameters was already seen in the output

flow control, it was opted to use similar tuning parameters in order to observe the slight differences

between them. To test this simulation, the same disturbances used in the previous case have been

introduced

Figure 4.35. System response for different parameters for the disturbances tested.

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Time (min)

20

30

40

50

60

70

80

Leve

l per

cen

tag

e (%

)

Tank level response for different tuning parameters

IMC (lambda = 4)IMC (lambda = 5)IMC (lambda = 6)


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Figure 4.36. Valve response of the different tuning parameters.

It can be seen that the control obtained for this process is really good as the tuning parameters are

small obtaining a really fast control with good disturbance rejection as well as set-point tracking. No

much difference can be appreciated between them.

Table 4.5. IAE, ISE and ITAE indexes obtained for the responses simulated.

IAE ISE ITAE

IMC (λ = 4) 99.46 168.97 8.28

IMC (λ = 5) 106.24 174.40 8.85

IMC (λ = 6) 120.80 181.14 10.07

The performance criteria confirm that each one of the three sets of parameters obtain good results,

being the ones obtained with the IMC for a tuning parameter of 4 the fastest in the group. Even though,

as already stated, all three controller parameters could be used as they obtain really good results in

the three indexes.

4.1.4.4. Cascade control

Even though the results obtained in both input and output flow cases provide a good control, it has

been simulated a cascade control scheme in order to test how much it improves disturbance rejection.

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In the cascade scheme, the PV of the primary controller is the liquid level inside the tank, while for the

secondary, the PV is the mass flow on the input stream. When it comes to the set-point, the set-point

of the primary controller will be given by the user, but for the secondary controller, the set-point will

be given by the primary.

Figure 4.37. P&ID of the cascade control scheme for the tank.

As it can be seen in the block diagram shown in Figure 4.38, the secondary process or the inner loop

process consists on the valve transfer function, which will be scaled to % in order to tune the controller.

Figure 4.38. Block diagram of the cascade control system.

As explained in the methodology, the first loop that has to be tuned is the inner loop, which is the flow

loop. The following graphic is obtained when a change in the controller output is applied while it is in

manual mode. It has been necessary to model the actuator with a first order model because an


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instantaneous response, as it was in the previous cases, would not provide a transfer function. A time

constant of 0.2 minutes was set arbitrarily. It does not really affect the main system since it is very small

compared to the large tank dynamics.

Figure 4.39. Inner loop response to the set-point change.

The transfer function of the system is:

𝑃(𝑠)

𝑈 (𝑠)=

179.45

0.2𝑠 + 1

𝑘𝑔

ℎ · %=

0.99


(Eq. 4.19)

The mass flow has been scaled in order to obtain the transfer function and the controller parameters.

The maximum and minimum parameters (PV range) are the ones obtained when the valve is fully

opened and fully closed. This range goes from 0 kg/h to 17960 kg/h.

If the Routh array is built for the inner loop controller, the margins of stability obtained are:

𝐾 > −1 (Eq. 4.20)

𝐾 > 0 (Eq. 4.21)

In order to tune the first controller, the IMC method has been used for a lambda parameter of 3:

𝐾 = 0.15 (Eq. 4.22)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Time (min)

8000

8500

9000

9500

10000

10500

11000Flow resposne to step change

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𝜏 = 0.20 (Eq. 4.23)

About the tuning of the master controller, the slave controller has been put in cascade mode with the

set of tuning parameters already placed in the flow controller. A step change has been introduced in

the master controller output and the open loop response has been obtained.

Figure 4.40. Fitting of the primary loop.

As it can be seen in Figure 4.40, the open loop response obtained resembles a second order model (Eq.

4.25), even though, as the second time constant of the system is really small, it could be also fitted into

a first order one (Eq. 4.24).

𝐻(𝑠)

𝑈 (𝑠)=

2.30


(Eq. 4.24)

𝐻(𝑠)

𝑈 (𝑠)=

2.30

25𝑠 + 26𝑠 + 1 [𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠] (Eq. 4.25)

In this case, if the first order model is chosen, the IMC controller is built like in the previous cases.

Otherwise, if the second order model is chosen, the IMC controller incorporates a derivative

component.

About the tuning of the first order transfer function, if a parameter of 5 is selected, the parameters

obtained are the ones shown in equations 4.26 and 4.27.

0 20 40 60 80 100 120 140 160 180 200

Time (min)

45

50

55

60

65

70

75

80

85

90Level resposne to step change in cascaded controller

Experimantal ValuesFirst Order ApproximationSecond Order Approximation


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𝐾 = 2.09 (Eq. 4.26)

𝜏 = 20 (Eq. 4.27)

About the tuning of the second order transfer function, for the same constant value, the parameters

obtained are the following:

𝐾 =2𝜉𝜏

𝜆 · 𝐾=

2 · 2.6 · 5

𝜆 · 2.30=

11.30

𝜆= 2.26

(Eq. 4.28)

𝜏 = 2𝜉𝜏 = 2 · 2.6 · 5 = 26 (Eq. 4.29)

𝜏 =𝜏

2𝜉=

5

2 · 2.6= 0.96

(Eq. 4.30)

In this case, the cascade scheme has been compared to the feedback scheme shown earlier; in order

to test it, two separate categories have been created, one consisting of set-point tracking, and the

other one consisting of disturbance rejection.

The set-point disturbances introduced to the system are:

1. From 50 % to 65 % in minute 100. 2. From 65 % to 25 % in minute 300. 3. From 25 % to 45 % in minute 500. 4. From 45 % to 50 % in minute 700.

The pressure disturbances introduced are:

1. From 140 kPa to 170 kPa in minute 100. 2. From 170 kPa to 150 kPa in minute 300. 3. From 140 kPa to 120 kPa in minute 500. 4. From 120 kPa to 140 kPa in minute 700.

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Figure 4.41. Different control schemes response to set-point tracking.

Figure 4.42. Different control schemes response to disturbance rejection.

From Figure 4.41, it can be seen that the three control systems are almost equally good at set-point

tracking, the main difference being in that the regular feedback produces less overshoot. Instead,

Figure 4.42 shows that the cascaded schemes perform much better at feed flow disturbance rejection

in both PI and PID cases than the feedback controller. The reason lies in the fastest detection of the

flow change due to the slave controller, so it mustn’t wait for a PV variation to start actuating.

Tem

per

atu

re (

ºC)

Tem

pera

ture

(ºC

)


73

4.2. Heat exchanger

Another important variable to control in chemical processes is temperature. Reactor or column feeds

must enter at a specific temperature for the process to work optimally. Moreover, the temperature

must be controlled for safety reasons. For instance, in an exothermic reactor, a too high reactor

temperature could lead to a dangerous conversion rate, activating secondary reactions, producing gas

and increasing the pressure. If there is not a good control system, this can translate into a reactor

explosion [32].

The chosen case study to get started with the temperature control is the heat exchanger. It is a very

common unit in chemical plants which allows energy integration and is used, for example, to

condensate a stream or just to change its temperature to fit the requirement of the next process unit.

Each heat exchanger has a hot stream that will be cooled down and a cold stream that will warm up.

The heat transfer depends on the available transfer area A, the overall heat transfer coefficient U, and

the temperature gradient. The following equations describe the heat exchanger system:

𝑄 = 𝑈 · 𝐴 · 𝐹 · ∆𝑇 (Eq. 4.31)

𝑄 = Ḟ · 𝑐𝑝 · ∆𝑇 (Eq. 4.32)

𝑄 = Ḟ · 𝑐𝑝 · ∆𝑇 (Eq. 4.33)

Where:

Q is the heat transfer, which is the same for both fluids if heat loss is negligible.

ΔTml is the logarithmic mean temperature difference through the heat exchanger, determined

by the two temperature profile, the cold fluid one and the hot fluid one.

Ft is a correction factor of the ΔTml which depends on the configuration of the heat exchanger

(counter or co-current).

Ḟ is the molar or mass flow of the hot or cold stream.

cp is the specific heat capacity, assuming as a simplification that it does not vary with

temperature in the temperature range of the process.

ΔT is the temperature difference between the outlet and inlet stream.

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In the proposed case, the process stream is hot water at 60ºC and 180 kPa, with a flow of 100 kg/h

which must be cooled down to 40ºC. The available coolant is water at 5ºC and 180 kPa. The hot stream

enters the tube side while the coolant goes through the shell. Figure 4.43 shows the steady state

flowsheet:

Figure 4.43. Steady state flowsheet.

The PV is the temperature of the Hot OUT stream and the SP is 40ºC. In such a system there could be

many disturbances that will make the PV move from its desired value:

Process stream (hot fluid) flow disturbance

Process stream (hot fluid) temperature disturbance

Utility stream flow disturbance

Utility stream temperature disturbance

Fouling can decrease the overall heat transfer coefficient [33]

Strong changes in the environmental conditions increase the heat loss

4.2.1. Dynamic simulation of a heat exchanger

As for the open tank, a steady state simulation has been performed and then properly converted to a

dynamic one. Here are the main aspects of the simulation remarking the differences between steady

state and dynamic simulation. For more details about the simulation see Simulation Manual - Heat

Exchanger in Appendix C2, for a step by step guide.

The only component used is water and the fluid package is ASME Steam. In order to run the steady

state simulation a heat exchanger configuration must be selected and the system fully specified. The

configuration used is a two tube passes and one shell pass, being the first a counter current pass. In

Figure 4.44, it can be seen how this configuration allows having a relatively high temperature

difference, which is the driving force of the heat transfer, all along the tube path.


75

Figure 4.44. Heat Exchanger with U-tube configuration. [34]

The specifications applied are the following:

UA to 440 kJ/h·ºC

Pressure drop in tube-side and shell-side to 30 kPa

Hot OUT temperature to 40ºC

As a rigorous design of the equipment is out of scope for this project, all the design parameters are left

to their default options. The steady state simulation returns the following results:

Figure 4.45. Steady state simulation results.

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As expected, the duty exchanged (8371 kJ/h) is the exact one to bring 100 kg/h of water from 60ºC to

40ºC, as equation 4.32 estimates. The used specifications allow the calculation of the Ft Factor and the

Cold stream flow. So, 53.57 kg/h is the amount of coolant needed to achieve the process objective.

A valve has been added to each inlet stream for control purposes discussed further in this chapter. In

steady state mode the pressure drop specification is used, while a Cv value is needed in dynamics mode.

For each valve, the Cv has been obtained by auto-sizing with the ANSI/ISA method, with a 50% opening

and Equal Percentage inherent characteristic since a temperature control is to be performed. The only

difference is the flow passing through each valve and the pressure drop. About the utility valve, a higher

pressure drop has been selected in order to give it a higher flow range, since it is going to be the OP

(see chapter 4.2.3). Specifically, for the process stream valve (VLV-100) the pressure drop has been set

to 50 kPa, while for the utility stream valve (VLV-101) it has been set to 100 kPa.

The Dynamics Assistant makes the following suggestions:

Figure 4.46. Dynamics Assistant suggestion.

The first two suggestions refer to pressure specifications for all boundary streams and no more

specifications. The last two refer to the heat exchanger. As the valve, the heat exchanger is a resistance

element and need pressure-flow specifications and two conductance values, one for both tube and

shell paths (k parameter in Eq. 2.1). It is possible to auto-calculate the conductance value, but first of

all it is important to set the heights of the equipment and activate the static head contribution in the

integrator as hydrostatic pressure can affect the flow through the heat exchanger. The stream nozzles

of the heat exchanger have been set as shown in Figure 4.47:


77

Figure 4.47. Nozzles height of the Heat Exchanger.

In this configuration, the hot fluid enters from above and exits at the bottom, while the cold fluid does

the opposite. The default maximum height is 1 m, so the process stream valve (VLV-100) height has

been set to 1 m, while the utility valve height to 0 m.

In the Dynamics Specs tab of the heat exchanger it is possible to visualize the dynamic specifications

and obtain the k values:

Figure 4.48. Conductance parameters k and pressure flow equation specification.

When simulating a heat exchanger in dynamics mode, three models are available: basic, intermediate

and detailed. The main difference is the possibility of specifying more or less geometry details. For this

project, the basic model is enough. This model allows selecting the tube and shell volume and the

overall UA only:

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Figure 4.49. Dynamic model of the Heat Exchanger.

The volume of the equipment is essential to determine the rate of accumulation and the hold-up of

the heat exchanger. To better visualize the importance of these specifications, two simulations have

been done. The first using the default tube and shell volume (0.1 m3 both) and the second one reducing

the tube volume to a ten part of its default value (0.01 m3). The results are shown using a strip chart

for the process temperatures and another strip chart for the enthalpies or duties of the process.

Figure 4.50. Temperature Stripchart Legend.


79

Figure 4.51. Temperature Stripchart (tube volume = 0.1 m3).

The expected behaviour was a flat Stripchart since no disturbance was induced to the process.

However, the temperatures of the outlet streams move from their steady state value until they reach

a new equilibrium.

Figure 4.52. Enthalpy Stripchart (tube volume = 0.1 m3).

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Figure 4.53. Enthalpy Stripchart Legend.

Figure 4.54. Flowsheet DYN1.

The Exchanger Cold Duty and Hot Duty are the steady state duties, while s_Shell duty and s_Tube duty

are the real ones. It can be seen how they decrease rapidly at the beginning and then increase until

they stabilize to a lower value. This means that the exchanged energy is lower than in steady state

simulation. This explains why, at the exit of the heat exchanger, the hot fluid temperature increases

while cold one decreases. The reason behind this behaviour is in the accumulation inside the heat

exchanger, as the energy balance in the heat exchanger demonstrates:

𝑄 = 𝐻 − 𝐻 − 𝑄 − 𝑄 (Eq. 4.34)

As much more accumulation, less heat exchanged. When switching to Dynamics Mode the volumes

are taken into account but the dynamic calculation is not initialized yet and there is not any option to

set a starting scenario. So, when running the simulation, the tube and shell of the heat exchanger start

filling up. Hence, the rate of accumulation at the beginning is maximum and then decreases with time,

which explains the great decrease of the duty exchanged and then its slower increase in the Enthalpy

strip charts.


