1 PID Feedback Controllers PID 反馈控制器 Shen Guo-jiang Institute of Industrial Control,...

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PID Feedback Controllers PID 反馈控制器

Shen Guo-jiang

Institute of Industrial Control,

Zhejiang University

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Last Lecture Defined the types of processes: self-

regulating and non-self-regulating processes, single- and multi-capacitance processes ;

Discussed the modeling from process dynamics;

Discussed process characteristic parameters K, T,τ, and their obtaining methods from process data.

Problem Discussion Control valve is divided into Fail-closed

valve and Fail-closed valve. what is the physical meaning of them? How to choose them?

What is the definition of the feedback controller action? According to the specific object, how to choose the controller action?

How to evaluate a performance of control system (qualitative and quantitative)

Problem Discussion

Describe the input and output relationship of P,PI and PID controller

For the common controlled process, why P controller will generate an offset and the PI controller can eliminate the offset?

Why the derivative effect of the PID controller dose not used in the most actual process?

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Contents

Selection of Valve Action Action of Feedback Controllers Performance Criterion of Process

Control Systems Understand P, PI and PID Controllers Problem Discussion

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Action of Control Valves Types of control valves

(1) Fail-closed valve : if no signal exists (or the input signal of valve is zero), the valve will be closed.(2) Fail-opened valve : if no signal exists, the valve will be opened completely.

Selection of valve typeIf one hope the valve closed when the power is off, he must select fail-closed valve; otherwise, he must select fail-opened valve.

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Types of Control Valves

..............

pc

Fail-openedValve

pc

..............

Fail-closedValve

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Action of Values Fail-closed valve

Direct Action ( 正作用 ) ---when the input signal of the value increases, its output signal also increases.

) Fail-opened valveReverse Action ( 反作用 )---when the intput signal from the value increases , its output signal decreases on the contrary.

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Control Valve Selection Examples

T

RV

RF , Ti

Steam（蒸汽）

Condensate（冷却水）

Process Fluid（过程流体）

Tsp

Tm

u(t)TC22

TT22

Heat Exchanger（热交换器）

Ex. 1 Ex. 2

ProcessFluid Inlet

（过程流体入口）

Coolant（冷却剂）

Fluid Outlet

u(t)

Fw

T

Tsp

Tm

TC25

TT25

ExothermicChemical Reactor（放热反应器）

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Action of Controllers Direct Action ( 正作用 )

when the signal from the transmitter increases, the controller output also increases.

Reverse Action ( 反作用 )when the signal from the transmitter increases, the controller output decreases on the contrary.

Note: The set point is not part of decision.

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Selection of Controller Action

Principle: to construct a negative feedback loop ?

ysp e(t)

+_

ym(t)

++ y(t)u( t) MV

D (t)Disturbance

Path

Sensor & Transmi tter

Final Control Element

Control Path

Controller

Controlled Plant

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Controller Action Selection Ex. 1

T

RV

RF , Ti

Steam

Condensate

Process Fluid

Tsp

Tm

u(t)TC22

TT22

Heat Exchanger

Considering the safety of the control system, the steam valve must be a fail-closed valve, so u↑→ RV↑. (Why ?)

Assume the controller is set to direct action. If T↑, then

Conclusion: the controller must be set to reverse action because if it is set to direct action, we cannot build a negative-feedback system.

Tm u RV T

Tm

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Controller Action Selection Ex. 2

The coolant valve must be a fail-opened valve, so u↑→ Fw↓. (Why ?)

Assume the controller is set to direct action. If T↑, then

Tm u FwT

Direct Action

FO Valve

T

Conclusion: the controller must be set to reverse action.

ProcessFluid Inlet

Coolant

Fluid Outlet

u(t)

Fw

T

Tsp

Tm

TC25

TT25

ExothermicChemical Reactor

Other methods ?

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Controller action selection based on loop analysis Ex. 1

T

RV

RF , Ti

Steam

Condensate

Process Fluid

Tsp

Tm

u(t)TC22

TT22

Heat Exchanger

Tsp e(t)

+_

Tm

T

TT 22

SteamValve

Heat Exchanger

TC 22u(t) RV

D (t)

Step 1: plot block diagram

Step 2: indicate the action direction for each block except the controller.

Step 3: determine the action of the controller to construct a negative feedback loop(+)

(+)(+)(+)

TC 22 must be reverse

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Controller action selection based on loop analysis Ex. 2

Tsp e(t)

+_

Tm

T

TT 25

CoolantValve

ExothermicReactor

TC 25u(t)

D (t)

Fw

( － )

(+)

(+)

TC 25 must be a reverse controller

ProcessFluid Inlet

Coolant

Fluid Outlet

u(t)

Fw

T

Tsp

Tm

TC25

TT25

FO

( － )

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Performance Criterion of Process Control Systems

ySP

y(∞ )

B

B'

y0

C

Offset ( 余差 ):

( ) ( )spe y y

Decay Ratio ( 衰减比 ):

Bn B

Overshoot ( 超调量 ):

100%BC

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Performance Criterion of Process Control Systems(cont.)

ySP

y(∞ )

y0

t0 t1 t2 t3 t4

Rise time ( 上升时间 ):

2 1rt t t Peek time( 峰值时间 ):

3pt t

Period of Oscillation

( 振荡周期 ): Setting Time ( 调节时间 ) ts

4 3T t t

Which is the best response ?

Problem Discussion

Describe the input and output relationship of P,PI and PID controller

For the common controlled process, why P controller will generate an offset and the PI controller can eliminate the offset?

Why the derivative effect of the PID controller dose not used in the most actual process?

