ERT 210/4Process Control

Hairul Nazirah bt Abdul HalimEmail: hairulnazirah@unimap.edu.my

Office: 04-9798840

CHAPTER 8Feedback Controllers

ExxonMobil Chemical Plant

Process Control in our daily life…

Process Control in our daily life…• Controlling the water temperature of a shower• Let’s analyze this process:

Control objective: to control the shower temp.

process: shower

sensor: person’s skin

Controlled variable (CV): shower temp.

Set point: desired shower temp.

Manipulated variable (MV): flow of cold water

Final control element: valve on cold water line

Controller: person in the shower

• Benefits of improved process control:

1. improve product quality

2. faster

3. greater production rates

4. less expensive process validation procedure

Overview – Temperature Control

• heat exchanger - uses steam to heat cold water. • How to control the temperature??

Manual ControlAutomatic Control

MANUAL CONTROL

Operator

Compare Temp. with desired value

open/close valve

To admit more/less steam

AUTOMATIC CONTROL

SENSOR - TRANSMITTER

(measure the temperature)

(transmits it to electronic signal)

FEEDBACK CONTROLLER

(compares the measured temp. to the set point value

& make corrective action)

I/P TRANSDUCER

(Convert electronic signal to pneumatic signal)

CONTROL VALVE

(Receive signal & adjust the manipulated variables (flow))

COURSE OUTCOME: CH 8, 9 & 10

CO2: Ability to identify, measure and investigate Feedback controllers, Control system instrumentation and the control system design.

CHAPTER 8: FEEDBACK CONTROLLERS

DEFINE and DISCUSS the standard feedback control algorithm (control laws), IDENTIFY and COMPARE Proportional-integral-derivative (PID) control and on-off control types of feedback control

Subtopic:

1. Definition

2. Basic Control Modes

3. PID Controllers

4. On-Off Controllers

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Figure 8.1 Schematic diagram for a stirred-tank blending system.

Feedback Controllers

• Basic components in a feedback control loop are:

1. Process being control (blending system)

2. Sensor-transmitter combination (AT)

3. Feedback controller (AC)

4. Current-to-pressure transducer (I/P)

5. Final control element (control valve)

6. Transmission line between the various instrument

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Figure 11.7 Block diagram for the entire blending process composition control system.

BLOCK DIAGRAM OF A FEEDBACK CONTROL SYSTEM

INDUSTRIAL PROCESS CONTROL EXAMPLES

• Flow Controller

• Level Control in a tank

• Aerobic Fermentation Process

• Fed-Batch Bioreactor

FLOW CONTROLLER• Control objective: to maintain the desired flow rate• The setpoint: desired flow rate• Controlled variable (CV): the outlet flow rate• Manipulated variable (MV): the inlet flow rate of the

process stream• Disturbances variable (DV): changes in the upstream

pressure for the process stream• Sensor: combination of an orifice plate and a device that

measure a pressure drop across the orifice, which directly related to the flow rate.

• Final control element: the control valve in the line• Controller – flow controller (FC) – compares the

measured flow rate with the specified flow rate (flow setpoint) and opens/closes the control valve accordingly.

Figure 8.2 Flow control loop

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LEVEL CONTROL IN A TANK• Control objective: to maintain the level in the tank• The setpoint: desired level in the tank• Controlled variable (CV): the level in the tank• Manipulated variable (MV): exit flow from the tank• Disturbances variable (DV): changes in the inlet flow

rate• Sensor: level indicator on the tank (LT)• Final control element: the control valve on the

outflow line• Controller – level controller (LC) – compares the

measured level with the setpoint for the level in the tank and makes a change to the control valve on the exit flow from the tank.

AEROBIC FERMENTATION PROCESS• Control objective: to maintain a specified dissolved oxygen

(DO) conc. in the fermentation reactor so that the cells in the process have adequate oxygen levels.

• The setpoint: desired DO concentration• Controlled variable (CV): the DO conc. in the fermentor• Manipulated variable (MV): air flow rate to the fermentor• Disturbances variable (DV): changes in the rpm of the mixer

impeller• Sensor: DO sensor-transmitter (AT)• Controller – DO controller (AC) – compares the measured

DO with the setpoint value and sets the air flow rate to the fermentor.