81

Figure 4.55. Temperature Stripchart (tube volume = 0.01 m3).

Figure 4.55 shows the same behaviour as Figure 4.51 but with a lower deviation of the outlet

temperatures. By reducing the tube volume, the accumulation in the tube side is reduced. The

exchanged energy (8084 kJ/h) is still lower than in the steady state simulation (8371 kJ/h), but higher

than in the previous case (7966 kJ/h). Even when the rate of accumulation is 0 and the system reaches

the equilibrium, the heat exchanged is lower than the calculated in steady state simulation. This is due

to the big difference between the residence time in tube and shell. A proper design would reduce the

duty deviation, however, the effect on the PV is negligible yet the temperature difference is less than

1 ºC (see Figure 4.57, PV=40.69ºC). In addition, it must be considered that the shell volume should be

designed with some tolerances since more coolant could be needed for control purposes.

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Figure 4.56. Enthalpy Stripchart (tube volume = 0.01 m3).

Figure 4.57. Flowsheet DYN2.


83

4.2.2. Disturbances and open loop responses

A set of disturbances was applied to the simulation in order to analyse the process dynamics.

1. 300-400 minutes: hot stream inlet pressure change from 180 kPa to 220 kPa. This is a flow

disturbance of 20 kg/h more approximately.

2. 400-600 minutes: hot stream inlet temperature change from 60ºC to 70ºC.

3. 600-800 minutes: cold stream inlet pressure change from 180 kPa to 160 kPa. This is a flow

disturbance of 5 kg/h less approximately.

4. 800-1000 minutes: cold stream inlet temperature change from 5ºC to 10ºC.

Figure 4.58. Temperature Stripchart: Open Loop response.

Observing Figure 4.58 and 4.60, the following conclusions can be done:

Disturbance 1: A higher flow means higher heat capacity and higher exchanged duty.

However, as this duty is going to be transferred by a greater amount of hot fluid than before,

the temperature difference will decrease and the PV will increase. The exchanged duty

increases at the beginning but then decreases when a new steady state is going to be reached,

since the temperature difference becomes lower.

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Disturbance 2: A higher temperature will increase the driving force obtaining a higher heat

transfer. However, this kind of disturbance will also make the outlet temperatures to be

higher than before (PV increases). The heat exchanged increases very fast at the beginning

but then falls smoothly until a new steady state is reached due to the decrease of the

temperature difference.

Disturbance 3: A coolant flow decrease means a heat capacity decrease which translates into

a lower exchanged duty. This leads to higher outlet temperatures (PV increases).

Disturbance 4: If the coolant enters the heat exchanger at a higher temperature, the driving

force will decrease and so does the exchanged duty. The outlet temperature will increase until

a new equilibrium is reached (PV increases).

Figure 4.60. Enthalpy Stripchart: Open Loop response.

The effect of each disturbance on the process variable depends on the type and on its magnitude.

However, if it is considered that the simulated disturbances are the limit cases for this process, the

temperature disturbance on the hot stream happens to be the most influent disturbance.


85

4.2.3. Feedback control loop

In the heat exchanger, the process variable is the process stream output temperature and the

manipulated variable is the service stream input, which will be modulated through a valve in order to

face the disturbances previously mentioned. The proposed control scheme for the feedback controller

is shown in Figure 4.61, where the transmitter is placed in the process stream output, and it is

controlled with the valve in the service stream input.

Figure 4.61. P&ID of the feedback control scheme for the heat exchanger.

Once the open loop response has been obtained, the process transfer function can be fitted into a first

order obtaining Eq. 4.35.

𝑇 (𝑠)

𝑈(𝑠)=

−0.624

64.35𝑠 + 1

º𝐶

%

(Eq. 4.35)

Now, in order to scale the transfer function obtained, the PV range must be known. In heat exchangers

set-point changes are not usual and in case they are demanded, the changes is really small. So, the

range selected is within 10 ºC of the nominal value and the range goes from 35 ºC to 45 ºC.

𝑇 (𝑠)

𝑈(𝑠)=

−6.24

64.35𝑠 + 1

%

%

(Eq. 4.36)

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The block diagram of the feedback control loop for the heat exchanger is almost the same as the

control loop for the tank liquid level, where only the process stream input disturbance has been

considered.

Figure 4.62. Block diagram of the heat exchanger feedback system.

The closed loop transfer functions of set-point change and disturbance are Eq. 4.37 and Eq. 4.38, which

again, have the same denominator.

𝑇(𝑠)

𝑇 (𝑠)=

𝐺 𝐺 𝐺 𝐺

1 + 𝐺 𝐺 𝐺

(Eq. 4.37)

𝑇(𝑠)

𝑇 (𝑠)=

𝐺

1 + 𝐺 𝐺 𝐺

(Eq. 4.38)

Both functions have the same characteristic equation, which means they both have the same margins

of stability that have been calculated via Routh-Hurwitz method.

1 + 𝐺 𝐺 𝐺 = 64.35𝑠 + 𝑠(1 − 6.24𝐾 ) − 6.24𝐾 = 0 (Eq. 4.39)

With the Routh array, the margins obtained are Eq. 4.41 and Eq. 4.42.

𝑠𝑠𝑠

64.35

1 − 6.24𝐾−6.24𝐾

−6.24𝐾00

(Eq. 4.40)

𝐾 < 0.16 (Eq. 4.41)

𝐾 < 0 (Eq. 4.42)


87

In order to obtain the tuning parameters, the IMC method has been used again for different values of

λ:

Table 4.6. Controller parameters obtained for different methods used.

Kc τI

IMC (λ = 5) -2.06 64.35

SKO (λ = 5) -2.06 20

SKO (λ = 7) -1.47 28

Several set-point changes and disturbances have been added to test the different set of tuning

parameters:

1. Set-point change from 40 ºC to 42 ºC in minute 100.

2. Process stream input temperature change from 60 ºC to 70 ºC in minute 400.


4. Process stream input temperature change from 70 ºC to 60 ºC in minute 1000.


Figure 4.63. Test disturbances for the feedback control system.

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Figure 4.64. Different tuning parameter responses to the disturbances introduced.

From Figure 4.64, some conclusions can be drawn. The first is that the fastest responses, which are the

ones obtained via the Skogestad’s method value present a light overshoot. This is due to big Kc value.

In this case, the values obtained without Skogestad’s limit provide the worst response due to the large

integral time, which makes the system really slow in both set-point tracking and disturbance rejection.

Figure 4.65. Valve response for the different tuning parameters.

Tem

pe

ratu

re(º

C)

Va

lve

Op

en

ing

(%

)


89

About the valve response, as it could be expected, the most aggressive responses are obtained for the

IMC where the limit value has been used.

In order to objectively compare the three tuning parameters proposed, the IAE, ISE and ITAE

performance criteria will be used again:

Table 4.7. IAE, ISE, ITAE obtained for the heat exchanger control system.

IAE ISE ITAE

SKO (λ = 5) 190.92 303.71 1.59

IMC (λ = 5) 366.88 451.30 3.05

SKO (λ = 7) 237.87 366.87 1.98

The performance criterion confirms that the IMC with the limit value and the tuning parameter of 5

obtains the best performance out of the three tested, closely followed by the one with the tuning

parameter of 7.

4.2.4. Cascade control loop

In a cascade control system, the main difference with the feedback control is that the output of the

temperature controller is fed into another controller instead of going directly to the valve. This second

loop, is responsible for ensuring that the flow rate of the cold liquid doesn’t change due to faults that

cannot be controlled, for example, irregularities in the cold liquid distribution. In this cascade scheme,

the process variable of the primary controller is the process stream output temperature, while the PV

of the second controller is the input mass flow of the service stream.

Figure 4.66.P&ID of the cascade control for the heat exchanger.

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By implementing cascade control, the flow controller will adjust the valve position in case that a

disturbance occurs in the service stream input. For instance, due to other users’ demands, the pressure

could drop leaving the system with less flow than usual. In a feedback control, in order to counter that

disturbance, the system would wait until the process variable has been modified, while in a cascade

control, the second controller would act immediately modifying the control valve stem position.

If the open loop response of the flow controller is obtained, it can be seen that the obtained transfer

function consists on the transfer function of the valve:

𝐹(𝑠)

𝑂𝑃(𝑠)=

2.19

0.2𝑠 + 1

%

%

(Eq. 4.43)

Building the Routh array for the first controller provides the margins of stability:

𝐾 > −0.45 (Eq. 4.44)

𝐾 > 0 (Eq. 4.45)

Before obtaining the open loop response of the primary controller, the secondary one has to be tuned

first and closed. In order to do so, the IMC method for a first order transfer function has been used

with a tuning parameter of 0.6, obtaining Eq. 4.46 and Eq. 4.47.

𝐾 = 0.15 (Eq. 4.46)

𝜏 = 0.20 (Eq. 4.47)

Once the inner loop has been closed, a step input can be introduced in the system and the open loop

response of the primary loop can be obtained. For this loop, the transfer function is Eq. 4.48 and the

fitting is shown in Figure 4.67.

𝑇(𝑠)

𝑂𝑃(𝑠)=

−2.30

55𝑠 + 1

%

%

(Eq. 4.48)


91

Figure 4.67. Primary loop fitting of the set-point change response.

Different constants have been tested for the IMC controller, obtaining the parameters shown in the

Table 4.8.

Table 4.8. Controller parameters obtained for the primary controller in the cascade scheme.

Kc τI

SKO (λ=7) - 3.41 28

SKO (λ=10) - 2.39 40

IMC (λ=15) - 1.60 55

About the testing of the cascade loop, the disturbances and SP change introduced in the system are:

1. Set-point change from 40 ºC to 42 ºC in minute 100. 2. Cold input pressure changes from 180 kPa to 210 kPa in minute 300. 3. Set-point change from 42 ºC to 40 ºC in minute 500. 4. Hot input temperature change from 60 ºC to 65 ºC in minute 700.

From the responses obtained for the different parameters it is clear that the ones that achieve the

fastest response are the two parameters that use the limit value of the integral constant. These

perform well in both set-point tracking and disturbance rejection; the only downside is that they

present overshoot.

0 50 100 150 200 250 300 350 400

Time (min)

38.5

39

39.5

40

40.5

41

41.5System response to a master controller change

Experimental ValuesFirst Order fitting

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Figure 4.68. Tuning parameters response to the tests introduced.

In terms of valve opening, as expected, the IMC with the limit value for the tuning parameter of 7

obtains the most aggressive valve openings.

Figure 4.69. Valve opening of the different tuning parameters for the cascade loop tests.

Tem

pe

ratu

re (

ºC)

Val

ve O

pen

ing

(%)


93

If the performance criterion is used the results shown in Table 4.9 are obtained. It can be seen that, as

expected, the Skogestad obtains the best performance followed by the IMC with a constant of 15.

Table 4.9. IAE, ISE, ITAE obtained for the different cascade parameters performance.

IAE ISE ITAE

SKO (λ = 7) 42.55 33.02 0.35

SKO (λ = 10) 53.09 38.64 0.44

IMC (λ = 15) 78.48 59.75 0.65

4.2.6. Feedforward control loop

Generally, feedforward control can be used when feedback cannot effectively control a process

variable. As previously said, a feedback controller must wait until disturbances affect the process

variable before actuating, but with feedforward control loop the controller can compensate this

disturbance before the process is affected.

In this case, a feedforward controller based on the steady-state energy balance of the heat exchanger

will be built [35]. It consists on calculating the valve opening as a function of the flow passing through

it. In order to implement this in HYSYS, the spreadsheet must be used to calculate the result of the

equation and export it to the valve.

Figure 4.70. Feedforward control block diagram.

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Figure 4.71. P&ID of the feedback plus feedforward control scheme.

In this case, it is desired to control the process stream output temperature, which will be named THout.

In order to maintain THout at a SP, the control valve will be open or closed depending on the required

action. The main disturbance considered is a temperature fluctuation in the process stream input (THin).

In order to determine the OP, the controller requires SP and THin.

The steady-state energy balance relates the stream flow to the disturbance of the process.

𝐹 𝐶 (𝑇 − 𝑆𝑃 ) − 𝐹 𝐶 (𝑇 − 𝑇 ) = 0 (Eq. 4.49)

Isolating FCin:

𝐹 = 𝐶 (𝑇 − 𝑆𝑃)

𝐶 (𝑇 − 𝑇 )· 𝐹

(Eq. 4.50)

A graphic of the valve opening vs the flow rate is obtained and, as Figure 4.72 shows the relation is

non-linear, an approximation to the third order has been done. Table 4.10 shows the numerical values

of the valve opening for each different flow value.


95

Table 4.10. Mass flow and Valve Opening relation for the feedforward valve.

Valve Opening (%) Flow rate (kg/h)

0 0

10 0.47

20 3.76

30 12.61

40 29.25

50 53.59

60 80.73

70 103.20

80 117.60

90 125.00

100 129.80

Figure 4.72. Valve opening and mass flow relation of the control valve.

By using the least squares method, a relation between x and y has been obtained:

𝑂𝑃(%) = (0.08 + 2.29 𝑥 − 3.99 𝑥 + 2.62 𝑥 ) · 100 (Eq. 4.51)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Mass flow (m3/h)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Va

lve

Ope

nin

g

Valve Opening vs Mass Flow

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Figure 4.73. Valve opening relation with mass flow curve fitting.

If in Eq. 4.51 the x is substituted by the mass flow, Eq. 4.52 is reached:

𝑂𝑃 (%) = 100 · 0.08 + 2.29 𝐹

129.8− 3.999

𝐹

129.8+ 2.618

𝐹

129.8

(Eq. 4.52)

However, mostly, feedforward-only control is not the best option because an accurate model of the

process is needed and sometimes it’s not available. The equation that relates the output of the valve

to the flow rate is not one hundred percent accurate, which leads to an offset between the control

valve desired percentage and the real mass flow passing through the valve.

