process control stydy of the ba6 cooling towers for...

PROCESS CONTROL STYDY OF THE

BA6 COOLING TOWERS FOR THE SPS ACCELERATOR

By Àlex Barriuso Poy

Escola Tècnica Superior d’Enginyeria

Universitat Rovira I Virgili

Tarragona, Spain

Acknowledgement

I would like to express my sincere acknowledgements to Didier Blanc and Maria

Carmen Morodo Testa, for his guidance and his excellent welcome at CERN. I would

also like to thank Michel Geoffory for his help during the fulfilment of this project, his

company, his comments and tips.

I’ve been Technical Student in the ST/CV group, I wish to thank all its

members. It has been a privilege to start my professional career in such a kind

environment. I also acknowledge the CERN for providing me all the tools needed for

the completion of this work.

I am grateful to Dr. Eduard Llobet, my eternal supervisor in the University

Rovira i Virgili, as well as, Dr. Luis Martínez Salamero for his help to go to CERN.

I thank Riichald, Juan, Sonia, Iván, Luis, Toni, Esther, Cocco, Bobo, Mirko,

Stefanos, Marcos, Albertos, Federico, Cristina, Arturo, Georgina, Eli, Giovanna,

Giuseppe, Andrea, Davide, Chiara, Rocio, Christos, Elena, Mario, Colum and Redwane.

You have done these 14 months unforgettable to me.

També voldria agrair pel seu afecte i ajut als meus pares Ignacio i Roser, el meu

germà Iñaki, als meus avis Joan i Carme i als meus oncles Jordi i Carme. Simplement,

gràcies per tot.

Per últim agrair a Gemma per la seva tendresa i suport des de sempre, quanta

paciència que has de tenir...

Report made by Àlex Barriuso Poy.

Industrial Electronics & Automatic Control Engineering student,

Escola Tècnica Superior d’Enginyeria, Universitat Rovira i Virgili, Tarragona, Spain.

Project carried out in the Controls and Electricity team of the ST/CV

(Technical Support/ Cooling and Ventilation) Design Unit,

European Centre for Nuclear Research (CERN), Geneva, Switzerland

CERN Supervisor: Didier Blanc

URV Supervisor: Eduard Llobet Valero

CONTENTS Part A: Introduction and System Discussion. 1 Introduction 8

1.1 Project Background. 9 1.2 Project Aim and Problem Formulation. 9 1.3 Main Studied Topics during the Project Development. 10 1.4 Project Outline (Plan). 11

2 The CERN & the LHC 13

2.1 High Energy Physics Today. 14 2.2 The CERN. 15 2.3 CERN Future, the LHC. 17 2.4 The SPS. 19

3 BA6 Cooling Towers Description 20 3.1 Generalities. 21 3.2 Modes of Operation. 22

3.2.1 Normal Mode. 22 3.2.2. Local Mode – Maintenance. 22 3.2.3. Defect Mode. 22

3.3 Control Loops Description and Characteristics. 23 3.3.1. Stopgap Tank Level Regulation. 25 3.3.2. Temperature Regulation of the BA6 Cooling Towers 33 3.4 Description of the Degrade Mode. 39 3.5 Description of the Safety Mode. 40 3.6 Conclusions. 41

Part B: System Identification and Control Enhancements. 4 Stopgap Tank Discussion 42

4.1 Problem Formulation. 43 4.2 Nonlinear System. 44 4.3 Linearization. 45 4.4 Non-linearities Effects & Static Test. 49 4.5 Dynamic Test: Water Tank Filling Time f(Qe). 57

5 First Approach: Single Feedback Control 58

5.1 Assumptions. 59 5.1.1 Storage Tank - Gp (s) -. 59 5.1.2 Actuator - Gv (s) - 61 5.1.3 Disturbance - Gd (s) - 63

5.1.3 Sensor, Transducer and Transmission - Gs (s) - 63 5.2 Developing a Robust Single-Loop PI Control. 64 5.2.1 Single-Loop Proportional Gain (Model 1). 66 5.2.2 Single-Loop PI Gain (Model 2) 71 5.2.2.1 Reset (Integral Windup). 72 5.2.3 Modelling the Single Feedback for the 4 Towers. 83

6 System Identification 87

6.1 Introduction. 88 6.2 The Input-Output Data. 90 6.3 Examining the Data. 95 6.4 Estimating Models. 98 6.5 Estimation Results. 100

6.5.1. Actuator Cooling Tower 2. 100 6.5.2. Actuator Cooling Tower 3. 104 6.5.3. Tank Level Contribution. 107 6.5.4. Pressure SIG Contribution. 110

6.6 Validating Models. 113 7 System Simulation and Optimization 117

7.1 Enhancements to Single-Loop PID Control. 118 7.2 Cascade Control. 118 7.3 Building the Present Control Architecture. 125 7.4 Optimizing the PI Controllers. 129

7.4.1 Tuning Cascade Controllers 131 7.5 Definitive PI Values for a Discrete-time Control 135 Part C: Further Work. 8 The Feedforward Control 138

8.1 Introduction 139 8.2 Feedforward Control Design Criteria. 140 8.3 Feedforward and Feedback are Complementary. 141 8.4 Is Feedforward Control Necessary? 143 8.5 Feedforward Controller Design. 144 8.6 Feedforward-Feedback Control Results. 146 8.7 Further Implementation of a Feeedforward Control. 150

9 The Digital RST Controller 152

9.1 Introduction to Computer Control. 153 9.2 Structure of Digital Controllers. 155 9.3 Digital Controller Design Methods. 158 9.4 Controller Design Procedure. 162 9.5 Controller Development. 163

10 Conclusions. 169 References 171 Appendix A: Keywords. 176 Appendix B: System Schema. 178

Part A: Introduction and System Discussion

CHAPTER 1: INTRODUCTION

1. Introduction Process Control Study of the BA6 Cooling Towers for the SPS accelerator

Àlex Barriuso Poy, Universitat Rovira i Virgili /182

1.1. PROJECT BACKGROUND.

This Project was carried out at CERN (European Center for Nuclear Research)

in the framework of the Controls and Electricity team of the ST-CV Design Unit. This

team is responsible for the control systems' engineering of the CERN cooling and

ventilation infrastructure. This includes the conception, design, implementation,

validation, evolution and dismantling of the CV control systems, which are built by

using industrial standard control hardware and software.

1.2. PROJECT AIM AND PROBLEM FORMULATION.

The target of this project is to develop a tool to simulate and improve the present

control system for the BA6 cooling towers which are a strategic part for the cooling of

the SPS accelerator.

The cooling system is based on a closed primary circuit around the SPS

accelerator that brings mineralized water by two ways, one with chilled water, and the

other one with warm water. The warm water outcomes from a heat exchanger with a

secondary circuit which transport demineralized water, this secondary circuit is in

charge directly of the magnets cooling. The warm mineralized water from the heat

exchanger with the secondary circuit, when finish its stretch, comes in a storage tank

that must remain at a constant level, in its turn, this stopgap tank feeds four cooling

towers assembled each one with a ventilator in charge of the water refrigeration; and

thus, the cooled water comes in the primary closed circuit again.

To carry out this study, an accurate model of the dynamic system has to be

obtained. This is the most important part of the project since, with a properly modeled

system, further work can be done. Each element that forms the system has been

modeled separately by two ways; firstly the elements were created using mathematical

modeling principles, and secondly, a more accurate modelization was achieved by using

the data extracted from a supervisory SCADA system and the System Identification

toolbox of Matlab®.

Once each element that shapes the system is identified, it is implemented the

present control architecture in order to check if the whole identified system matches

with the real one. Thus, the present parameters for the PID controllers that form the

system can be optimized.



Finally, after optimizing the present control system, new proposals for the kind

of control architecture and for the type of controllers are studied, simulated and

compared with the actual behaviour of the plant for a further upgrade of the BA6

cooling towers control system.

1.3. MAIN STUDIED TOPICS DURING THE PROJECT DEVELOPMENT.

During the modelization and study of the control system the following “tools”

were used:

• System Identification Toolbox of Matlab©: This toolbox allows us to find out

mathematical models of dynamics systems based on the observed input/output

data extracted from the supervisory SCADA system. These mathematical

models can be used later to create the overall system block diagram. This

toolbox was created by Lennart Ljung and has been chosen over another tools,

as WINPIM of Adaptech®, due to the variety of possibilities that provides

during the identification, and because its facility of use.

• Cascade Control Architecture: This is the present control architecture

implemented on the BA6 cooling towers for the controls. It is one of the most

successful methods for enhancing single-loop control performance. It can

improve the performance of control strategies, reducing both the maximum

deviation and the integral error for disturbance responses. Cascade control uses

an additional, “secondary” measured process input variable that has the

important characteristic that it indicates the occurrence of the key disturbance.

The important feature in the cascade structure is the way in which the controllers

are connected.

• Feedforward Control Architecture: This is a first proposal for a further upgrade

on the present control system. Feedforward uses the measurement of an input

disturbance to the plant as additional information for enhancing single-loop PID

control performances. This measurement provides an “early warning” that the

controlled variable will be upset some time in the future. With this warning the

feedforward controller has the opportunity to adjust the manipulated variable

before the controlled variable deviates from its set point.



• RST digital controller: The use of a digital computer or microprocessor in the

control loop offers numerous advantages: (a) Considerable choice of strategies

for controller design, (b) possibility of using algorithms which are both more

complex and efficient than the PID, and, (c) this is a technique perfectly suited

for the control of systems with time delay. Moreover, by combining the

controller design methods with the system model identification techniques, a

rigorous, high performance controller design procedure can be implemented. A

tri-branched structure called R-S-T has been studied, and the main performance

that it provides us with is the possibility to optimize separately the tracking of

the set point and the plant regulation.

1.4. PROJECT OUTLINE (PLAN).

This report is divided into 10 main chapters. The first introductory part of the

project is formed by Chapter 1, 2 and 3. After this introduction, the second chapter

makes a general explanation about what CERN is, its history and future with a brief

discussion about the new LHC accelerator. Chapter 3 is focused on the definition of the

BA6 cooling towers control system that is on operation nowadays for the cooling of the

SPS accelerator.

The second part of the project shaped by Chapters 4, 5, 6 and 7 is based on the

identification of the system and a regulation discussion, first using single-loop strategies

,and afterwards, using the present multi-loop cascade control architecture. Chapter 4

talks about the non-linearities that the storage tank of the system has and its effects, as a

result, a linearization has been carried out. In Chapter 5 starts the control discussion, a

first modelization of the elements that forms the system is done and, when each element

is identified, an initial control approach with the single-loop PI control is simulated in

order to compare the results with the more complex control architectures used later. The

stability of the system is the main target, then, robust PI controllers with anti-windup

are used in this Chapter 5. In Chapter 6 an accurate identification of the elements that

shape the control system is done. Mathematical models were obtained by using the

System Identification Toolbox of Matlab®, input/output data was extracted from the

supervisory SCADA system. The resultant transfer functions were transported to a

Simulink® environment for the simulations. In Chapter 7, once accurate and tested

elements are obtained, the overall cascade control architecture is assembled. Moreover,



after validating the whole control system, it was carried out the optimization of the old

parameters for the PI controllers achieving faster the steady-state.

In the last part of the project, Chapters 8, 9 and 10, it is discussed the possibility

of new control strategies and a final conclusion is presented. In Chapter 8 the

feedforward control is introduced comparing its results with the ones already obtained

with the optimized cascade control. At the end of this chapter it is proposed a

feedforward architecture for the temperature regulation. In Chapter 9 the digital RST

controller is introduced as well a new Matlab® toolbox developed to calculate this kind

of controllers. In Chapter 10 a brief project conclusion is presented.

The main references are presented after Chapter 10. Appendix A contains the

keywords used in this report and Appendix B contains a detailed schema of the overall

SPS cooling architecture.

CHAPTER 2: THE CERN & THE LHC

2. The CERN & the LHC Process Control Study of the BA6 Cooling Towers for the SPS accelerator

Àlex Barriuso Poy, Universitat Rovira i Virgili 14/182

2.1. HIGH ENERGY PARTICLE PHYSICS TODAY

Particle physicists have found that they can describe the fundamental structure

and behaviour of matter within a theoretical framework called the Standard Model. This

model incorporates all the known particles and forces through which they interact, with

the exception of gravity. It is currently the best description we have of the world of

quarks and other particles. However, the Standard Model in its present form cannot be

the whole story. There are still missing pieces and other challenges for future research

to solve.

The masses of the particles vary within a wide range of masses. The photon,

carrier of the electromagnetic force, and the gluons that carry the strong force, are

completely massless, while the conveyors of the weak force, the W and Z particles, each

weight as much as 80 to 90 protons or as much as reasonably sized nucleus. The most

massive fundamental particle found so far is the top quark. It is twice as heavy as

theWand Z particles, and weights about the same as a nucleus of gold. The electron, on

the other hand, is approximately 350,000 times lighter than the top quark, and the

neutrinos may even have no mass at all.

Why there is such a range of masses is one of the remaining puzzles of particle

physics. Indeed, how particles get masses at all is not yet properly understood. In the

simplest theories, all particles are massless which is clearly wrong, so something has to

be introduced to give them their various weights. In the Standard Model, the particles

acquire their masses through a mechanism named after the theorist Peter Higgs.

According to the theory, all the matter particles and force carriers interact with another

particle, known as the Higgs boson. It is the strength of this interaction that gives rise to

what we call mass: the stronger the interaction, the greater the mass. If the theory is

correct, the Higgs boson must appear below 1 TeV. Experiments at Tevatron and LEP

have not found anything below 110 GeV.

Another open question is the unification of the electroweak and strong forces at

very high energies. Experimental data from different laboratories around the globe

confirm that within the Standard Model this unification is excluded. When scaling the

energy dependent constants of the electroweak (a1 and a2) and strong (a3) interactions to

very high energies, the coupling constants do not unify. Grand Unified Theories (GUT)



explain the Standard Model as a low energy approximation. At energies in the order of

1016 GeV, the electromagnetic, weak and strong forces

unify. One of the GUT theories is the supersymmetry (SUSY) that predicts new

particles to be found in the TeV range. Many other GUT theories predict new physics at

this energy scale.

These and other questions like the elementarity of quarks and leptons, the search

of new quark families and gauge bosons or the origin of matter-antimatter asymmetry in

the Universe, will be addressed by CERN's next accelerator, the Large Hadron Collider,

which is currently under construction [1].

2.2 THE CERN

The creation of a European Laboratory was recommended at a UNESCO

meeting in Florence in 1950, and less than three years later a Convention was signed by

12 countries of the 'Conseil Européen pour la Recherche Nucléaire'. CERN was born as

the prototype of a chain of European institution in space, astronomy and molecular

biology. The laboratory sites on both sides of the Franco-Swiss border west of Geneva

at the foot of the Jura Mountains [URL1].

CERN is today composed of 20 member States which are Austria, Belgium,

Bulgaria, Czech Republic, Denmark, Finland, France, Germany, Greece, Hungary, Italy,

The Netherlands, Norway, Poland, Portugal, Slovak Republic, Spain, Sweden,

Switzerland and the United Kingdom. Some 6500 scientists use CERN's facilities,

representing 500 universities and over 80 nationalities.

CERN primary aim is to provide the European scientific community with the

facilities to probe the structure of matter and reach a better understanding of the way the

universe is made and works: pure science with no immediate technological or

commercial objectives. Specifically, it has built and operates the particle accelerators

needed as tools for such research in a centre which allows European physicists to

collaborate more fruitfully than if each country maintained an independent program.

However, even in the short term this fundamental research, with its stringent demands

for accuracy and ultra-fast response pushes modern technology to the limit.

For high interaction energies, the laboratory has developed several fixed target

and colliding beam machines. The first ones were the Proton Synchrotron (PS), that



came into operation in 1959 supplying fixed target experiments with 28 GeV beams of

protons, and the Intersecting Storage Rings (ISR) proton-proton collider, which began

to act in 1971. The next step was represented by the Super Proton Synchrotron (SPS),

which was later made into the proton-antiproton collider (at 450 GeV/beam energy)

which started to work in 1981. It led to the discovery of the W and Z particles -the

carriers of the weak nuclear force - confirming the elegant theory unifying

electromagnetic and weak forces ('electroweak' theory). This discovery by Carlo

Rubbia's team, together with the development of a new technique - 'stochastic cooling' -

to control the anti-protons and shape them into an intense beam, by Simon var der Meer,

earned them the Nobel Prize for Physics in 1984.

Since 1989, these accelerators have also represented the elements of a chain

(Fig. 2.1) to pre-accelerate and inject electrons and their antiparticles, positrons, into the

Large Electron-Positron collider (LEP), where their energy was increased up to 46 GeV,

while bunches containing 1011 particles were made travel in opposite direction in the

same ring, before the head-on collision of two bunches occurred within a detecting unit.

By means of this machine physicists could make a detailed study of Z boson, that were

abundantly produced at 92 GeV energy. At 1996, the LEP energy doubled, thanks to

superconducting accelerating cavities, reaching 105 GeV per beam.

Figure 2.1: The CERN network of interlinked accelerators and colliders [URL1].



The intense experimental and theoretical effort of the last decades has provided

knowledge about the constituents of matter and the forces acting between them. These

advances have culminated in the construction of the 'Standard Model' (SM) which

describes the interaction between quarks and leptons. The predictions of the SM about

the strong and weak interactions agree with experimental observation in atomic, nuclear

and particle physics, at the ~0.1% level.

LEP is almost certainly the last in line of the circular machines of colliding

leptons. Electron and positron beams emit energy while following a circular path, as

they are relativistic charged particles. This synchrotron radiation is a great drain in the

operation of machines for particle physics. The mean energy loss of electrons in a

circular orbit due to synchrotron radiation per revolution can be written as following:

rEC

r

cmE

e

Wr

4

4

20

32

34

⋅=

⋅

=

βπ

being r the bending radius, E the energy of the particle, e the electron charge, β the

velocity of the particle divided by c (the speed of light in vacuum), m0 the rest mass of

the particle and C = 8.85x10-5 [GeV-3/m].

For LEP working at beam energy of 50 GeV the energy loss (per electron) is

about 150 MeV, while working at 100 GeV the loss increase up to 3.2 GeV. It increases

dramatically as the beam energy rises, and a machine like LEP would be extremely

expensive to operate much above 100 GeV per beam. Therefore, attention has turned

again to proton-proton machines, as mp=1836me; such beams can be accelerated to TeV

energies without unreasonable operation costs [2], [3].

2.3. CERN FUTURE, THE LHC

The LHC machine is a proton-proton collider that will be installed in the 26.6

km circumference tunnel currently used by the LEP electron-positron collider at CERN

(Lef 95). Superconducting dipole magnets with a field of 8.4 tesla, operated at 1.9 K,

will allow a beam energy of 7 TeV to be achieved. The beams intersect at four points

where experiments are placed. Two of these are high luminosity regions and house the

ATLAS (ATP 94) and CMS (CMS 94) detectors. Two other regions house the ALICE

detector (ALI 95), to be used for the study of heavy ion collisions, and LHCb (LTP 98),

(1.1)



a detector optimized for the study of B-mesons, particles composed either by a bottom-

quark and an up-antiquark or a bottom-antiquark plus a down quark, and B-baryons.

The bunches cross every 25 ns and the peak luminosity is 1034 cm-2 sec-1 at

which there is an average of around 20 pp interactions per bunch crossing. The machine

will also be able to accelerate heavy ions resulting in the possibility of Pb-Pb collisions

at 1150 TeV at the center of mass and luminosity up to 1027 cm-2 sec-1.

The main goals are (Wom 97):

• Discover or exclude the Standard Model Higgs and/or the multiple Higgses of

supersymmetry.

• Discover or exclude supersymmetry over the entire theoretically allowed mass

range.

• Discover or exclude new dynamics at the electroweak scale.

The Higgs is the boson that carries the mass, the responsible that particles have any

mass. Supersymmetry links the matter particles (the quarks and the leptons) with the

force-carrying particles (the gauge bosons: photon, graviton, gluons, W, Z plus the

Higgs), every fundamental matter particle should have a massive “shadow” force carrier

particle and every force carrier should have a massive “shadow” matter particle. These

shadow-particles have not been seen, as they are very massive, but the lightest shadow-

particles should be only around ten times heavier than the heaviest particles studied so

far. This puts them in range of the LHC.

Figure 2.2: Layout of the Large Hadron Collider [URL 1].



In Fig. 2.2 the placements for the four different experiments can be seen. Those

detectors are located in the available collision points. Also can be seen the beam

injection and ejection.

2.4. THE SPS The control system for the BA6 cooling towers is in charge of the SPS

accelerator cooling. The 6 km in circumference Super Proton Synchrotron (SPS) started

its operation at CERN in 1976 accelerating protons and making them hit fixed targets

with a peak energy of 500 GeV. In 1968 the possibility of accelerating and storing

intense beams of particles using the “stochastic cooling technique” proposed by Simon

van der Meer in 1968, opens the door to convert SPS into a proton-antiproton collider.

This enable CERN to have face-to-face collisions up to 800 GeV which brings CERN to

the historic discovery of the W-bosons and the Z-bosons in 1983, the long-sought

carriers of the weak nuclear force, confirming the electroweak theory unifying weak and

electromagnetic forces and providing CERN with the Nobel Prize for Physics of 1984 to

Carlo Rubbia and Simon van der Meer.

Currently SPS is the injector of the largest CERN accelerator, LEP, accelerating

electrons and positrons. SPS is not working as a collider any more, and the experiments

in it are restricted to the fixed targets running protons, making research in many

different fields of physics such as CP violation or relativistic nucleus-nucleus collisions,

and lead ions for the study of the quark-gluon plasma which may have occurred shortly

after the big bang. Although LEP is going to be dismantled after the summer run in year

2000, SPS will remain in service as injector of the future LHC.

The experiments at SPS are placed in the North and the West Experimental

Areas. In each of this areas the accelerated and stored beam hits a metallic target

emitting all sorts of particles in the incident direction, some of this particles are

recovered (after collimation, selection, and focusing) again for addressing them to other

targets and experiments downstream [URL 1].

CHAPTER 3: BA6 COOLING TOWERS

DESCRIPTION

3. BA6 Cooling Towers Description Process Control Study of the BA6 Cooling Towers for the SPS accelerator


3.1. GENERALITIES

The target of this document is to present an overview about the basic operation

related to the control of the ensemble of the S.P.S (Super Proton Synchrotron) cooling

towers located in the auxiliary buildings BA6 at CERN, Geneva (CH).

This installation already existed, was brought to work in a different way

(circulation of cooling waters not rejected into the lake like previously). The raw water

necessary for the S.P.S cooling is provided by SIG station. A piping distributes this

water, around the auxiliary buildings, with a pressure approximately of 7 Bars. Prickings

are carried out on this collector to feed the cooling stations of the auxiliary buildings. Hot

water is then collected in another piping and feeds the whole of the towers in the BA6.

The differential pressure between the source collector and the return collector is

maintained at 4 Bars by adjustment the speed of the pump in the SIG station (pumps

speed set point controls the measured differential pressure).

A storage tank, opened at the atmosphere, is used as hydraulic safety for the

coolant circuit. The storage tank is part of the circuit and it makes possible to fix a

reference pressure on the circuit, which supplies the cooling towers. The cooling water

flow coming from the auxiliary buildings is variable according to the request coming

from these buildings. The level fluctuations in this tank are the reflection of the water

flow variations at exit of buildings BA6.

The flow regulation is carried out by measuring the level variations between 2 and

3 meters and while acting on the opening of five automatic valves. Among these five

valves, four feed the corresponding cooling towers, the fifth sends water directly to a

recovery basin. Five flowmeters measure the flow in each circuit. According to the

request, the four towers will be starting the ones after the others.

The fifth circuit is not affected by any tower. It will be used in particular cases of

operation. It does not take part directly on the flow regulation of the installation.

A safety valve makes possible to isolate the feeding circuit from the towers.

A temperature measurement is taken on the collector that supplies the towers. A

temperature measurement is also taken in each basin as well as a temperature

measurement complementary in the point of fall of water.



The recovery basins for each tower are compartmentalized. However they

communicate between each other by a recovery channel. One can conclude from it that

the water level is appreciably the same one everywhere.