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Proportional Controller

ysp e(t)

+_

ym(t)

++ y(t)MV

D (t)

Sensor & Transmitter

ValveControlled

PlantController

%CO

u(t)

%TO

0( ) ( ) ,cu t K e t u ( ) ( ) ( )sp me t y t y t

KC is the controller gain ( 控制器增益 ).

( ) cG s K

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Effect of Controller Gain on Controller Output

0 10 20 30 40 5049

50

51

52

%

% TO

0 10 20 30 40 5049

50

51

52

%

% TO

0 10 20 30 40 5049

50

51

52

53

%

Time, min

% CO

0 10 20 30 40 5047

48

49

50

51

%

Time, min

% CO

setpoint setpoint

measurement measurement

Kc = 2

Kc = 1 Kc = 1

Kc = 2

Direct-acting P Controller

Reverse-acting P Controller

Kc establishes the sensitivity of the controller to an error

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0 10 20 30 40 5048

50

52

54

56

58

60

62

Time, min

%

TO of Liquid Level

Kc = 0.5

Kc = 1.0

Kc = 2.0

Kc = 4.0

Simulation of P Control Loop

Fi(t) increases from 10 to 11 liter/min at 10 min.

See ../PIDControl/LevelPControlLoop.mdl

u(t) % CO

% TOh(t)

Fi(t)

Fo(t)

A

ysp

y(t)LC41

LT41

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Effect of Proportional Gain on Control Performances

P controllers have only one tuning parameter, Kc. However, they suffer a major disadvantage - there exists an Offset of the controlled variable from the set point. (Why ?)

For a given step disturbance, the magnitude of the offset depends on the value of the gain. The larger the gain, the smaller the offset.

Above a certain Kc, most processes go unstable.

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About the Proportional Band

Definition: proportional band （比例带） refers to the error (expressed in percent-age of the range of the controlled variable) required to move the output of the controller from its lowest to its highest value.

100%c

PB K

5025 75 1000

50

25

75

100

0

% CO

% TO

100% PB

200% PB

50% PB25% PB

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0 5 10 15 20 25 3049

50

51

52

%

% TO

0 5 10 15 20 25 3048

50

52

54

56

58

60% CO

Time, min

%

1% set point

Kc

Kc

TI

Proportional-Integral (PI) Controller

0

0

1( ) ( )

,

t

ci

u t K e edT

u

)1

1()(sT

KsGi

cc

Ti is the integral time, or the reset time

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0 10 20 30 40 50 60 7048

49

50

51

52

53

54

55

56

57

58

Time, min

%

TO of Liquid Level

P (Kc=1)

PI (Kc = 1, Ti = 10 min)

set point

Simulation of PI Control Loop

Fi(t) increases from 10 liter/min to 11 liter/min at time = 10 min.

See ../PIDControl/LevelPIControlLoop.mdl

u(t) % CO

% TOh(t)

Fi(t)

Fo(t)

A

ysp

y(t)LC41

LT41

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Effect of Integral Action on Control Performances

PI controllers have two tuning parameter: the gain or proportional band, and the integral time or the integral rate (1/Ti ). The advantage is that the integration removes the offset. (Why ?)

The disadvantage of PI controllers is that the addition of integration adds some amount of instability to the system. The smaller the integral time, the stronger the integral action, the faster the system removes the offset, but the weaker the stability of the system.

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Proportional-Integral-Derivative (PID) Controller

00

1 ( )( ) ( ( ) ( ) ) ,

t

c di

de tu t K e t e d T u

T dt

1( ) (1 )c c d

i

G s K T sT s

Td is the derivative time.

Ideal PID Controller

Industrial PID Controller

1 1( ) 1

1

dc c

d i

d

T sG s K

T T ssA

Ad is called the derivative gain ( 微分增益 ).

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0 1 2 3 4 5 6 7 8 9 1049

50

51

52

%

% TO

0 1 2 3 4 5 6 7 8 9 1050

60

70

80

90

Time, min

%

% CO

Td = 0Td = 2.5 min, Ad = 10Td = 2.5 min, Ad = 20

set point

Kc = -2, Ti = 10 min

Response of Real PID Controller

Discuss the effect of Td and Ad on the output of the controller.

Please see PIDControl /PIDController.mdl

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0 10 20 30 40 50 6058

59

60

61

62

63

64

Time, min

%

% TO

set point

P (Kc =1)

PI (Kc =1, Ti = 6 min)

PID ( Kc =1, Ti = 6 min, Td = 1.5 min, Ad =10 )

Simulation of PID Loop

Ti(t) increases from 50 Cent. to 60 Cent. at time = 10 min.

See ../PIDControl/PIDLoop.mdl

Process Fluid

Fuel Oil

T(t)

u(t)

y(t) %, TO

%, CO ysp(t)

Ti (t)

TC27

TT27

Furnace

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Effect of Derivative Action on Control Performances

PID controllers have three tuning parameter: the gain, the integral time and the derivative time. The derivative action gives the controller the capability to anticipate.

PID controllers are recommended for use in slow processes with long time constants, such as temperature loops, which are usually free of noises. For fast processes with noises, such as flow loops and pressure loops, the use of derivative action will amplify the noise and therefore should not be used.

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Problem Discussion For a stable controlled process, there exist

offset when a P controller is used. Why? When we use a PI controller, there is no

offset if the closed-loop system is stable. Please explain its reason.

It is well known that derivative action is helpful to improve the stability of a closed-loop system, however, derivative action is not used in most industrial processes. Why?

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Next Lecture How to select types of PID controller How to tune parameters of PID

controller How to tune parameters of flow control How to tune parameters Level Control What is the Reset Windup and Its

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1 PID Feedback Controllers PID 反馈控制器 Shen Guo-jiang Institute of Industrial Control,...

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