In order to eliminate the offset, a feedback controller will be used in conjunction with the feedforward

controller. The feedback controller used will have the same tuning parameters as the normal feedback

controller already calculated (IMC with λ = 7). In order for the variable to reach the set-point, its output

value will be reduced to create a positive offset that allows the feedback controller to act and reach

the set-point.

In order to test the feedback controller, different disturbances will be introduced into the system:

1. Disturbance of 10ºC in the input flow temperature (from 60 to 70ºC). 2. Disturbance of 5ºC in the input flow temperature (from 70 to 65ºC). 3. Disturbance of 5ºC in the input flow temperature (from 65 to 60ºC).

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Mass flow (m3/h)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Va

lve

Op

enin

g

Relation between the mass flow and the valve opening

Experimental valuesLeast squares fitting


97

Figure 4.74. Feedforward plus feedback controller response to temperature disturbances.

From the last graphic it can be seen that the feedforward plus feedback controller does a good job at

the input disturbance rejection, even though it takes a long time for the temperature to stabilize.

4.2.7. Comparison of the different control schemes

In order to compare the different control systems, three different tests have been carried out. These

have been classified as set-point changes, temperature disturbances and flow disturbances.

About the set-point changes:

1. Set-point change from 40 ºC to 43 ºC in minute 100. 2. Set-point change from 43 ºC to 41 ºC in minute 400. 3. Set-point change from 41 ºC to 37 ºC in minute 700. 4. Set-point change from 37 ºC to 39 ºC in minute 1000. 5. Set-point change from 39 ºC to 40 ºC in minute 1300.

About the temperature disturbance:

1. Temperature change from 60 ºC to 55 ºC in minute 100. 2. Temperature change from 55 ºC to 58 ºC in minute 400. 3. Temperature change from 58 ºC to 68 ºC in minute 700. 4. Temperature change from 68 ºC to 64 ºC in minute 1000. 5. Temperature change from 64 ºC to 60 ºC in minute 1300.

Tem

pera

ture

(ºC

)

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About the flow disturbance:

1. Pressure change from 180 kPa to 250 kPa in minute 100. 2. Pressure change from 250 kPa to 210 kPa in minute 400. 3. Pressure change from 210 kPa to 160 kPa in minute 700. 4. Pressure change from 160 kPa to 260 kPa in minute 1000. 5. Pressure change from 260 kPa to 180 kPa in minute 1300.

For this test, the parameters for the three controllers have been selected to be not the most aggressive,

choosing more conservative approaches instead.

Table 4.11. Tuning parameters used for the comparison.

Kc τI

Feedback -1.47 28

Cascade (Primary loop) -2.39 40

Feedforward (feedback controller) -1.47 28

Figure 4.75. Different control schemes response to set-point changes.

About the response to SP changes, it can be seen that the most effective is the feedback controller,

followed closely by the cascade controller, which has a bit more of overshoot and a longer stabilization

time.

Tem

pera

ture

(ºC

)


99

Table 4.12. IAE, ISE and ITAE obtained for the SP disturbances introduced.

IAE ISE ITAE

Cascade 138.66 203.78 1.15

Feedback 95.14 135.88 0.79

Feedforward 310.35 400.59 2.50

The temperature results are shown in Figure 4.76.

Figure 4.76. Different control schemes response to temperature disturbances.

About the temperature response, it can be seen that even though the feedforward plus feedback

controller obtains good results in the rejection of the temperature disturbance, it is the control

scheme with a longer stabilization time, which penalizes the control scheme when it comes to the

performance criteria.

Table 4.13. IAE, ISE and ITAE obtained for the temperature disturbances.

IAE ISE ITAE

Cascade 80.60 59.57 0.67

Feedback 53.95 32.62 0.44

Feedforward 99.10 54.46 0.82

Tem

pera

ture

(ºC

)

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The responses obtained to the flow disturbances are shown in Figure 4.77.

Figure 4.77. Different control schemes response to flow disturbances.

It can be seen that the cascade controller achieves the best performance, obtaining much better

results than both the feedforward and the feedback controller.

Table 4.14. IAE, ISE and ITAE obtained for the flow disturbances introduced.

IAE ISE ITAE

Cascade 1.86 0.03 0.02

Feedback 16.39 1.33 0.136

Feedforward 53.25 6.785 0.44

For the heat exchanger studied in this case, the results have proven that the best control schemes

are the feedback and the cascade control loops, obtaining good results in the three tests. The final

decision should be made considering if utility stream disturbances happens frequently and taking

into account the budget available. Actually, one of the advantages that feedback controllers have

over cascade ones is that they are less expensive because they need one less controller.

Tem

per

atur

e (º

C)


101

4.3. Heated tank

The third case consists on a tank heated by steam passing through a coil. This is a system that could be

used for preparing the outlet stream before entering the next unit when some more capacitance than

the one provided by a heat exchanger is wanted. In such a system, the feed enters the tank at a certain

temperature, while the hold-up liquid in the tank is at a higher temperature provided by steam

condensation. Accepting the perfect mixing hypothesis inside the tank, the outlet stream has the same

temperature than the hold-up liquid. There are two PV: the liquid level and the temperature of the

tank. A change in one of them can affect the other. On one hand, if the temperature increases, the

water density increases too and the liquid level rises. On the other hand, if the liquid level decreases,

the heat is absorbed by a smaller amount of liquid, so the temperature increases.

In the proposed case, the feed is water entering the tank at 25ºC and 140 kPa. The tank is open to the

atmosphere and the SP for the liquid level is 50%, while the temperature desired is 50ºC. The utility

stream is steam at 250 kPa (2.5 bar).

Figure 4.78. Heated Tank: Flowsheet in Aspen HYSYS.

In such a system there could be many disturbances that will make the PV move from their desired

value:

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Feed flow disturbance.

Feed temperature disturbance.

Utility stream flow disturbance.

Utility stream pressure disturbance.

Steam quality change.

An ambient temperature decrease could increase the heat loss.

4.3.1. Dynamic simulation of a heated tank

The tank is the same as in the first case, with the same geometry, feed and open to the atmosphere.

The coil was simulated using the tube bundle. The first part of the simulation is simulating the tank.

The steps are exactly the same as for the Tank Liquid Level case, but in this case the Separator vessel

module was used since it is the only one to support the tube bundle option. The second part is

simulating the tube bundle. For details about the steps of the simulation see Simulation Manual -

Heated Tank in Appendix C3.

The components used are water, nitrogen and oxygen and the fluid package is Peng-Robinson. The

separator was run in dynamics mode until the SP (50% liquid level) is reached.

Since the tube bundle is only available in dynamics mode, the simulation has been quite different to

the previous ones. In fact, when in dynamics mode, the material streams added are given automatically

some specifications just to get them initialized. For instance, pressure and temperature are given

ambient default values (1 atm and 25ºC) while the composition is equally distributed. Probably these

specifications will not be the correct ones, but they can be changed to have a desired initial point.

The steam has been simulated at 250 kPa and fully saturated. To obtain the utility requirement, the

modelling was done at the maximum conditions for the nominal feed, in order for the process to be

able to heat the hold-up liquid up to 87ºC approximately. The steam inlet valve was simulated wide

open and a 1000 kg/h flow was set. Then, when the simulation converged to the equilibrium, the valve

opening was reduced until the vessel temperature was 50ºC (SP value).

Figure 4.79 shows a typical tube bundle:


103

Figure 4.79. Tube Bundle for heated tanks. (Source: Cooney [36]).

In the simulation, it was placed at the bottom of the tank. As the heat exchanger, it is another resistance

element and requires sizing. The specifications used when preparing the simulation for the maximum

conditions are the following:

Figure 4.80. Tube bundle specifications.

The selection of the heat transfer coefficients depends on the tube material and chemical species

inside and outside the tubes. In order to avoid such details, as a mean of simplification, these

coefficients were left at their default values. The tube volume, heat transfer area and the tube pressure

drop were specified instead. This allows the global UA calculation. As the simulation has not been run

yet, the Tube liquid volume percent is 0, so the tube is empty. For the same reason, the shell duty does

not have a value yet.

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104

Further relevant details about this simulation are:

The dynamic specifications were set in order to force a certain flow through the tube bundle.

The flowsheet with the dynamic colour code is shown in Figure 4.81. The Steam IN stream has

both pressure and flow specifications and VLV-104 has the Total Delta P specification instead

of the Pressure Flow Relation. The tube bundle has a delta P specification too as shown in

Figure 4.80, so the VLV-105 does not need any specification since the pressure has been fixed

both before and after it. This method is necessary since these material streams have been

initialized in dynamics mode.

VLV-104 has an Equal Percentage Operating Characteristic since it is going to control

temperature and has been auto-sized at the maximum steam flow condition scenario.

All the other valves, including VLV-105, are linear valves and have been auto-sized excluding

the vapour valve and the liquid outlet valve.

The Cv for the liquid outlet valve (VLV-102) has been obtained by simulating a stream with the

same flow but at 50ºC and 111.3 kPa passing through a linear valve with 50% opening, and a

pressure drop equal to the hydrostatic pressure of 1.024 m of water at 50ºC (9.94 kPa).

Figure 4.81. Heated Tank: Flowsheet at intermediate simulation.

The final results of the simulation are shown in Figure 4.82 and 4.83:


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Figure 4.82. Heated Tank: Final flowsheet.

It can be seen that both SP are reached and the utility requirement for that objective is 367 kg/h of

saturated steam at 250 kPa. The worksheet shows that the steam exits the tube totally condensed and

sub-cooled down to 27.2 ºC. This means that the global UA is very high. However, for the case purposes

it can be accepted.

Figure 4.83. Heated Tank: Worksheet results.

The process has been modelled taking into account one important simplification: the heat loss to the

environment is null and all the heat goes to the hold-up liquid. However, as the vessel is closed, Aspen

HYSYS calculates a temperature increase also for the air above the liquid surface (1.5 m3 at SP

conditions). By analysing the hold-up material, it can be considered that all the heat goes to the liquid

water since the vapour amount is negligible compared with the aqueous amount (Moles column):

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Figure 4.84. Heated Tank: Vessel holdup.

4.3.2. Disturbances and open loop responses

A set of disturbances is simulated in order to analyse the dynamic behaviour of the system:

1. 9500-9700 minutes: feed inlet pressure change from 140 kPa to 160 kPa. This is a flow

disturbance of 2 m3/h more approximately.

2. 9700-9900 minutes: feed temperature change from 25ºC to 15ºC.

3. 9900-10100 minutes: steam inlet valve opening change from 64.72% to 90%. This simulates a

valve malfunctioning.

The results are shown using three different strip charts. Figure 4.86 shows the liquid percent level

together with the vessel flows. Figure 4.87 shows the process temperatures and the duty exchanged,

while Figure 4.88 shows steam mass flows and pressures. Figure 4.89 is a zoom of the Steam Stripchart

to better visualize the effect of the second disturbance on the steam pressure and flow.

Figure 4.85. Temperature Stripchart Legend.


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Figure 4.86. Liquid level Stripchart: open loop response.

Figure 4.87. Temperature Stripchart: open loop response.

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Figure 4.88. Steam Stripchart: open loop response.

Figure 4.89. Steam Stripchart: open loop response zoom in disturbance 2.


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Figure 4.90. Steam Stripchart Legend.

Disturbance 1: When the feed flow increases, the level rises until a new equilibrium is reached.

This means that the hold-up amount also increased and, as the amount of steam is the same,

the same heat will be absorbed by more mass of water. This leads to a lower tank temperature.

Disturbance 2: When the feed enters the tank at a lower temperature there is a rapid change

in the heat exchanged. This is due to the mixing of the colder feed with the hold-up liquid. The

driving force, so the temperature difference, is higher now and maximum at the beginning,

decreasing with time until a new steady state is reached. This explains why the duty drops but

to a higher value than before. However, the duty is not enough to maintain the tank

temperature to the previous value. Instead, it decreases down to 37ºC approximately. The

condensed water exits the tube bundle at a lower temperature too, yet more heat is being

exchanged. This disturbance has much more effect on the temperature than on the liquid

level. As the feed stream is now at 15ºC, the density is higher and more water is entering the

tank, which justifies the small feed and liquid flow increase. This scenario, should lead to a

liquid level increase, however, as the holdup liquid passes from 45ºC to 37ºC its density

decreases too occupying less volume, which means that the liquid level drops. Figure 4.89

shows the condensed steam behaviour to disturbance 2. It can be seen that during 5 minutes

the aqueous phase flow and steam out flow oscillate, showing rapid positive and negative

accumulation inside the tube bundle. This can be due to the rapid increase of the heat

exchanged and its relatively fast stabilization. This leads to a rapid change in the tube hold-up

temperature and its density.

Disturbance 3: If the steam valve suddenly opens, more steam will enter the tube bundle. This

means that more latent enthalpy is available, which justifies the great increase in the heat

exchanged. When the valve opens, the pressure drop decreases, which makes Steam IN 2

pressure higher. When talking about a saturated steam, a pressure increase means a saturated

temperature increase, increasing the driving force of the heat transfer. The result is a vessel

temperature increase, which causes the water density to be lower and occupy more volume,

so the liquid level to drop.

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4.3.3. Multiloop control

In order to control this process, multiloop techniques must be used. In this case, the output variables

are going to be the vessel temperature (y1) and the liquid percent level (y2). The manipulated variables

are going to be the tube bundle input stream (u1) and the tank output stream (u2), as shown in the

diagram below.

Figure 4.91. Heated tank P&ID.

4.3.3.1. Variable pairing and system identification

As it is a MIMO system, the changes on both input streams values affect both process variables. This

means that in the process there are four transfer functions, as it is a 2x2 system. Gp11 is the transfer

function of the vessel temperature variable when a change is applied in the tube bundle input stream.