A water supplement is carried out by a local regulation (standard water hunting

with float) to compensate the losses due to evaporation in the towers.

A whole for purging to the sewer of the basin is in place. It includes two circuits

with two automatic valves and a measurement of flow on a joint base.

Station SIG provides the water temperature measurement on the outlet side of the

towers, as well as flow and pressure measurements to the deliveries.

Each cooling tower has a ventilator driven by an engine, itself controlled by a

variator. Each engine is equipped with thermostat for the overheating temperature

control, as well as temperature measurement per probe type Pt 100. A whole of detection

of vibrations engine/ventilator is also envisaged. Variator defect information is available

by variator.

The installation is controlled starting from a supervision station.

Three functionalities are identified:

- Cooling functionality (towers)

- Level regulation functionality (tank of regulation)

- Safety & degrade functionality (dysfunction)

The general way the cooling process always starts is according to cooling

requirements. The level regulation varies according to the flow consumption of the

buildings in service. The safety functionality enables us, in the event of defect in one of

the towers, not to stop the SPS and thus to be able, if possible, to finish the experiment in

progress without influencing the water temperature too much.

The objective is to maintain the physical and dynamic parameters of the

installation thanks to 4 towers of cooling. The cooling towers are supplied with raw water

and in closed loop operation.

The selection of the operation modes is made with the Wizcon supervision.

The control process program is made up mainly with regulations and a safety

mode [4].



3.2 MODES OF OPERATION

3.2.1 Normal mode

It is the operating mode in steady operation. The installation is controlled

automatically by the control system (PLC installed under this study + supervision in the

control room).

3.2.2 Local mode - maintenance

The installation is controlled manually, by the operator, from the supervision

station.

3.2.3 Defect mode

(a) Safety mode : It is an operating defect mode established to manage the failure

on the cooling capacities of a cooling tower. In this case, the "safety" circuit comes to

replace the failing circuit, water is rejected through the sewer.

SIG station will be informed of this operating condition and will have to ensure a

flow complement equal to that sent to the sewer.

(b) Degrader mode : It is an operating mode used in two fold cases:

- When staging an increase in the flow when the four valves are opened

to the maximum.

- When a regulation valve in a tower is failing, this is the equipment in

the "safety" circuit that comes to substitute the defective valve.

In both cases, no information is sent to the SIG station, any water discharge is

carried out (the rejection valves remain closed) [4].



3.3. CONTROL LOOPS DESCRIPTION AND CHARACTERISTICS

Within the framework of the reorganization of the water distribution networks

inside the CERN, accelerator SPS Super Proton Synchrotron, and more precisely the BA6

cooling towers must undergo significant functionality modifications.

The raw water or cold source necessary for the various magnets cooling in the

SPS accelerator, is pumped from the lake Léman by the station then filtered and treated.

The raw water is then distributed on the whole SPS site by the pumping station "Bern"

located in building 862. After use, the raw water is cooled by cooling towers and then

rejected.

This operation in open loop has been abandoned, a new closed-loop operation is

set up. Thus the raw water cooled by the BA6 towers is re-used and again injected into

the distribution loop.

This new functionality leads us to set up a temperature control on the BA6 towers

and to modify the existing level regulation on the stopgap tank. On these regulations

several types of constraints are identified:

- Process constraint.

The stopgap tank should never overflow, it should not never reach the very high

level (except breakdown) which thus corresponds to a stop of the SPS cooling and

to the accelerator.

- Performance constraint.

The outlet water temperature in the basins must always be lower than 24°C.

The rejections to the river must remain exceptional.

The water addition by the SIG must mainly compensate the evaporation losses

and the possible escapes. The rejections to the river in the safety mode must

remain exceptional. The regulation valves technology, on the stopgap tank, not

having a linear operation that will force to us to carry out a distribution of the

flow valves control signal and so balance the load of the towers (it is preferable to

have two valves opened at 70% rather than a valve at 100% and the other at 40%

to optimize the work of the towers).



- Network constraint.

The auxiliary buildings are distributed along the SPS ring, which has a

circumference of 7 Km approximately. No information is exchanged between the

several BA’s systems and the BA6 towers. Otherwise one would need to rebuilt

all the network wires, which is not considered.

- SIG constraint .

The total flow information on the distribution loop is available by a flowmeter.

This measurement is exploited by the SIG installations. We cannot guarantee a

reliable use to this measurement, we will hold of it like a measurement for

comparison.

- Mechanical constraint.

The minimum operation speed for the ventilators is of 900 rev/min (1500 rev/min

to the maximum).

Due to the system inertia, it is inconceivable to start, and then to stop, in an

inopportune way the ventilators. Their starting is carried out when the valve is

opened at 50 %, if the temperature is correct, and their stop at 30 %.

3.3.1 STOPGAP TANK LEVEL REGULATION

Description of the level information in the stopgap tank.

The water distribution loop is equipped with a storage tank that allows to absorb

the flow variations caused by the starting of any of each BA circuits.

This tank is equipped with the following instruments:

- LSHH very high level switch (Action SIG for stopping of SIG pump).

- LAH high level switch (Alarm)

- LAL low level switch (Alarm)

- LSLL very low level switch (Action SIG locking of an additional request).

This information is sent and processed by SIG.

- LT 01 Delta transmitter P (Measurement bracket between 2 and 3 meters

being measured 1 meter).




being measured 5 meters).


being measured 5 meters).

- LT 01 will be used with priority for the level regulation.

- LT 02 allows to supervise the level variations between 0 and 5 meters.

Used in help of LT 01 if LT 03 is at fault.

- LT 03 used in help of LT 01 or LT02.

A selection between the transmitters is carried out. This commutation of

transmitters is carried out from the control system, one generates an alarm. On the signal

resulting from this selection:

1) Four level thresholds are elaborated with alarm:

- A very high level threshold having for action the opening of the five valves.

- A high level threshold with alarm.

- A bottom grade threshold with alarm having for action the closing of the

five valves.

- A very low level threshold having for action to close the valve of safety for

stage to a defect on the return piping (escape or possible rupture).

2) If decided by the operator and in the case of a defect on LT 01; LT 02 (or LT

03) replaces LT01.

When the very high level is reached the pumps are stopped. When the very low

level is reached no additional pump is put on service by SIG station.

Operation principle for the stopgap tank transmitters

On the storage tank exists three regulation transmitters. The transmitter of

regulation 2-3 m ensures operation in normal mode for the installation. It is used for the

level regulation. The normal transmitter of regulation 0-5 m ensures the measurement of

the tank like its retransmission. Alarms are created starting from this transmitting signal,

it is in help with the regulation transmitter. The failure transmitter ensures the

measurement of the tank in the event of failure.



The difference of measurement between the normal transmitter of regulation 0-5

m and the failure transmitter of regulation is controlled, if a defect appears a

commutation to the failure measure is carried out on the site and then with the Wizcon

supervision.

The incautious levels with contact ensure the ultimate safeties on the tank

regulation in the event of problem with the analogical measures.

Information swings of transmitter or the sensors defects are transmitted like

stopgap tank general defect of regulation to the TCR.

Figure 1: Level regulation for the Stopgap tank I



Level regulation description for the storage tank.

A study of the towers carried out by the CERN informs us that when the tower

operation is lower than 50% of its load, then its performance is practically null. On the

top part, a water cloud vaporizes thus creating a better AIR/WATER calorific exchange

in the tower. The achievement of a good tower performance is made by balancing the

regulation valves control signal.

The maximum flow that a tower absorbs is 300 l/s (1080 m3/h). The total amount

for the four towers is 1080 m3/h X 4 = 4320 m3/h. The towers optimal performances are

ranges between 70% and 100% of its maximum flow.

The regulation system must continuously analyze the relationship between the

flow, which passes in a tower, and the total flow of water to be cooled (total request for

flow).

The system will calculate and adjust the set points for the flow regulators to allow

an operation of 2 or 3 towers into a simultaneous way and between 70 and 100% of their

capacity.

The selected measurement signal for the level regulation is sent to a P.I.D.

regulator (measurement on the LIC). The set point of this regulator corresponds to 2,5

meters height. After treatment and shunting, the output signal of this regulator gradually

tackles the four flow regulators set points.

The level regulator output signal (LIC) is divided into 4 and is recalibrated on a

4/20 mA scale. These four values will be used as a set point for the water flow regulators,

which water cross the towers (cascade control), after treatment and shunting on the

selected regulator.

A fifth value is calculated and directed, as a set point, towards the flow regulator

non-affected for a tower (Safety). This last circuit is used in special cases and does not

take part in the general flow regulation.

Flow measurements (four for the towers supply and one for towers derivation) are

used like measures that affect the flow regulators. The set points of these four regulators

are defined next.



Cd

e V

aria

teu

r

Ver

s ré

gu

lati

on

mis

e ég

ou

t

Ver

s B

assi

n

Ver

s to

ur

N°1

Ver

s to

ur

N°2

Ver

s to

ur

N°3

Ver

s to

ur

N°4

Cd

e V

aria

teu

r

Cd

e V

aria

teu

r

Cd

e V

aria

teu

r

ZSF

XSVFCVFCVFCV

FCV

Niveau 0 -- 5 m

Niveau 0 -- 5 m Alarmes

Comparateur

Niveau 2 -- 3m

Selecteur Arrêt pompe SIGOrdre desélection

Ordre de Selecteur

sélection

Mesure

Consigne2,5 mètres

4-20 ma

Relais à Arrêt pompe SIGseuil Fermeture vanne

sécurité

4-7,2 7,2-10,4 10,4-13,6 13,6-16,8 16,8-20Diviseur Diviseur Diviseur Diviseur Diviseur

Consigne A Consigne B Consigne C Consigne D Consigne E4-20 4-20 4-20 4-20 4-20

Pilotage Pilotage Pilotage Pilotage PilotageConsigne A Consigne B Consigne C Consigne D Consigne E

Arrêt d'unetour

Consigne Consigne Consigne Consigne Consigne

Mesure Mesure Mesure Mesure Mesure

++ + + + +

+ + + +

Anticip. Anticip. Anticip. Anticip. Anticip.Débit 1 Débit 2 Débit 3 Débit 4 Débit 5 AIR

SELECTION TOURS AIGUILLAGE DES CONSIGNES

FIC

FT

FIC

FT

FIC

FT

FIC

FTFT

FIC

LIC

LT 01

LT 02

LT 03

LSHH

LSH

LSL

LSLL

LAHH

LAH

LAL

LAHH

AlarmeEcart

SOVSOV

ZSF

Figure 2: Level regulation for the Stopgap tank II [4]



On a request of the primary circuit the first selected tower is requested from 0 to

100% of its capacity. If the request continues increasing, the second selected tower is

requested (1st being at 100%).

The second tower set point moves normally between 0 and 40%. At 40%, the

required total flow is: 100% for the 1st tower and 40% for the 2nd tower, being a total of

140%. This can be brought back to twice 70% for each of the two towers that are on duty.

In order to rebalance the system and so to achieve a better output on the 2nd tower, the

set points will be modified simultaneously in the following way: The first tower set point

will be decreased from 100% to 70% and the second tower set point will be increased

from 40% to 70%.When both set points are equal, and if the request continues increasing,

the two set points will evolve in the same way from 70% to 100%.

If the set point continues increasing the third selected tower is solicited (1st and

2nd being at 100%). The third tower set point moves normally between 0 and 10%. At

10%, the required total flow is 200% for the two first towers and 10% for the third one,

being the whole 210%. This corresponds to three times 70% for each of the three towers.

Evolution des Consignes

1+2+3+4 Tours + By Pass 100 90 80 70 60 50 40 30 20 10 0

0% 20% 40% 60% 80% 100% Sortie LIC

1ére Tour 1 ère + 2 ème Tours

1 ère + 2 ème + 3 ème Tours 1+2+3+4 Tours

A

B

C D E

Figure 3: Balancing the regulation valves in order to work between the 70 to the 100 % of the towers capacity



In order to rebalance the system and to obtain a better performance on the 3rd tower, the

set points will be modified simultaneously in the following way: The first and second

towers set points will be decreased from 100% to 70%. The third tower set point will be

increased from 10% to 70%. When the three set points are equals, and the request

continues increasing, the three set points evolve in the same way from 70% to 100%.

If the request continues to increase the fourth selected tower is solicited (1st, 2nd

and 3rd being at 100% of their capacity). The three first towers being at 100%, being the

whole 300%, the fourth tower will move from 0 to 100% following the demand for flow.

The operation principle will be symmetrical when a reduction on the flow demand

occurs (including a possible failure in one tower).

Selection of the flows set points

A towers priority selection is envisaged from the Wizcon supervision. Each unit

(measurement of flow, control valve, flow regulator) affects one tower:

- Tower N° 1. - Tower N° 2.

- Tower N° 3. - Tower N° 4.

Each set point treatment (A, B, C, D) is affects one order for a tower start:

- Instruction A: 1st tower has been brought into service.

- Instruction B: 2nd turn has been brought into service.

- Instruction C: 3rd turn has been brought into service.

- Instruction D: 4th turn has been brought into service.

According to a selection carried out starting from the control system a set point

will be assigned to a given tower. This represents (4!) possible combinations being 24 in

all (without the possible towers failures). If a tower is declared out of service, the tower,

which must work thereafter, will take the changing and the others towers will be shifted.

Example: Only one tower on service and it is declared out of service, then, the

second that has to start becomes 1st; the third becomes 2nd; and the fourth becomes 3rd.



Particular case of the safety loop

The fifth flow regulation (non-affected with a tower) controls a valve that can be

regarded as a safety valve. If the 4 towers are at 100% of their capacity, the flow value in

S.P.S. primary circuit is of 1200 l/s or 4320 m3/h. In this case, it is planned to use the

fifth circuit to treat an additional flow variation.

This 5th circuit can also be requested in the event of incident of one of the cooling

towers. The system configured like that must maintain the tank level (within the safety

limits).

This 5th circuit does not intervene directly in the towers selection. It must always

be requested the last for its starting and the first one for its outage when demand

decreases. Before requesting this last circuit, it is useful to make sure that the manual

valves of selection in the basins are open. These valves does not have end of race, thus

the operator must inform the system about the valves selection that he chose.

The startup of this 5th circuit causes that hot water is sent to the basin. In order to

avoid recycling this hot water in the installation, it is envisaged a purging to the sewer

with the same quantity of water. Water is drawn from one or two different basins, and the

valves selection for the sewer depends on the selection carried out by the manual valves

quoted above, therefore of the place where water was sent.

The flow regulation for the sewer will have to be controlled by the flow of the

fifth circuit. The quantity of water put at the sewer has to be equal to that brought.

For stage the lack of water carried out by the purging to the sewer, a supplement

must be requested from SIG station. The station will be informed, via a TOR contact,

about the setting of the sewer in progress.

Moreover the value from the flowmeter for setting the sewer is also sent to the

SIG station in order to inform it about the quantity of water to be added.



Checking of the measurements coherence

A checking of the valve position compared to the flow is carried out. If a too

significant variation is detected an alarm is generated “DEFAUT DEBIT/POSITION

VANNE TOUR INCORRECT”.

A checking of the towers flows is carried out compared to the total flow. If a too

significant variation is detected an alarm is generated “DEFAUT DEBITS

TOURS/DEBIT TOTAL INCORRECT”.

Linearization of the regulation valves.

A linearization of the valves of regulation type butterfly is envisaged. An object

“vanne”(valve in French) is available in the library of the created objects.

3.3.2 TEMPERATURE REGULATION OF THE BA6 COOLING TOWERS

The setting in closed loop of the water distribution loop as the augmentation of

the temperature at the exit of the BA' s leads us to conceive a regulation on the BA 6

towers very precise.

New evaluation on the BA6 towers.

In steady state operation the four towers are envisaged to be under operation.

A study shows us that if an auxiliary building is brought into service, a

temperature disturbance will affect us some time afterwards. The transmission is

deterministic.

In the same way an increase in the storage tank level will have a direct impact on

the cooling towers operation.

On the other hand, if variations in temperature occur on the towers, it is probable

that a disturbance will occur on the auxiliary buildings due to the pumping.

Among the auxiliary buildings of the SPS ring, only BA 6 is not more connected

to the BA 6 towers. It will be taken on the SF1 towers of the LEP (future LHC ring).



Temperature control

The goal is to obtain water with a temperature close (by lower value) to 24°C on

the outlet side of the towers. The elements at our disposal are as follows:

(a) Measurements:

- Flow in each tower.

- Water temperature at the entry of the towers on general circuit.

- Water temperature arriving in the basins with regard to each tower.

- Water temperature inside the basins.

- Water temperature in the resumption collector of the basins (supply by SIG).

(b) Possible actions:

Towers heat exchange capacity, being related to the towers dimensioning, the

atmospheric conditions, and the crossing water flow.

The cooling air forcing in the towers by ventilators at variable speed.

(c) Assumptions:

One can admit that an increase in the water flow corresponds to an increase in the

calories to evacuate, with or without increase in the temperature at the entry of the

towers.

The ventilator will be requested if the temperature in the basin tends to increase

above 24 °C; on an increase in flow above a certain value; and on an increase in the

temperature variation at the entry (by anticipation).

The adopted principle, takes into account the following complementary

assumptions: (a) All the towers are identical, and (b) a tower (pulverizers unit +

ventilators) is a body with linear response according to the requests in the operating range

of the equipment that makes it up (ventilators speed, pulverizers flow, etc).

(d) Principles selected:

d.1 Guiding principle:

For any temperature exchange, the quantity of evacuated heat is related to the variation in

temperature by the following fundamental equation:

TMCTTMCQ initialinitial ∆=+= )1(



With

Q : heat quantity, energy in Joules (or Kcal). M : mass in kg

C : specific heat in J/kg°C (or Kcal/kg°C). T : temperature in °C.

The power to be evacuated is function of the temperature variation, but also of the

mass variation, therefore the mass throughput of the coolant fluid.

This concept is used in the anticipation envisaged on the temperature regulators

for each tower. The principal temperature regulation (via the variator in each tower), can

thus be influenced by the variation in the calorific power to be dissipated. We will retain

the calorific power variation, like input datum influencing (or not according to the state

of the system) the temperature control anticipation. This can be schematized as follows:

Consigne 24

k2

+

-

? Ti

TTi

Température tour n°1

FTi débit

tour i Fonction F (Fti ;

?Ti)

Dif. δt (F)’

Régulateur Puissance calorifique

Régulateur Débit i

+

+

Vanne i Sur débit

k1

Régulateur Principal

Température Ecart température tour i

Ventilateur i

+ +

+

-

Consigne puissance calorifique à variation

nulle 0

Figure 4: Temperature regulation schema [4]



F = K1 ?Ti+ k2 FTi, where, K2 and K1 are parameters to be envisaged in the

supervision system and are useful in the establishment of the general behavior law of

each tower.

d.2. Differential Function:

This function makes it possible to determine the power variation to evacuate at

every moment. The principle of anticipation on the flow and the temperature uses the fact

that this variation of calorific power to evacuate must be nearest possible to the zero

value (even negative!!).

A positive variation in the calorific power to evacuate must show a more

significant request of the exchanger (thus of the towers).

That can be carried out through instantaneous flow (via the regulation valve that

supply the tower) and/or through the number of revolutions in the ventilator (via the

ventilator variator of the corresponding tower).

d.3. Regulators

- Main Regulator: Type PID or predictive, it allows a control on the temperature set point

while operating directly to the corresponding ventilator. Action direction: direct.

- Flow Regulator: Type P.I.D., it allows the tank level control. Action direction: direct.

- Calorific Power Variation Regulator: Type PID, it makes possible to control a power

variation the lowest possible (even negative). It makes possible to carry out (with 2

correction factors k1 and k2) anticipations on flow and temperature controls. Action

direction: opposite.

d.4. Parameters

Per tower: 1 regulation flow + 1 regulation temperature + 1 regulation power + 2

modulations of anticipations, being 5 parameters/tower.

Exchanger i (tower i) Flow i

Input Tª i Wi (Evacuated calorific power)

Function = f (FTi ; ∆Ti)



If it is considered that the towers are identical, the calorific variation power

control will be identical to the whole of the towers.

Exchangers model, 2 parameters (function F). Being on the whole 4 (2 + 5) = 7 X

4 = 28 parameters to be left accessible on supervision.

The parameters of the modeling function for the exchanger could be established:

- In a theoretical way (if the data manufacturer allow it),

- In a graphic way (using statements taken from essays on the load).

The parameters modulating the impact of flow & temperature anticipations lie

between 0 and 1. Their action could be minimized, if after experimentation, one realizes

that the influence of anticipation must be reduced (ex: flow via regulation valve).

Description of the temperature regulators

Due to the system regulation complexity and its little margins, it is envisaged to

set up a predictive regulation. This regulation results from the regulation library

QUANTUM. The used block is the EF1 [5].

Definition of the regulating block QUANTUM EF1

The system regulator is type first order with intake of disturbance tendency,

transfer of constraint and automatic compensator. Regulator EF1 is envisaged with intake

of disturbance essential in our project, the choice of this predictive regulator is even

imposed for that disturbance. Block EFB PCR_EF1 is a regulator improved for a 1st

order system with delay. The algorithm of this block is based on the predictive principles:

- An internal model, composed for three parameters, makes possible to predict the future

behavior of the system:

- KM: Static Gain

- TM: Time-constant

- DM: Lag Time

- Constraints on the handled variable (Y) can be taken into account:

- YMIN: Minimal value of Y



- YMAX: Maximum value of Y

- YRATE: Constraint of speed per second on Y

- INTAKE DISTURBANCE TENDENCY:

This block takes into account the influence of a disturbance calculated by a model

block (FF1) or by another block EF1

- CONFIGURATION SPLIT-RANGE:

This block can be associated to another block EF1 in case of Split-range

- AUTO-COMPENSATOR:

This makes it possible to reject the disturbances in not-measured slope. Block

EF1 uses a prediction horizon, a trajectory for reference. This trajectory,

initialized to the measure of the variable to be controlled tends towards its set

point (constant or not) according to a defined way mainly by the derivative of

rallying. This duration is directly interpretable as the time response in closed loop.

The action to be applied to the process is then calculated in order to make

coincide the future output of the model with the trajectory of reference on a

horizon (often limited to a point) known as prediction horizon.

Figure 5: Model Predictive Controller trajectory [4], [5]



Checking the coherence of measurements

A checking between the basin temperature and the tower surface temperature is

carried out. If a too significant variation is detected an alarm is generated “DEFAUT

ECART TEMPERATURE SURFACE /BASSIN”.

Ventilators commands

The speed of the ventilators cannot be lower than 900 rev/min, and their

maximum speed is fixed at 1500 rev/min. The action and operating range is thus reduced.

Moreover it is inconceivable to start and to stop inopportunely the ventilator

because of its wheel inertia. The regulation action field will be reduced.

3.4. DESCRIPTION OF THE DEGRADE MODE

First case:

In the extreme case where the four regulation valves are put at 100 % of their

race, if the storage tank level increases until a preset threshold then not to stop the SPS,

one controls the safety valve. The output signal of the regulator in not more, in this case,

divided into four since is divided into five identical parts. Calculation is carried out on the

automat. In this case, the four regulation valves of the towers remain opened at 100% and

only the safety valve is controlled to compensate a level increase. In this degraded mode,

no information is sent to the SIG and any water rejection is carried out (the rejection

valves remain closed).

Second case:

When a valve of the BA6 towers is at fault, it is the safety valve that compensates

for flow losses after the other valves are already opened at 100%. The regulator output

signal remains in this case divided into four parts. The treatment is carried out by the

automat. In this degraded mode, no information is sent to the SIG and any water rejection

is carried out (the rejection valves remain closed). Caution: To prevent a locking on

degrade and safety mode. Available only on Wizcon high level.



3.5. DESCRIPTION OF THE SAFETY MODE

The normal operation of the cooling towers is in tended flow, to prevent a

possible rise of temperature beyond 24°C, a safety mode is created. This mode is made

up with a regulation valve and two manual valves in entry. At exit, two regulation valves

can be selected under Wizcon supervision. The safety mode is engaged when there is a

failure on the temperature of one tower and when the three others are already under

operation. So if more than one tower is at fault the safety circuit is ineffective.