• Final control element: variable speed air compressor

FED-BATCH BIOREACTOR• Control obj:

to maintain a specified cell concentration in the bioreactor.

• What is the CV, MV, DV, sensor & final control element?

• Control objective: to maintain a specified cell concentration in the bioreactor.

• The setpoint: desired cell concentration• Controlled variable (CV): the cell conc. in the bioreactor• Manipulated variable (MV): the feed rate of glucose and

nutrients mixture to the bioreactor.• Disturbances variable (DV): changes in the concentration

of glucose in the feed.• Sensor: turbidity meter (AT) which provides a

measurement that correlates with the cell conc. in the broth.

• Controller – controller (AC) – compares the measured cell conc. with the setpoint value and sets the glucose feed rate.

• Final control element: variable speed pump

Three basic control modes:

1) Proportional Control

2) Integral Control

3) Derivative Control

Next, we consider :

Proportional-Integral-Derivative (PID) Control

BASIC CONTROL MODESC

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PROPORTIONAL CONTROL

Objective: To reduce the error signal to zero.

(8-1)sp me t y t y t

error signal

set point

measured value of the controlled variable

(or equivalent signal from the sensor/transmitter)

sp

m

e t

y t

y t

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For proportional control, the controller output is proportional to the error signal,

(8-2)cp t p K e t

where:

controller output

bias (steady-state) value

controller gain (usually dimensionless)c

p t

p

K

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Some controllers have a proportional band setting instead of a controller gain.

The proportional band PB (in %) is defined as

100%(8-3)

c

PBK

PB correspond to Kc and vice versa

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The transfer function for proportional-only control:

(8-6)cP s

KE s

Disadvantage of proportional-only control:

Offset : Steady-state error occurs after a set-point change or a sustained disturbance.

-Offset can be eliminated by manually resetting the set point, ysp or by using controller with integral action.

Applications•P-only control: for process with non-sluggish dynamic behavior & offset is not important. (pressure @ level)

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INTEGRAL CONTROL

Controller output depends on the integral of the error signal over time.

0

1* * (8-7)

τ

t

I

p t p e t dt

τI = Integral Time (adjustable parameter) - units of time (min)

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Integral control action is widely used: elimination of offset.

Integral control action is normally used in conjunction with proportional control as the proportional-integral (PI) controller:

0

1* * (8-8)

τ

tc

I

p t p K e t e t dt

Proportional-Integral (PI) Control

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Transfer function for the PI controller:

τ 111 (8-9)

τ τI

c cI I

P s sK K

E s s s

• Response to unit step change in e:

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Figure 8.6. Response of PI controller to unit step change in e(t).

Disadvantage of integral control:

Tend to produce oscillatory responses of the controlled variable.

-Oscillatory response can be eliminated by proper tuning of the controller or by including derivative action.

Applications•PI control: when offset elimination is important (Flow, Temp., Composition, DO)

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RESET WIND-UP

• When a control loop is in control with a minimal error, then wind-up is not a problem.

• Wind-up is only a problem when a control loop is temporarily taken out of control.

• Occur during start-up of a batch process or after a large set-point change.

• The integral term becomes quite large due to a sustained error

• The controller output eventually saturates.

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RESET WIND-UP

• Further build-up of integral term while the controller is saturated.

• undesirable because the controller is already doing all it can to reduce the error.

• Commercial controllers provide antireset wind-up.

• Antireset wind-up reduce the windup by temporarily halting the integral control action whenever the controller output saturates.

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Reset windup

ysp

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DERIVATIVE CONTROL

anticipate the future behavior of the error signal by considering its rate of change.

•ideal derivative action,

= derivative time, has units of time.

τ (8-10)D

de tp t p

dt

τD

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• “ideal” PD controller has the transfer function:

1 τ (8-11)c D

P sK s

E s

• Derivative control action tends to improve dynamic response of the controlled variable

• The process measurement is noisy if it contains high frequency or random fluctuations.