Gp12 is the transfer function of the vessel temperature variable when a change in the outlet flow is

applied. Gp21 is the transfer function of the tank liquid level when a change in the tube bundle input

stream is applied, and Gp22 is the transfer function of the tank liquid level when a change in the tank

outlet flow is applied.

In this case, in order for the attendee to be aware on different pairing methods, RGA, SVA, and NI will

be used.

It is important to remark that, for this case, the gains of the transfer function had to be obtained in

dynamics mode, because the steady state mode does not support the tube bundle module.


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Table 4.15. Transfer function gains.

K11 [%/%] K12 [%/%] K21 [%/%] K22 [%/%]

2.45 2.6e-3 0.1 -1.5

It can be seen that with a λ being really close to 1, the pairing for the variables obtained with the RGA

method is the 1-1, 2-2 configuration.

𝜆 = 1

1 −0.0026 · 0.1

2.448 · (−1.5)

= 1

1.0001= 0.99

(Eq. 4.53)

𝜆 1 − 𝜆1 − 𝜆 𝜆

=0.99 0.010.01 0.99

(Eq. 4.54)

If the Niederlinski index is calculated a positive value is obtained, which means that it cannot be

concluded if the system will be stable or not.

𝑁𝐼 = |𝐾|

∏ 𝑔 =

−3.6723

−3.672= 0.99

(Eq. 4.55)

In case that the singular value analysis is used, the first thing to do is to see if the gain matrix is linearly

independent.

|𝐾 − 𝛼𝐼| = 2.448 − α 0.0026

0.1 −1.5 − α= 𝛼 − 0.948𝛼 − 3.66 = 0 (Eq. 4.56)

𝛼 = 2.44; 𝛼 = −1.49 (Eq. 4.57)

From equations Eq. 4.56, as the values obtained were different than 0, it can be stated that the gain

matrix is linearly independent.

In order to calculate the singular values, the eigenvalues of the KTK matrix must be obtained.

𝐾 𝐾 = 2.44 0.1

0.0026 −1.52.13 0.00260.1 −1.5

= 5.19 −0.14

−0.14 2.25 (Eq. 4.58)

𝐾 𝐾 − 𝛼 𝐼 =5.19 − 𝛼 −0.14

−0.14 2.25 − 𝛼= 𝛼 − 7.44𝛼 + 11.65 (Eq. 4.59)

And the values obtained are σ1 (Eq. 4.61) and σ2 (Eq. 4.62).

𝛼 = 5.19; 𝛼 = 2.24

(Eq. 4.60)

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𝜎 = 𝛼 = 2.28 (Eq. 4.61)

𝜎 = 𝛼 = 1.49 (Eq. 4.62)

Finally, the CN number is shown in Eq. 4.63.

𝐶𝑁 = 𝜎

𝜎=

2.28

1.49= 1.5

(Eq. 4.63)

With the SVA, in this case, as the value is really close to one, it can be said that the 2x2 matrix is really

well conditioned.

About the transfer function of the vessel temperature, when a change is applied in the tube bundle

input stream a second order identification has been selected (Eq. 4.64).

𝑌 (𝑠)

𝑈 (𝑠)=

2.44

11.05𝑠 + 10.64𝑠 + 1

%

% =

1.22

11.05𝑠 + 10.64𝑠 + 1

º𝐶

%

(Eq. 4.64)

Instead, when a change is applied in tank output flow stream, a first order fitting has been used (Eq.

4.65).

𝑌 (𝑠)

𝑈 (𝑠)=

0.0026

9.9𝑠 + 21.8𝑠 + 1

%

% =

0.0013

21.52𝑠 + 1

º𝐶

% (Eq. 4.65)

In the case of the transfer function of the liquid percent level, when a change is applied to the heat

exchanger input stream, a second order fitting has been obtained (Eq. 4.66).

𝑌 (𝑠)

𝑈 (𝑠)=

0.1

15.73𝑠 + 1

%

%

(Eq. 4.66)

Instead, when a change is applied to the output flow stream, a first order model has been selected (Eq.

4. 67).

𝑌 (𝑠)

𝑈 (𝑠)=

−1.53

28.80𝑠 + 1

%

%

(Eq. 4.67)

So, taking into account the RGA, SVA, and NI results, the selected pairings for this case are y1-u1 and y2-

u2, and it can be concluded that the system is stable, obtaining a 1-1, 2-2 configuration. In this case, the

dynamic considerations are not a key factor in pairing the variables because there is not a great

difference in the time constants obtained.


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Figure 4.92. Block diagram of the heated tank.

According to [21] the characteristic equation of the 2x2 system is the following.

1 + 𝐺 𝐺 1 + 𝐺 𝐺 − 𝐺 𝐺 𝐺 𝐺 = 0 (Eq. 4.68)

Eq. 4.68 can be simplified considering that the gains of the transfer functions Gc12 and Gc21 are really

small and thus the controller parameters can be approximated considering that both transfer functions

are 0.

Note that to obtain the stability parameters, both controllers have been considered to be PI.

1 + 𝐺 𝐺 = 11.05𝑠 + 10.64𝑠 + (1 + 2.44𝐾 )𝑠 + 2.44𝐾 = 0 (Eq. 4.69)

With the Routh-Hurwitz method, the limit parameters for the first controller are Kc1 and KI1.

𝐾 > 2.53𝐾 − 1

2.44

(Eq. 4.70)

𝐾 > 0 (Eq. 4.71)

For the second controller:

1 + 𝐺 𝐺 = 28.80𝑠 + (1 + 𝐾 ) − 1.5𝐾 = 0 (Eq. 4.72)

And the final limit parameters for the controller are going to be Kc2 and KI2.

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𝐾 < 0.66 (Eq. 4.73)

𝐾 < 0 (Eq. 4.74)

4.3.3.2. Tuning the controllers

In order to obtain the controller parameters of the system, the independent loop method explained in

chapter 2.3.6.5 will be used. In this method, both controllers are tuned based on their open loop

responses.

The IMC method will be used and, in this case, as the temperature loop is a second order function, a

PID will be obtained. However, in order to compare the PID with the PI, the transfer function will be

approximated to a first order plus time delay in order to obtain a PI controller.

The P&ID diagram of the Heated Tank is shown below, where the two controllers can be seen in action.

Tuning the first controller

In the temperature controller, using a tuning parameter equal to 5 the proportional, integral and

derivative parts obtained are shown in Eq. 4.75, Eq. 4.76, Eq. 4.77, respectively.

𝐾𝑐 =2𝜉𝜏

𝐾𝜆= 0.90

%

%

(Eq. 4.75)

𝜏 = 2𝜉𝜏 = 10.64 (Eq. 4.76)

𝜏 =𝜏

2𝜉= 1.03 (Eq. 4.77)

In order to obtain the PI controller, as said earlier, Skogestad’s half rule has to be used, but first, the

denominator of Eq. 4.64 has to be rearranged in the form of Eq. 4.78.

𝑌 (𝑠)

𝑈 (𝑠)=

1.22

(9.47𝑠 + 1)(1.16𝑠 + 1)

º𝐶

%

(Eq. 4.78)

The next step is to transform the two time constants into one, so the new time constant will be

obtained by adding the largest time constant plus half of the next largest:

𝜏 = 9.47 + 1.166

2= 10.06

(Eq. 4.79)


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And the time delay is going to be the second largest time constant divided by 2 plus all the other time

constants, but in this case there are none.

𝛳 = 1.166

2= 0.58

(Eq. 4.80)

The resulting FOPTD transfer function is shown in equation 4.81:

𝑌 (𝑠)

𝑈 (𝑠)=

1.22

10.06𝑠 + 1𝑒 .

º𝐶

%

(Eq. 4.81)

In order to tune a first order plus time delay system, the equations shown in appendix C5 can be used,

with a tuning parameter of 4. The PI values obtained are:

𝐾 = 𝐾 =𝜏

𝐾 · (𝜆 + 𝛳)=

10.06

2.44 · (4 + 0.58)= 0.90

(Eq. 4.82)

𝜏 = 𝜏 = 10.06 (Eq. 4.83)

Tuning the second controller

For the second controller, the first order equations of the IMC method have been used. For this case,

several tests will be performed with different values of λ. The Skogestad controller parameters have

also been calculated for the case when the tuning constant is equal to 5.

Table 4.16. Controller parameters obtained for the liquid level controller.

Kc τI

IMC (λ = 5) -3.84 28.8

IMC (λ = 10) -1.92 28.8

IMC (λ = 15) -1.28 28.8

Skogestad (λ = 5) -3.84 20

4.3.3.3. Testing the control system

In order to test the control parameters obtained for the first controller, different set-point changes and

disturbances were introduced to the system with both loops closed. In this case, as the RGA pointed

out, the interaction between both loops is minimal. However, to test the first controller, the

parameters used for the second one were Kc2 = -3.84 and τI2 = 20. The final disturbances applied were:


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2. Pressure disturbance in the tube bundle input steam from 250 kPa to 280 kPa in minute 300.

3. Temperature disturbance in the Feed stream from 25 ºC to 20 ºC in minute 600.


5. Pressure disturbance in the tube bundle input steam from 280 kPa to 250 kPa in minute 1200.

Figure 4.94. Different control schemes response to different disturbances.

Figure 4.95. Valve response of the PID obtained with the IMC method.

Tem

per

atur

e (º

C)

Tem

pera

ture

(ºC

)


117

From the Figure 4.94, it can be seen that both PI and PID parameters obtain very good and very similar

results. In Figure 4.95, it can be seen the oscillation of the controller output when the derivative action

is added. In this case, as in the simulation there is no noise it is not critical, but in other cases where in

the plant there is external noise or interferences that cannot be shielded off, the derivative action

should never be added. Another characteristic of the derivative action that can be seen in the graphic

is the derivative kick, around 600 minutes. The derivative kick occurs because the value of the error

changes suddenly when the set-point is adjusted, thus causing a really large error and saturating the

controller output. In Figure 4.96, the controller output of the PI shows a much smoother response.

Figure 4.96. Valve Opening response for the PI obtained with the IMC method.

Table 4.17. IAE, ISE and ITAE obtained for the first controller.

IAE ISE ITAE

PI 243.93 223.52 2.03

PID 258.23 231.29 2.15

As expected, as the two controllers behave really similar, the performance parameters are identical.

Due to the small oscillations in the PID controller output, for the tests of the liquid level controller, the

PI was used.

In the liquid level loop, the different set-point changes and disturbances were:

1. Set-point change from 50 % to 70% in minute 0.

Tem

pe

ratu

re (

ºC)

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2. Input disturbance from 140 kPa to 170 kPa in minute 300. 3. Heat exchanger set-point change from 50 ºC to 60 ºC in minute 600. 4. Set-point change from 70 % to 50% in minute 900. 5. Input disturbance from 170 kPa to 140 kPa in minute 1200.

Figure 4.97. Different responses for the test disturbances proposed in the liquid level loop.

From the last graphic, it can be seen that the best response of all the tuning parameters are the ones

obtained with the Skogestad tuning method.

Figure 4.98. Valve opening responses for the tuning parameters.

Liq

uid

Lev

el (

%)

0 500 1000 1500

Time (min)

0

10

20

30

40

50

60

70

80

90

100Outflow valve responses to disturbances

IMC (lambda = 5)IMC (lambda = 10)IMC (lambda = 15)SKO (lambda = 5)


119

From the valve graphics, it can be seen that the Skogestad and the IMC for a constant of 5 give the

most aggressive controller outputs, especially when a set-point change occurs. On the other hand, the

other two tuning methods are not as much aggressive.

The performance criteria return the results shown in Table 4.18. It can be seen that the Skogestad

parameters obtained are the best in terms of the error, as they achieve better results in all the

categories, followed by the IMC when a constant of 5, and with the last being the IMC with the higher

constant.

Table 4.18. IAE, ISE and ITAE obtained for the second controller.

IAE ISE ITAE

IMC (λ = 5) 713.90 3123.30 5.94

IMC (λ = 10) 951.30 5150.90 7.92

IMC (λ = 15) 1437.90 8954.30 11.98

SKO (λ = 5) 496.70 2514.50 4.13

So, attending the results obtained, the controllers selected are the PI option for the temperature

control and IMC with a tuning parameter of 5 with the Skogestad limit of value for the tank level loop.

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4.4. Distillation column

The final case reunites all the knowledge assimilated by the moment, adding some more difficulty in

both process simulation and control. The process chosen is a binary distillation column for a non-

azeotropic mixture with a total condenser. For such a system, there are 5 PV to be controlled and so 5

OP to be chosen. The selection process will be discussed later in chapter 4.4.5. As all these variables

affect each other, a multivariable control will be performed and, as the relation between each variable

can be more troublesome, a brief distillation theory review is presented in chapter 4.4.1.

4.4.1. Distillation column theory

The distillation is a separation process based on the volatility of the chemical species. Disregarding the

nature of the mixture to separate (binary or multicomponent, azeotropic or non-azeotropic), the

separation is easier if the relative volatility is higher. The mixture is heated up to its boiling point

obtaining a vapour with a higher composition of the component with the lower boiling temperature,

being the heat provided the separator agent. The system obtained is a two-phase system described

by the vapour-liquid equilibrium (VLE), which can be represented with the diagram in Figure 4.99b.

Figure 4.99. Continuous distillation with reflux and total condenser (a) [33], VLE diagram description (b) [37].

The simplest case for a continuous distillation column is the one shown in Figure 4.99a. Inside the tower

there is an ascending vapour flow and a descending liquid flow which are brought into contact on

plates. Figure 4.100a shows the control volume for plate n and Figure 4.100b how the purification takes

place. Two streams enter plate n: the liquid coming from the above stage (Ln-1) and the vapour coming

from the previous plate (Vn+1). These two streams are not in equilibrium and, when brought into

(a) (b)


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contact, they try to reach it exchanging heat of vaporisation, which allows the transport of the volatile

component from the liquid to the vapour. As Figure 4.100b shows, the result is a higher molar fraction

of the light component in the vapour and a lower molar fraction in the liquid (x is the molar fraction of

component A in the liquid phase, y is the molar fraction of component A in the vapour phase). A

composition gradient is obtained in the column where the molar fraction of the heavy component

decreases while the molar fraction of the light component increases from the bottom to the top of the

column.