When the safety mode is engaged, the tower parameters at fault are recovered and

applied to the regulation safety valve. The flow is then controlled by the safety mode

flow measurement and retransmitted to the SIG. In this case the tower at fault is to

declare out of service.There exist on the safety circuit two valves controlled manually

without any communication with the system. The operator winnows manually the valve 1

or 2. It must indicate then on the supervisor the valve opened (No control is carried out

by the system).

According to the manual valve choices, a corresponding rejection valve is

controlled:

- Manual valve 1 selected then water rejection by the controlled rejection valve 1

- Manual valve 2 selected then water rejection by the controlled rejection valve 2

When the valve of regulation safety is controlled, these parameters are recovered

and applied to the selected valve of safety rejection. The flow is controlled at the exit of

the valves in rejection safety mode. The input flow to the basin is then equivalent to the

rejected flow.

The safety flow is transmitted to the SIG station to allow the cold water

complement for the regulation loop.



Figure 6: Safety Mode

3.6 CONCLUSIONS

This theoretical approach must be supported by programmed tests and detailed in

advance in order to:

- To validate the established principle,

- To determine the missing parameters graphically,

- To configure the whole of the regulators.

In addition, only note that when maximum flow is on a valve, then it corresponds

to a maximum speed on the ventilator.

Lastly, the basin and return temperatures even available are not used in this

model, it is a consequence of the used regulation. At the most, they could be used as

measurements on which alarms could be calculated and announced by the control system

[4].

Part B: System Identification and Control

Enhancements

CHAPTER 4: STOPGAP TANK DISCUSSION

4. Stopgap tank discussion Process Control Study of the BA6 Cooling Towers for the SPS accelerator


4.1. PROBLEM FORMULATION.

The problem consists of the storage water tank modeling located in the BA4 for a

further liquid level regulation.

It is considered a vertical tank, which is opened, possessing an outlet, or a

restriction in the discharge, just as a valve, and which for the moment will be constant.

That storage tank, with a cross-sectional area St equal to 59.45 m², that correspond to a

diameter of 8.7 m, has a volume input flow rate Qe (m³/s) that enters from the top and a

volume output flow rate Qs (m³/s) that leaves at the bottom through a valve, these flow

rates move from 0 to 1.3 m³/s.

The flow rate passes through a restriction following a quadratic law with the

differential pressure. In the case studied, with the stopgap tank opened to the atmosphere,

the differential pressure on the outlet corresponds to a hydrostatic pressure, which exists,

as a consequence of the liquid level in the tank. Thus, as higher the level is, higher the

output flow rate is.

For a fact, it is known that for a constant input flow rate, the level will stabilize on

a certain point when the output flow rate will equalize the input flow rate.

In this exercise one first will obtain a model from the tank; however the

conservation equation will be nonlinear. Although to find out an equilibrium level is

trivial for the nonlinear system, since in that point Qe=Qs, we must obtain a linear model

in order to build the system control because this tank will be just a piece in a chain and

Figure 4.7.: Level in draining tank

Qe

H

Qs

Pa = P2

Pa = P1

Sp St

k

dtdh



because of the computation difficulties in transitory conditions. This linearization will

bring disadvantages with him that will be tried to handle though different ways.

4.2. NONLINE AR SYSTEM

Being h the liquid level or height, and a the coefficient that depends on the outlet

geometry and the liquid density, the output flow rate is (considering Bernoulli’s equation,

and supposing the atmospheric pressure zero) [6] [7]:

gS

HHgSQ

p

ps

⋅=

=⋅⋅=

2

2

α

α (4.1)

Because of the level depends on the total amount of liquid in the tank the

conservation equation selected is an overall material balance of the system.

dtdH

SQQ

onAccumulatiOutputInput

tse ⋅=⋅−⋅

=−

ρρρ (4.2)

The system with equations 4.1 and 4.2 and with two variables, Qe and H, is

exactly specified. After the equations are combined, the model is finally obtained, by

canceling ?, due to the fluid density remains constant, and rearranging the equation in the

standard input-output differential equation.

QeHdt

dHS

dtdH

SHgSQe

t

tp

=+

=⋅⋅−

α

2

System state equation :

( )∫ ⋅⋅−+=t

pt

dHgSQeS

htH0

)(2)(1

)0()( τττ

Thus, the schematic of the nonlinear system state equation is,



4.3. LINEARIZATION

One encounters a nonlinear element in the differential equation describing the

system’s model. It is quite easy to compute the equilibrium height h, given a certain input

flow rate since Qe is equal to Qs in the equilibrium point. However to seek a solution for

such systems in closed-form is at times a formidable task, and very difficult to achieve.

Besides, this element can be a piece in a chain more or less complex, where this nonlinear

equation combined with other lineal equations would complicate the calculations

excessively.

Hence, one uses linearization in the flow and as a consequence it is found an

approximate equation. A linear model can be developed by approximating each nonlinear

term with its linear approximation, in our case, we have just one nonlinear term, the

square root in the outlet flow (eq. 4.1). A nonlinear term can be approximated by a Taylor

series expansion to the nth order about a point if derivates up to nth order exist at the set

point; the general expression for functions of one variable about Xs is [9]:

Rxxdx

Fdxx

dxdF

xFxF sxsxs ss+−⋅+−⋅+= 2

2

2

)(!2

1)()()(

In the case studied, function F(x) correspond to outlet flow function Qs(t), and Xs

to Ho. Developing a first order approximation:

_

Qe (t)

gS p 2

tS1

∫t

0

h (0)

H (t) +

Figure 4.8: Non-Lineal System [8]



)(2

00

0 HHH

HH

HQs

−+≈

=α

αα

α (4.3)

The factor R means the accuracy of the linearization. It can be estimated by

comparing the magnitude of the remainder, R’, to the linear term. For a linear Taylor

series approximation in one variable,

22

2

)(21

' sx xxdx

FdR −⋅= =ξ with ? between x and xs

The successful application of linearization to process control systems is typically

justified by the small region of operation of a process when under control. Although the

uncontrolled system might operate over a large region because of the disturbances in

input variables, the controlled process variables should operate over a much smaller

range, where the linear approximation often is adequate. Note that the accuracy of the

linearization in general depends on the operating point xs.

Looking at Equation 4.3 we realize that our output flow rate function has been

replaced by a lineal function that corresponds to the tangent in the static point. In order to

make that, we must choose a tank level average value (Ho), being the static work level

point the best choice. That Equation 4.3 has provided us with:

• Slope m from the tangent line: 02

0HdH

dQm

HH

s α==

=

• Average outlet flow Qo: 00 HQ α=

Then, 0

0

H

Q=α

And, therefore, 0

0

2HQ

m =

Nonetheless, starting from now, we must deal with the variables values referred to

the ones defined as average, Qo and Ho; it means, we work with the deviations to the

“normal” values. Mathematically, this is equivalent to make an axis change to [Ho,Qo].



See on the Figure 4.3 below, where H and Qs represent the absolute values of the

variables, and qs and h the deviations around the static point.

+=+=+=

)()(

)()(

)()(

tqQtQ

tqQtQ

thHtH

sos

eoe

o

Figure 4.9: Linearization of the outlet flow function. Axis change.

In this way, we say: mhhdhdq

q ss ==

Hence, the overall material balance equation after the linearization is defined as:

dtdh

Smhq te =−

That differential equation can be rearranged and solved taking the Laplace

transform:

)()()()()( msSshshmsSshsqe tt +⋅⋅=⋅+⋅⋅=

then, the transfer function will be,



0

0

0

001

1

2

221

11

11

)()(

)(

QSH

mS

antConstTimeSystem

QHH

mGainSystemK

sK

msS

mmsSsq

shsT

tt

tte

===

====

+⋅=

+⋅

=+⋅

==

τ

α

τ

Transfer function allows us to identify and to define the resistance and the

capacity from our level system, related to an atmospheric tank, with a cross-sectional

area St and operating with a level H submitted to a restriction from which the flow goes

through.

Since t= RC and we have t= S t / m, identifying terms from both equations we

obtain:dqdh

mR ==

1.

The resistance R of a restriction is a coefficient that indicates the relationship

between the level variation and the outlet flow variation.

The capacity C corresponds to the tank cross-sectional area surface, C = St.

Notice that the capacity is equivalent to the cross-sectional area instead of the volume,

which is the relationship between level and content. In fact, the cross-sectional area is,

what changing the level, absorbs the flow input and output.

Summarizing [10]:

• Resistance R = Level variation / Flow variation

• Capacity C = St (Tank cross-sectional area)

_ qe (s)

gS p 202

1

H

tS1

s1 h (s)

+

Figure 4.10: Lineal System [8]



4.4. NON-LINEARITIES EFFECTS & STATIC TEST

Recall that for the validation of our linearization we assumed that the implicated

variables just moved on a small region around the static point; it means, the deviations

with the “normal” work point was little in magnitude.

Nonetheless, in many cases of real process happens that as a consequence of

heavy changes in the load, the variables appears in points quite far apart from the static

point. In a non-linear element this implies, at least, that the static gain will be different

depending on which point the system is situated. Thus, it transpired that for a specific

zone or work point the controller parameters are the very best, then, changing this point,

the controller gain, which compensates the gain variation of the non-linear component,

will change as well. In this way, the global feedback gain will remain constant, and will

obtain the same kind of response. In practice, it means that an optimized loop can

becomes unstable if the change has gone to a region with more gain or, on the contrary,

becomes slow if the change has been in the other-way. In other words, the non-linearities

can affect heavily the stability of our system because of the deeply dependence on the

work point.

The water level in the case studied can work between 2 and 3 meters in normal

conditions. The following table 1 has been provided as for the static test. The input flow

rate, between 0 to 1.3 m³/s, has been scaled from 0 to 100 %. The same think happens

between Ho (m) and Ho (%), moreover Lcv (mA) follows a linear relationship with Ho.

Note that this values has been obtained using Bernoulli’s equation and as a result Ho

follows a non-linear relationship with Qe.

Qe (ma) 4 7.2 8.8 10.4 12 12.5 13.2 13.6 15.2 18.4 20

Qe (%) 0 20 30 40 50 53.5 57.4 60 70 90 100

Lcv (ma) 4 4.6 5.6 7.2 9.4 10.4 12 13.3 17.7 19.7 20

H0 (m) 2 2.04 2.1 2.2 2.3 2.4 2.5 2.58 2.86 2.9 3

H0 (%) 0 4 10 20 34 40 50 58 86 98 100

Qe (l/s) 0 260 390 520 650 695.5 746.2 780 910 1170 1300

Table 4.1: Static Test Result I with controlled valves in opened position



First of all, we had a linear model computed around the static point, Ho = 2.5 m

and Qo = 0.7462 m³/s, which has been fed with a step series between 0 and 1.3 m³/s.

Figure 4.11: Linear Model

The Table 2 below compares the steady-state values obtained after linearization

with the real steady-state heights values, which depends on the input flow rate (Qe) taken

from the table above. That table also presents the different time constants for each case.

H0 (m) 2 2.04 2.1 2.2 2.34 2.4 2.5 2.58 2.86 2.98 3

H (m) linear -2.5 -0.757 0.113 0.984 1.854 2.160 2.5 2.726 3.597 5.34 6.211

Sp (m^2) 0 0.041 0.06 0.078 0.095 0.1 0.106 0.109 0.12 0.152 0.168

Tau (sec) 8 933 640 503 428 410 399 394 374 303 275

Table 4.2: Static Test Result II with controlled valves in opened position

As we can see in the Figure 4.6 below, as in Table 2, the solution to the

approximate linear model is accurate for the small step due to the sharp slope; however, it

is inaccurate for a large step, even predicting an impossible negative level at the final

steady state. The general trend that the linearized model should be more accurate for a

small than for a large step conforms to the previous discussion of the Taylor series.

Figure 4.12: Steady-state Comparison



In order to compensate the non-linearity, we added a new block that performs the

inverse function. Since our system follows a quadratic function in steady state: 2

2

=

gS

Qh

p

e

It is added a new block based in a square root function that minimizes the steady

state error of our linear function. As a result the approximation achieved is quite accurate,

the correlation coefficient between the real data and the obtained thought the square root

function is 0.994. To reach this approximation one chose a constant value ‘a’ equal to

0.258, which minimizes the deviation to the real solution for each sample (see Figure 4.9

below). Nonetheless, to introduce a non-linear function as a square root to correct a non-

linear effect is a contradictory philosophy.

Figure 4.13: Non-Linearity Correction I

Figure 4.14: Steady-State Comparison I through a square root function



Figure 4.15: Constant 'a' selection

The next step was to use curve fitting or regression to seek out some smooth

curve that “best fits” the steady-state data obtained by Bernoulli equation showed in table

1, it means that it does not necessarily pass through any data points. “Best fit” is

interpreted as minimizing the sum of the squared error at the data points and the curve

used is restricted to polynomials, curve fitting is fairly straightforward. Mathematically,

this is called least squares curve fitting to a polynomial.

To achieve a better curve fitting first of all we increase the number of samples, as

we can see in table 1, we just work with 11 samples, so let’s use one-dimensional

interpolation to reach 100 samples. At this moment, using linear interpolation, one

guesses that intermediate values fall on a straight line between the entered points.

Figure 4.16: Linear interpolation to increase the number of samples



Once we have increase the number of samples we apply curve fitting to find out a

proper “transfer function” between the real level steady-state and the obtained with the

linearized system in order to correct the steady-state error for large steps:

Figure 4.17: Steady-Sate comparison II through least squares curve fitting

0733.20797.00404.00038.00014.0

0377.21242.0049.0007.0

1167.21432.00083.0

1086.21748.0

2344

233

22

1

+++−=

+++−=

++=

+=

xxxxy

xxxy

xxy

xy

In the figure 4.11 above, we can check that the 3rd and 4th order polynomials

obtained are really accurate; however, to introduce a correction that simulates that in our

system imply to increase the difficulty. We are looking for an easy to model solution that

reduce the steady-state error, thus, for us the 1st order polynomial would be the best

choice. Nevertheless, if we zoom in the set point, we realize that an error exists at that

point for any polynomial, thus if we take the assumption that error zero must exists at that

point the least square curve fitting has to be rejected.

Once we have rejected the proposals based on a square root function and on curve

fitting, one arrives to a crossroad. We can leave the level transmitter gain Km equal to

1(without taking account the scaling and the possible delay yet) even though the linear

tank solution predicts an impossible negative level at the final steady state (see figure 4.6)

hoping that our controller will be so fast that will avoid to reach that impossible steady-

state



On the other hand, one can try to change the slope of our linear tank (see figure

4.6 again) by adding a constant level transmitter gain Km that minimizes the steady-state

error although that will involve a lower overall gain change that will must be corrected

through a quicker controller. Below, we find out the value of Km equal to 0.1432 that

minimizes the steady-state error for the case studied.

Figure 4.18: Reducing ess through Km selection

The relationship between the real steady-state height and the solution achieved by

adding Km has a correlation coefficient equal to 0.96.

Figure 4.19: Steady-State Comparison III by changing the slope, adding Km

The data, which we are using, is in m³/s for the flow and in meters for the level;

these are the input and output variables for the real process. Now, if we want to scale our

system using some normalized physic variables as 4 ..20 mA, 1 ..5 V…or variables for a



simulated system as 0 ..100%, we must to change the overall static gain that at this

moment we have (static gain Kp):

))(())((

minmaxminmax

minmaxminmax

uuyyxvxx

kpk−−−−

⋅=

x: Real process input variable

y: Real process output variable

u: Simulated or physic process input variable

v: Simulated or physic process output variable

To summarize and compare the different responses to a step function located

between 0 and 1300 l/s one can see figure 4.14 below. As we mentioned before, our

linear tank (cyan line) presented a good accuracy for small steps around the set point [Qo

= 746.2 l/s, Ho = 2.5 m]; however, for distant steps to the static point the response can

reach an impossible value as a negative height. Applying the corrections we realize that

the ess diminish considerably, as we can see with the square root correction (red line) and

with the constant value correction (blue line).



Figure 4.20: Step Responses



4.5. DYNAMIC TEST: WATER TANK FILLING TIME f(Qe)

To carry out the dynamic test, one has just to close the valve making Sp equal to

zero. That is equivalent to open the loop in our linear system presented in figure 4.4.

Using an electrical analogy, the capacity of our system is equivalent to the tank

cross-sectional area, the resistance is equal to the inverse slope and the intensity is

equivalent to the flow. Thus, the dynamic test, which studies the filling time function of

Qe, is equivalent to the voltage in the capacity, Feeding the system with steps between

130 l/s to 1300 l/s and opening the loop we obtain the time response:

∫∫ ⋅= →←⋅= dtqS

thdtiC

tv et

yanaby

1)(

1)( log

Figure 4.21: Simulink Representation and electrical analogy

Figure 4.22: Dynamic test time response

CHAPTER 5: FIRST APPROACH.

SINGLE FEEDBACK CONTROL

5. First Approach: Single Feedback Control Process Control Study of the BA6 Cooling Towers for the SPS accelerator


5.1. ASSUMPTIONS

Let’s assume a typical feedback control system where all the different elements,

which form the studied cooling process, are introduced. Each transfer function is

discussed below.

SP(s)Gc(s) Gv(s) Gp(s)

Gd(s)

Gs(s)

+E(s) U(s)

D(s)

Y(s)

-

+

Gc(s) = ControllerGv(s) = Transmission, transducer, and valveGp(s) = ProcessGs(s) = Sensor, transducer, and transmissionGd(s) = Disturbance

Figure 5.23:Block diagram of a feedback control system

5.1.1. Storage Tank - Gp(s) -

It is considered a vertical storage tank with a cross-sectional area St equal to 59.45

m² that correspond to a diameter of 8.7 m. That storage tank has a volume input flow rate

Qe (m³/s) that enters from the top and a volume output flow rate Qs (m³/s) that leaves at

the bottom through four valves that feed the four cooling towers.

Using SIMULINK® it has been created the tank model. The process gain, which

will be the integration factor, must be explained in terms of speed of the level variation

(m/s) in the tank, by the overall flow variation (m³/s), it means:

]/[0168,045,59

11 23 −===== mmmStq

dtdh

K t

Then, the transfer function that represents the storage tank will be:

sG p 45,59

1=



One justifies this calculations recalling that the speed of the level variation in a

tank is function of the overall flow q (qin - qout) and the cross sectional area St

qSdt

dh

t

1=

and so, clearing up dh and integrating both sides of the equality, the level equation

results:

∫ ⋅= dtqS

ht

1

and expressing the equation in Laplace transforms:

sSsQsH

t ⋅=

1)()( or also

sSsQsH

t ⋅=

1)()(

An unitary integrator block presents an operational transfer function 1/s and, as a

consequence, the factor 1/St could be extracted to a separated block, so, let’s show the

transfer function as the product (1/St)(1/s). Thus, the factor 1/St can be interpreted as a

static gain applied to a dynamic function 1/s.

Factor St is called integration time Ti and it is expressed in seconds. Ti must be

interpreted as follows: when the overall of the contribution (or extraction) flow to the

tank is a unitary value (q = 1), the necessary time to increase (or decrease) the level one

length unit (?h = 1) is equivalent to the constant St (tank cross sectional area) and it is Ti.

Figure 5.24: SIMULINK storage tank model



5.1.2. Actuator - Gv(s) -

The actuator can be represented by the cascaded block diagram of Figure 5.3, with

the transmitter, transducer and valve in series.

C o n t r o l l e rC o m m a n d

%

u( t )

G v 1T r a n s m i t t e r

G v 2T r a n s d u c e r

G v 3V a l v e

C u r r e n t , m A

ic ( t )

P r e s s u r ep s i

pc ( t )

F l o wm ^ 3 / s

q i ( t )

Figure 5.25: Actuator block diagram

Transmitters carry signal from controller to final element and from sensor to

controller. Transducer I/P converts a current input signal to a linearly proportional

pneumatic output pressure. Based on several samples taken from the plant, the overall

transmitter-transducer is modelled as a first order delay elements with a typical dynamic

response t = 1.5 seconds. With the valve completely close, 6 seconds time (4 t ) pass from

a command (opening at 100%) until the valve reacts to. This block is taken into account

due to the delay that it causes, a unitary gain is assumed.

15,11

12,1

2,12,1 +

=+⋅

=ss

KG

v

vv τ

Valve

TTLevelMeter

Process

SignalConversion

Feedback

0...100 %

4...20mA

Display

2…3 m

mV

Storage tank

I/P

Compressedair

3-15 psi

Figure 5.26: Process and instruments in the control loop



Concerning the final control elements, they are high-performance butterfly valves

8510 by Fisher© [URL 2][16]. After several experiments on the plant, the valves has been

modelled as a first order delay elements with a typical dynamic response t = 3 seconds.

Around 12 seconds (4 t ) are needed to reach the travel limit switch fixed at 55% of the

valve capacity. Once again, an static gain 1 is assumed since during the simulations real

flow in m³/s is used.

Figure 5.27:SIMULINK controlled valve model

The aim to oversize the valves have been to achieve a proper heat exchanger

performance inside the cooling towers. To exceed the 55%, which depending on the

pressure, match with around 260 l/s flow, means to feed the tower with too much warm

water. As a consequence, the outgoing water from the cooling towers come in the closed

cooling circuit not enough cooled, making a non proper cooling in the different BA’s, and

in turn, causing an increase in the cooled water demand from the BA’s. This fact causes

severe problems on the process regulation due to the increase in the cooled water demand

from the BA’s. As more water is demanded by the BA’s, more water is fed by SIG

station, making possible to exceed the maximum amount of water that the cooling towers

can absorb, and, as a consequence, an unsafe level in the storage tank can be reached

quickly.

In practice, the maximum flow that each tower absorbs is around 260 l/s (936

m3/h). The total amount for the four towers is 936 m3/h X 4 = 3744 m3/h or 1040 l/s.

The operation capacity for each valve moves from 0 l/s to 473 l/s and the operation flow



range goes from 0 l/s to 260 l/s. Thus, the valve only will work up to 55 % of its real

capacity.

For the simulation, one uses the “real” signals, meters for the level measurements

and m³/s for the flow data to make the results easier to understand at first sight.

5.1.3. Disturbance - Gd(s) -

Concerning the transfer function that corresponds to the disturbance Gd(s) it is

assumed a static gain 1 and an instantaneous transmission. In fact, the disturbance

represents the warm water coming from the SPS cooling process. Since no flowmeter is

installed in the inlet of the storage tank, the disturbance signal D(s) is assumed as an

unknown parameter for the regulation. During the simulation this value moves within a

range between 0 to 1040 l/s.

5.1.4. Sensor, Transducer and Transmission - Gs(s) -

It is assumed gain 1 and instantaneous dynamics for the Gs(s) block. It is

supposed no delay in the sensor data acquisition as well as in the signal transmission. The

transmitted signal is an electronic one and moves within a range from 4 to 20 mA.



5.2. DEVELOPING A ROBUST SINGLE-LOOP PI CONTROL

The overall model located at BA6 presents several elements to be modeled, which

are, mainly, the tank and the four valves. These controlled valves also have a

complementary system in charge of the set points tracking that introduces more

complexity for a further implementation of a linear system.

Therefore, the chosen manner to face the problem of creating a “complex” model

has been to start from a simple control system Figure 5.6 with just one tank (process), one

valve (final element) and its I/P transducer. The single valve with its I/P converter

representing the overall of the four valves keeps the same transfer function since it is

retained the same gains and the same dynamics for each valve (t = 3 seconds) and each

I/P (t = 1,5 seconds). To create a simple model reduces the complexity when linear

analysis is used in order to study the system behavior and its stability.

Once, the first model has been studied, one will compare the results with a more

detailed model in order to check if the obtained results has been the same.

Figure 5.28: Simple Single-Loop PI Control (1)

As said before, the inflow is taken as an unknown disturbance in m³/s. This is

positive since the inflow acts adding; whereas, the outlet flow, passing through the valve,

acts taking away water from the tank. The simple feedback loop presented above follows

a set point fixed at 2,5 m. For the set point tracking, the controller must send a positive

action U(s), to drain the tank while opening the controlled valve, or a negative one -U(s),

to fill the tank closing the controlled valve.



Example 1:

Let’s see the response for an ideal, linear level control system, which has no

sensor or final element dynamics and it is perfectly linear to a step change in the inlet

flow for a case with a proportional-only control.