• Disadvantage: derivative action will amplify the noise unless the measurement is filter

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• the transfer function for “real” PD controller,

τ1 (8-12)

ατ 1D

cD

P s sK

E s s

• Eq. 8-12 includes a derivative filter that reduces the sensitivity of the calculations to high frequency noise in the measurement.

• the value of α constant : 0.05 < α <0.2,

(0.1 being a common choice)

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Proportional-Integral-Derivative (PID) Control

Combination of P, I & D Control modes

3 most common forms of PID Control:

1.Parallel

2.Series

3.Expanded

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Figure 8.8 Block diagram of the parallel form of PID control (without a derivative filter)

Parallel Form of PID Control

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Parallel Form of PID Control

Transfer function for “Ideal” PID control is:

11 τ (8-14)

τc DI

P sK s

E s s

Transfer function for “Real” PID control, with derivative filter is:

1

11

)(

)(

1 s

s

sK

sE

sP

D

Dc

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Series Form of PID Control

Transfer function for “Ideal” PID control is:

Figure 8.9 Block diagram of the series form of PID control (without a derivative filter)

Series Form of PID Control

Commercial versions of the series-form controller have a derivative filter @ “Real PID control”:

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τ 1 τ 1(8-15)

τ ατ 1I D

cI D

P s s sK

E s s s

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Expanded Form of PID Control

Use in MATLAB

Control parameters are 3 gains: Kc, KI and KD

0

* * (8-16)t

c I Dde t

p t p K e t K e t dt Kdt

PID - Most complicated to tune (Kc, I, D) .- Better performance than PI- No offset- Derivative action may be affected by noise

PI - More complicated to tune (Kc, I) .- Better performance than P- No offset- Most popular FB controller

P - Simplest controller to tune (Kc).- Offset with sustained disturbance or setpoint change.

Controller Comparison

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Automatic and Manual Control Modes

Automatic Mode• Controller output, p(t), depends on e(t),

controller constants, and type of controller used. ( PI vs. PID etc.)

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Manual Mode

• Controller output, p(t), is adjusted manually.• Manual Mode is very useful when unusual

conditions exist:i) plant start-upii) plant shut-downiii) emergencies

On-Off Controllers

• Simple type of feedback controllers• Cheap• Used in residential heating and domestic refrigerators• Limited use in process control due to continuous cycling of controlled variable• Less widely used than PID controllers – not

versatile @ effective. • Two mode of control action:

1.Full control action2.No control action

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On-Off Controllers

• Consider Figure 1.6.1

• The on-off heater applies heat to the system as long as the controlled temperature is below a specified upper limit.

• When upper limit is reached, the addition of heat is stopped.

• Heat is not added to the process until the controlled temp. becomes less than a specified lower limit

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Figure 1.6.1 An example of the operation of an on-offtemperature controller.

Typical Response of Feedback Control SystemsC

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Figure 8.12. Typical process responses with feedback control.

No control: the process slowly reaches a new steady state

P – speed up the process response & reduces the offset

PI – eliminate offset & the response more oscillatory

PID – reduces degree of oscillation and the response time

Figure 8.13. Proportional control: effect of controller gain.Ch

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-Increasing Kc tends to make the process response less sluggish (more faster)

-Too large of Kc, results in undesirable degree of oscillation or even become unstable

-Intermediate value of Kc usually results in the best control.

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-Increasing τI tends to make the process response more sluggish (slower)

-Too large of τI, the controlled variable will return to the set point very slowly after a disturbance change @ set-point change occurs.

Figure 8.14. PI control: (a) effect of reset time (b) effect of controller gain.

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Figure 8.15. PID control: effect of derivative time.

-Increasing τD tends to improve the process response by reducing the maximum deviation, response time and degree of oscillation.

-Too large of τD: measurement noise is amplified and process response more oscillatory.

-The intermediate value of τD is desirable.

Selection of Controller• Should consider the combination of dynamic

behavior of:- final control element- process- sensor

• P-only control: for process with non-sluggish dynamic behavior & offset is not important. (pressure @ level)

• PI control: when offset elimination is important (Flow, Temp., Composition, DO)

• PID: for sluggish process (Biomass Concentration, Temp., Composition)