Figure 4.100. Material balance in stage n (a) and rectification in stage n (b) [38].

Obtaining high purity components depends on many variables and design parameters:

Stage efficiency: the contact between the two phases is crucial to have a maximum mass

transport. This happens when the equilibrium is reached. However, in real plates, equilibrium is

never truly reached and the separation degree is lower. In the designing procedures, it is common

to consider stage efficiency equal to 1, the maximum value, and sometimes it can be a very good

simplification for real processes.

Stage number: as more plates are in the column, the separation degree is higher since more

contact phases are added. However, adding plates means increasing equipment cost.

Feed stage number: it is very important for the feed to enter the column in a plate where the

conditions (composition, temperature) are as similar as possible. The feed can enter the tower in

four different scenarios: at its boiling point, sub-cooled liquid, saturated vapour or mixture of

liquid and vapour phase. Depending on this condition, the amount of liquid or vapour in the

column will be higher or lower since the liquid fraction will go down to the bottom while the

vapour fraction will go up to the top.

Reflux ratio: it is the relation between the flow returned to top of the column (L) and the distillate

product extracted (D). For each distillation column there is a minimum reflux ratio at which the

(a) (b)

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number of plates required to accomplish the separation objective is infinite. As much more reflux,

more liquid is returned to the column and more contact is allowed between the phases. This

achieves higher purities or reduces the stage number requirement for the same separation

objective. Nevertheless, this equipment cost saving is countered by an increase in utility needs,

yet there is more mass in the tower and the reboiler (the heat exchanger placed at the bottom of

the column) needs more heat to maintain the boiling temperature. There exists a relation for

selecting the optimal reflux ratio that states that it should lie between 1.2 and 1.5 times the

minimum reflux ratio [33].

Pressure: the VLE changes at different pressures, which makes it essential to work at constant

pressure. Normally, the operating pressure is referred to the pressure at the top of the column.

Its selection will depend on the dew point of the top vapour to condensate. As pressure increases,

the dew point also does, which allows using a coolant stream at a higher temperature.

Environmental changes must be taken into account when designing the condenser yet the

maximum summer temperature of cooling water is 30ºC [33].

In such a system, the degrees of freedom can be determined by the phase rule [33]:

𝐹 = 𝐶 − 𝑃 + 2 (Eq. 4.84)

Where:

F is the number of degrees of freedom

C is the number of components of the system (binary = 2)

P is the number of phases of the system (vapour and liquid = 2)

Which results into 2 degrees of freedom. Considering the steady state material balance in the column

in Figure 4.99a, these 2 degrees of freedom can be assigned to achieve the separation objectives:

𝐹 = 𝐷 + 𝐵 (Eq. 4.85)

𝐹 · 𝑥 = 𝐷 · 𝑥 + 𝐵 · 𝑥 (Eq. 4.86)

Where:

F is the feed flow.

D is the distillate flow.

B is the bottom flow.

xi is the molar fraction of the light component in each stream.


123

4.4.2. Steady state simulation of a distillation column

The chosen case is the distillation of n-butane and n-pentane mixture, a common process in oil refining

[39]. The feed stream has the following specifications:

Table 4.19. Feed specifications.

FEED Vapour / Phase Fraction 0.0000 Pressure 520 kPa Molar Flow 800 kmol/h Molar fraction n-butane 0.55 Molar fraction n-pentane 0.45

The 0.00 specification in the vapour phase fraction indicates that the feed enters at its boiling point.

The objective of the separation is obtaining a distillate product with a 98% n-butane purity and a

bottom product with a 98% n-pentane purity. The operating pressure has been decided to be 500 kPa,

which assures a dew point of the top vapour mixture around 50ºC (Source: Aspen HYSYS). This makes

it possible to condensate the vapour using water at 5ºC.

Figure 4.101a shows the VLE for the n-C4 and n-C5 mixture at different pressures (units in lb/in2) [40].

Even if the chosen operating pressure is not represented (100 lb/in2 = 689.5 kPa), the graphic shows

that the mixture is not azeotropic. The Peng-Robinson fluid package was selected to model the VLE and

the thermodynamics properties of the system, as suggested by HYSYS through the Method Assistant.

In Figure 4.101b, it is shown how this fluid-package predicts the VLE for the binary mixture at 500 kPa.

Figure 4.101. VLE data (a [40]) and VLE obtained through a HYSYS case study (b).

(a) (b)

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In order to design the column, the Shortcut module was implemented. However, there are graphical

methods such as the McCabe-Thiele one that can also be used for a binary mixture [38]. Estimating a

pressure drop of 40 kPa along the column, the number of plates, the reflux ratio and the feed stage

have been obtained (Figure 4.102). These results have been used to simulate the Distillation Column

module.

Figure 4.102. Shortcut Column: Performance tab.

Once the plates have been set to be 21 and the feed stage to 10, as said in the previous chapter, there

are 2 degrees of freedom to be specified in order to determine the separation degree. In this case, the

reflux ratio and the distillate flow were specified, both coming from the Shortcut calculation. The

steady state simulation converged to a result shown in Figure 4.103. It can be seen how the separation

objective is achieved and the column design correct.

Figure 4.103. Distillation Column: Results.


125

Further analysis implies plotting the temperature and composition profiles. In Figure 4.104, it can be

seen how the temperature changes at each stage proving that every stage is working and separation

is taking place in all of them. This means that there is not an excessive number of stages and, as the

98% of purity objective has been reached, no more stages are needed.

The same can be observed in the composition plot. As said before, the separation takes place in every

stage. In a distillation column, changes in temperature mean changes in composition as the VLE

diagram in Figure 4.100b shows.

Figure 4.104. Distillation Column: Temperature Profile.

Figure 4.105. Distillation Column: Composition Profile.

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4.4.3. Dynamic simulation of a distillation column

In order to perform a dynamic simulation of this process a different methodology was used. Instead of

converting the current steady state simulation into a dynamic one, the column was assembled starting

from a tower and the material streams, adding the required equipment one by one (sump, reflux drum,

pump and heat exchangers). The Absorber module was used in this case. The tray diameter was

changed from 1.5 to 2.5 m, just to give some more slack to the system, and the flow path was set to 2,

in order to allow 2 paths through the plates instead of only 1. In the next chapter, a brief description

about each equipment is presented. For more details about the steady state and dynamic simulation

see Simulation Manual - Distillation Column.pdf in Appendix C4.

4.4.3.1. Equipment Analysis

Assembling the column from zero implies properly designing both bottom and top recycle loops. In

Appendix A4, details about the design decisions and calculations are shown. The bottom recycle loop

extracts the liquid from the column and returns it as vapour after passing through a heat exchanger

(the reboiler). The following equipment are required:

Sump: it is a vessel added at the bottom of the column that assures that there is always some

liquid in the column and adds inertia to the system as a disturbance prevention. A vertical flat

cylinder Separator was used with a diameter of 2.5 m and a height of 4 m. The design liquid level

is at 65%. The Boilup stream enters the sump at 90% of total height, which is a way to assure that

the vapour does not mix directly with the hold-up liquid.

Figure 4.106. Distillation Column: SUMP.

Reboiler: it is the heat exchanger used to vaporise the liquid exiting from the Sump for then

returning it to the column. The utility stream is saturated steam at 7.5 bar and goes tube-side

while the cold stream goes shell-side. The same model as in the Heat Exchanger case was used.

The tube volume is of 0.535 m3 while the shell volume is 1.605 m3.


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Figure 4.107. Bottom recycle loop: reboiler and divisor tee.

Divisor Tee: it is a module which allows the separation of the liquid stream coming from the Sump

into the bottom product and the Boilup streams. The flow of the outlet streams depends just on

the pressure difference when in dynamics mode.

The top recycle loop extracts the vapour from the last stage and brings it to the ground level where it

is totally condensed. This is then accumulated in a closed vessel called Reflux Drum. The liquid exiting

from the bottom of this vessel goes to a pump, necessary to bring it back to 14 m high. The outlet

stream is then divided into two streams, the distillate product and the reflux stream, using the Divisor

Tee module. Figure 4.108 shows the flowsheet for this loop. Some information about each equipment

is resumed below:

Condenser: it is the heat exchanger used to condensate all the vapour exiting the top of the

column. The coolant is water at 5ºC. Again, the hot fluid goes tube-side while the coolant goes

shell-side. The tube volume was designed to be 0.94 m3, while the shell volume is of 2.09 m3.

Reflux Drum: a flat horizontal cylinder Separator was used with a total volume of 30 m3. The HYSYS

relation between height and diameter returns a height of 2.942 m. The designed liquid level is

50% [2]. In Figure 4.108, it can be seen that there is a purge stream. However, it is just a simulation

building feature yet the vessel must have two outlet streams. Actually, the vessel is closed and

pressurized when switching to dynamics mode.

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Figure 4.108. Top recycle loop.

Pump: it is necessary to gain the pressure to reach the top of the column from the ground level.

The head specification together with speed and efficiency specifications allow the creation of

pump curves, which add a more realistic point to the simulation since the head supplied by the

pump will vary with the flow passing through it. The curve can be seen in Appendix A4 (Figure A5).

All the equipment height was defined at ground level, except for some valves where the height has

been set equal to the nozzle height of the previous or next unit. It should be noted that there are many

valves and sometimes also 2 valves in series. However, the majority of them are simulation building

choices in order to facilitate the integration task. For instance, when there is a height change or an

equipment change, the valve can help dividing the pressure calculation into two more points, the inlet

point and the outlet point. For such valves, a big value of Cv was selected (1E+05) or a very small

pressure drop (0.001 kPa) for then obtaining the Cv through auto-sizing. Some valves show a pressure

drop, but it is only due to the hydrostatic pressure for the height change. The only valves that can be

used as OP are the following:

Feed (VLV-100), Reflux (VLV-113), Bottoms (VLV-103) and Distillate (VLV-112) valves: as they are

going to be OP for flow or level control, they have been set with a Linear operating characteristic.

Steam (VLV-105) and Coolant (VLV-108) valve: as they are going to be OP for pressure or

temperature control, the Equal Percentage operating characteristic was selected.

4.4.3.2. Transition to Dynamics Mode

This chapter serves to highlight the most important features when switching from steady state to

dynamics mode:

Integrator: as the simulation is much more complex than the previous ones, a smaller integration

step is required. Instead of the default one (0.5 s), a 0.2 s step was used. Furthermore, it has been


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necessary to bring the execution frequencies to the lower value, solving all the calculations

simultaneously. This is due to the amount of flash processes and composition change tray by tray.

Dynamic specifications: as in the previous cases, the pressure specification was left in each

boundary stream and each valve has got the pressure flow relation active. About the heat

exchangers, the conductance values were obtained by auto-sizing after specifying the flow and

the steady state pressure drop estimated. The same was done for the valves.

UA and k reference flows: a new feature has been implemented for this case. Once the dynamic

simulation reached the equilibrium, the two heat exchangers were given flow reference values.

The UA reference flow is used to model the UA variation with flow through the tubes or shell. The

following equation describes the relation [5]:

𝑈𝐴 = 𝑈𝐴 ·𝑚𝑎𝑠𝑠 𝑓𝑙𝑜𝑤

𝑚𝑎𝑠𝑠 𝑓𝑙𝑜𝑤

,

(Eq. 4.87)

The reference flows were set as the steady state values. If the flow gets higher, the UA will also

be higher, while the opposite happens if the flow drops. The k reference flow is important for

start-up and shut-down operations yet it provides a more linear relation between flow and

pressure at low flow region. The k reference flows were set at 40% of the steady state flow, as

recommended in the HYSYS Help. The relation that will be applied only in the case that the flow

is lower than the reference flow is the following:

𝑘 = 𝑘 ·|𝐹𝑙𝑜𝑤|

𝑅𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝐹𝑙𝑜𝑤

(Eq. 4.88)

Controllers: in order to make the simulation converge and reach the equilibrium, another

common building feature has been implemented. The controllers help in stabilizing the system

that without this help would probably not converge due to the big differences between steady

state simulation and dynamic simulation. The feed controller is absolutely artificial. In real plants,

the feed flow and pressure is determined by the previous unit, a reactor or another distillation

column for example, but here there is no another unit. If the feed is set to be free, it will change

if there is a change in the pressure profile inside the column, and as the boundary pressure has

been specified, the pressure drop will vary and so does the flow. The vessels controllers are added

to stabilize the system, which would be very difficult for the big inertia of these equipment. The

last is the reflux controller, which helps in getting the desired distillate, and so the bottom,

product.

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Figure 4.109. Distillation Column: Dynamic Simulation Flowsheet.

All these controllers are just PI controllers. As no tuning has been done yet, they have been given

common parameters. The flow controllers were set to reverse action, yet if the flow increases, valve

must close, and with K=0.1 and Ti=0.25. The level controllers were set to direct action with K=2 and

Ti=10 [5].

4.4.3.3. Results Analysis

The simulation reaches the equilibrium and the results show that the separation objective is achieved

(98% purity). A further analysis can be done by comparing the dynamic simulation results with the

steady state ones:

Table 4.20. Steady state vs Dynamics.