The linear model for the process and the controller are:

soutcout

toutin

QLSPKQdtdL

SQQ

onAccumulatiOutputInput

)()( +−=

=−

=−

(5.1.)

Expressing variables in deviation form, equating the set point and the initial

steady state (i.e., L’ = L – Ls = L - SP) and combining them into one equation, the result

is:

dtdL

SLKQ tcin'

'' =−

By taking the Laplace transform and rearranging, the transfer function for this

system can be derived as:

1

1

')(

+

−

−=

sKS

KQ

sL

c

t

c

in

Since the system is simple, the following analytical solution to the equations can

be derived from the step change in the inlet flow, F’in(s) = ? Qin/s.

)1(' τt

c

in eKQ

L−

−−∆

=

with )( ct KS −=τ . As can be seen, the controller gain affects the time constant of the

feedback system, increasing the magnitude of the controller gain, which gives negative

feedback control (in our case Kc < 0), decreases the time constant as well as reducing the

steady-state offset.

Note that for this first order system the controller gain can be set to a very large

magnitude without causing instability. This conclusion can be demonstrated by analyzing

the expression for the time constant, which would have to change sign to cause

instability. Since the time constant is positive and the analytical solution has a negative



exponent for all gains (Kc<0), this idealized system is stable for any negative feedback

controller gain. Recall that this analysis is only valid for the ideal, linear level control

system described by Equation 5.1, which has no sensor or final element dynamics and is

perfectly linear [9].

5.2.1. Single-loop Proportional Control (Model 1)

Let’s see what happens when it is inserted an actuator represented as a valve and

an I/P converter. Both are first order delay and the used controller is a simple

proportional one with gain Kc. The corresponding schema is the already introduced in

Figure 5.6.

The level L(s) and the set point SP(s) responses against the disturbance D(s) are:

IPvctIPvttvIP

IPvIPv

tIP

IP

v

vc

t

kvalvePIcontroller

k

KKKsSsSsS

ss

sSsK

sK

K

sSGGGG

GsDsL

−⋅+⋅++⋅+⋅++⋅

=

⋅⋅

+⋅⋅

+⋅⋅−

⋅=

−=

23

2

tan/

tan

)(

1)(1

111

1

1)()(

ττττττττ

ττ

IPvctIPvttvIP

IPvc

tIP

IP

v

vc

tIP

IP

v

vc

kvalvePIcontroller

kvalvePIcontroller

KKKsSsSsS

KKK

sSsK

sK

K

sSsK

sK

K

GGGGGGGG

sSPsL

−⋅+⋅++⋅−

=

⋅⋅

+⋅⋅

+⋅⋅−

⋅⋅

+⋅⋅

+⋅⋅

=−

=23

tan/

tan/

)(111

1

111

1)()(

ττττττ

ττ

Note that either transfer function could be considered, because the characteristic

equations of both are identical. Thus, the stability analyses for the set point changes and

for the disturbances yield the same results. Setting the characteristic polynomial to zero

produces the characteristic equation [12], [13].

0)( 23 =−⋅+⋅++⋅ IPvctIPvttvIP KKKsSsSsS ττττ

Using Routh criterion for stability, one obtains the values that makes stable the

system.

IPvc

IPvt

tIPIPvvcIPvt

IPvcIPvt

ttvIP

KKKsS

SKKKSs

KKKSsSSs

−+

++−+

0

21

2

3

)()(

)(

ττττττ

ττττ



Being: tv = 3 sec t IP = 1,5 sec St = 59,45 m²

Kv = 1 KIP = 1

Therefore, to keep the system stable it must comply with the following conditions:

00 1 < →>− ==c

KKIPvc KKKK IPv

45,590)(

)( 245,59sec5,1

sec31

2

−> →>+

++ ==

===

cmS

KK

IPvt

tIPIPvvcIPvt KS

SKKKSt

IPv

IPv

ττ

ττττττ

045,59 <<− cK

We have arrived to similar conclusion than for an ideal level control system

presented in the Example 1. Let’s see separately the step response against disturbance and

the step response following the set point and how both systems keep stable for any

negative values of Kc within the range from 0 to 57,45.

Matlab® provide us with the “Control System Toolbox” [11]. From a Simulink

model it is possible to create a transfer function establishing some input and output

points. From the model studied one adds two input points, one for the set point set at 2,5

meters, and another one for the disturbances set at 1 m³/s; the output point is obviously

the controlled variable, the level. Simulink provides us with a powerful tool that creates a

linear system from the Simulink model. Once the Linear Time Invariable model is

achieved, conclusions can be extracted making the analysis of the linear model with LTI

Viewer.

Figure 5.29: To specify the inputs and the outputs of the analysis model

The linear system with three different values of Kc is analyzed fixing the

disturbance at 1 m³/s and the set point at 2,5 meters. Firstly, one proves how the system

becomes unstable for a positive value of Kc, later it is tested the response against two

negatives Kc’s with different magnitude.



Figure 5.30: Proportional gain positive makes unstable the system

As seen in figure above, a positive value for Kc produces positive feedback

control, locating a pole in the right side of the pole-zero map and forcing the system

unstable.

Figure 5.31: Small negative Kc makes the system stable but not satisfactory



Inserting negatives values for Kc, one achieves to pass all the poles to the left side

of the pole-zero map. However, the offset is too heavy for a fine performance, one checks

in Figure 5.9 how manage to follow perfectly the set point against a step response;

however the disturbance effect is unacceptable since an offset of 10 meters is inserted.

Finally, one tries with a high negative proportional gain, Kc = -50 close to the

stability limit fixed at –St and finally it is achieved what it was expected, a stable system

with two imaginary poles well located in the left side of the zero pole map. Also, a

perfect tracking of the set point is done, getting one as a steady-state value, and almost a

zero offset since the steady-state response against the disturbance is 0.012. Depending on

the demanded specification, we could vary the damping coefficient (?), the rise time (Tr),

the decay ratio, the period of oscillation, the manipulated-variable overshoot, the offset

and the settling time by adjusting the proportional gain.

Figure 5.32: A big enough Kc makes the performance suitable

As introduced in Example 1 for the ideal, linear level control system, the

controller gain affects the time constant of the feedback system, increasing the magnitude

of the controller gain, which gives negative feedback control (in our case Kc < 0),



decreases the time constant as well as reducing the steady-state offset. The magnitude of

Kc can be increased up to St that represents the stability limit.

Figure 5.33: Kc = St puts the system on the stability limit

Also check that only with negative values of Kc we can drive our system to

stability by taking a look to our system and studying the equations with the closed loop:

)()()(

)()(

tleveltspte

teKtu c

−=⋅=

Depending on the position of the valves the sign of Kc changes [URL 3]:

Direct acting controller Kc < 0 Inverse acting controller Kc > 0



The type of controller to be used is with direct action since our controlled valves

are located in the outlets.

If the output increases, then u(t) decreases with Kc positive (and the opposite for

Kc negative). This kind of system has only two possible control actions: to fill or to drain.

a) Have a 2 meters level in the tank and the set point is set at 2,5 meters, so

the error is positive (0,5 m). Then one has to close the valve to increase

the level, this means to act in a negative way against the valve. With a

negative Kc an u(t) negative is achieved.

b) Equally, if have a 3 meters level in the tank and the set point is set at 2,5

meters the error becomes negative (-0,5 m). Then the valve has to be

opened to decrease the level. This means to act in a positive way against

the valve. With a negative Kc an u(t) positive is achieved.

To ensure no steady-state error, let’s insert also an integral time, converting our

controller in Proportional-Integral.

5.2.2. Single-loop PI Control (Model 2)

Figure 5.34: Single-Loop PI Control (1)

Before studying the stability in our new system it is important to check that a new

block composed by a PI controller and by an anti wind-up system has been added.



5.2.2.1 Reset (Integral Windup)

The integral mode is included in the PI controller to eliminate steady-state offset

for step like disturbances, which it does satisfactorily as long as it has the freedom to

adjust the final element. If the final element cannot be adjusted because it is fully open or

fully closed, the control system cannot achieve zero offset. This situation is not

deficiency of the control algorithm; it represents a shortcoming of the process and control

equipment. The condition arises because the equipment capacity is not sufficient to

compensate the disturbance, which is presumably larger than the disturbances anticipated

during the plant design. The fundamental solution is to increase the equipment capacity.

However, when the final element (valve) reaches a limit, an additional drawback

is encountered that is related to the controller algorithm and must be addresses with a

modification to the algorithm. When the valve cannot be adjusted, the error remains

nonzero for long periods of time, and the standard PI control algorithm continues

calculating values for the controller output. Since the final element can change only

within a restricted range (e.g., 0 to 100% for a valve), these large magnitudes for the

controller output are meaningless, because they do not affect the process, and should be

prevented [9], [14].

The situation just described is known as reset (integral) windup. Reset windup

causes very poor control performance when, because of changes in plant operation, the

controller is again able to adjust the final element and achieve zero offset. Suppose that

reset windup has caused a very large positive value of the calculated controller output

q

ω

4-20 mA

Figure 5.35: Final element can change only within a restricted range [URL3]



because a nonzero value of the error occurred for a long time; thus, the controller

maintains the final element at the limit for a long time simply to reduce the (improperly

"wound-up") value of the integral mode.

The improper calculation can be prevented by many modifications to the standard

PI algorithm that do not affect its good performance during the normal circumstances.

These modifications achieve anti-reset windup. The modification used is termed external

feedback and is offered in many commercial analog and digital algorithms. The external

feedback PI controller has been modelled with Simulink and it is shown in Figure 5.14

below. The system behaves exactly like the standard algorithm when the limitation is not

active, as it is demonstrated by the following transfer function, which can be derived by

block diagram manipulation on Figure 5.16.

)()('

11

)()('

sUsU

sTK

sEsU

ic

=

⋅

+=

Figure 5.36:Anti-Windup System

However, the system with external feedback behaves differently from the standard

PI controller when limitation is encountered. When a limitation is active in Figure 5.16,

the following transfer function defines the behavior.

1)('

)()(

tan)('

+⋅+=

=

sTsU

sEKsU

tConssU

ic



with U'(s) at its upper or lower limit. In this case, the controller output approaches a

finite, reasonable limiting value of )(')( sUsEKc + . Thus external feedback is a

successful in providing anti-reset windup. These calculations can be implemented in

either analog or digital systems.

Anti-reset windup should be included in every control algorithm that has integral

mode, because limitations are encountered, perhaps infrequently, by essentially all

control strategies due to a large changes in operating conditions.

Reset windup is relatively simple to recognize and correct for a single-loop

controller outputting to a valve, but it takes on increasing importance in more complex

control strategies such as cascade.

Once presented the kind of controller used in the simulations in order to improve

the performance, let's take a look to the stability. The level response L(s) against the

disturbance D(s) and the set point SP(s) is:

IPvciIPvctivIPtiitvIP

iiIPvIPvi

tIP

IP

v

v

ic

t

kvalvePIcontroller

k

KKKsTKKKsSTsSTsTSsTsTsT

sSsK

sK

sTK

sSGGGG

GsDsL

−⋅−+⋅++⋅⋅+⋅++⋅

=

=

⋅⋅

+⋅⋅

+⋅⋅

⋅

+−

⋅=

−=

234

23

tan/

tan

)()(

111

111

1

1)()(

ττττττττ

ττ

IPvciIPvctivIPtiitvIP

vIPcivIPc

tv

v

IP

IP

ic

tv

v

IP

IP

ic

kvalvePIcontroller

kvalvePIcontroller

KKKsTKKKsSTsSTsTSKKKsTKKK

sSsK

sK

sTK

sSsK

sK

sTK

GGGGGGGG

sSPsL

−⋅−+⋅++⋅−⋅−

=

=

⋅⋅

+⋅⋅

+⋅⋅

⋅

+−

⋅⋅

+⋅⋅

+⋅⋅

⋅

+−=

−=

234

tan/

tan/

)(

111

111

111

11

1)()(

ττττ

ττ

ττ

Setting the characteristic polynomial to zero produces the characteristic equation.

0)( 234 =−⋅−+⋅++⋅ IPvciIPvctivIPtiitvIP KKKsTKKKsSTsSTsTS ττττ



Using Routh criterion for stability one obtains the values that makes stable the

system.

IPvc

iIPIPvvcvIPti

vIPiIPvctvIPiIPIPvvcvIPIPvcti

IPvcvIP

iIPIPvvcvIPti

iIPvcvIPti

IPvctiitvIP

KKKsTKKKST

TKKKSTKKKKKKSTs

KKKTKKKST

s

TKKKSTsKKKSTTSs

−++

+++−+−

−+

++−+

−

0

2222221

2

3

4

)()()()(

)()(

ττττττττττττ

ττττττ

ττττ

Being: tv = 3 sec t IP = 1,5 sec St = 59,45 m²

Kv = 1 KIP = 1

From these values and following the Routh criterion for stability that force the

signs on the first column to be positive one can define the following conditions over the

proportional gain and the integral time to keep the stability:

00 1 < →>− ==c

KKIPvc KKKK IPv

0)(

>+

++

vIP

iIPIPvvcvIPti TKKKSTττ

ττττ

45,59)( 245,59

sec5,1sec3

1

−> →+−

> ==

===

cmS

KK

IPIPvv

ivIPtc K

KKS

K t

IPv

IPv

ττ

ττττ

45,590 −>> cK (1)

ci

mS

KK

IPIPvvcvIPt

vIPti

iIPIPvvcvIPti

vIPiIPvctvIPiIPIPvvcvIPIPvcti

KT

KKKSS

T

TKKKSTTKKKSTKKKKKKST

t

IPv

IPv

+⋅

> →++

+>

>++

+++−+−

==

===

45,595,445,59

)()(

0)(

)()()(

245,59sec5,1

sec31

2

222222

ττ

ττττττ

ττττττττττττ

c

i KT

+⋅

>45,59

5,445,59 (2)



For the linear analysis, only negative Kc between the range specified are used

since previously has been deeply discussed in Example 1 and Model 1 the need for

stability of negative values of Kc.

Figure 5.37: )45,59()5,445,59( ci KT +⋅< lead the system to the instability

Using again LTI Viewer we can check how for Ti < 5.41, which does not obey the

stability condition when Kc=-10, the system becomes unstable. Two imaginary poles are

located on the right side of the pole-zero map leading the system to a positive feedback

control.

The stability limit 41,5)45,59()5,445,59( =+⋅= ci KT is reached for Kc = -10.

Both tracking for SP(s) and the disturbance oscillates indefinitely within margins since

two imaginary poles are placed exactly in the imaginary axis with non-real part. This

poles placement causes a weak system in terms of robustness since a small change can

lead the system to the instability.



Figure 5.38: )45,59()5,445,59( ci KT +⋅= lead the system to the stability limit

Moving away from the stability limit, Ti equal 10 is applied. The poles are now

well placed on the left side of the pole-zero map leading the system to a negative

feedback control. In this case, the signal tracking is well done, one and zero for the set

point and the disturbance respectively. Thus, the steady-state level for a constant

disturbance is 2,5 m as shown in figures 5.17 and 5.18 below.

Figure 5.39:Storage tank level response against a 1m³/s disturbance and 2.5 m set point



Figure 5.40: )45,59()5,445,59( ci KT +⋅> lead the system to the stability

Once known the conditions for stability, let’s tune the PI controller in order to

find some suitable parameters that ensure a good dynamic performance.

Acting on the controlled-variable performance the system can be improved. The

well-tuned controlled should provide satisfactory performance for one or more measures

of the behavior of the controlled variable. We shall select to minimize the IAE [9] of the

controlled variable. The meaning of the integral of the absolute value of error, IAE, is

represented and implemented on a Simulink model [15].

Zero-steady state offset for a steplike disturbance system input is ensured by

integral mode appearing in the controller.

Values between -4 and –24, and from 5 to 25 seconds, have been given to the

proportional gain and to the integral time respectively, and then, the error has been

calculated from the controlled variable, the level. The experiment takes 500 seconds time

dttLeveltSPIAE ∫∞

−=0

)()(



and initially with the storage tank at the desired level by the set point (2,5 m), so when

the disturbance occurs the initial error is zero. The conclusion extracted from the IAE is

that no heavy variance in the accumulated error appears for changes in Kc (when it is

bigger in magnitude than around 15), and Ti, between the ranges studied that satisfy the

conditions of stability.

Figure 5.41: IAE evolution depending on the PI coeficients.

Linear dynamic models always have errors, because the plant is non-linear and its

operation changes. This error can be appreciated, for instance, in the IAE experiment just

introduced. For instance, using the non-linear Simulink model with Kc = -23 and Ti = 2

the system remains stable although these coefficients does not satisfy the stability

conditions of the linear analysis (for Kc=-23, Ti must be bigger than 7.3). Tuning

procedure should account for these errors, so that acceptable control performance is

provided as the process dynamics changes. The changes are defined as ± percentage

changes from the base-case or nominal model parameters. The ability of a control system

to provide good performance when the plant dynamics change is often termed robustness.

The amplitude margin Am and the phase margin F m are the classical robustness

margins. Their definitions are illustrated for a Nyquist curve in Fig. 5.20. The amplitude



(or gain) margin is the gain the loop transfer can be amplified with before stability is lost.

The phase margin is the amount of phase loss of the loop that can be tolerated before

stability is lost. Phase loss is related to time delay. The phase margin can therefore be

translated to a delay margin cmd ωτ Φ= , where cω is the cross-over frequency (which is

where the loop gain is 1)( =− cieL ω ). While the amplitude and phase margins are

accounted for because of uncertainties of the plant, the delay margin is also of interest

because of the uncertainty in the controller implementation [URL 4].

Figure 5.42: Nyquist curve of a loop transfer and definition of amplitude margin Am and phase margin

F m. Delay margin is cmd ωτ Φ=

Using the function margin to determine these margins, Matlab® returns the gain

and phase margins as well as the corresponding crossover frequencies. Also, one can plot

the Bode response and displays the margins graphically.

To compute the margins, first we form the unity-feedback open loop by

connecting the controller, the final element and the process. The resulting open-loop

transfer function is:

234tan/ )(1

111

1sSTsSTsST

KKKsTKKKsSs

Ks

KsT

KGGGGtivIPtitIPvi

IPvciIPvc

tv

v

IP

IP

ickvalvePIcontroller ⋅+⋅++⋅

+⋅=

⋅⋅

+⋅⋅

+⋅⋅

⋅

+=ττττττ



With the previous transfer function values to the PI coefficients has been given in

order to follow the evolution of the phase and gain margins. The gain margin, for PI

coefficients that satisfy the conditions for stability, varies from almost zero to up to 40dB.

Concerning the phase margin, it changes with the PI coefficients. In a 400

samples experiment, where we have been giving values from 8 to 40 for Ti, and from -1

to –20 for Kc, finally, it is checked how the phase margin moves from 0 to almost 50

degrees. So, for all the different given coefficients, our system remains always stable

since the phase margin is always positive, as well as the gain margin, reaching zero at the

stability limit for Ti equal to (59,54 · 4.5) / (59.45 + Kc).

Figure 5.43:Gain and Phase margin evolution depending on the PI coefficients.

Having a quick look at Figure 5.21 it is extracted that, as small in magnitude Kc

is, better the gain margin is. Concerning the phase margin, the best performance is

achieved for Kc’s around 6 and big Ti’s. Thus, one can conclude saying that within the

range of PI coefficients studied, the design is robust and can tolerate an important dB

gain increases, as well as, phase lag in the open-loop system without going unstable.

At this point one must reach a compromise between IAE and robustness in order

to choose some proper PI coefficient. Small values in magnitude for Kc (-1 to -5)



combined with high values of Ti (30 to 50 sec) makes a good performance in terms of

robustness but a poor one in terms of accumulated error (IAE). Increasing Kc, the IAE

performance improves.

Thus, Ti = 50 and Kc = -8 has been selected because they drive the system to a

gain margin of 6,7 dB and a phase margin of 49,6 deg, which corresponds to the relative

uncertainty of the plant transfer function around the 60% range around the crossover

[URL 5]. The obtained IAE for these coefficients has been 15.9; the experiment has been

done using a 1m³/s disturbance and zero initial error with the tank at the desired level.

Below, the Bode diagram is presented for the open loop system with both margins

specified, gain and phase. The level response against a 1 m³/s step disturbance is also

showed.

Figure 5.44: Good robustness performance for Ti = 50 sec & Kc = -8

Figure 5.45: Step response against 1m³/s disturbance wit Kc=-8 and Ti=50



The most important variable, other than the controlled one is the manipulated one.

We shall choose the common goal of preventing “excessive” variation in the manipulated

variable by defining limits on its allowed variation. By applying the anti wind-up as well

as defining a valve dynamics that cannot be exceeded on the simulation one protects the

manipulated variable.

5.2.3. Modelling the Single Feedback for the 4 Towers.

In the last section, it has been presented the core of the system to be modelled in a

simple way. The aim to model the system as easy as possible is that an analytical

expression could be found out, and so, results in terms of stability and system behavior

have been obtained more accurately. Once the simple system has been created, the next

step is to model the system in more detail and then compare the results with the obtained

previously.

Because our system is not only composed by one valve and it is composed by four

(there is also a fifth one only used for safety that will not be taken into account) one must

model this fact.

On the other hand, in the BA6 Functional analysis [4], it is explained the way the

valves are put in operation due to the plant optimization. To reduce the model it is

supposed that priorities does not change and the first valve will be always the one with

highest priority and the fourth one with lowest. Let’s summarize that in pseudo-code

assuming that the action going out from the controller, which represents the overall set

point, has a range between 0 and 400 %, 100 % for each valve:

Case SP = 100%

SP valve 1 = SP

SP valve 2 = 0 %

SP valve 3 = 0 %

SP valve 4 = 0 %

Case 100% < SP = 140%

SP valve 1 = 100 %

SP valve 2 = SP – 100 %

SP valve 3 = 0 %

SP valve 4 = 0 %

Case 140% < SP = 200%

SP valve 1 = SP / 2

SP valve 2 = SP / 2

SP valve 3 = 0 %

SP valve 4 = 0 %

Case 200% < SP = 210%

SP valve 1 = 100 %

SP valve 2 = 100 %

SP valve 3 = SP- 200 %

SP valve 4 = 0 %

Case 210% < SP = 300%

SP valve 1 = SP / 3

SP valve 2 = SP / 3

SP valve 3 = SP / 3

SP valve 4 = 0 %

Case 300% < SP = 400%

SP valve 1 = SP / 4

SP valve 2 = SP / 4

SP valve 3 = SP / 4

SPvalve4=SP/4



Thus, a block with Simulink has been created following the pseudo-code specified

above which controls the set points for the four valves. The conditions and actions that

correspond to the pseudo-code have been implemented inside each subsystem.

Figure 5.46: Set point management block

At this point, one inserts the four valves that will be controlled by the single PI

with anti-wind up block previously introduced. The Simulink schema is like follows:

Model 3:

Figure 5.47: Single PID loop (2)



With the new model appears an increase in the difficulty to create a numerical

expression to study the stability and behavior of the new model if we compare with

Figure 5.12.

Hence, previously the system has been modelled with a single valve that

corresponds exactly to the overall system with the four valves in terms of static and

dynamic gain. The circuit corresponding to the set point management does not act in a

relevant form in the system behavior since the computation is instantaneous. However,

for the linear analysis and the tool “LTI Viewer” [11] this block represents a handicap for

the system modelling. In fact, the linear system that corresponds to the overall system

becomes unstable, something that does not correspond with the real system behaviour

when one checks the time response against a step disturbance.

Figure 5.48: Incorrect linear response against 1m³/s disturbance due to the set point management block

Let’s check that the system is well modelled and the only problem is the increase

on the difficulty of the model. The same disturbance with white noise has been inserted in

both schemas, Figure 5.12 and Figure 5.25, and identical time responses are obtained.



Figure 5.49: The single and the overall systems time responses are identical

Using the Matlab® function “corrcoef” one achieves 100% correlation

between the two models, the simple and the overall, which means they are identical.

Thus, the overall system with the four valves can be summarized in a system with just

one single valve and, as a consequence, we can use the same transfer functions obtained

previously in order to study stability and system behavior. So, the same coefficients for

the PI controller have been selected (Kc = -8 and Ti = 50). Note that it is just an

approximation to make easy a first study of the system, obviously the dynamics of the

whole system cannot be modelled perfectly using just one valve. However, as a first

approach it has been accepted. Later, in Chapter 7, the overall system is identified in an

accurate way, which means that the dynamics of the system corresponds to the four

towers working together.

