1 process characteristics 过程特征 shen guo-jiang institute of industrial control, zhejiang...

1

Process Characteristics过程特征

Shen Guo-jiang

Institute of Industrial Control,

Zhejiang University

2

Last Lecture Discussed three basic operations in every

type of control system; Defined Controlled Variable, Setpoint,

Manipulated Variable and Disturbance; Discussed The objective of an automatic

process control system ; Defined Regulatory Control and Servo

Control; Discussed Feedforward Controland

Feedback Control .

Example

For the above pressure control system, please describe its CV, SP, MV, DVs, control diagram as well as control objective.

2211 FKFKdt

dPV

PPfKF V 1111

2222 PPfKF V

Variable relations are as follows:P

P1

P2Psp Pm

u

f1

f2

F1

F2PC51

PT51

uf 1001

If the is increased suddenly, How the feedback control maintain the P at its set point.

1P

Problem Discussion

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.

5

Contents Process and Importance of Process Cha

racteristics Introduction of Final Control Elements Types of Processes Obtaining Characteristics from Process

Dynamics Obtaining Characteristics from Process

Data Summary

6

Heat Exchanger Temperature Control System

Tsp Tm(t)u(t)Transmitter

HeatexchangerController

mA, CO

I/P& valve

Flow

Sensor

T mV

mA, TO

The extended controlled process ( 广义对

象 ) is anything except the controller.

T

RV

RF , Ti

Steam

Condensate

Process Fluid

Tsp

Tm

u(t)TC22

TT22

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Importance of Process Characteristics

Every process has different characteristics

Not easy to change the controlled process

Very easy to change the controller tuning What we can do is to adapt the controller

to the process A good controller is the controller best

adapted to the process characteristics

Heat Exchanger Temperature Control

System

Process description and signal flow diagram?

换热器T

RV

RF , Ti

蒸汽

凝液

工艺介质

Tsp

Tm

u(t)TC22

TT22

温度控制系统的信号流程图

Tsp

Tm

T(t)RV (t)

RF (t), Ti (t)

气动控制阀

换热器控制器TC 22

u(t)

热电偶温度变换器 ℃mVmA

TT 22

mA T/hr

电气转换器 MPa

p(t)

10

Pneumatic Control Valves

功能：根据阀头气压的大小，通过阀杆改变阀体中阀芯的位置，进而调节流经阀体的流体流量。

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

pc

薄膜片弹簧

阀杆

密封填料

阀芯

阀体

0.02 ~ 0.1MPa

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I/P Converter 功能：将电流信号（ 4 ~ 20mA ）转换成气动模拟量信号 0.02 ~ 0.10MPa

12

Principle of Transducer 应用意义 改变交流电机供电的频率和幅值，因而改变其运动磁

场的周期，达到平滑控制电动机转速的目的 异步电动机的变频调速原理

异步电动机定子三相对称绕组空间相隔 120 角，当通以三相对称电流后，便产生了旋转磁场；其旋转磁场的转速（亦称同步转速）为

n = 60 f 1 / p （ r / min ）式中， f 1 为定子绕组电源频率； p 为磁场对数。

实现方法

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变频调速主电路

Ud

整流器 滤波器 逆变器

a

bc

a

bc

D3D1 D5

D4D2 D6

Tr1 Tr3 Tr5

Tr4 Tr6 Tr2

C 0IM

三相电源

电机

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变频器基本组成

DC0 - 10V

整流器 IM滤波器 逆变器

电动机

基极驱动电路

直流电源

保护电路.电压过载.电流过载等

V / F转换器

加减速调节器

函数发生器

电压发生器

PWM正弦波发生器

相序切换器

手动操作状态检测

AC200-230V50-60Hz

主电路电源

DC4 - 20mA

CPU

触摸式操作面板, 包括.操作按键.状

变频器运行状态信号输出

Problem Discussion

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.

16

Types of Processes Self-regulating processes (or stable

processes, 自衡过程 / 稳定对象 )(1) Single-Capacitance Processes(2) Multi-Capacitance Processes

Non-self-regulating processes (or unstable processes, 非自衡过程 )Ex.: some level processes and some reactors

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A Self-regulating Process

The controlled process is stable. Why ?

Steam

Tsp

Tm

T

RV

RF , Ti

u(t)

Condensate

Process Fluid

TC22

TT22

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A Non-self-regulating Process

h

Qi

Qo

ysp

y(t)

u(t)

LC41

LT41

The controlled process is unstable. Why ?

19

A Self-regulating Liquid Level Process

h

Qi

Qo

y(t)

u(t)

The process is self-regulating. Why ?