Steady State Dynamics Distillate 441.9 kmol/h 442.5 kmol/h Distillate purity 97.98% 98.03% Bottoms 358.1 kmol/h 357.5 kmol/h Bottoms purity 98.02% 98.28% Recovery n-C4 98.40% 98.59% Recovery n-C5 97.50% 97.60% Reflux Ratio 1.373 1,371 Qreboiler 2.152E+07 kJ/h 2.168E+07 kJ/h Qcondenser 2.072E+07 kJ/h 2.101E+07 kJ/h Top stage pressure 500 kPa 503.5 kPa Inlet stage pressure 520 kPa 516.9 kPa Bottoms pressure 540 kPa 549.6 kPa Stages 21 21 Inlet stage 10 10


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The great difference resides in the column pressure. Even if at the top of the column the difference is

relatively small, it affects directly to the vapour-liquid equilibrium and so to the temperatures and

compositions. It is also relevant that the feed enters at a lower pressure than in the steady state

simulation, yet the temperature and vapour phase condition will be different. The pressure profile in

the column has changed and this is due to the hydrostatic pressure, caused by the liquid inside the

column and the adding of the sump, and the resistance of each stage. As the heat exchangers and the

valves, the stages of a distillation column have a resistance equation associated as well. Figure 4.110

shows the conductance values for each plate. These values have been obtained automatically,

however, if it is necessary, they can be set to other values.

Figure 4.110. Trays conductance values.

If the temperature profiles of both columns are compared it can be seen how similar they are and no

visible difference can be distinguished between Figure 4.104 and 4.111. Globally, the results are a little

better in the dynamic simulation, but they are very similar to the steady state results. Hence, it can be

said that the column was properly simulated in dynamic mode and reliable results can be obtained.

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Figure 4.111. Distillation Column: Dynamic Temperature Profile.

4.4.3.4. Disturbances, Open Loop Responses and Process Variables Relation

As said at the beginning of Chapter 4.4, the distillation column is a more complex case of multivariable

control. So, in order to study the process variables relation, a set of disturbances is induced to the

system and the open loop responses are analysed. This is a clear circumstance in which the dynamic

simulation enhances a deeper understanding of the process and the relation of its variables.

Usually, previous to the distillation column, there is a reactor or another distillation column. A

disturbance in this unit will modify the feed conditions inducing a disturbance in the distillation unit.

So, possible disturbances are:

Feed flow disturbance.

Feed composition disturbance.

Feed temperature disturbance.

Other possible disturbances are:

Valve malfunctioning: it could happen in many process spots (bottoms, distillate, reflux, utility

streams).

Environmental changes: if there is no protection against summer temperature, the coolant will no

longer be available at 5ºC.

Before analysing the disturbances effect, some concepts must be revised. The pressure inside the

column is due to the amount of vapour inside of it. As more vapour, more pressure. The amount of


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vapour can be reduced by reducing the heat supplied or increasing the heat absorbed by the coolant.

In fact, the reflux temperature can cause a higher or lower heat transfer between the liquid and

vapour inside the column. For instance, if the reflux returns with a lower temperature, more vapour

will be condensed and the pressure drops.

Next, the first three types of disturbances are tested and the system responses are shown in three

different Stripcharts to better appreciate the results. In order to get the open loop response, all the

controllers were set on off mode, except for the feed stream. This controller is in fact used to simulate

a feed flow disturbance through a SP change.

Figure 4.112. Stripchart legend.

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Feed flow disturbance from 800 to 850 kmol/h

Figure 4.113. Feed flow disturbance: Open loop response (flows, liquid levels, temperature).

A higher feed flow means that more matter enters the column. According to the conservation of the

matter, the system will tend to an equilibrium where what goes out equals what goes in. However,

the sum of the output flows (Distillate Out and Bottoms Out) does not equal the feed flow. The reason

is that the liquid level of the reflux drum is still changing, which means that there is still some

accumulation in the process. With some more simulation time, equilibrium will be reached.

As the heat supplied is the same but the heat capacity has increased, the steam is not enough to

vaporise the proportional quantity of inlet stream and the column results in having more liquid than

vapour than before. The Boilup flow increase demonstrates it, together with the great liquid level rise

of the sump. This greater amount of liquid causes a Bottoms Out flow increase. If compared with the

Distillate Out flow, the variation has been much higher, however, the distillate flow also increases a

little since some more volatile component enters the column. The Reflux flow presents a very small

increase due to the additional amount of vapour exiting the column from the top. However, this top

flow increase affects the liquid level in the reflux drum, causing a positive accumulation. As said

before, as the heat supplied is fixed, the temperature measured in stage 17 is lower than before.


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Figure 4.114. Feed flow disturbance: Open loop response (flows, composition, pressures).

The liquid level increase will cause the bottom pressure of the sump to increase. Furthermore, as there

is more vapour than before, the top pressure increases changing the pressure profile of the column.

This explains why the feed pressure also changes. Generally, as the heat supplied is not enough to

provide the right temperature, the separation quality gets worse and both distillate and bottoms purity

are lower than before.

The resulting temperature profile (Figure 4.115) shows some differences with Figure 4.111: in the

rectifying zone (above the feed stage), the temperature has increased, which indicates a higher

presence of the heavy component; in the stripping zone (below the feed stage), the temperature has

decreased due to a higher amount of light component. Both phenomena demonstrate the purity loss

caused by this type of disturbance.

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Figure 4.115. Feed flow disturbance: Temperature profile inside the column.

Feed composition disturbance from 55% to 70% of n-C4

Figure 4.116. Feed composition disturbance: Open loop response (flows, liquid levels, temperature).


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The simulated disturbance consists on entering more volatile component (and so less heavy

component) than before. In this case, the feed flow is constant, so if the outlet flows vary is due to

column internal changes.

As before, the heat supplied is fixed but, this time, the amount of matter inside the column does not

change. Nevertheless, there is a top flow increase due to the generation of vapour. This is due to the

greater amount of light component, which allows the steam to vaporise more mixture than before.

For the same reason, the liquid amount decreases and so does the Boilup flow. This causes a liquid

level drop in the sump leading to a higher flow in the bottom. The Reflux flow is not really affected by

this disturbance having all the vapour amount exiting through the distillate output.

Figure 4.117. Feed composition disturbance: Open loop response (flows, composition, pressures).

As said before, firstly there is a net evaporation due to the higher amount of n-butane. This causes the

top pressure to increase changing the pressure profile inside the tower. As expected, the distillate

product is purer than before, however, the light component is not fully recovered in the top of the

column. A significant part of it exits through the bottoms, making this product much less pure. This

explains why the reflux drum level drops and the sump bottom pressure does not vary significantly.

As the composition varies a lot, the temperature of each outlet stream also changes, which has a direct

impact on the density. If the density increases, the liquid level drops.

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Figure 4.118 shows a very different temperature profile from the one shown in Figure 4.111. The next

three stages below the feed plate show a very small temperature difference, which means that they

are not needed or that the feed should enter another stage.

Figure 4.118. Feed composition disturbance: Temperature profile inside the column.

Feed temperature disturbance from 66.97 to 80ºC (0.002 to 0.1087 vapour phase)

Figure 4.119. Feed temperature disturbance: Open loop response (flows, liquid levels, temperature).


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A higher feed temperature was set in order to simulate a change in the feed condition. In particular,

the feed now enters the column with more vapour fraction than before.

As more vapour enters the column, a light top pressure increase should be registered, but above all a

flow increase exiting the top of the column. This translates into a distillate flow increase. The vapour

phase oscillation is due to pressure changes induced by the disturbance itself. As the amount of matter

inside the column is the same (feed flow is the same), less liquid than before enters the column. This

leads to a sump liquid level drop and the bottoms flow to increase consequently. However, both outlet

flows come back to their initial values approximately. This can be due to a reflux flow increase, which

reduces the top pressure restoring the initial pressure profile more or less.

Figure 4.120. Feed temperature disturbance: Open loop response (flows, composition, pressures).

As the feed enters the column at a different temperature, it is to expect that the temperature profile

changes. As a higher part of the inlet stream is already vapour, the heat supplied can be used to

vaporise a greater amount of mixture than before. The vapour is richer in the light component,

resulting in a purer distillate product, while the bottoms purity decreases below the 97%. This is due

to the higher temperature of the inlet liquid that goes to the bottom of the column. In Figure 4.121, it

can be seen how the temperature is a little bit higher in the stripping zone than in Figure 4.111. Instead,

as expected, a high purity is accompanied by lower temperatures in the rectifying zone.

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Figure 4.121. Feed temperature disturbance: Temperature profile inside the column.

Among all these scenarios there is an important feature to be highlighted. The vessels take a very long

time to stabilize due to their big volumes, and so to their inertia. This demonstrates that the system

has a big amount of capacity to face disturbances.

4.4.4. Tray Selection for Temperature Measurements

As previously said, if the pressure is constant, the temperature is an indicator of the mixture

composition. In most of the cases, an online composition measurement (such as chromatography) is

not available, and temperature measurements turn to be essential to have information about the

separation quality. Indeed, it is important to select the right location for the temperature sensor.

E. S. Hori and S. Skogestad suggest to locate the measuring point at the stage were the slope is steep.

By calculating the temperature difference between consecutive stages, the graph in Figure 4.122 is

obtained. A further analysis can be done by measuring the temperature gain to a reflux flow step [41].

In order to do so, the steady state simulation was used. The gain is calculated by dividing the

temperature difference between the nominal temperature in a stage and the one after the step

change. The results are shown in Figure 4.123.


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Figure 4.122. Temperature slop for consecutive stages.

Figure 4.123. Steady state gain for each stage.

Both graphics show a maximum for stage 17. This means that this stage is the most sensitive to changes

in the composition, yet it provides a faster temperature response. So, all the control schemes proposed

have got the temperature measurement point at stage 17, as a composition indicator. The SP is just

decided to be equal to the value obtained in the dynamic simulation once the equilibrium has been

reached (TSP, Stage 17 = 83.64ºC).

0 2 4 6 8 10 12 14 16 18 20 22

Stage

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Incr

emen

tT/I

ncre

men

tN

Temperature slop

IncT/IncN

Incr

eme

ntT

/Inc

rem

ent

L

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4.4.5. Distillation column control

As explained in chapter 4.4.1, in a distillation column with a total condenser and two product streams,

there are two degrees of freedom in steady-state, which needs to be specified in order to determine

the top and bottom compositions. In dynamics, the number of degrees of freedom turns to be 5. The

new three degrees of freedom need to be specified to define the column inventory variables within

the column. These variables are the pressure, the condenser level (reflux drum) and the column base

level (sump). In a real plant, the 5 degrees of freedom (5 PV) are specified through 5 valves opening (5

OP), as shown in Figure 4.124.

Figure 4.124. Distillation column P&ID with the five valves used for the control.

Each valve determines a flow that controls one or more process variable. In fact, in this case, multiple

configurations are possible and multiple variable pairings can be used in order to obtain good results.

Hence, the RGA method already presented in case 3 will be used in order to determine the best pairing.

4.4.6. Multivariable control of a distillation column

In this case, the RGA will be used to find the most appropriate pairing for the five process variables in

the distillation column. However, in order to control the pressure, the manipulated variable used will

be the coolant flow rate in the condenser. There are other ways, but this is a very common strategy

[2].


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The four process variables are:

Bottom composition. Top composition. Condenser level. Column base level.

The four manipulated variables are:

Reboiler duty QR Reflux flow L Distillate flow D Bottom product flow B

In order to build the distillation column control, the example shown in [2] was followed, where a similar

distillation column was shown and it explained simple guidelines on how to obtain the variable pairing.

In this case, the reason why the reflux ratio is not considered a manipulated variable is because of the

ratio. Modifying the ratio implies modifying two flows, losing controllability.

As there are 4 PV and 4 MV, there are 24 (4!) possible configurations shown in Table 4.21, even though,

only three of those twenty-four are viable. Generally, PV and MV cross between top and bottom of the

column must be avoided.

Combinations 1, 3, 5, 9, 11, 13, 15, 19, 20, 23, 24 were discarded since they involve control of the

column base level with the reflux or distillate flows, which in reality is not viable because those streams

cannot provide good control of that variable.

Combinations 6, 8, 14 and 19 were discarded since they involve manipulating flow rate of the bottom

product or reboiler heat to control the liquid level in the reflux drum, which again, is not viable because

those streams cannot provide good control of that variable.

Combinations 21 and 22 were discarded since they do not regulate the material balance.

Combinations 2, 12 and 17 were discarded since each involves the control of one or both compositions

at the end of the column using a manipulated variable at the other end of the column.

That leaves only case 4, 10 and 18 as possible options to evaluate.

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Table 4.21. All the possible options for the control of the distillation column [2].

In order to obtain the RGA, the steady-state gains for the compositions will be used, and the best

controller pairings will be determined for the bottoms and the distillate composition. Since the

inventory loops can be considered as independent on the quality level, the multiloop is a 2x2 system.

The initial steady state simulation will be used to calculate the open loop gain and the closed loop gain.

Case 4

In this case, the MV to control top and bottom composition are the distillate flow and the heat supplied

by the reboiler respectively. In order to obtain the open loop gain (K11), the steady state simulation was

given the distillate flow and the reboiler duty as specifications. Then, a step (+60 kmol/h) was made in

the distillate flow to see how top composition changes. About the closed loop, it was simulated

specifying the bottom composition (as a controller was fixing it) and the distillate flow. The same step

was introduced and the variation of the molar fraction of the volatile component is calculated, for then

obtaining the closed loop gain (K11*).


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Figure 4.127. Distillation column control scheme (case 4).

The open loop gain is:

𝐾 = ∆𝑥

∆𝐷=

0.8755 − 0.9798

501.9 − 441.9= −1.74 · 10

(Eq. 4.89)

For the closed loop gain and the λ:

𝐾∗ = ∆𝑥

∆𝐷=

0.8649 − 0.9798

501.9 − 441.9= −1.92 · 10

(Eq. 4.90)

𝜆 = 𝐾

𝐾∗ = −1.74 · 10

−1.92 · 10= 0.91

(Eq. 4.91)

Finally, the RGA can be built (Eq. 4.92). It can be seen that case 4 is a strong contender when it comes

to paring the variables, as the value obtained is really close to 1.