CHAPTER 6: SYSTEM IDENTIFICATION

6. System Identification Process Control Study of the BA6 Cooling Towers for the SPS accelerator


6.1. INTRODUCTION.

In the previous chapter has been presented a model of the cooling plant. From the

point of view of the plant dynamics, it is mainly composed by a set of valves, I/P

transducers and a storage tank. These elements, which form the system, were modelled

through experiments that took place in the plant. Having the valves completely closed the

opening time at 55% was measured (a travel limit switch is fixed at 55% of the valve

capacity). In this operation two elements have to be taken into account, the I/P

transducer, which converts a current input signal to a linearly proportional pneumatic

output pressure, and the controlled valve.

Using a chronometer, the time to charge the transducer with the needed pressure

was measured and it varied between 5,5 to 6,7 seconds. Once the transducer is charged

the valve starts to run. It needed between 11,5 to 12,3 seconds to reach the set point fixed

at 55%. Thus, both elements, the I/P transducer and the valve, were modelled as a first

order delay elements with a typical dynamic response of t = 1,5 seconds for the I/P

transducer (̃ (6,7-5,5) / 4) and t = 3 seconds in the case of the valve (˜ (13,3-11,5) / 4).

Adding both dynamics an overall system with t = 4,5 seconds as a time response is found

out.

15,11

)(13

1)( /tan +

=+

=s

sHs

sH PIk

From a rigorous point of view, the way in which the elements have been modelled

can seem weak. Although the elements are quite well built (it will be proved later), a new

mode to create them in a more accurate way is discussed. Moreover, additional variables

are taken into account in order to make the system more accurate.

The System Identification Toolbox provided for Matlab® has been used to

improve the transfer functions of our elements [17].

What is System Identification? The System Identification Toolbox is for

building accurate, simplified models of complex systems from noisy time-series data. It

provides tools for creating mathematical models of dynamic systems based on observed

input/output data. How is that done? Essentially by adjusting parameters within a given

model until its output coincides as well as possible with the measured output. How do



you know if the model is any good? A good test is to take a close look at the model’s

output compared to the measured one on a data set that wasn’t used for the fit

(“Validation Data”).

NO SI

PROCEDURE

INGREDIENTS

Model good

enough?

The input-output data

A set of candidate models (the model structure)

A criterion to select a particular model

Collect input-output data from the process to be identified.

Examine and polish the data

Select and define a model structure within which a model is to be found

Compute the best model in the model structure according to the input-output

data and a given criterion of fit

Examine the obtained model’s properties

STOP!



6.2. THE INPUT-OUTPUT DATA

The System Identification problem is to estimate a model of a system based on

observed input-output data. A database is stored in a PC where the local supervision take

place with an interface Ethernet TCP/IP. The database is composed for the corresponding

information to the last three days and it is refreshed everyday in a FIFO stack. The

supervisor program is independent of the PLC. For this project is used a Wizcon

supervisor with an Schneider PLC type Quantum [5]. The set of available variables

provided for the Wizcon data base is shown in Figure 6.1 .

Figure 6.50: System Architecture

The input-output data used for the identification of the overall actuator, composed

for the I/P transducers and the valves, corresponds to the following IDs: 957, 958, 959,

960 as the output data, and, 1375, 1376, 1377, 1378 as the input data.



Figure 6.51: Available SCADA data base.



Valve

SignalConversion

I/P

Compressed air

0...55 % 4...20mA 3-15 psi

Valve positionset point Flow

(l/s)

Figure 6.52: Actuator schema

The input data (ID 1375, 1376, 1377 and 1378) match with the position set point

of each valve, which does not exceed the travel limit switch fixed at 55%. A variation in

the diaphragm of the valve causes a change in the flow (ID 957, 958, 959, 960), this flow

corresponds to the output data. There is no a direct linear relationship between the

position of the valve and the flow due to two main reasons:

• The non-linear effect of the butterfly valve diaphragm.

• The pressure due to the stopgap tank level and due to the SIG pump also

varies over the time.

There is a lack of pressure measurement before the valves, however, it exists two

relevant variables on the database which can be linked with the pressure before the valve.

1. Firstly, the storage tank level (ID 933) is always known. A variation on the

stopgap tank level produces a change on the outlet pressure due to the volume

variation.

2. Secondly, it exists a pressure measurement “Pression eau primaire SPS SIG” (ID

961) near the point of interest. The differential pressure between the source

collector and the return collector is maintained at 4 Bars by adjustment the speed

of the pump in the SIG station, this is our second variable and is located at

building BA5 just next to the cooling towers. See Figure 6.4.

At the end, a model based on a valve and on an I/P transducer is identified. The

resultant transfer function is equivalent to the whole formed by both elements. This

model has been modeled also taking into account the disturbance produced by pressure

variations.

DPsFlow

sLevelTanksFlow

sPositionValvesFlow

sH∆

∆±

∆∆

±=)(

)()(

)()(

)(



Figure 6.53: Location of the primary water pressure measurement SPS SIG.

From Wizcon is extracted a database containing all the different variables that

take part in our system, this database has a .dbf format. Then, using a database viewer,

the relevant data corresponding to the selected ID’s is filtered to achieve a “clean” data to

use for the system identification. Once the relevant variables are filtered, a temporal

window has to be chosen since the database corresponds to the whole day. In order to

chose data which brings proper information for a further system identification three

criterion are followed:

1. The variable used for identification is the flow, then, it is important to notice

flow variation on the SIG pumping station.

2. To extract data from periods in which the system is working between two

cooling towers. It means a critical region where a tower is reaching its limit

and the following in priority one starts to act. In that way relevant data can be

extracted from two towers, the point is to take data from towers which don’t

work neither at maximum or minimum.

3. Two temporal windows are chosen or just one large enough. The aim is to

have a set data, which will be used for the model creation, and another

different set of data, which will be used for the model validation. The data



used for the identification has to be different than the used for the validation,

because using the same data the validation will be incorrect.

In order to model the second and third cooling towers it was selected data from

the 30th and 31st of August, as well as from the 1st of September. Below it is showed the

extracted data. Notice that the flow at SIG pumping station for the selected periods has

important variations (in normal conditions it is quite constant). These flow variations

produce a change in the cooling towers behavior, activating or defusing towers.

Figure 6.54: Set of data from 30th of August




Figure 6.56: Set of data from 1st of September

6.3. EXAMINING THE DATA

Plot the data. Look at them carefully. Try to see the dynamics with your own

eyes. Can you see the effects in the outputs of the changes in the input? Can you see

nonlinear effects, like different responses at different levels, or different responses to a

step up and a step down? Are there portions of the data that appear to be “messy” or carry

no information. Use this insight to select portions of the data for estimation and

validation purposes [17], [18].

Do physical levels play a role in your model? If not, detrend the data by removing

their mean values. The models will then describe how changes in the input give changes

in output, but not explain the actual levels of the signals. This is the normal situation. The

default situation, with good data, is that you detrend by removing means, and then select

the first half or so of the data record for estimation purposes, and use the remaining data

for validation.

Once a temporal window has been chosen from the huge dbf file, the data has to

be treated to achieve a set of “polish” data. Hence, several problems have to be faced up:



a. Depending on the variables, the sample period varies. The level measurement

is sampled each second, the flow measurements are sampled each 3 seconds,

and the pressure measurement at SIG is sampled each 10 seconds. It is

important to get arrays of input-output data with the same size, as the point is

to prepare data for system identification. For that reason, a resample is carried

out, interpolating one achieves input-output data with a constant sampling

period of 1 second time. Thus, data objects for identification routines are

created. This data is also exported to the Simulink environment, where the

final model is tested.

b. Measurements carry always an inherent error due to different circumstances.

The measurement error due to the sensor precision, as well as, the error

introduced on the sampling lead the data to a noisy state. Can be checked on

graphics above how the extracted data from the Wizcon supervisor is quite

steeped, thus it has to be treated. With the Signal Processing toolbox of

Matlab the signal is treated in order to get a smoother set of data. With the

new smooth data the system identification is more accurate since it is more

direct to find out a proper relationship between input and output.

Figure 6.57: Input-Output data treatment



The specified data has been smoothed. In that case, the data is the valve position

set point and the flow through the valve. The method used has been a moving average

filter and the selected number of data points in the average (the span) has been 30.

Once a smooth data is obtained the data is ready be used to identify the system.

As can be checked on figure 6.5, 6.6 and 6.7 a long set of data has been captured, between

one to two hours time have the temporal windows. Thus, this data has been decomposed in

two parts [17], [19]:

1. Estimation Data: is the data set that is used to fit a model to data.

2. Validation Data: A good test is to take a close look at the model’s output

compared to the measured one on a data set that wasn’t used for the fit

(“Validation Data”). Validation Data is the data set that is used for

model validation purposes. This includes simulating the model for these

data and computing the residuals from the model when applied to these

data.

On figure 6.9 below, the input-output data corresponding to the actuator of the

2nd tower, extracted from the Wizcon supervisor the 1st of September 2003, is showed.

Relevant data has been separated for the estimation and the validation.

Figure 6.58: Decomposing data for identification



This process has been repeated several times for each actuator that takes part in

the cooling process at BA6, with several sets of data from different days.

6.4. ESTIMATING MODELS

Estimating models from data is the central activity in the System Identification

Toolbox of Matlab®. One can distinguish between two different types of estimation

methods:

1.Direct estimation of the Impulse or the Frequency Response of the system. These

methods are often also called nonparametric estimation methods, and do not

impose any structure assumptions about the system, other than that it is linear.

2. Parametric methods. A specific model structure is assumed, and the parameters

in this structure are estimated using data. This opens up a large variety of

possibilities, corresponding to different ways of describing the system.

Dominating ways are state-space and several variants of difference equation

descriptions.

How to Know Which Structure and Method to Use?

There is no simple way to find out “the best model structure”; in fact, for real

data, there is no such thing as a best structure. It is best to be generous at this point. It

often takes just a few seconds to estimate and validate a model, you can quickly find out

if the new model is any better than the ones you had before. There is often a significant

amount of work behind the data collection, and spending a few extra minutes trying out

several different structures is usually worthwhile.

The chosen way to identify the model has been using parametric methods since

these methods provide us with more flexibility during the model building and mainly

because the obtained results have been the best ones. The parametric models have been

described using state-space equations, which are a useful way to export the model to a

Simulink environment. During the simulations, these state-space equations can be applied

directly or can be transformed in continuous or discrete transfer functions.



State-Space Models. The Model Structure

The basic state-space model in innovations form can be written:

)()()()()()()()1(

tetDutCxtytKetButAxtx

++=++=+

The System Identification Toolbox supports two kinds of parametrizations of

state-space models: black-box, free parametrizations, and parametrizations tailor-made to

the application.

Entering Black-Box State-Space Model Structures, which will be the used one,

the most important structure index is the model order; i.e., the dimension of the state

vector x. Moreover, you can affect the chosen model structure. Fixing K to zero gives an

Output-Error method; i.e., the difference between the model’s simulated output and the

measured one is minimized. Formally, this corresponds to an assumption that the output

disturbance is white noise. The delays from the input can be chosen independently for

each input. It will be a row vector nk, with nu entries. When the delay is larger than or

equal to one, the D-matrix in the discrete time model is fixed to zero. For physical

systems, without a pure time delay, that are driven by piece-wise constant inputs, nk = 1

is a natural assumption.

Estimation Methods

There are two basic methods for the estimation:

• PEM: Is a standard prediction error/maximum likelihood method, based on

iterative minimization of a criterion. The iterations are started up at parameter

values that are computed from n4sid. The parametrization of the matrices A, B, C,

D, and K is free. The search for minimum is controlled by a number of options as

the focus estimation that can be the prediction, simulation filter or stability, the

initial state or the covariance.

• N4SID: Is a subspace-based method that does not use iterative search. The quality

of the resulting estimates may significantly depend on some options called

N4Weight and N4Horizon. If N4Horizon is entered with several rows, the models



corresponding to the horizons in each row are examined separately using the

Working data. The best model in terms of prediction (or simulation, if K = 0)

performance is selected. A figure is shown that illustrates the fit as a function of

the horizon.

A feature available for black-box state-space models, is to estimate using n4sid.

When a good order has been found, try the PEM estimation method, which often

improves on the accuracy [17], [20].

6.5. ESTIMATION RESULTS

Since it does not exists identical elements (valves and I/P transducers) it has been

tried, when it has not been beyond our means, to identify each element separately. The

data used on that section comes from the actuators of towers 2 and 3. Concerning cooling

tower 1 and 4, one was working at maximum and the other one at minimum during the

time when the data was extracted. Thus, it is kept the obtained transfer functions for

tower 1 and 4 whereas the actuators identification has been focused just in cooling tower

2 and 3 that brings data with enough information.

At the end, a model based on a valve and I/P transducer has been identified. The

resultant transfer function is equivalent to the whole formed by both elements. The

accuracy has been improved taking into account the disturbance produced by pressure

variations.

DPsFlow

sLevelTanksFlow

sPositionValvesFlow

sH∆

∆±

∆∆

±=)(

)()(

)()(

)(

6.5.1. Actuator cooling tower 2 ( )()( sPositionValvesFlow ):

The model was extracted from data corresponding to the 1sf of September 2003.

Around 1 hour time was used to estimate the process and another hour time to the

validation. Anyhow, this routine was done again for all the set of data available

corresponding to the 30th and 31st of August. Just comparing input and output one sees a

hard relationship between the signals, so a proper identification is expected.



Figure 6.59: Examined data for the identification of actuator corresponding to cooling tower two.

Using several types of models it has checked that a similar result has been

obtained. Thus, a 3rd order state-space model has been chosen and the best result is

presented below.

( )

=

+⋅+=

+

+

=+

71.7631.4171.1161

)0(

)()(0)(0.00783232.3793-287.02)(

)(0.130250.09937-

0.005238)(

2.58050.738370.013297

)(0.78446-0.0072408-0.0074676-0.41716-0.782690.0714530.000726-0.019224-0.99769

)(

2

2

2

x

tetutxty

tetutxTtx s

To calculate the steady-state equations has been used PEM (standard prediction

error/maximum likelihood method), it is based on iterative minimization of a criterion,

the criterion in which the identification has been focused has been the prediction, this

means that the model is determined by minimizing the prediction errors. It corresponds to

a frequency weighting that is given by the input spectrum times the inverse noise model.

Typically, this favors a good fit at high frequencies.

The state-space model has been transformed in a continuous 3rd order transfer

function and, like that, the model is transported to a Simulink environment.



5- 23

-52

2 1.908e + s 0.006727 +s 0.1611 + s9.583e + s 0.04208 + s 0.5113

(s) =G

The output yh that results when the model m is simulated with the input u has

been computed. The results are plotted together with the corresponding measured output

y (black). The percentage of the output variation that is explained by the model is also

computed and displayed.

)))((

)(1(100

ymeanynormyyhnorm

fit−

−−⋅=

Comparing with the real data (black) it has been obtained a best fit of 79,48 %.

Note a thin improvement of 3% respect the old transfer function used in the previous

Chapter 5.

222,01.1

15,11

131

)()()( 2/tan ++=

+⋅

+=⋅=

sssssHsHsOld PIk

Figure 6.60: Best Fits

Figure 6.61: Errors respect the real model



The same results, but now plotted in terms of error between the real model and the

predicted ones, has been plotted above.

In terms of stability, it is presented below the discrete time zero and pole map. As

can be seen all the poles and zeros are enclosed on the unitary circle, which means that all

the predicted models are stable.

Figure 6.62: The pole and zero map reflects the system stability

Residual Analysis

In a model )()()()()( tezHtuzGty += the noise source e(t) represents that part of

the output that the model could not reproduce. It gives the "left-overs" or residuals. For a

good model, the residuals should be independent of the input. Otherwise, there would be

more in the output that originates from the input and that the model has not picked up.

To test this independence, the cross-correlation function between input and

residuals is computed. It is wise to also display the confidence region for this function.

For an ideal model the correlation function should lie entirely between the confidence

lines for positive lags. If, for example, there is a peak outside the confidence region for

lag k, this means that there is something in the output y(t) that originates from u(t-k) and

that has not been properly described by the model. The test is carried out using the

Validation Data. If these were not used to estimate the model, the test is quite tough.

For a model also to give a correct description of the disturbance properties (i.e.,

the transfer function H), the residuals should be mutually independent. This test is also

carried out, by displaying the auto-correlation function of the residuals (excluding lag



zero, for which this function by definition is 1). For an ideal model, the correlation

function should be entirely inside the confidence region.

Figure 6.63: Residual analysis for the selected model

Any estimated model has a degree of uncertainty. This will affect the reliability of

the various model properties. The different model views come with estimated accuracy

measures. The uncertainty region is marked by two dash-dotted lines on either side of the

nominal model curve and has the same color as the curve. The statistical interpretation is

that (with the indicated probability) the true system's response will be found within the

confidence region marked.

6.5.2. Actuator cooling tower 3 ( )()( sPositionValvesFlow ):

Figure 6.64: Examined data for the identification of actuator corresponding to cooling tower three.



Like in the previous identification, data from the 30th of August 2003 was treated

and decomposed for estimation and validation. To calculate the steady-state equations

PEM method was used again but the best performance in terms of best fit was achieved

with N4SID method. The obtained model was focused as well on the prediction and it

was a 4th order system.

( )

=

+⋅+=

+

+

=+

18.74326.13112.055

0.66023

)0(

)()(0)(0.42829-0.560193.0993- 253.99)(

)(

0.0114110.0218680.048103-

0.0046913

)(

0.0802021.03670.48399

0.017323

)(

0.16984-0.720930.0207080.068590.89061-0.17950.149620.073583-0.19104-0.44289-0.840780.155790.00649-0.00139-0.037898-1.0108

)(

3

3

3

x

tetutxty

tetutxTtx s

The state-space model has been transformed in a continuous 4 th order transfer:

0.0001754 + s 0.02038 + s 0.2768 + s 0.2294 + s

0.0005329 + s 0.1172 + s 0.2583 + s 1.716(s) 234

23

3 =G




The plots show the simulated (predicted) outputs of selected models. The models

are fed with inputs from the Validation Data set, whose output is plotted in black (in

white on a black blackground).The percentage of the output variations that is reproduced

by the model is displayed at the side of the plot. A higher number means a better model.


Note that for that actuator the improvement on the modelization has been pretty

important since, for that set of data, the best fit corresponding to the old transfer function

is a poor 18,99% whereas the best fit achieved with the identification toolbox has been a

67,50%.

In that case the selected model is also stable, can be checked below how for the

best fitted model all the poles and zeros are inside the unity circle.





For the selected model, the residuals (prediction errors) are computed for the data

selected as the Validation Data set. The autocorrelation function for the residuals as well

as the cross correlation function between input and residuals are computed and displayed.

The confidence interval for these functions is fixed at 99%. Comparing the results with

the actuator two one can conclude, that for the set of data used, the identification has been

worst, the best fit has decreased and the degree of uncertainly has increase since our

system acts often outside the confidence region marked.

6.5.3. Tank Level contribution ( )(/)( sLevelTanksFlow ∆∆ ) :

Figure 6.69:A tank volume variation provoques a variation on the pressure.



In figure above it is checked how a variation on the stopgap tank level produces a

change on the outlet pressure due to the volume variation. This contribution has been

tacking into account to improve the accuracy of the model even if the contribution is

quite thin, a more important contribution in terms of pressure variation is studied later

and it comes from the SIG pumping station.

To identify the model data has been extracted from cooling tower 1 because

during those days it was working at maximum of its capacity, it means that there was not

variations in the valve position having the diaphragm always with the same gap. Thus, all

the flow variations were due to pressure changes.

Tacking a look to the figure above it is noted that the input-output data

relationship is quite weak. Thus, to model this contribution, data is preprocessed

removing the trends from output-input data, as can be seen in figure 6.20. In that way

when identification is carried out the offset is not taken into account and the model is

based just on signal variations, as a consequence, a better fit is achieved. Moreover, the

obtained transfer function work over variations on the level operational point located at

2,5 meters, it means, the resultant flow from this transfer function can be added directly

to the total flow corresponding to percentage of valve opening.

( )

=

+⋅+=

+

+

=+

0.003559-0.042601-

)0(

)()(0)(4.3363-279.99)(

)(0.16835-

0.0103)(

0.00355780.000106-

)(0.948340.023550.07457-1.0203

)(

2

2

2

x

tetutxty

tetutxTtx s

A second order continuous transfer function is calculated from the steady-state

equations:

0.0007194 + s 0.03115 + s0.07668 - s 0.007284-

(s) 22 =G

The following figures represent the models best fits and the errors respect the real

solution, the achieved best fit for the level contribution on the flow across the valves is

just a 25 % due to the weak relationship between both.



Figure 6.70:Best Fits


For the selected transfer function all the poles and zeros are inside the unity circle,

which means a stable system.





For a good model, the residuals should be independent of the input. To test this

independence, the cross-correlation function between input and residuals is computed.

Check how the cross-correlation function is entirely between the confidence lines. It

means the output has been properly described by the model.

However, disturbance properties are not properly described, the residuals are not

mutually independent. It is displayed on the auto-correlation function of the residuals.

For an ideal model, the correlation function should be entirely inside the confidence

region. Any estimated model has a degree of uncertainty, and this will affect the

reliability of the various model properties. In that case, there is not a direct relationship

between input-output data, which makes a weak model in terms of best fit.

6.5.4. Pressure SIG Contribution ( DPsFlow ∆∆ /)( ) :

Like in the previous model, output data (flow) has been extracted from the first

cooling tower which is working at maximum. Secondly, the input is collected from a

pressure measurement on the pumping station “Pression eau primaire SPS SIG” near the

point of interest. The differential pressure between the source collector and the return

collector has a set point maintained at 4 Bars by adjustment the speed of the pump in the

SIG station.



Figure 6.74: A pressure variation on the pumping station provokes a variation on the flow.

The contribution of a pressure variation over the flow through the valve is quite

thin. Thus, as before, the trends have been removed to improve the identification tacking

out the offset. The resulting model is located on the working point, it means, just

variations are taken into account and are added directly to the model. A second order

steady-state corresponds to the best model:

( )

=

+⋅+=

+

+

=+

0.16419- 0.008465

)0(

)()(0)(4.7299-339.9)(

)(0.16419-

0.00846)(

0.0003244-0.00039691

)(0.965480.0140050.064368-1.0125

)(

2

2

2

x

tetutxty

tetutxTtx s

A continuous transfer function is calculated to be used later on a Simulink

environment:

0.0004767 + s 0.02182 + s0.01184 + s 0.132

(s) 22 =G





For the selected set of data the best fit achieves is just a 38%. Like before it is also

a low contribution, but anyway both added makes the system more accurate as will be

seen later. In terms of stability the system have all poles and zeros inside the unity cercle,

which means a stable system.

Figure 6.77: Pole and zero map




Check how the cross-correlation function is entirely between the confidence lines.

It means the output has been properly described by the model. On the other hand, the

auto-correlation is weak and therefore the estimated model has a degree of uncertainty

which will affect the reliability of the model properties.

6.6. VALIDATING MODELS

The main propose to identify each different element is to implement them in a

Simulink environment. In that way, the present control architecture can be studied and

simulations over the actual behavior of the cooling plants can be done. At this moment,

the control architecture is based on cascade control, a master controller take care of the

storage tank level and several slave controllers acts on the valves. An extended

explanation about the actual system and cascade control will be done afterwards in

Chapter 7. The point is to improve, if possible, the present parameters located on the

standard PI controllers and propose new kind of controllers or even a new kind of control

architecture.

Each actuator has been implemented on the Simulink environment, a schema of

them can be seen on Figure 6.3. The obtained transfer functions after identification has

been written taking into account also the corresponding pressure contributions. In figure



below the Simulink can be seen. To validate the model data from the data base

corresponding to the 30th and 31st of August, and 1st of September, has been treated and

polished. Firstly Acces has been used due to the large .dbf file to extract the data from the

selected temporal window. Secondly, all the selected variables have been ordered in

Excel since the standard .xls extension can be exported to a Matlab framework. Finally, a

Matlab program .m imports the data, makes the last arrangements, and send it to the

Simulink engine. There, in the Simulink environment, it is checked if the models are

good enough using the real data extracted from the cooling towers to feed the linear

systems and in that way to see the evolution of the dynamics.