0( ( )) ( )oQ KA u t h h t

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Approaches to Obtain Process Characteristics

Based on Process Dynamics ( 机理建模 )Describe process characteristics with some mathematical equations based on the chemical and/or physical mechanism of a controlled process.

Based on Process Data ( 测试建模 )To obtain process characteristics, manually change the input of a controlled process and record the input and output data, then find an appropriate model based on process data.

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Modeling Example #1

H

Qi

Qo

A

oi QQdt

dHA

HkQo

HkQdt

dHA i

Material balance equation ：

Problem Discussion:

How to build the controlled process with SimuLink?

(\Simulink\ LevelProcess01.mdl)

Relationship between flow and level ：

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Modeling Example #1

( ) ( ) ( )i oAsH s Q s Q s

0

( ) ( )2

o

kQ s H s

h

02 hR

k

H

Qi

Qo

A

oi QQdt

dHA

HkQo

( )

( ) 1i

H s R

Q s RAs

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For the level controlled process, h2 is selected as its controlled variable, and Qi is the manipulated variable, Qd is the main disturbance variable. The rates of outlet flow are assumed to satisfy the following equations:

Modeling Example #2

,111 hkQ 222 hkQ

Please obtain the process characteristics by dynamic equations, and build the corresponding Matlab/SimuLink model.

h1

Qi

Q1

A1

h2

Q2A2

Qd

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Modeling Example #2

212

211

1 , QQdt

dHAQQ

dt

dHA i

222111 , HkQHkQ

22112

2

111

1 ,

HkHkdt

dHA

HkQdt

dHA i

Simulation ex.: \simulink\ LevelProcess02.mdl

H1

Qi

Q1

A1

H2 Q2

A2

State equation and linearization ?

Material balance equation ：

Relationship between flow and level ：

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Modeling Example #2

1 1 1 2 2 1 2( ) ( ) ( ), ( ) ( ) ( )iA sH s Q s Q s A sH s Q s Q s

222111 , HkQHkQ

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1 1

( ) ( )1 i

RH s Q s

R A s

212

211

1 , QQdt

dHAQQ

dt

dHA i

1 1 2 21 2

10 201 2

1 2

1 1( ) ( ), ( ) ( )

2 2,

Q s H s Q s H sR R

h hR R

k k

H1

Qi

Q1

A1

H2 Q2

A2

2 2 2 21 1

1( ) ( ) ( )

1 iA sH s Q s R H sR A s

2 2

1 1 2 2

( )

( ) 1 1i

H s R

Q s R A s R A s

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Single-Capacitance Processes Ex.1

Ti (t)

T (t)

0 5 10 15 20 25 30 35 40 45 5025

30

35

40

45

50

55

60

65

Time, min

Tem

pera

ture

Inlet Temp.

Outlet Temp.

speepest slope

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Single-Capacitance Processes Ex.2

H

Qi

Qo

A

0 5 10 15 20 25 30 35 40 45 5025

30

35

40

45

T/h

r

Inlet Flow

0 5 10 15 20 25 30 35 40 45 504

6

8

10

Time, min

met

er

Liquid Level

( )?

( )i

H s

Q s

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Single-Capacitance Processes Ex.3

h

Qi

Qo

u(t)

( )?

( )

H s

u s

0 5 10 15 20 25 30 35 40 45 5030

40

50

60

70

%

Valve Position

0 5 10 15 20 25 30 35 40 45 50

4

6

8

10

Time, min

met

er

Liquid Level

Problem Discussion

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.

30

Terms that Describe the Process Characteristics

Process Gain (K)Ratio of the change in output (or responding variable) to the change in input (or forcing function).

final initial

final initial

O OOutputK

Input I I

Process Time Constant (T) Process Dead Time (τ)

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Process Gain Calculation Ex.1

0 5 10 15 20 25 30 35 40 45 5025

30

35

40

45

50

55

60

65

Time, min

Tem

pera

ture

Inlet Temp.

Outlet Temp.

speepest slope

(45 30) Cent

(60 50) Cent

Cent outlet temp.1.5

Cent inlet temp.

final initial

final initial

OutputK

Input

O O

I I

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Process Gain Calculation Ex.2

(9 5)

(40 30) /

0.4/

final initial

final initial

OutputK

Input

O O

I I

meter

T hr

meter

T hr

0 5 10 15 20 25 30 35 40 45 5025

30

35

40

45

T/h

r

Inlet Flow

0 5 10 15 20 25 30 35 40 45 504

6

8

10

Time, min

met

er

Liquid Level

33

Process Gain Calculation Ex.3

(4 9)

(60 40) %

0.25%

final initial

final initial

OutputK

Input

O O

I I

meter

meter

0 5 10 15 20 25 30 35 40 45 5030

40

50

60

70

%

Valve Position

0 5 10 15 20 25 30 35 40 45 50

4

6

8

10

Time, min

met

er

Liquid Level

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Notes to Process Gain Process gain describes the sensitivity

of the output variable to a change in input variable.