𝜆 1 − 𝜆1 − 𝜆 𝜆

=0.91 0.090.09 0.91

(Eq. 4.92)

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Case 10

In this case, the MV are the reflux flow and the bottoms flow. In order to obtain the open loop gain,

the steady state simulation was given the reflux and bottoms flows as specifications. Then, a step (+60

kmol/h) was made in the reflux flow and, as before the variation of top composition is calculated. About

the closed loop, it was simulated specifying the bottom composition and the reflux flow. The same step

was introduced to calculate the closed loop gain.


The open and closed loop gains are the following:

𝐾 = ∆𝑥

∆𝐿=

0.9869 − 0.9798

666.6 − 606.6= 1.18 · 10

(Eq. 4.93)

𝐾∗ = ∆𝑥

∆𝐿=

0.9904 − 0.9798

666.6 − 606.6= 1.77 · 10

(Eq. 4.94)

𝜆 = 𝐾

𝐾∗ = 1.18 · 10

1.77 · 10= 0.67

(Eq. 4.95)


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The RGA matrix shows worse results than case 4 (λ farer from 1), which indicates that case 10 should

not provide the best pairing for the controller.

𝜆 1 − 𝜆1 − 𝜆 𝜆

=0.67 0.330.33 0.67

(Eq. 4.96)

Case 18

In this case, the MV are the reflux flow and the heat supplied by the reboiler. In order to obtain the

open loop gain, the steady state simulation was given the reflux and reboiler heat specifications. Then,

a step (+60 kmol/h) was made in the reflux flow. About the closed loop, it was simulated specifying the

bottom composition and the reflux flow. The same step was introduced to calculate the closed loop

gain.


The open and closed loop gain are:

𝐾 = ∆𝑥

∆𝐿=

0.9958 − 0.9798

666.6 − 606.6= 2.67 · 10

(Eq. 4.97)

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𝐾∗ = ∆𝑥

∆𝐿=

0.9904 − 0.9798

666.6 − 606.6= 1.77 · 10

(Eq. 4.98)

𝜆 = 𝐾

𝐾∗ = 2.67 · 10

1.77 · 10= 1.51

(Eq. 4.99)

Finally, the RGA matrix can be constructed. The results show a worse pairing than the other two cases:

𝜆 1 − 𝜆1 − 𝜆 𝜆

=1.51 −0.51

−0.51 1.51 (Eq. 4.100)

In order to test the validity of these results, the RGA matrixes of the three cases have been also

calculated for a different step (+10 kmol/h). The results obtained were similar, pointing at case 4 as the

best option for pairing.

Case 4:

𝜆 1 − 𝜆1 − 𝜆 𝜆

=0.65 0.350.35 0.65

(Eq. 4.101)

Case 10:

𝜆 1 − 𝜆1 − 𝜆 𝜆

=0.62 0.380.38 0.62

(Eq. 4.102)

Case 18:

𝜆 1 − 𝜆1 − 𝜆 𝜆

=2.71 −1.71

−1.71 2.71 (Eq. 4.103)

In order to provide another indicator to check the stability of the system, the Niederlinski Index (NI)

was used. This index can be calculated from the steady state gain matrix of the distillation column.

𝐾 =𝐾 𝐾𝐾 𝐾

(Eq. 4.104)

𝐾 = ∆𝑥

∆𝐷=

0.8755 − 0.9798

501.9 − 441.9= −1.74 · 10

(Eq. 4.105)

𝐾 = ∆𝑥

∆𝑄𝑟=

0.9832 − 0.9798

2.2 · 10 − 2.152 · 10= 7.08 · 10

(Eq. 4.106)


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𝐾 = ∆𝑥

∆𝐷=

0.020 − 0.0198

501.9 − 441.9= 3.33 · 10

(Eq. 4.107)

𝐾 = ∆𝑥

∆𝑄𝑟=

0.0155 − 0.0200

2.2 · 10 − 2.152 · 10= −8.96 · 10

(Eq. 4.108)

𝑁𝐼 = |𝐾|

∏ 𝐾 =

1.56 · 10

(−1.74 · 10 ) · (−8.958 · 10 )= 0.99

(Eq. 4.109)

As NI > 0, the system will be stable [2].

Even though the RGA matrix specified that the optimal pairing is number 4, all the other pairings will

be tuned and compared in order to verify the results.

4.4.7. Tuning the controllers of the distillation column

In order to tune the different loops of the distillation column, the independent loop method will be

used for simplicity reasons. This method obtains the open loop system identification of each process

before closing all the individual loops. Note that all the open loop responses of the different loops are

shown in Appendix B4.

Pressure loop

About the pressure controller, all the cases have the same transfer function, thus, all of them have the

same tuning parameters. From the response obtained, a first or second order model could be built.

Nevertheless, to avoid introducing a derivative action in the controller that could potentially destabilize

the distillation column, the first order transfer function has been selected (Eq. 4.110). The tuning

parameters have been obtained with a constant of 1.3:

𝑃(𝑠)

𝑂𝑃(𝑠)=

16.25

10.72𝑠 + 1 [𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠] =

13

10.72𝑠 + 1

𝑘𝑃𝑎

%

(Eq. 4.110)

𝐾 = 0.51 (Eq. 4.111)

𝜏 = 10.7 (Eq. 4.112)

Column level

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In order to control the sump level, two transfer functions must be obtained, as case 4 and case 18

control it with the bottoms flow, where case 10 controls it with the reboiler duty. For case 4 and case

18, the transfer function obtained is shown in Eq. 4.113, which is a first order model. The tuning

parameters were obtained with a constant of 7.

𝐿(𝑠)

𝑂𝑃(𝑠)=

−2.3


(Eq. 4.113)

𝐾 = −3.21 (Eq. 4.114)

𝜏 = 28 (Eq. 4.115)

When it comes to case 10, the response obtained was also a first order model, but with a much lower

time constant (Eq. 4.116), and its tuning parameters were obtained with a constant of 9.

𝐿(𝑠)

𝑂𝑃(𝑠)=

−1.59


(Eq. 4.116)

𝐾 = −1.09 (Eq. 4.117)

𝜏 = 15.7 (Eq. 4.118)

Distillate drum

When it comes to the distillate drum, case 4 controlled the tank via the reflux flow, and the transfer

function could be fitted into a first order model (Eq. 4.119). In order to obtain the controller

parameters, the IMC method was used for a constant of 8.

𝐿(𝑠)

𝑂𝑃(𝑠)=

−13.19

313𝑠 + 1 [𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠]

(Eq. 4.119)

𝐾 = −2.96 (Eq. 4.120)

𝜏 = 32 (Eq. 4.121)

For cases 10 and 18, the manipulated variable was the distillate flow, and again, the function followed

a first order model (Eq. 4.112) and the tuning was obtained for a parameter of 8.

𝐿(𝑠)

𝑂𝑃(𝑠)=

−15.19

280𝑠 + 1 [𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠]

(Eq. 4.122)


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𝐾 = −2.24 (Eq. 4.123)

𝜏 = 32 (Eq. 4.124)

Distillate Composition

In order to control the distillate composition, case 4 uses the distillate flow, while cases 10 and 18 use

the reflux flow. The two transfer functions obtained, are the transfer functions of the valve, as flow

controllers were used. For case 4 (Eq. 4.125), the used tuning parameter was 4, obtaining Eq. 4.126

and Eq. 4.127. And for cases 10 and 18 (Eq. 4.128), the used parameter was 3, obtaining Eq. 4.129 and

Eq. 4.130.

𝑅(𝑠)

𝑂𝑃(𝑠)=

0.931


410

0.2𝑠 + 1

𝑘𝑔

ℎ·

1

%

(Eq. 4.125)

𝐾 = 0.05 (Eq. 4.126)

𝜏 = 0.2 (Eq. 4.127)

𝑅(𝑠)

𝑂𝑃(𝑠)=

0.934


445

0.2𝑠 + 1

𝑘𝑔

ℎ·

1

%

(Eq. 4.128)

𝐾 = 7.2 · 10 (Eq. 4.129)

𝜏 = 0.2 (Eq. 4.130)

Bottom composition

When it comes to controlling the bottoms composition, a temperature control will be used because

these type of controllers are affordable, reliable and fast compared to composition sensors [2]. While

cases 4 and 18 use the reboiler duty (Eq. 4.131), case 10 uses the bottoms flow (Eq. 4.134). The tuning

parameter used for cases 4 and 18 is 8 and for case 10 is 0.95.

𝑇(𝑠)

𝑂𝑃(𝑠)=

8.75


1.05

7.33𝑠 + 1 [º𝐶/%]

(Eq. 4.131)

𝐾 = 0.9 (Eq. 4.132)

𝜏 = 7.33 (Eq. 4.133)

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𝑇(𝑠)

𝑂𝑃(𝑠)=

−29.08

64𝑠 + 1 [𝑑𝑖𝑚𝑒𝑛𝑠𝑖𝑜𝑛𝑙𝑒𝑠𝑠] =

−3.49

64𝑠 + 1 [º𝐶/%]

(Eq. 4.134)

𝐾 = −0.42 (Eq. 4.135)

𝜏 = 20 (Eq. 4.136)

4.4.8. Testing the system

In order to compare the three systems, feed flow and temperature disturbances have been introduced.

Figure 4.130 is an example of the oscillatory responses provided by case 10, which makes its

implementation unviable. This is the reason why, in the following graphics, its response has been

omitted.

Figure 4.130. Temperature in stage 17 response to temperature disturbances (case 10 included).

For the comparison, 6 different graphics have been obtained. These graphics provide helpful insight in

the different process variables of the systems as well as the composition obtained in both bottoms and

distillate.

1300 1400 1500 1600 1700 1800 1900 2000 2100 2200

Time (min)

82.5

83

83.5

84

84.5Column temperature response to temperature disturbances

Case 4

Case10

Case 18


153

About the flow disturbances introduced, in order to make it more real, they have a short duration.

Normally, if there is a controller in the previous unit, the disturbance will be attenuated and the process

is more likely to experience oscillating flow disturbances.

1. Feed flow disturbance from 800 kmol/h to 700 kmol/h at minute 1300 with a duration of 5 minutes.



The responses obtained for the column pressure, distillate and bottoms composition, column

temperature and the distillation drum and column liquid levels are shown in the following graphics:

Figure 4.131. Column pressure response to the flow disturbances tested.

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Figure 4.132. Distillate composition response to the flow disturbances tested.

Figure 4.133. Bottoms composition response to the flow disturbances tested.


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Figure 4.134. Column temperature response to the flow disturbances tested.

Figure 4.135. Reflux drum response to the flow disturbances tested.

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Figure 4.136. Column base level response to the flow disturbances tested.

About the temperature disturbances, again, short lasting disturbances have been introduced.

1. Temperature disturbance from 66.94 ºC to 71.94 ºC in minute 1300 during 5 minutes.




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Figure 4.137. Column pressure response to the temperature disturbances tested.

Figure 4.138. Distillate composition response to the temperature disturbances tested.

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Figure 4.139. Bottoms composition response to the temperature disturbances tested.

Figure 4.140. Colum temperature response to the temperature disturbances tested.


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Figure 4.141. Reflux drum level response to the temperature disturbances tested.

Figure 4.142. Column base level response to the temperature disturbances tested.

Once all the responses have been obtained, the first thing that can be noted is that both systems

provide good control, achieving good disturbance rejection in both flow and temperature, obtaining

acceptable levels of composition in both distillate and bottoms parts. The responses of case 4 look

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smoother than the ones of case 18. Moreover, in Figure 4.132, the distillate purity falls down to 97%

in case of a feed flow disturbance. Keeping in mind that the objective of the control system is to

attenuate the disturbance presenting the minimum deviation from the SP and with a stabilization time

as fast as possible. In addition, taking into account that the objective of this distillation process is

obtaining products with 98% purity, the case 18 is the one that suits the best these requirements.

The conclusion disagrees with the RGA method prediction. In order to explain why the pairing obtained

with the RGA is not the optimal one, few arguments can be made. The main one is that the RGA method

is based on the steady-state simulation, where the system dynamics are not accounted. So, it is possible

that the dynamic system introduces some changes that the RGA does not consider.


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5. Economic analysis

In order to state the viability of the project, an economic analysis has been carried out. It is divided in

five parts: the investment, a fixed cost; the variable cost, associated to the teaching of the course; the

market study, where an offer analysis has been done to give a competitive price to the course; the

project viability, evaluated through a VAN analysis; and finally, the pilot test, analysing the results

obtained by surveys done to UPC students, which attended the Process Control subject where some

cases of this project have been implemented.

It has been considered that the project is financed by a fictitious consultancy company named

“CHEMICON”. The name is totally invented and there is no relation with other possible homonymous

companies.

5.1. Investment

The investment is the cost associated to the realization of the project. So, it can be defined as the cost

of designing and preparing the course material. To determine the cost, the investment has been

divided in three categories: the human resources, the cost of the equipment and other expenses.

Moreover, the human resources subdivision has been broken down into three main activities:

Table 5.1. Hours destined by the designers of the course.

Task Hours Design of the course 200 Simulation 900 Documentation 200 TOTAL 1300

The amount of hours of work corresponds to the dedication time of both engineers (650 hours each).

To determine the cost of each employee for the company, the gross salary plus the social welfare tax

(30% of total salary) was contemplated. Considering that most sources agree that the mean gross

salary for the junior engineer is around 25000 €/year, the final cost per hour and designer is show in

Table 5.2.

Table 5.2. Cost/hour per designer.

Salary Cost/hour Net salary (€/h) 10,35 Gross salary (€/h) 13,02 Total cost for the company (€/h) 18,60

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In terms of calculating the cost of the equipment used, only the price of the licences has been

considered. The software used are Aspen HYSYS, MATLAB-SIMULINK and Microsoft Office. As the

company it is supposed to use those software for other projects, an amortization calculation was done

using a ratio of the hours spent for each software to the total workable hours of the year.