Figure 6.79: Simulink models for the actuators



Figure bellow shows the results obtained for each actuator, it is represented the

flow through each valve. The flow in the cooling towers 2 and 3 (“Debit T2 and T3”)

follows a variable set point, then the results depends on the set point and the pressure

contribution. The best approximations have been achieved with the continuous transfer

functions obtained from the system identification. On the other hand, the flow on the

cooling tower 1 (“Debit T1”) has a fixed set point located at maximum, all the flow

variations come from pressure changes that were taken into account using system

identification. It can be checked that it has been achieved a pretty good approximation to

the real values.

Figure 6.80: Comparison between real and obtained data



As can be seen in figure above, some transfer functions representing the actuators

(see red line “Debit T3”) have an important error when the valve works at low capacity,

this is due to the non-linearity that the valve butterfly presents. This error always exists

when a non-linear system is modelled as a linear transfer function, anyway the error has

been minimized as possible and the best fits are pretty good.

CHAPTER 7: SYSTEM SIMULATION AND

OPTIMIZATION

7. System Simulation and Optimization Process Control Study of the BA6 Cooling Towers for the SPS accelerator


7.1 ENHANCEMENTS TO SINGLE-LOOP PID CONTROL

Several factors that define the behavior of a controlled system are, the kind of

process, the disturbance situation and amplitude, and the controller features and tuning.

Often, the process is submitted to large load changes or disturbances, thus a typical

feedback control based on a PID controller is not satisfactory. Focusing on our process,

one realizes several troubles that take place:

1. Important dead-time due to the long supply pipe of about 8 km.

2. There is no predictive action against heavy variations on the input flow

rate that enters in the storage tank.

3. Nonlinear elements.

Hence, one has to resort to modify the control strategy in order to improve the

response. In this Chapter 7 we will introduce the multi-loop control strategy called

cascade control. The feedforward control, also a multi-loop strategy, will be discussed

afterwards in Chapter 8.

7.2. CASCADE CONTROL

The configuration based on cascade control is used when the manipulated

variable (output flow rate) suffers heavy disturbances that affect excessively the

controlled variable (storage tank water level). In our case that disturbances corresponds to

the input flow rate, which is unknown, depending on the SPS conditions and depending

on the cooling demand from the different BA’s. The strategy consists on the implantation

of a secondary control loop (slave) inside the main control loop (master), by then to

control both variables separately.

The best way to introduce cascade control is with reference to our process, which

goal is to keep in the level between some limits thought a tight control of the out flow

rate [9].

The conventional feedback controller, with integral mode, attempts to maintain

the level near its set point in response to all disturbances and ensures zero steady-state

offset for step like disturbances.



Suppose that one particularity frequent and large disturbance is the input flow rate

Qe. As has been said in the previous Chapter 5, the input flow rate is unknown and it is

taken as disturbance. Studying the evolution of the flow that pass for the SIG station, the

same that will end in the cooling towers after a dead time due to the long supply pipes, it

is checked that the warm flow is quite stable apart from some sporadic but important

variations. When this flow increases, the initial response of the level is to increase, then

the feedback controller opens the valve to compensate the increase in the input flow rate,

and in that way to maintain the level near the set point. While the effect of the

disturbance is ultimately compensated by the single-loop strategy, the response is slow,

because the level must be disturbed before the feedback controller can respond.

Cascade control design considers the likely disturbances and tailors the control

system to the disturbance(s) that strongly degrades performance. Cascade control uses an

additional, “secondary” measured process input variable that has the important

characteristic that it indicates the occurrence of the key disturbance [21].

For the level in our storage tank water, all measured variables are shown in Figure

7.1. The schema complexity has been reduced by grouping the four outlet controlled

valves of the towers in a single one. The secondary variable is selected to be the output

flow rate managed by the “whole” valve, because it responds in a predictable way to the

disturbances in the input flow. The control objective (tight control of the storage tank

water level) and the final element are unchanged.

The manner in which the additional measurement is used is shown in Figure 7.1.

The control system employs two feedback controllers, both of which can use the standard

PID controller algorithm. The important feature in the cascade structure is the way in

which the controllers are connected. The output of the water level controller adjusts the

set point of the flow controller in the cascade structure; that is, the secondary controller

set point is equal to the primary controller output. Thus, the secondary flow control loop

is essentially the manipulated variable for the primary level controller. The net feedback

effect is the same for the single-loop or cascade control; in either case, the valve is

adjusted ultimately by the feedback. Therefore the ability to control the storage tank

water level has not been changed with cascade.



As described previously, the single-loop structure makes no correction for the

input flow rate disturbance until the tank level is upset. The cascade structure makes a

faster correction, which provides better control performance. The reason for the better

performance can be seen by analyzing the initial response of the cascade system to an

input flow increases. The valve position is initially constant; therefore, the input flow

increases. The level sensor detects a level increase as a consequence of the inlet flow

increase, then the master controller, which is connected to the slave input, acts on the

slave with a new set point. Because the flow sensors and the valves constitute a very fast

process, compared with the tank level process, the flow controller can rapidly achieve its

desired flow. By responding quickly to the level increase and compensating by opening

the control valve, the secondary controller corrects for the disturbance before the tank

level is significantly affected by the disturbance [14].

A few important features of the cascade structure should be emphasized:

- First, the flow controller has to be much faster than the level controller, thus,

often the slave controller is just a proportional one. The improvement results

from the much shorter dead time in the secondary loop than in the original

single-loop control. If the flow controller were not faster, the cascade design

would have no advantage.

- Second, the level controller with an integral mode remains in the design to

ensure zero offset for all disturbance sources. The primary controller is

essential, because (1) the secondary variable may not totally eliminate the

effect of the disturbance, (2) other disturbances that are not affected by the

cascade will also occur, and (3) the ability to change the primary set point

must be retained.

LC

FC

SetPoint

Qe

Q s

H

Figure 7.81: Storage tank water level



In Figure 7.1 above, the basics of the multiple control loop system to be studied is

showed. Two control loops are related in cascade mode, a flow control and a liquid-level

control. Having made the distinction, it can be seen that each category of control system

has its own peculiar properties regarding linearity, self-regulation, and dynamic response.

As a result, each has its own requirements as to valve characteristics, and the selection

and settings of control modes. The recommendations for ach loop is summarized in Table

7.1 below, each loop has been analyzed as to dynamics, steady-state modes and their

approximate ranges, and appropriate choice of valve characteristics.

Property Flow Liquid-Level

Deadtime No No

Capacity Multiple non-iterating lags Integrator

Period 1-10 s 2-20 s

Linearity Linear/square Linear

Kp 1-5 -

Noise Always Always

Proportional band 50-500% 5-50%

Integral 0,3-3 s 1-10 min

Derivative No No

Valve Linear/modified-percentage Linear/modified-percentage

Table 7.3: Common properties for flow and liquid-level control loops [9]

Concerning the cascade design criteria, in Table 7.2 is summarized in a concise

form so that they can be applied in general.

Cascade Control is desired when

1. Single-loop control does not provide satisfactory control performance

2. A measured secondary variable is available

A secondary variable must satisfy the following criteria:

1. The secondary variable must indicate the occurrence of an important disturbance.

2. There must be a causal relationship between the manipulated and secondary variables.

3. The secondary variable dynamics must be faster than the primary variable dynamics.

Table 7.4: Cascade control design criteria [9]



The first two items address the selection of cascade control. Naturally, only when

single-loop control does not provide acceptable control performance is an enhancement

such as cascade control necessary. Single-loop control provides good performance when

the dynamics are fast, the fraction dead time is small, and the disturbances are small and

slow. Also, the second criterion requires an acceptable measured secondary variable to be

available or added at reasonable cost.

A potential secondary variable must satisfy three criteria. First, it must indicate

the occurrence of an important disturbance; that is, the secondary variable must respond

in a predictable manner every time the disturbance occurs. Naturally, the disturbance

must be important (i.e., have a significant effect on the controlled variable and occur

frequently), or there would be no reason to attenuate its effect. Second, the secondary

variable must be influenced by the manipulated variable. This casual relationship is

required so that a secondary feedback control loop works properly. Finally, the dynamics

between the final element and the secondary must be faster than the dynamics between

the secondary variable and the primary controlled variable. The secondary must be

relatively quick so that it can attenuate a disturbance before the disturbance affects the

primary controlled variable. A general guideline is that the secondary should be three

times as fast as the primary.

In the previous Chapter 4 it was studied and modeled the dynamics of the stopgap

tank, a dynamic test filling the tank with different flow rates was carried out, the results

are displayed below. As can be checked, to exceed the safe limit just 50 seconds are

needed in nominal conditions with a typical flow rate of 700 l/s.

Figure 7.82: Dynamic test time response



On the other hand, the actuator dynamics (transmitter-transducer-valve) was

studied over experiments carried out in the same cooling towers. To open completely the

valve from zero it takes between 16 to 18 seconds time. It means that the actuator

dynamics (secondary loop) is faster than the tank dynamics (primary loop).

The relative dynamics between the secondary and the primary loop is defined by

the variable ?, this value has to follow the requirement of three times more quick the

secondary than the primary process. For instance, for a huge step like disturbance of 780

l/s flow, and working on the level set point (2,5 m), the dynamics of the actuator (˜ 18

sec) is around 2 times faster than tank dynamics to exceed the secure level (˜ 40sec).

Thus, for a huge disturbance of 780 l/s the system has a relative dynamics of ?=2 and it

means that the cascade control does not improve the system response in an important way

if it is compared with the typical single loop. However, this kind of disturbance is not real

in normal operation the flow disturbance are quite smooth and due to that fact cascade

control improve the system behavior against disturbances. In figure below an importance

disturbance in terms of flow is presented and can be seen how a progressive disturbance

of 300 l/s flow occurs and takes around 10 minutes time.




Figure 7.84: Block diagram of cascade control



Summarizing, the principal advantages of using cascade control are [14]:

1. Phase lag existing in the secondary part of the process can be reduced

significantly by closing the secondary loop, thereby increasing the speed

of the primary loop.

2. Load changes arising within the secondary loop can be corrected by the

secondary controller often before they affect the primary controller

variable.

3. Gain variations in the secondary part of the process affect only the

secondary loop, which removes them from the primary loop.

4. The secondary loop may permit precise manipulations of the flow by the

primary controller.

Cascade control is recommended wherever high performance is mandatory in the

face of frequent load changes, or where the secondary part of the process contains an

undue amount of phase lag or nonlinearity.

The most common secondary loops are valve positions, like the studied case,

which overcomes the damping phase lag of deadband, and flow, which in addition

eliminates the nonlinearity of the installed valve characteristic and supply-side

disturbances [10].

7.3. BUILDING THE PRESENT CONTROL ARCHITECTURE

In Figure 7.4 above the Simulink® cascade schema is showed. This cascade

controller is composed for two layers, a master controller drives the level control for the

storage tank and, four slave controllers drive the flow for each cooling tower. As one can

check in the “Analysis functionnelle des tours du BA6” [4] the output signal coming from

the level controller (master) is divided in four, and these values following the cascade

concept will be the set points for the flow controllers (slave). Since there is a study that

recommends to work between the 70% and the 100% of the tower capacity

The next step, once the overall structure of the control system has been

implemented, is to find out if the model is correct or not. In previous Chapter 6 was

checked how the actuators were well modeled, this proofs was done using real data



extracted from the supervisor SCADA system. Now, the same test will be carried out but

using the overall structure of the control system. As can be seen in Figure 7.4 above, an

incoming flow is passed, this flow corresponds to the real measurement took at the SIG

pumping station. In order to verify if the overall model is correct, all the PI controllers

that take part of the system has to be modeled with the same parameters used when the

data acquisition was carried out. The corresponding model and explanation for the PI

controllers with anti-reset windup can be found in previous Chapter 5.

Primary level controller Kp = 25 Ti=15

Secondary 1st cooling tower controller Kp = 0,35 Ti = 1.8

Secondary 2nd cooling tower controller Kp = 0,35 Ti = 1.8

Secondary 3rd cooling tower controller Kp = 0,35 Ti = 1.8

Secondary 4 th cooling tower controller Kp = 1 Ti = 1.5

Table 7.5: Old PI parameters

Note how for the 4th cooling tower the parameters are different. It is the

consequence of the plant behavior during the summer. The normal load for the cooling

towers used to be between 600 to 900 l/s of warm water. During this period of time the

4th tower was the latest one in priority, it means that for that load the normal operation

was with the 1st and the 2nd tower at maximum, and working between the 3rd and the 4th

ones. As a consequence, with Kp = 0,35 the 4th cooling tower responded too slow against

flow variations, normally it took around 1 hour time to reach the steady-state. Thus the

correction was to increase the proportional gain and decrease the integral time to achieve

a faster system and the before steady-state. This was an important point to be improved

for the new proposed PI parameters that will be taken from the simulations of the

identified system.

Hence, it has been simulated the behavior of the overall plant for the 30th, 31st of

August and 1st of September using real data. Below a comparison of the most relevant

parameters is showed.



Figure 7.85: Storage tank and total flow behavior (1st of September 2003)

In figure above the comparison between the real level and the modeled one is

showed. Also three flows are presented, the SIG flow is the used as an incoming

disturbance for the simulations. Remark that this flow corresponds to the outgoing one

that is pumped for the SIG station to the distribution ring, but since there is not

measurement at the input, just for the simulations it is used the output measurement as

input. In fact, the outgoing flow is the same that will income the stopgap tank after going

around the ring, it can be supposed that the input is advanced in time. It introduce an

error which is not crucial in such a slow system, the time that pass between the flow

incomes the tank to it reaches the SIG pumping station is around 45 seconds to 1 minute

time, the distance between the cooling towers to the SIG pumping station is around 100

meters.

In the following Figure 7.6, the real measured flows as well as the modeled ones

are presented. It has been also represented the set points corresponding to each cooling

tower, since in the cascade structure the set point of the secondary loop varies with the

error correction introduced by the primary controller.



Figure 7.86: Flow and set point for each cooling tower

As can be observed in both, figures 7.5 and 7.6, the model of the entire system is

pretty approximate to the reality. Thus, once the point of having the system modeled is

reached two main actions can be proposed:

1. To keep the present control architecture and to optimize the system by:

a. Changing the PI controller parameters.

b. Changing the kind of controllers for proposed digital RST controllers.

2. To propose a new control structure strategy as a feedforward control to achieve a

better system behavior against steep flow disturbances. This kind of control

strategy could be even better if would be applied over the control of the

ventilators.



7.4. OPTIMIZING THE PI CONTROLLERS.

The actual parameters, which can be seen in Table 7.2, make the cooling towers to

work properly during all the period in which the SPS accelerator is in motion. However,

to improve the functioning of the system is desired.

Problem 1:

There is one thing that can lead the system to the disaster, this is to surpass the

cooling capacity of the towers. It happens if the SPS accelerator increases in an important

way its demand of cooled water, when the SPS hot up it contributes with warm water, at

higher temperature than usual, to the closed cooling system. However, the cooling

capacity remains constant, and to keep the storage tank between the safe limits, the water

that comes in has not to exceed 1050 l/s. Once, in summer 2002, working the SPS at

maximum and in extreme environmental conditions the accelerator had to be turned off.

It happened because the cooling towers were not capable to reach the temperature set

point established around 24ºC, when it happen the SIG pumping station adds cold water

coming from the lake until the set point is satisfied, however if the amount of warm water

inside the ring reaches the cooling limit, the accelerator has to be stopped. The definition

of this critical situation is showed in Figure 7.7. To solve this problem there are two

possible actions:

a. To improve the control parameters or the controls structure to optimize the

cooling process. Predictive actions can be used or a feed-forward structure to

minimize the contribution of the disturbances on the system. This solution

cannot guarantee a proper functioning of the system, it can be optimized but

the physical limitations of the system cannot be surpassed.

b. The adopted solution was to vary the physical parameters of the system.

Recall that there are two water circuits, the primary brings the cooled water

for towers and the secondary brings demineralized water that cools directly

the magnets. Between both circuits there is a heat exchanger, the SPS magnets

are hot magnets and the temperature set point for the demineralized water is

fixed at 34ºC. Then the proper solution is to acts over this set point increasing



its value as possible in order to increase the cooling capacity the cooling

towers, and so to be able to keep the storage tank between the safe limits.

Figure 7.87: Critical process Problem 2:

During the normal operation in summer is normal to work with a typical load

between 600 to 800 l/s. This load makes to work at maximum two and often three cooling

towers and acting on the threshold of the third or fourth tower. To be functioning in the

threshold, between two cooling towers with the present parameters for the PI controllers

YES

NO

NO

YES

(a) (b)

Cooling towers satisfy Tª set point

Cooling towers don’t satisfy Tª set point

SIG station pumps cold water from the lake

Is the Tª set point

satisfied?

Is the cooling capacity

exceeded?

SPS accelerator hot up

OK

Storage tank overloaded !!!

OK



introduces a handicap, the system reach the steady-state late. The valves’ set points are

driven by the level controller, this level controller presents a quite big proportional gain

that amplifies the level error. Nonetheless, the valves controllers are quite slow since the

integral constants dominate over the proportional gains. As a consequence, the tracking

of the set point takes a lot of time and the valves vary over all their ranges (between the

0% to the 55%) during large periods until the steady-state is reached. In Figure 7.8 below

can be checked how when the third tower starts to operate it needs a large time to set the

steady-state, after 20 minutes the flow through the valve is not stabilized yet.

Figure 7.88: Slow response working in the threshold between two towers

7.4.1. Tuning Cascade Controllers

Because the secondary loop is an element within the primary loop, the secondary

controller must be properly tuned before the primary controller, with the primary in

manual mode. The secondary controller should be tuned optimally for load changes

originating at its output, and tested by stepping its output in manual before transferring to

automatic, exactly as recommended for single loops. Then the primary controller should

be tuned in the same way, with the secondary in automatic mode and set from the

primary [9], [10].



Following the previous criteria for tuning the controllers in a cascade

configuration a Matlab® program has been developed to minimize the IAE making

iterations for different values of the PI controllers and so to obtain optimal values.

Let’s make a simple introduction of the used criteria to tune the different

controllers separately. Integrated error (IE) is a very useful measure of controller

performance, both for comparison of different controllers applied to the same process and

for arriving at optimum tuning as well. Fortunately, it is possible to estimate the IE

resulting from a load change for any controller having integral action. For the integral

controller, this is simply:

∫ ∆⋅=⋅= mIdteIE Eq. 7.1

where m∆ is the change in the value of the controller output between any two steady

states, e.g., before and after a load change.

From Equation 7.1 it appears that minimizing IE for a given load change simply

requires minimizing integral time I. But the lowest allowable of I is Iu, representing the

stability limit. So simply minimizing IE is unsatisfactory- dumping must be assured as

well. The most satisfactory single criterion meeting both objectives is the minimization of

the integral absolute error (IAE):

∫ ⋅= dteIAE Eq. 7.2

IAE accumulates rather then canceling deviations of opposite sign. Consequently it can

reach a final value following a load change only in the absence of cycling, and

minimizing IAE results in a well-damped response curve having little set-point

overshoot.

Thus, using the identified system which has been modeled with Simulink a

Matlab® program has been written in order to find out the values that minimizes the IAE

error. Each of the iterations done to found out the proper parameters took 1200 seconds

time. A disturbance of 610 l/s was applied to the system; a white noise of 60 l/s

magnitude each 15 seconds time was added to the disturbance. As has been mentioned

before the slave controllers were tuned in first position, secondly the master one. The

following results in terms of IAE have been obtained:



Figure 7.89: IAE for the storage tank level

Figure 7.90: IAE for cooling towers flows



Figure 7.9, which is the most representative, shows the accumulated error for the

level in the storage tank. As can be seen, increasing the proportional gain of the

secondary controllers the system becomes faster and as a consequence the error

decreases. Concerning the integral time, the opposite occurs, as bigger the integral time

is, the system has more accumulated error. Figure 7.10 shows the IAE for each cooling

tower, these results are less appreciates because they depend strongly with the applied

disturbance, recall that these valves are driven by the primary controller and depending

on the disturbance they switch on or not. In Table 7.4 below the recently obtained PI

parameters are compared with the old ones.

Old PI parameters New PI parameters

Primary level controller Kp = 25 Ti=15 Kp = 45 Ti=15 Secondary 1st cooling tower controller Kp = 0,35 Ti=1,8 Kp = 4 Ti=1 Secondary 2nd cooling tower controller Kp = 0,35 Ti=1,8 Kp = 4 Ti=1 Secondary 3rd cooling tower controller Kp = 0,35 Ti=1,8 Kp = 4 Ti=1 Secondary 4 th cooling tower controller Kp = 1 Ti = 1,5 Kp = 4 Ti=1

Table 7.6: Parameters for the PI controllers

To check if the new values fit the system to achieve faster the steady-state the

critical case has been simulated. As mentioned before, a step disturbance of 650 l/s has

been passed, this disturbance has a white noise with a magnitude of 60 l/s with a period

of 15 seconds time. This disturbance forces the system to work in the threshold of the

third cooling tower, the final steady-state would have to be with the first and second

cooling towers at maximum and the third one with almost 100 l/s flow. In Figure 7.11

below, a comparison between the responses with the new and old PI parameters is

presented. Underline the response corresponding to the third cooling tower, it is proved

how the overall system has become more than twice faster. The carried out actions have

been to increase the proportional gain in both, primary and secondary controllers, to

maintain the integral time in the primary controller and to reduce it in the secondary one.



Figure 7.91: With the new PI parameters the steady-state is reached faster

7.5. DEFINITIVE PI VALUES FOR A DISCRETE-TIME CONTROL

In Figure 7.4 the schema of the overall system was presented. In that model, all

the different parts of the system, valves, transducer, controllers, etc, were taken in

continuous time. This fact can lead the simulations to an error since the real model driven

by a PLC Schneider Quantum obviously works in discrete time. To model the system

properly D/A and A/D converters were added to the schema in the same way showed in

Figure 7.12. The PLC use the following sampling times: ts = 3 sec for the flow

measurements and ts=1 sec for the level measurements. Thus, zero-order holds with these

sample times are used.

Figure 7.92: Discrete-time control of a continuous-time plant [URL 5]



Simulating the system again, now in discrete-time, it is observed that for the used

sample times the new values for the PI controllers exceed the capacity of response for the

elements of the system. A really tight level control is achieved, however the different

valves work excessively, they make the tracking of the set point given by the master

controller suffering too much wear, changing their opening position without stop.

Hence, next step is to reach a compromise between the speed of the response and

a proper/smooth functioning of the different elements that shape the system. Using the

discrete-time model and trying to obtain the best system in terms of smooth functioning

and minimizing as well the IAE, the following PI parameters has been chosen.

Primary level controller Kp = 25 Ti=15

Secondary 1st cooling tower controller Kp = 1 Ti = 1.5

Secondary 2nd cooling tower controller Kp = 1 Ti = 1.5

Secondary 3rd cooling tower controller Kp = 1 Ti = 1.5

Secondary 4th cooling tower controller Kp = 1 Ti = 1.5

Table 7.7: Definitive PI parameters

These parameters improve the system behaviour against a critical disturbance,

reaching before the steady-state and keeping the smooth functioning of the system.

Figure 7.13 presents a comparison between the three obtained results. Can be

observed the slow response obtained with the old PI parameters which need more than

half an hour to reach the steady-state (red). It is also showed the fast but sudden response

obtained with the firsts proposed PI parameters extracted wrongly from the continuous-

time model (green). Finally, it is checked the fast and smooth response obtained with the

last obtained PI parameters which have been inserted by the supervisor SCADA system

and are the ones used at the moment for the controllers (blue).



Figure 7.93: System response in discrete-time against a 650±60 l/s disturbance

Finally to mention the improvement obtained with the cascade configuration. A

200 l/s disturbance has been passed to two systems modelled with the elements obtained

from the system identification. The first one is modelled in single loop and a second one

in cascade configuration. Both systems operate with the same level controller that

minimizes the IAE, an IAE improvement of 14,7 % results from the utilization of a

cascade configuration instead of the typical single loop (see Figure 7.14).