Process gain includes three parts: Sign, Numerical value and Units.

Process gain relates only steady-state values, so the gain is a steady-state characteristic of the process.

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0 5 10 15 20 25 30 35 40 45 503

4

5

6

7

8

9

10

Time, min

met

er

Liquid Level

9+(4-9)*63.2% = 5.84

T

Process Time Constant (T ) Definition

The process time constant for a single-capacitance process is defined as the amount of time counted from the moment the variable starts to respond to reach 63.2% of its total change.

36

Process Dead Time (τ) Definition

the finite amount of time between the change in input variable and when the output variable starts to respond. 0 5 10 15 20 25 30 35 40 45 50

25

30

35

40

45

50

55

60

65

Time, min

Cen

t

Inlet/Outlet Temp.

Inlet Temp.

Outlet Temp.

T

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Notes to Parameters K, T, τ These numerical values describe the basic

characteristics of a real process, which K describes the steady-state characteristic, and T, τ are related to the dynamics of the process.

These numerical values depend on the physical parameters of the process as well as its operating conditions. In most cases, they vary with operating conditions, or most processes are nonlinear.

The ratio, τ/ T, has significant adverse effects on the controllability of control systems.

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Mathematical Description of Single-Capacitance Processes

The transfer function for a first-order-plus-dead-time (FOPDT) process is given by

seTs

K

su

sy

1)(

)(

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Multi-capacitance Processes Ex.2

Ti (t)

T1(t)

T4(t)

T5(t)

T2(t)

0 10 20 30 40 5045

50

55

60

65

Ti(t)

0 10 20 30 40 5045

50

55

60

65

T1(t

)

0 10 20 30 40 5045

50

55

60

65

T2(t

)

0 10 20 30 40 5045

50

55

60

65

T5(t

)

Time, min

40

Mathematical Description of Multi-Capacitance Processes

High-Order Model:

Second-order-plus-dead-time Model

First-order-plus-dead-time Model

( )

( ) 1sO s K

eI s Ts

1

( )

( ) ( 1)

sn

ii

O s Ke

I s T s

1 2

( )

( ) ( 1)( 1)sO s K

eI s T s T s

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Characteristics of Real Processes

Most controlled processes are self-regulating except some liquid level processes;

Processes have some amount of dead time; The step responses of controlled processes

are often monotonous( 单调的 ) and slow; Most processes are nonlinear, so the

numerical values of model parameters vary with operating conditions.

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Parameters Describing Process Characteristics

Process Gain (K)Ratio of the change in output (or responding variable) to the change in input (or forcing function).

final initial

final initial

O OOutputK

Input I I

Process Time Constant (T) Process Dead Time (τ)

Problem Discussion

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.

44

Obtaining Process Characteristics from Process

Data

Obtain the necessary process data by step response testing;(1) Set the controller to manual mode;(2) Make a step change in the controller output;(3) Record the process variable.

Obtain parameters K, T, τ from process testing data.

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0 10 20 30 40 5045

50

55

60

65

%

Controller Output

0 10 20 30 40 50148

150

152

154

156

158

160

time, min

Cen

t

Heat Exchanger Outlet Temp.

The Step Response Curve for a Heat Exchanger

Steam

Tsp

Tm

T

RV

RF , Ti

u(t)

Condensate

Process Fluid

TC22

TT22

46

Obtain the Dynamic Terms from the Step Response

Curve

0 10 20 30 40 5045

50

55

60

65

%

Controller Output

0 10 20 30 40 50148

150

152

154

156

158

160

time, min

Cen

t

Heat Exchanger Outlet Temp.

63.2%

28.3%

T0

T1

T2

?0632.0

TTt O

?

5.1 283.0632.0

OO ttT

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Obtain Process Gain from the Step Response Curve

0 5 10 15 20 25 30 35 40 45 5045

50

55

60

65

%

Controller Output

0 5 10 15 20 25 30 35 40 45 50148

150

152

154

156

158

160

time, min

Cen

t

Heat Exchanger Outlet Temp.

If the span of the temperature transmitter is 100 to 300 ℃, then the change in transmitter output is 4%. Therefore, the total process gain is

?

%,'

%,'

outputscontrollerinchange

outputsrtransmitteinchangeK

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Summary 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.

Next Lecture 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)

Next Lecture(Cont.)

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?