𝐶𝑜𝑠𝑡 = 𝐶𝑜𝑠𝑡 ·𝐻𝑜𝑢𝑟𝑠 𝑢𝑠𝑒𝑑

𝑇𝑜𝑡𝑎𝑙 ℎ𝑜𝑢𝑟𝑠 (Eq. 5.1)

About the licences, they are all professional licences with the accessories needed for the course:

Aspen HYSYS: Professional license.

MATLAB: Professional license, plus SIMULINK.

Microsoft Office: Business standard license.

Table 5.3. Licenses used, with its percentages and the final cost.

License Price/year Hours used Percentage Cost Aspen HYSYS 33000 800 0.38 12692.30 MATLAB 2000 200 9.6·10-2 192.30 Office 144 500 0.24 34.62 TOTAL 12919.23 €

The other expenses subdivision takes into account multiple things, such as electricity and internet bills

or computer maintenance. In order to approximate this cost, it has been considered a 2.5% of the sum

of the other two. The final values for the investment cost can be seen in Table 5.4.

Table 5.4. Total cost and the subdivisions for the investment in the course.

Human resources 24180 € Cost of equipment 12919.23 € Other expenses 927.48 € TOTAL 38026.71 €

5.2. Variable cost

In order to calculate the variable cost of the course, the same three categories in which the investment

was divided can be accounted.

About the human resources, it is needed a professor who can be a professional of the company. His/her

salary has been decided to be the same as the junior engineer one. His/her tasks, can be divided in two

categories, which are the teaching part and the preparation part.


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Table 5.5. Human resources number of hours for the variable cost.

Task Hours Course teaching 20 Preparing 10

The course will take place in rented offices. As an estimation, the cost of renting the computer

classrooms in the Barcelona East School of Engineering (EEBE-UPC) was considered. For the concession

of this classroom, the price is of 515€ per day used. This expense is taken into account in the cost of

the equipment subdivision, together with the software cost.

Figure 5.1. PC classroom in EEBE.

The software will be used by the students and the teacher (Table 5.6), and the same calculation shown

in Eq. 5.1 has been used. Finally, the last expense added in this subgroup are the computers used and

its maintenance. In order to approximate this cost, a 2.5 % of the sum of the classroom rent and the

software used has been contemplated. Considering 10 attendees and 1 teacher, the cost associated to

a 3 days course is:

Table 5.6. Cost of the software and its reduction for the variable cost.

License Price/year Hours used Percentage Total Aspen HYSYS 33000 230 0,11 3649.03 € MATLAB 2000 230 0,11 221.15 € Office 60 230 0,11 6.63 €

Table 5.7. Partial and total cost of the rented classroom.

Classroom Price/day Days Total Computer class 515 € 3 1545 €

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Furthermore, the course includes lunch and coffee break for the attendees and the professor, yet it

will be given in the morning and in the afternoon (7h/day). This cost has been accounted in “Other

expenses”.

Table 5.8. Cost of the other expenses category for the variable cost.

Diet €/attendee Nº attendees Days Total Lunch 30 11 3 990 € Coffee breaks 5 11 3 165 €

In the end, the total value for each course is 7270.37€ (Table 5.9). It can also be seen that the major

expense in the variable cost are the simulation software used.

Table 5.9. Final table for the variable cost.

Human resources 558.00 € Cost of equipment 5557.37 € Other expenses 1155.00 € Total 7270.37 €

5.3. Market study

In order to present a competitive product market study has been carried out. The offer of three other

companies has been analysed. They offer multiple courses oriented in the field of chemical process

simulation and process control. The information is summarized in Table 5.10.

Table 5.10. Market study comparison for different companies.

Days Nº attendees Location Price Inprocess (Aspen HYSYS) [42] 3 Unknown Barcelona (Spain) 1650 € Chemstations (CHEMCAD) [43] 3 10 USA 1750 €

PSE (gPROMS) [44] 1 Unknown England, Japan, Korea, USA 650 € 2 Unknown England, Japan, Korea, USA 1050 €

It has been decided that the maximum number of attendees has to be 10 in order to have small classes

and allow the professor to be able to train all the attendees accordingly. Finally, the price decided for

the 3 days course is 1600 €, without VAT.

5.4. Project viability

In order to state if the project is viable or not, a VAN analysis has been carried out. Analysing the other

companies, the frequency of the course has been estimated to be 4 courses per year. The inflation task

has been considered to be 0.79%, which is the current value in Spain [45].


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Table 5.11. VAN formula applied to the course viability.

Year 0 Year 1 Year 2 Year 3 Investment -38026.71 0 0 0 Variable cost 0 -29081.49 -29081.49 -29081.49 Income 0 64000.00 64000.00 64000.00 Annual -38026.71 34918.50 34918.50 34918.50 VAN -38026.71 34644.81 34373.26 34103.84 Accumulated -38026.71 -3381.89 30991.37 65095.21

From Table 5.11, it can be seen that in a bit more than one year the investment will be recovered, and

by the end of the third year, the winnings of the course could potentially be of 65095.21 €.

5.5. Pilot test

The project proved economically viable. Nevertheless, to evaluate the contents quality and the interest

of recently graduated engineers, two of the course’s cases (Tank Liquid Level and Distillation Column)

were introduced into the lab sessions of the subject Process Control of the Master’s degree in Chemical

Engineering – Smart Chemical Factories, taught by the UPC in the EEBE. Two surveys have been carried

out: one at the beginning and one at the end of the course.

The objective of the initial survey is to know about the starting level of the potential attendees that

have just finished their degree or their master’s degree. Basically, they were asked about their

knowledge on both chemical and process control. This information can be useful in order to know if

the cases presented could provide them with the knowledge predicted.

This survey was made with Google Forms, a survey administration tool that is included with Google

Drive. This app allows collecting information from the users using personalized surveys anonymously.

The questions asked to the master’s degree students were:

What is your background degree? In a scale from 1 to 5, what is your interest in the Chemical Process Control subject? Have you ever attended a Chemical Process Simulation course? Have you ever used a professional process simulator (Aspen HYSYS, UniSim, ChemCAD,

gPROMs, PRO/II, VMGSim or others)? Have you ever used Aspen HYSYS in steady state mode? (If yes, to which extent?) Have you ever used Aspen HYSYS in dynamic mode? Have you ever used a controller in HYSYS? Have you ever used MATLAB? Before starting the course, did you know basic coding in MATLAB? Have you ever plotted arrays in MATLAB? Have you ever used SIMULINK?

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Before starting the course, did you know the difference between an open loop and a closed loop system?

Before starting the course, did you know what a transfer function was? Before starting the course, did you know block diagram algebra? Have you ever tuned a PID? Before starting the course, did you know about cascade control?

All the results of the surveys can be found in Appendix D. Here are some relevant ones. The results

provided helpful insight into the master’s degree students’ education. 90% of them had previously

obtained a bachelor’s degree in chemical engineering, and more than 60 % of them had great interest

in the subject.

Figure 5.2. Student’s response to the “What is your background degree” question.

As expected from chemical engineers, 95% of the tested had previously used a process simulator,

having the majority used Aspen HYSYS, even though, a vast majority of them hadn’t used Aspen HYSYS

in dynamic mode and hadn’t had experience in building a controller in any simulation software.

Figure 5.3. Student’s response to the question “Have you ever used a professional process simulator”.


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Furthermore, as expected, the majority of the students had previously used MATLAB and SIMULINK,

as well as they knew the basic concepts in process control, even though, 81 % had never tuned a PID

and 71 % of them had never seen beyond surface level control schemes, such as cascade control.

Figure 5.4. Student’s response to the question “Before starting the course, did you know about cascade

control?”.

From the initial survey, some conclusions can be drawn. The potential attendee of the course has

knowledge in chemical process as well as in basic use of the professional simulators. He/she also has

the very basic control theory background, even though, most of the attendees would not know the

essentials of dynamic simulation, system identification or controller tuning.

Once all the students had been presented with the cases and had time to work with them, another

survey was sent in order to obtain their final feedback.

In this second survey, the potential attendees were asked:

Your grade of interest on the cases has been (1- Not interested at all; Extremely interested). Your grade of satisfaction with the contents and the didactic materials provided is (1- Not

satisfied at all; Extremely satisfied). How difficult have you found the cases addressed? (1- Not difficult at all; Extremely difficult). The increasing difficulty of the cases addressed was conveniently structured and has helped

in the learning process and assimilation of concepts (1- Strongly disagree; Extremely agree). Your knowledge and ability on assembling and controlling a dynamic simulation increased as

the course proceeded concepts (1- Strongly disagree; Extremely agree). Do you think that simulating an open tank is a good starting point to learn about dynamic

simulation and chemical process control? (1- Strongly disagree; Extremely agree). Do you think that the open tank control gave you enough knowledge about selecting the

right control strategy in chemical processes? (1- Strongly disagree; Extremely agree). Do you think that simulating the same open tank with both MATLAB and HYSYS was useful

for providing deeper understanding of the concepts behind? (1- Strongly disagree; Extremely agree).

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Do you think that MATLAB, and so mathematical modelling, is a good resource/strategy for chemical process control? (1- Strongly disagree; Extremely agree).

Simulating the distillation column in Aspen HYSYS is easier, time saving and allows a better understanding of the process dynamic that if it was to be done in MATLAB. (1- Strongly disagree; Extremely agree).

Through the simulation of a distillation column, you gained strong knowledge about multivariable control. (1- Strongly disagree; Extremely agree).

The laboratory sessions helped you integrating the control and chemical engineering concepts and vocabulary. (1- Strongly disagree; Extremely agree).

How relevant are the cases addressed for the professional career of a chemical engineer? (1- Not relevant at all; Extremely relevant).

How do you feel about the amount of information presented? (1- Too little information; 5- Too much information).

How likely is it that you would attend an "Advanced" part of the course, should it exist? (1- Not likely at all; Extremely likely).

How likely is it that you would recommend this course to a friend or colleague? (1- Not likely at all; Extremely likely).

What did you like the most about the course? What did you dislike the most about the course? If you have got any suggestion to improve the course, please, let us know about it!

The results were really helpful in order to determine their grade of interest as well as if the material

proposed was the right fit. It can be stated that the satisfaction with the didactic material and the grade

of interest in the cases has been excellent.

Figure 5.5. Student’s response to the affirmation “Your grade of satisfaction with the contents and the didactic

materials provided is”.


169

It can also be seen that most of the students appreciated the increasing difficulty of the cases, as almost

84 % of them argued that their knowledge progressively increased along with each case.

Figure 5.6. Student’s response to the affirmation “Your knowledge and ability on assembling and controlling a

dynamic simulation increased as the course proceeded”.

When it comes to the cases presented, most of them agreed that the tank is a good starting point to

learn about process control. However, when it comes to questions regarding the use of MATLAB, such

as if they thought that simulating the tank in both software was useful in order to introduce the

concepts and if they thought that MATLAB was a good strategy for chemical process control, mixed

reviews were obtained.

Figure 5.7. Student’s response to the affirmation “Do you think that MATLAB, and so mathematical modelling is

a good resource/strategy for chemical process control?”.

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In addition, most of the surveyed said that they would attend an Advanced part of the course as well

as recommend it to a friend or a colleague.

Figure 5.8. Student’s response to the question “How likely it is that you would attend an Advanced part of the

course, should it exist”.

When it comes to the student’s opinions, most of them pointed that they liked the new concepts, the

usefulness of it as well as the implementation in HYSYS. When it comes to what they had disliked the

most about the course, some pointed the work-load, while others didn’t point to anything in particular.

Finally, it can be concluded that the surveys returned a good review on the course content. This means

that the potential client will probably be satisfied with this product and recommend it to other

professional. This reinforces the project viability.


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173

Conclusions

This project allowed designing a course to train engineers in the simulation of chemical process control.

The potential attendee profile was defined and, basing on that, the educational objectives and the

course scope were determined. Moreover, the cases were selected to provide an easier approach for

those attendees that do not have a solid chemical engineering background, applying an increasing

difficulty level.

The economic analysis of this project returned positive results. A three-day course for 10 attendees

and with a frequency of 4 times per year allowed recovering the investment in a little more than one

year, still being competitive with other companies that offer similar courses. In addition, the surveys

carried out to the master’s students revealed that the potential attendee profile has been chosen

properly and has the basic knowledge to face the course. Furthermore, the surveyed students

demonstrated interest and satisfaction with the proposed contents and are very likely to continue with

an advanced part of the course. Hence, it can be stated that the course is a viable project.

The course is based on the Svrcek’s approach to process control. The use of a chemical process

simulator enhanced the control design of four different chemical processes by applying control

methods (system identification, variable pairing, IMC tuning method) to what could be real

experimental data. The dynamic simulation in Aspen HYSYS allowed familiarizing with the process

dynamics and understanding the relations between the process variables. Furthermore, it has

enhanced testing different control strategies in a relatively quick way, picking the best one for each

case. So, process simulation proved to be a very useful tool since it allows a deeper insight into the

process and can save a lot of time and money. However, experience with the simulator and a critical

analysis by the process engineer is needed in order to obtain coherent results. Special attention must

be paid when modelling the system with a good knowledge of the thermodynamics properties and

chemical interactions of the chemical species of the process. Moreover, the simulation can be more or

less detailed, so the simulator must be aware with his/her objective in order to reproduce coherently

the desired system.

This training course serves as an introduction to process control starting from the basic knowledge,

passing through the simulation of different control schemes, and ending with a multivariable process

such as the distillation column. These contents, together with the motivation provided by the positive

results of the pilot test, can be the basis for an advanced part of this course, where plant wide control,

split range control and optimal control might be addressed.


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Environmental impact analysis

The project has no direct impact on the environment as it consists on designing a course, where the

design of the different processes is tested by simulation.

However, indirectly, the course could prove beneficial for the environment. The course teaches the

attendees how to control different chemical processes, which if done right can lead to better trained

engineers and in the future more safety for chemical plants. A good control system helps avoiding

liquid spill and gas releasing to the atmosphere.


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