Figure 7.94: Enhancement obtained using a cascade configuration instead of a single loop

Part C: Further Work

CHAPTER 8: THE FEEDFORWARD CONTROL

8.The Feedforward Control Process Control Study of the BA6 Cooling Towers for the SPS accelerator


8.1. INTRODUCTION

Feedforward uses the measurement of an input disturbance to the plant as

additional information for enhancing single-loop PID control performance. This

measurement provides an “early warning” that the controlled variable will be upset some

time in the future. With this warning the feedforward controller has the opportunity to

adjust the manipulated variable before the controlled variable deviates from its set point.

Note that the feedforward controller does not use an output of the process! This is the

first example of a controller that does not use feedback control; hence the new name

feedforward. As it will be seen, feedforward is usually combined with feedback so that

the important features of feedback are retained in the overall strategy [9].

Feedforward control is effective in reducing the influences of disturbances,

although not usually as effective as cascade control with a fast secondary loop. Since

feedforward control uses an additional measurement and has design criteria similar to

cascade control, engineers often confuse the two approaches.

Figure 8.95: Illustration of feedforward control [URL 3]

In previous chapters, the theoretical limits of feedback control were presented with

two purposes:

1. To show what was the best possible in the way of feedback controller response

to load changes, and therefore a standard by with measure controller

performance.

2. To show what was not possible using feedback control, and therefore recognize

the need for an alternative technology.

U(s) Y(s)

D(s) GF

G

Gp



The alternative technology feedforward uses measured values of load variables

and the set point to calculate the requisite value of the manipulated variable to keep the

controller variable at the set point. Because the load variables and set point can change

with time and the process contains dynamic elements, the calculations must be dynamic

as well. However, the most important component of the feedforward calculations is the

steady-state.

8.2. FEEDFORWARD CONTROL DESIGN CRITERIA

In Table 8.1 the design criteria are summarized in a concise form so that they can

be applied in general. Adherence to these criteria ensures that feedforward control is used

when appropriate.

The first two items in the table address the application of feedforward control.

Naturally, only when feedback control does not provide acceptable control performance

is an enhancement like feedforward control employed. The second criterion requires that

an acceptable measured feedforward variable be available or that it can be added at

reasonable cost.

Feedforward is desired when

1. Feedback control does not provide satisfactory control performance

2. A measured feedforward variable is available

A feedforward variable must satisfy the following criteria:

3. The variable must indicate the occurrence of an important disturbance.

4. There must not be a causal relationship between the manipulated and feedforward variables.

5. The disturbance dynamics must not be significantly faster than the manipulated-output variable

dynamics (when feedback control is also present).

Table 8.8: Feedforward control design criteria [9]

A potential feedforward variable must satisfy three criteria. First, it must indicate

the occurrence of an important disturbance; that is, there must be a direct, reproducible

correlation between the process disturbance and the measured feedforward variable, and

the measured variable should be relatively insensitive to other changes in operation.

Naturally, the disturbance must be important (i.e., change frequently and have a



significant effect on the controlled variable), or there would be no reason to attenuate its

effect. Second, the feedforward variable must not be influenced by the manipulated

variable, because the feedback principle is not used. Note that this requirement provides a

clear distinction between variables used for cascade and feedforward. Finally, the

disturbance dynamics should not be faster than the dynamics from the manipulated to the

controlled variable.

The final requirement is related to combined feedforward-feedback control

systems. Should the effect of the disturbance on the controlled variable be very fast,

feedforward could not affect the output variable in time to prevent a significant variation

from the set point. As a result, the feedback controller would sense the deviation and

adjust the manipulated variable. Unfortunately, the feedback adjustment would be in

addition to the feedforward adjustment; thus, a double correction would be made to the

manipulated variable; remember, the feedforward and feedback controllers are

independent algorithms. The double correction would cause an overshoot in the

controlled variable and a poor performance. In conclusion, feedforward control should

not be used when the disturbance dynamics are very fast and PID feedback control is

present. Naturally, if feedback is not present(perhaps due to the lack of real-time sensor),

feedforward can be applied regardless of the disturbance dynamics.

8.3. FEEDFORWARD AND FEEDBACK ARE COMPLEMENTARY

Feedforward and feedback control each has important advantages that compensate

for deficiencies of the other, as summarized in Table 8.2. The major advantage of

feedback control is that it reduces steady-state offset to zero for all disturbances. As we

can seen, it can provide good control performance in many cases but requires deviation

from the set point before it takes correction action. However, feedback does not provide

good control performance when the feedback dynamics are unfavorable. In addition,

feedback control can cause instability if not correctly tuned.



Feedforward Feedback

Advantages - Compensates for the disturbance

before the process output is affected.

- Does not affect the stability of the

control system.

- Provides zero steady-state offset.

- Effective for all disturbances.

Disadvantages - Cannot eliminate steady-state offset.

- Requires a sensor and model for each

disturbance.

- Does not take control action until the

process output variable has deviated

from its set point.

- Affects the stability of the closed-loop

control system.

Table 8.9: Comparison of feedforward and feedback principles [9].

Feedforward control acts before the output is disturbed and is capable of very

good control performance with an accurate model. Another advantage is that a stable

feedforward controller cannot induce instability in a system that is stable without

feedforward control. This fact can be demonstrated by analyzing the transfer function of a

feedforward-feedback system shown in Figure 8.2, which accounts for sensors and final

element explicitly:

)()()()(1

)()()()()(

)()(

sGsGsGsG

sGsGsGsGsG

sDsCV

cfbspv

dffffspv

m +

+=

As long as the numerator is stable, which is normally the case, stability is

influenced by the terms in the characteristic equation, which contain terms for the

feedback process, instrumentation, and controller. The disturbance process, feedforward

instrumentation, and feedforward controller appears only in the numerator. Therefore, a

(stable) feedforward controller cannot cause instability, although it can lead to poor

performance if improperly designed and tuned. The major limitation to feedforward

control is its inability to reduce steady-state offset to zero. As explained, this limitation is

easily overcome by combining feedforward with feedback.



Figure 8.96: Block diagram of feedforward-feedback control system with sensors and final element

8.4. IS FEEDFORWARD CONTROL NECESSARY?

Sometimes engineers have the impression that because feedforward is generally a

good idea, it should be applied in all process control strategies. This is not the case. As

strongly emphasized in the first design criterion, feedforward is applied when feedback

control does not provide satisfactory control performance. Thus, feedforward is not used

if a tight control is not needed or if feedback control provides good performance. An

example of this situation is generally our studied case, a stopgap tank where level can

vary within limits without influencing the plant economics or safety, thus feedforward

would be not applied.

However, in our case, the typical feedback control is not sure enough when

important changes on the SPS accelerator cooling demand occur. As a consequence, the

first design criterion for feedforward control is satisfied. To surpass the level limits

means an increase of just half a meter on the stopgap tank level, and this can happen

when an important variation on the inflow takes place. To prevent this circumstance

feedforward control is a useful tool, it will lead the system to a safe operation when a

huge disturbance appears, since the main feature of a feedforward loop is to minimize the

effects of the disturbances.

SP(s) CV(s) Gv(s)

Dm(s)

Gd(s)

+ -

Gff(s)

Gfbs(s)

Gp(s)

CVm(s)

Gffs(s)

+ Gc(s)

_ _ +



8.5. FEEDFORWARD CONTROLLER DESIGN

The point is to find out an equation or mathematical function that represents the

feedforward controller. Figure 8.2 shows the generalized block diagram for a

feedforward-feedback control system where can be seen blocks with the following

transmittances:

Gd = Disturbance Gffs= Sensor for the disturbance variable

Gff= Feedforward controller Gc= Feedback controller

Gv= Controlled valve Gp= Process

Gfbs= Sensor for the controlled variable

Note that the disturbance Dm follows two different paths to reach the output CV:

the “normal” path though the block disturbance, and the path in charge of the

compensation. The equation connecting the output CV with the disturbance Dm will be

composed by the addition of both effects. The contribution of the “normal” path is:

)()()()(1)(

)()()( sGsGsGsGsG

sDsCVfbspvc

dmd −

=

and, following the Mason’s rules, the contribution corresponding to the path in charge of

the disturbance compensation is:

)()()()(1

)()()()()()()( sGsGsGsG

sGsGsGsGsDsCV

fbspvc

pvffffsmff −

=

then, the combined effect due to the addition of both elements is:

)()()()(1

)()()()()()()()()( )()( sGsGsGsG

sGsGsGsGsGsDsCVsCVsCV

fbspvc

pvffffsdmffd −

+=+= Eq. 8.1

Now, it is the most important part. Let’s try to make null the fraction

corresponding to Equation 8.1, as a result, the effect due to the disturbance Dm will be

compensated completely (CV = Dm·0 = 0). Thus, it is only needed to make the numerator

null, and it is carried out by designing the parameters of the feedback controller:

0)()()()()( =+ sGsGsGsGsG pvffffsd

which is the same that:



)()()()()( sGsGsGsGsG pvffffsd −=

this equation shows that the transmittances for each one of both paths has to be equals in

magnitude to be cancelled. The negative sign means that the proportional term of the

feedforward controller will have to be also negative, it is the only way to make the

disturbance zero. Recall from Chapter 5 which are the position of the controlled valves,

they are located after the tank, and as a consequence, the controllers (feedback and

feedforward) will be direct acting controllers with Kc < 0.

Finally, the equation representing the feedforward controller, when a typical

feedforward architecture is used, corresponds to:

)()()()(

)(sGsGsG

sGsG

pvffs

dff −

=

Note that disturbance in the studied case is added before the process, the

disturbance corresponds to the inflow that feeds the tank (process) with chilled water.

Thus, a variation is made on the typical block diagram for the feedforward-feedback

control system presented in Figure 8.2. As can be seen in Figure 8.3, where the Simulink

schema for the feedforward-feedback architecture is developed, the disturbance is added

before the process, in that way, the final representation for the feedforward controller

suffers a variation as well. The equation corresponding to the feedforward controller for

the studied case is:

)()()(

)(sGsG

sGsG

vffs

dff −

=

If it is managed to do a device that satisfy exactly this expression of transmittance

then a perfect compensation will be achieved. It means that a disturbance would not

provoke any effect over the process, which is the same to say that it would not be

negative effects against the controlled variable. Normally this will be a complex

expression almost impossible to synthesize and, in addition, a perfect knowledge of the

real elements that compose the system is never had. As a consequence, the obtained

expression will be just an approximation and, at the end, what is searched is the best

possible approximation. On the other hand, in practice, it is not needed an exact

compensation since small deficiencies or vagueness due to the feedforward control will

be later compensate by the feedback controller. Hence, the feedforward control is just a



way to minimize the effect of disturbances over the process, sometimes it is more useful

than a cascade structure in order to compensate effects due to disturbances but sometimes

the enhancements are less [10].

8.6 FEEDFORWARD-FEEDBACK CONTROL RESULTS

The target of this point is to show the enhancements introduced thanks to the

feedback control architecture when an important disturbance occurs. The results are

compared with the obtained ones from the simple feedback system, at first sight, the

improvements in terms of time response against a disturbance, accuracy and safety can be

seen. A tight level control in the storage tank is achieved with the feedforward correction.

This feedforward-feedback control architecture would be just a proposal for a

hypothetical future upgrade of the BA6 cooling towers control system. Thus, a

comparison with the present cascade control architecture is presented as well. As it will

be seen, no improvements are achieved comparing with the cascade control architecture

already implemented, in the cascade configuration the internal or slave loop that

corresponds to the I/P-valve elements is pretty well fixed. The slave controllers, as it was

discussed in Chapter 7, are faster than the master one, in that way, for the studied case,

corrections against disturbances are achieved faster than using feedforward control.

Three kinds of disturbances will be applied to the system, a step like disturbance,

a sine wave and a band-limited white noise. The used disturbances for simulations were

high in magnitude because what is desired on the simulations is to see which is the

system behavior when a strange operation mode is required. As it was said before, the

demand of cooled water from the SPS accelerator is quite constant over the time and just

in sporadic instants during the year it varies in a steep way, that moments are critical and

has to been controlled as possible. The worst period of the year is obviously summer,

when high temperatures combined with high cooling demand from SPS can lead the

system to the saturation. In Figure 8.3 below is showed what happened is summer 2002, a

huge increase in the cooling demand leaded the system to exceed the safe SPS operation

temperature fixed at 24ºC.



Figure 8.97: SPS temperature and flow demand 17/6/2002



Figure 8.98: Simulink model for the feedback-feedforward control

( )s

ssssm

sssGsG

sGsG

vffs

dff 5,41

103,422,0

15,422,0/103,4

1

22,0103,4

1

%55/064,1

131

15,11

1

1)()(

)()( 33

2

33+⋅

⋅−

=

+⋅−

≈

++⋅−

=

+

+

−=

−= −−−

)5,41(51)( ssG ff +⋅−≈ Proportional-Derivative Feedforward Controller with:

• Kc (Proportional Gain) = -51

• Td (Derivative Time) = 4,5



Using the feedforward controller with the obtained parameters in the previous

page and comparing it with the previous configurations the results are the following:

Figure 8.99: System response against a 0,6 m3/s step like disturbance

Figure 8.100: System response against a 1,2 m3/s absolute sinus disturbance

For all kind of disturbances is demonstrated that cascade configuration is the best

which fits the modeled system. To compare the different results it has been used the IAE

(integral of absolute value) coefficient. Note how both, feedforward and cascade, achieve



important enhancements comparing with the behavior of the feedback system,

nevertheless, the cascade configuration makes the best disturbance compensation.

Figure 8.101: System response against a band-limited white noise disturbance

8.7. FURTHER IMPLEMENTATION OF A FEEDFORWARD CONTROL.

It has been demonstrated in previous point 8.1.5 that feedforward control does not

provide us with any improvement respect the present cascade control. However, there is a

new possibility to use feedforward. As it has been introduced in Chapter 3, the cooling

system is composed by two main parts:

• The storage tank controlled by four valves.

• The four cooling towers with its ventilators.

The used disturbance, in the previous point 8.1.5 corresponds to the SIG flow

measurement. This flow is an essential value for the control system, actually, this flow is

the outflow which is pumped to the ring, nevertheless, after an approximate period of a

quarter of hour that flow becomes the inflow that comes in the storage tank and has to be

cooled.

The new proposed idea is to use this flow value from SIG pumping station to a

new feedforward control system applied to the temperature control of the cooling towers.

This idea is based on the fact that water demand (flow) has a direct relationship with the



cooling necessities at the SPS accelerator, as much water is pumped by SIG station much

cooling is required. It is known that if there is an increase on the water demand, SIG

station is in charge of the cold water supply from the lake. Then, if SIG station provides

more water to the circuit, the control system will have around a quarter of hour to

improve its functioning. Thus, if an important disturbance occurs at SIG (normally flow

remains constant) one can use this information to increase the power on the ventilators of

the cooling towers, and in that way, to optimize the cooling process advancing the

operation on the ventilators. Obviously, if SIG supplies water until surpassing the cooling

capacity, then the only possible solution would be to increase as well the temperature set

point over 24ºC. The idea is presented in the following schema:

+ 24ºC Tª surface

Flow SIG

Gd(s)

+ -

Gff(s)

Gfbs(s)

Gp(s)

Gffs(s)

Gc(s)

+ _ + Tª

Ventilator

Feedforward Action

Power

Figure 8.102: Possible implementation of feedforward control on the temperature control loop

CHAPTER 9: THE DIGITAL RST

CONTROLLER

9.The Digital RST Controller Process Control Study of the BA6 Cooling Towers for the SPS accelerator


9.1. INTRODUCTION TO COMPUTER CONTROL

The first approach for introducing a digital computer or microprocessor into a

control loop is indicated in Figure 9.1. The measured error between the reference and the

output of the plant is converted into digital form by an analog-to-digital converter (ADC)

at sampling instants k defined by the synchronization clock. The computer interprets the

converted signal e(k) as a sequence of numbers that it processes using a control

algorithm, and generates a new sequence of numbers [u(k)] representing the control. By

means of a digital-to-analog converter (DAC), this sequence is converted into an analog

signal which is maintained constant between the sampling instants by a zero holder hold

(ZOH). The set ADC - computer - DAC should behave the same as an analog controller

(PID type), which implies the use of a high sampling frequency and the algorithm

implemented on the computer is very simple [20].

Figure 9.1: Digital realization of an analog type controller

A second, much more interesting approach for introducing a digital computer or

microprocessor in a control loop is illustrated in Figure 9.2, which can be obtained from

the diagram given in Figure 9.1 by displacing the reference-output comparator after the

analog-to-digital converter. The reference is now specified digitally across the keyboard.

In Figure 9.2, the set DAC - plant – ADC is interpreted as a discretized system

whose control input is the sequence [u(k)] generated by the computer, the output being

the sequence [y(k)] resulting from the A/D conversion of the system output y(t). This

_ +

CONTROLLER

u(t) e(t) e(k) u(k)

ADC COMPUTER DAC + ZOH

PLANT

CLOCK

r(t) y(t)



discretized system is characterized by a discrete-time model, which describes the relation

between the sequence of numbers [u(k)] and the sequence of numbers [y(t)]. This model

is related to the continuous-time model of the plant. [23]

Figure 9.2: Digital control system

This approach offers numerous advantages, from which one may derive the

following:

1. The sampling frequency is chosen in accordance with the bandwidth of the

continuous-time system.

2. There is the possibility of a direct design of the control algorithms tailored to the

discretized plant models.

3. Intelligent use of the computer becomes possible since the considerable increase

of the sampling period permits the computation capacity to be used in order to

implement algorithms that are “intelligent” but more complex than a PID and

require a greater computation time.

In fact, if one really wants to take advantage of the use of microprocessors in a

control loop, the language must also be changed. This may be achieved by replacing the

continuous-time system models by discrete-time system models, and the continuous-time

controllers by digital control algorithms, as well as by adding intelligence capabilities in

the algorithms.

_ +

DISCRETIZED PLANT

u(t) e(k)

u(k) u(t) y(t) y(k)

ADC COMPUTER DAC + ZOH

PLANT

CLOCK

r(k)



9.2. STRUCTURE OF DIGTAL CONTROLLERS

Figure 9.3 gives the diagram of a PI-type analog controller. The controller

contains two channels (a proportional channel and an integral channel) that process the

error between the reference signal and the output. In the case of sampled systems, the

controller is digital and the only operations it can carry out are additions, multiplications,

storage, and shift. All the digital control algorithms have the same structure. Only the

memory of the controller changes, according to the numbers of coefficients [20].

Figure 9.3: Diagram of a PI analog converter

Figure 9.4 illustrates the computation structure control u(t) applied by the

controller to the plant at instant t. This control is an average of the output measured at

instants t, t-1,…., t-n, of the previous control values at instants t-1, t-2,…, t-m, and of the

reference signal weighted by the coefficients of the controller.

This type of control law can even be obtained by the discretization of a PI or PID

analog controller. It can be considered the discretization of the PI controller used

previously in the simulations. The control law for the analog PI controller is given by:

[ ])()(1

1)( tytrpT

Ktui

−

+=

For the discretization of the PI controller, p (the derivation operator) is approximated by

1-z-1. One then obtains (t is now the mormalized time):

∫ −

−

−≈=

−=−−≈=

)(1

11)()1()1()()/(

1

1

txz

xp

xdt

txztxtxpxxdtd

e(t)

+

+

_ +

u(t) PLANT

r(t) K

K/Ti ∫

y(t)



and the equation for the PI controller becomes:

[ ])()(1

)1()( 1

1

tytrz

TK

zKtu i −

−

+−= −

−

(Eq. 9.1)

Figure 9.103: Digital controller

By multiplying both sides of Equation 9.1 by (1-z-1), the equation of the digital PI

controller is written as:

)()()()()()( 111 tyzRtrzTtuzS −−− −= (Eq. 9.2)

in which:

110

111

11

111

)1

1()()(

)1(11)(

−−−−

−−−

+=−+==

=+=−=

zrrKzT

KzTzR

szszzS

i

which leads to the diagram represented in Figure 9.5.

Taking into account the expression S(z-1), the control u(t) is computed using the

formula:

)1()()1()()1(......)()()()()1()(

1010

11

−++−−−−=−+−−= −−

trrtrrtyrtyrtutyzRtrzTtutu

which corresponds to the diagram in figure 9.5.

On the other hand, dividing both sides of Equation 9.2 by S(z-1), one obtains:

u(t)

PLANT

r(t) y(t)

t0

t1 z-1

r1 z-1

s1 z-1

s2 z-1

r0



)()()(

)()()(

)( 1

1

1

1

tyzSzR

trzSzT

tu −

−

−

−

−=

which leads to the canonical structure of the digital controllers represented in Figure 9.6

(tri-branched structure R-S-T).

Figure 9.5: Digital PI controller

Figure 9.6: Canonical structure of digitals controllers

Given that:

)()(

)( 1

11

−

−− =

zAzB

zH

is the pulse transfer function of the group DAC + ZOH + continuous-time system + ADC,

the transfer function of the closed-loop system using a digital controller with a canonical

structure is written as:

)()()(

)()()()()()(

)( 1

11

1111

111

−

−−

−−−−

−−− =

+=

zPzRzB

zRzBzSzAzRzB

zH CL

in which:

....1)()()()()( 22

11

11111 +++=+= −−−−−−− zpzpzRzBzSzAzP

PLANT +

r(t)

T

_

1/S

R

B/A

u(t) y(t)

+ + + - -

u(t)

PLANT

r(t) y(t)

t0

t1 z-1

r1 z-1

z-1

r0

Digital PI



defines the poles of the closed loop system.

The objective of the digital controller design may thus be seen as the computation

of R, S and T in order to obtain a closed-loop transfer function able to achieve the

required performances.

This is the reason that the desired closed-loop performances will be expressed (or,

of this is not the case, converted) in terms of desired closed-loop poles [P(z-1)] and

eventually in terms of desired zeros.

The polynomial [P(z-1)] corresponding to the desired closed-loop poles defines the

essential performances. It is generally chosen as a second-order polynomial

corresponding to the discretization of a second-order continuous-time system having a

given ? 0 and ?. Both coefficients can be obtained either from an abacus figure or by

software. In both cases, the sampling period (Ts), natural frequency (? 0), and the damping

factor (?) must be specified. The relation between ? 0 and Ts, obviously must be respected.

17,05,125,0 ≤≤≤≤ ξω soT

9.3. DIGITAL CONTROLLER DESIGN METHODS

First, the design of digital PID controllers is presented, which puts in evidence

the general structure of digital controllers (tri-branched structure known as R-S-T), the

special features of the general approach, and the limitations of the digital PID. The

following design methods can be chosen: poles placement, tracking and regulation with

independent objectives, and tracking and regulation with weighted input. These methods

permit the control of the system of any order with or without pure time delay.

The use of a digital computer or microprocessor in control loops offers numerous

advantages. These include:

• Considerable choice of strategies for controller design.

• Possibility of using algorithms which are both more complex and efficient than

the PID.

• Technique perfectly suited for the control of systems with time delay.



Moreover, by combining the controller design methods with the system model

identification techniques, a rigorous, high performance controller design procedure can

be implemented.

The available digital controller design methods are four, they are related to single

input – single output control in the presence of deterministic disturbances.

• Digital PID.

• Poles placement (closed-loop poles).

• Tracking and regulation with independent objectives.

• Tracking and regulation with weighted input (weighted control energy).

All the controllers, irrespective of their design method, will have the same R-S-T

tri-branched structure (See Figure 9.6). Only the “memory” of the controller (number of

coefficients) will vary depending on the complexity of the system.

The design and tuning of the different types of controllers requires the knowledge

of the parametric discrete-time model of the plant to be controlled.

This controller design method makes it possible to obtain the desired tracking

behavior (changing of reference) independent of the desired regulation behavior

(rejection of a disturbance). For example, the performance specifications illustrated in

Figure 9.7 correspond to a situation for which the desired regulation response time is

significantly smaller than the desired response time for a change in reference, but the

reverse situation may be considered.

Figure 9.7: Tracking and regulation performances

Plant output

Regulation Tracking

Reference

t



A standard digital pole placement configuration using a polynomial controller

(denoted R-S) is shown in Fig. 9.8. The plant model G(z_1) is of the form:

nAnA

nBnB

d

zazazbzbz

zAzB

zG −−

−−−

−

−−

+++++

==...1

)...()()(

)( 11

11

1

11

Figure 9.8: Considered closed loop configuration.

The R-S part of the controller has the transfer function:

)()()()(

)()(

110

110

1

1

−−

−−

−

−

=zHzSzHzR

zSzR

S

R

where HR(z-1) and HS(z-1) denote the fixed parts of the controller (either imposed by the

design or introduced in order to shape the sensitivity functions). R0(z-1) and S0(z-1) are

solutions of the Bezout equation (poles of the closed loop):

44 344 21)(

11110

1110

1

1

)()()()()()()()(−=

−−−−−−−− =+zP

FDRS zPzPzHzRzBzHzSzA

where P(z-1) represents the desired closed loop poles, PD(z-1) defines the dominant poles

(specified) and PF(z-1) defines the auxiliary poles (which in part can be specified by

design specifications and the remaining part is introduced in order to shape the sensitivity

function).

The tracking part T(z-1) of the controller is used to compensate the closed loop

dynamic in such way that the entire system transfer function (from r(t) to y(t)) has the

dynamic of the reference model mm AB . The polynomial T(z-1) is considered to have

three basic forms:



• T contains all closed-loop poles given by the polynomial P = AS + BR and its

static gain is adjusted so the static gain of the transfer function from y*(t) to y(t) is

1. Hence,

)1()(

)(1

1

BzP

zT−

− =

• T contains dominant closed-loop poles given by the polynomial PD and its static

gain is adjusted so the static gain of the transfer function from y*(t) to y(t) is 1.

Hence,

)1()1()(

)(1

1

BPzP

zT FD−

− =

• T is a gain with the value )1()1(

BP

T = .

The reference model mm AB is considered to be either 2nd order transfer function

with dynamics defined by natural frequency and damping, or two same 2nd order transfer

functions connected in cascade.

Sensitivity function shaping is one of the way how to assure controller and closed-

loop performances, since the sensitivity functions are one of the crucial indicator of these

performances. The considered sensitivity functions are [27]:

The output sensitivity function:

)()()()(

)( 1

110

11

−

−−−− =

zPzHzSzA

zS Syp

The input sensitivity function:

)()()()(

)( 1

110

11

−

−−−− −

=zP

zHzRzAzS R

up

The complementary sensitivity function:

)()()()(

)( 1

110

11

−

−−−− =

zPzHzRzB

zS Ryb

where Syp is shaped to obtain a sufficient closed-loop robust stability, the shaping of Sup

allows to limit controller gain and hence actuator effort and Syb shaping help to limit

noise sensitivity of the closed loop and it serves to fix a desired closed-loop tracking

performance.



We can now introduce the following parameterization:

)()()(

)()()(

)()()(

)()()(

11''1

11'1

11'1

11'1

−−−

−−−

−−−

−−−

=

=

=

=

zzPzP

zzPzP

zzHzH

zzHzH

SFF

RFF

SSS

RRR

δ

δ

γ

γ

With these notations we get:

)()(

)()()()(

)(

)()(

)()()()(

)(

1

1

1'

1'10

11

1

1

1''

1'10

11

−

−

−

−−−−

−

−

−

−−−−

=

=

zz

zPPzHzRzA

zS

zz

zPPzHzSzA

zS

R

R

FD

Rup

S

S

FD

Syp

δγ

δγ

where the filters )()()( 111 −−− = zzzF SSyp δγ and )()()( 111 −−− = zzzF RRup δγ consist of

several 2nd order notch filters (2zeros/2poles band-stop filters with limited attenuation)

simultaneously tuned. The tuning means in fact searching for appropriate frequency

characteristics of )( 1−zFyp and )( 1−zFup . Specifically in our case, we are interested in

frequency band-stop with limited attenuation characteristics and thus the tuning concerns

the frequency of band-stop, its bandwidth and the maximum attenuation in the band-stop

frequency [20].

9.4. CONTROLLER DESIGN PROCEDURE

Suppose to dispose with a digital model G of the plant to be controlled. The

controller design consists of the following steps:

1. Design specifications - Determine desired closed loop and tracking performances

closed loop performances, such as robust stability, disturbance rejection, etc., has

to be expressed by some templates imposed on sensitivity functions. The tracking

properties include rise time, maximal overshoot, or settling time.

2. Closed-loop part R-S design - The sensitivity functions are shaped to satisfy

design specifications (to enter the frequency responses to imposed templates). As

we can see from the previous section, one disposes with the following design

parameters:



• PD polynomial of desired dominant (the slowest) closed loop poles

• '''FF PP polynomial of desired auxiliary closed loop poles.

• HR fixed part of the controller numerator.

• HS fixed part of controller denominator.

• Fyp 2nd order digital notch filters on Syp.

• Fup 2nd order digital notch filters on Sup.

which allow us to shape appropriately the sensitivity functions Syp, Sup, Syb.

3. Tracking part design - If the tracking properties are not satisfied by closed loop

controller part R-S, the tracking part has to be designed. One has to choose an

appropriate structure of T and to design the reference model mm AB corresponding

to the desired tracking performances. For reference model adjusting the natural

frequency and damping of the reference model denominator is modified.

9.5. CONTROLLER DEVELOPMENT

Next step will be to design RST controllers to implement them as slave controllers

on the cascade configuration. The point will be to create a fast tracking of the set point,

studying independently the regulation and the tacking of the system. Thus, it is expected

to improve the functioning of the system against two main problems: (a) when an

important disturbance takes place, or, (b) when the cooling towers operate in the

threshold between two towers and the system has problems to reach the steady-state.

In order to build properly RST controllers using the poles placement method it

was chosen the Poles Placement Master (briefly PPMaster) [27] toolbox programmed in

MATLAB® 5.3 environment (it works also under MATLAB® 6.0 and higher). It is user

friendly application with graphical user interface (GUI) for design of digital SISO

(single-input, single-output) robust controller. The implemented controller design

procedure is combined pole placement with sensitivity shaping design technique.

The toolbox was developed in Laboratoire d'Automatique de Grenoble as a part of

doctoral thesis "H. Prochazka".

First of all let’s transform our continuous time plant into a digital plant, the model

to be introduced in the toolbox has the following appearance:



mnzAzB

zazazazbzbzbz

zG nn

mm >=

+++++++

= −

−

−−−

−−−−−

)()(

...1)...(

)( 1

1

22

11

22

11

11

Then, the studied continuous-time plant representing the I/P transducer and the valve has

been converted to discrete time using a zero order hold on the input as follow:

21

211

2 05,0508,01146,0396,0

)(22,0

22,013

115,1

1)( −−

−−−

+−+

= →++

=+

⋅+

=zz

zzzG

sssssG ZOH

Once the system is defined, let’s create the RST controller. One of the relevant

points about a RST controller is the robustness, which is the ability of a control system to

provide good performance when the plant dynamics change. The amplitude margin G∆

and the phase margin ∆Φ are the classical robustness margins. The amplitude (or gain)

margin is the gain the loop transfer can be amplified with before stability is lost. The

phase margin is the amount of phase loss of the loop that can be tolerated before stability

is lost. Phase loss is related to time delay. The phase margin can therefore be translated to

a delay margin CRd ωτ ∆Φ= , where CRω is the cross-over frequency (which is where

the loop gain is 1)( =− CRieL ω ).

Figure 9.9: Nyquist Curve [URL 6]



The typical values for the robustness margins are presented next:

Taking a look to the Nyquist curve (fig. 9.9):

( )1

max1111

111

max

1

min

11

min

1

)()()()()()(

)()()(1−

−−−−

−−−−−−−

+===+=∆

zRzBzSzAzSzA

zszszHM ypypBO

fjez π21 −− =

Finally, it has been found a direct relationship between the Module margin and

the output sensitivity function:

dBMdBMdBeS jyp ∆−=∆= −− 1

max)( ω

Figure 9.10104: Module margin and sensitivity function [URL 6]

A module margin 5,0≥∆M implies 2≥∆G and º29≥∆Φ

Caution! There is no reciprocity!

Gain margin: 2≥∆G (6 dB) [min: 1,6 (4 dB)]

Phase margin: º60º30 ≤∆Φ≤

Delay margin ( dτ∆ ): it is a fraction of the system delay (10%), or a fraction of the raising time (10%).

Module Margin: 5,0≥∆M (-6 dB) [min: 0,4 (-8 dB)]



Launching the command “ppmaster” on the Matlab® workspace, the principal

window for closed-loop controller (R/S) design is opened, see figure 9.11. First of all, the

digital plant already presented in Figure 9.8 is edited with a sampling time fixed in 3

seconds. The next step is to specify the dominant poles modifying the natural frequency

and the damping. To reach a robust closed loop controller (R/S) one has followed as a

reference the sensitivity functions, overcoat Syp the output sensitivity function. Recall that

it has a direct relationship with the Module Margin. The templates that normally define a

robust controller are plotted in dark, it can be seen in Figure 9.11 how the designed

controller for Hzn 025,0=ω and 8,0=ξ (plotted in red) is inside the templates that

define the robustness.

Figure 9.1051: PPMaster Toolbox closed loop window

Next step will be to design the tracking of the controller. The tracking part design

window enables to design the tracking part T of the controller and the tracking model

Bm/Am. Three graphs display (time domain) properties of the closed loop system.



1. System output y(t) step response.

2. Desired trajectory y*(t) step response.

3. Command u(t) step response.

By sliding the natural frequency and the damping factor, the tracking part of the

RST controller is designed. In Figure 9.12 below, it is showed the three graphs for

Hzn 0711,0=ω and 757,0=ξ (plotted in red). These values are compared with the ones

obtained using the same values that in the closed-loop window (green dashed), it can be

seen how the new ones makes the system faster against variations on the set point. This is

one of the imposed objectives at the beginning of the discussion, in that way the valves

will react faster against a new operation mode of the cooling towers.

Figure 9.12: PPMaster Toolbox Tracking window



Finally the RST controller with regulation and tracking independent of each other

is found out. More proofs and simulations would be desired before a possible

implementation of this kind of controller on the control system. The resultant expressions

that have to be inserted in the way, already shown in Figure 9.8, are the following:

211 1314,046442,01)( −−− +−= zzzAm

211 22185,04452,0)( −−− += zzzBm

11 2398,024554,0)( −− −−= zzR

11 708,01)( −− −= zzS

211 017115,004811,003674,0)( −−− −+= zzzT

CHAPTER 10: CONCLUSIONS

10. Conclusion Process Control Study of the BA6 Cooling Towers for the SPS accelerator


CONCLUSIONS

The point of this project is the study of the BA6 cooling towers which form part

of the cooling installations for the SPS accelerator.

The first step was to model the system as much as possible to the reality. At the

end an accurate model of the system was identified, element by element. To find a

suitable model of the overall system has provided us with a blank board, in which to be

able to find out enhancements over the present control system by optimizing the

parameters of the present controllers and by changing the kind of control architecture.

Once the system was modelled the second step was to optimize it. The old

values of the controller in charge of the level in the storage tank have been changed as

well as the parameters of the controllers in charge of the opening of the valves that feed

the cooling towers. As a result, the steady-state is reached around a 30% before when

the system operates in the threshold between two cooling towers.

Finally, it was investigated the possibility to add a feedforward control

architecture over the present system. After the simulations, it was assessed that any

enhancement has been obtained comparing with the present cascade architecture.

However, this technology was proposed for the ventilators control on the cooling

towers. Afterwards, it was also discussed the chance of changing the typical PID

controller for digital RST controllers. Both proposals, the feedforward control and the

digital RST controllers, were possible to study thank to the modelled system obtained

previously, it can allow in the future further studies about the BA6 cooling towers.

REFERENCES

Bibliography

[1] Antonio Vergara Fernandez. 2003. ‘Reliability of the Quench Protection System

for the LHC Superconducting Elements’. CERN & Universitat Politècnica de

Catalunya.

[2] Pierre Germain ULB, Bruxelles, Belgique. 1989. ITRODUCTION AUX

ACCÉLÉRATEURS DE PARTICLES. Édité par D. Dekkers.

[3] Simon Baird, 1997. ACCELERATORS FOR PEDESTRIANS. PS/OP/ Note 95-

17, CERN –PS Division.

[4] J. Perez, D. Blanc. 2001. PROCES CONTROL UPGRADE OF THE COOLING

INSTALLATIONS FOR THE SPS ACCELERATOR, ANALYSIS

FUNCTIONNELLE DES TOURS DU BA6. CERN contract f349, ST/CV.

[5] LA COMMANDE PRÉDICTIVE POUR L’INSTRUMENTISTE AVEC UN

MODICON TSX QUANTUM, Fiche Tématique 1. Schneider Electric

[6] Walter Driedger, P. Eng., 2001. CONTROLLING VESSELS and TANKS. First

published in Hydrocarbon Processing March 2000.

[7] Ljung V. Vu, Ramis S. Esfandiari. 1998. DYNAMIC SYSTEMS, Modeling and

Analysis. McGraw-Hill International Editions.

[8] Javier Calvente, 2002, MODELATGE I SIMULACIÓ DE SISTEMES

DINÁMICS, Apunts de l’assignatura. Universitat Rovira i Virgili, Tarragona.

[9] Thomas E. Martin. 1995. PROCESS CONTROL, Designing Processes and

Control Systems for Dynamic Performance. McGraw-Hill International

Editions.

[10] Alfred Roca Cusido. 1994. CONTROL DE PROCESOS. Edicions UPC,

Universitat Politèctica de Catalunya.

[11] CONTROL SYSTEM TOOLBOX for use with MATLAB 02. The MathWorks Inc.

[12] Martínez Salamero L., Poveda A., Garcia L., 1991. FUNCIONS

ELECTRÒNIQUES. Edicions UPC, Universitat Politèctica de Catalunya.

[13] Franklin G., Powell J., Emami-Naeini A. 1991. CONTROL DE SISTEMAS

DINÁMICOS CON RETROALIMENTACIÓN.Addison-Wesley

Iberoamericana.

[14] Shinskey F.G. 1996. PROCESS CONTROL SYSTEMS, Applications, Design

and Tuning, fourth edition. McGraw-Hill Companies, Inc.

[15] H. Rasmussen, 2002, Automatic Tuning of PID-regulators. Aalborg University,

Dept. of Control Engineering

[16] Product Flier PF51.6:8510B.1997. High-Performance Butterfly Valves, Fisher-

Rosemount.

[17] Lennart Ljung. 2001. SYSTEM IDENTIFICATION TOOLBOX for use with

MATLAB. The MathWorks Inc.

[18] Ljund L., Gjad T. 1994. MODELING OF DYNAMICS SYSTEMS. Prentice

Hall Information and System Sciences Series.

[19] Stéphane Colinges. 2002. IDENTIFICATION DES SYSTEMES EN BOUCLE

FERMEE. Laboratoire d’automatique Centre Paris.

[20] Ioan Doré Landau. 1992. SYSTEM IDENTIFICATION AND CONTROL

DESIGN. Prentice Hall Information and System Sciences Series.

[21] Carlos A. Smith, Armando B. Corripio. C. 2001. CONTROL AUTOMÁTICO

DE PROCESSOS, Teoría y Práctica. Limusa, Noriega Ediciones.

[22] Kart J. Aström, Björn Wittenmark. 1995. ADAPTATIVE CONTROL, Second

Edition. Addison-Wesley Publishing Company.

[23] Kart J. Aström, Björn Wittenmark. 1990. COMPUTER-CONTROLLED

SYSTEMS, Theory and Design, Second Edition. Prentice Hall International

Edition.

[24] L. Dugard, M. M’Saad, I.D. Landau. 1992. ADAPTATIVE SYSTEMS IN

CONTROL AND SIGNAL PROCESSING. Published for the International

Federation of Automatic Control.

[25] Nanfred Morari, N. Lawrence Ricker. 1998. MODEL PREDICTIVE

CONTROL TOOLBOX for use with MATLAB. The MathWorks Inc.

[26] E. Blanco, C. de Prada, J. Casas, S. Cristea, 1999, PREDICTIVE

TEMPERATURE CONTROL OF THE LHC SUPERCONDUCTING

MAGNETS. LHC Division, CERN.

[27] Hynek Prochazka. 2003. USER’S GUIDE FOR POLE PLACEMENT MASTER

MATLAB, graphical toolbox for robust digital controller design. Laboratoire

d'Automatique de Grenoble, Institut National Polytechnique de Grenoble

[28] J.G. Pett. 2003. FEED 02 ‘Analogue and digital techniques in closed-loop

regulation applications’. Lecture Notes CERN.

[29] Didier Dumur, 2002, CONTRIBUTION À L’ANALYSE ET AU

DEVELOPPEMENT D’ALGORITHMES DE COMMANDE PREDICTIVE,

Universite Paris XI, U.F.R. Scientifique d’Orsay. [30] F. Bordry, H. Thiesen. RST Digital Algorithm for controlling the LHC Magnet

current. CERN

[31] D. Blanc. Distributed control software for high performance control loop

algorithm. ST-Division CERN.

Universal Resource Locator (URL) Addresses

[URL 1] http://www.cern.ch

% CERN webside

[URL 2] http://www.emersonprocess.com/fisher/

% Butterfly valves 8510 by Fisher©

[URL 3] http://www.isa.cie.uva.es

% Process Control course by Prof. Prada, UVA

[URL 4] http://www.hh.se/staff/ulho/Digital/Digital.html

% Process Control course by U. Holmberg, ULHO

[URL 5] http://www.stanford.edu/class/ee392m/Lecture7_Design.pdf

% System Robustness

[URL 6] http://www-lag.ensieg.inpg.fr/landau/bookIC/

% Process Control and RST controller by I.D. Landau

[URL 7 ] http://www.bgu.ac.il/chem_eng/pages/Courses/oren%20courses/

% Process Control

[URL 8] http://www.personal.rdg.ac.uk/~shs99vmb/notes/ce/Lecture5.pdf

% Feedforward Control

[URL 9] http://csd.newcastle.edu.au/control/

% Process Control Course both English and Spanish

[URL 10] http://lorca.umh.es/isa/es/asignaturas/cas/

% GPC Controller

[URL 11] http://proj-lti.web.cern.ch/proj-lti/

% SPS piping schemas

[URL 12] http://st-div.web.cern.ch/st-div/Groups/cv/controlsection/Controls/bak/welcome.htm

% Controls and Electricity (ST-CV Design Unit)

APPENDIX A: KEYWORDS

ALICE A Large Ion Collider Experiment

ATLAS A Toroidal LHC ApparatuS

BA “Bâtiments Auxiliaires”, Auxiliary Building

CERN Centre Européen pour la Recherche Nucléaire

CMS Compact Muon Solenoid

FIFO First In First Out

GUT Grand Unified Theories

IAE Integrated Absolute Error

IE Integrated Error

ISR Intersecting Storage Rings

LEP Large Electron-Positron Collider

LHC Large Hadron Collider

LHCb The Large Hadron Collider beauty experiment

PI Proportional Integral Controller

PID Proportional Integral Derivative Controller

PS Proton Synchrotron

SCADA Supervisory Control And Data Adquisition System

SIG “Services Industriels de Genève”, Geneva’s Industrial Utilities

SM Standard Model

SPS Super Proton Synchrotron

SUSY SUperSYmmetry

TCR Technical Control Room

APPENDIX B: SYSTEM SCHEMA

P

PG

21

10

5

T4

T6

B A 1

B A 2

B A 3

B A 4

E C X 4B A 5

ECX5BA6

B A 7

BA80 BA81

TCC8ECN3

TT61TCC6

BIW295

E H W 3

SPS

PS

N O R T H E X P E R I M E N T A L A R E A

W E S T E X P E R I M E N T A L A R E A

Booster

BA3 DEMINERALISED -WATER

COOLING STATION

SIG ( GENEVA INDUSTRIAL PUBLIC UTILITIES )

PUMPING STATION


COOLING STATION


COOLING STATION


COOLING STATION


COOLING STATION


COOLING STATION

DISCH

AR

GE

LOO

P

HO

T LO

OP

SPS - BA6 COOLING -TOWERS STATION

The Cooling Towers are fitted : With a group of 4 discharge regulation valves which make it possible to maintain, with a level-flow rate multiloop control system, the water level in the regulating tank.

With a group of 4 variable speed motor-pumping sets which make it possible to maintain, with a multivariable control system, the water discharge temperature within the operating conditions.

CO

OL

ING

-TO

WE

RS

WA

TE

R S

UP

PLY

THE COOLING STATIONS ARE SUPPLIED BY THE RAW WATER PRIMARY

PUMPING STATION (SIG). EACH STATION HAS, AS A FUNCTION OF THE

MACHINE CARACTERISTICS, A VARYING NUMBER AND TYPE OF SECONDARY

DEMINERALIZED COOLING WATER CIRCUITS.

THE NEW CONCEPT OF COOLING THE SPS ASSESSES A COMPLETE STUDY

FOR THE REQUIREMENT OF PROCESS OPTIMISATION CONTROL SYSTEMS.

THE STABILITY AND RELIABILITY OF THE PROCESS TEMPERATURE COOLING

FOR THE MAGNETS ARE HIGHLY IMPORTANT FOR THE OPERATION

OF THE SPS MACHINE.

THE OBJECTIVE IS TO USE INTELLIGENT SYSTEMS BASED ON ROBUST

BEHAVIOUR HIGH PERFORMANCE CONTROLLERS, IN A

DISTRIBUTED CONTROL SOFTWARE TO SATISFY THE PEFORMANCE

SPECIFICATIONS.

SPS DEMINERALIZED WATER

PUMPING STATIONS

SPS PRIMARY CIRCUITREGULATING TANK

The regulating tank is located at the high point of the discharge pipe. It ensures that the pipe is filled and sets a reference pressurein relation to the distribution pipe.The variation in the SPSconsumption results in a variation level in the regulating tankwhich is to be kept constant at 2.5 m

CO

OL

ING

-TO

WE

RS

WA

TE

R S

UP

PLY


COOLING STATION

COOLING TOWERS

PUMPING STATION


COOLING STATION


COOLING STATION


COOLING STATION

SPS NORTH AREA COOLING STATIONS

DISTRIBU

TION

LOO

P

COLD LOO

P

TOUR 2

CV20001

CM

2000320002

XM

FT

20001

FI

20001

20004

TT

20004

TI

20005

TT

20005

TI

TOUR 1

CV

10001

CM

1000310002

XM

FT

10001

FI

10001

10004

TT

10004

TI

10005

TT

10005

TI

TOUR 4

CV

40001

CM

4000340002

XM

FT40001

FI

40001

40004

TT

40004

TI

40005

TT

40005

TI

TOUR 3

CV

30001

CM

3000330002

XM

FT30001

FI

30001

30004

TT

30004

TI

30005

TT

30005

TI

LI

60004

CV50001

FT

50001

FI

50001

50002

ZS

50003

ZS

CV

50006

FS50006

FS

50006

REJET

VANNES MANUELLESDE VIDANGE

INSTRUMENTATIONSIG

(NON EXPLOITABLE)

PT FT

STATION SIG

APPORT D'EAU

XV

LS

SIG

XH

XL

CV

50005

FS

50005

FS

50005

TT

90001TI

90001

LI

6000360003

LT

60004

LT

60005

LT LI

60005

LSLL

60004

LSL

60003

LSH

60002

LSHH

60001

RESERVOIR

60004

LS

60003

LS

60002

LS

60001

LS5 m

3 m

0 m

2 m

ZX

50002

O

F

ZX

50003

O

F

LI

50004

LT

50004

TT

9000390003

TI

BA

1B

A 7

BA 2B

A 3

BA

5

BA

4

BA 80BA 81

BA 82

BA 6

TSP 1

FERLAZZO Lucio BLANC Didier

BB

3

BA1 Demineralised -WaterCOOLING STATION









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PROFIBUS-DP

MODBUS NETWORK

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ION

HAZEMEYER CUBICLES

ELECTRICAL POWER SUPPLY

LOCAL MONITORING STATION

ETHERNET TCP-IP SERVICE

DECENTRALISED PERIPHERYDRAIN WATER STATION

SIEMENS S7-400

SIEMENS S7-200

MODBUS NETWORK


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PRIVATE NETWORK

Distributed Process Control Architecture of the Cooling Plants for the SPS Accelerator, CERN ST/CV

process control stydy of the ba6 cooling towers for...

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