Process Characteristics （过程动态特性分析）

Lei Xie

Institute of Industrial Control, Zhejiang University, Hangzhou, P. R.

China

Contents Importance of Process Characteristics (

过程对象特性的重要性) Introduction of Final Control Elements

( 执行机构介绍 ) Types of Processes ( 过程特性分类 ) Obtaining Characteristics from Process

Dynamics ( 过程特性机理建模法 ) Obtaining Characteristics from Process

Data ( 过程特性测试建模法 ) Summary

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

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

Pneumatic Control Valves( 气动调节阀 )

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

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

A Self-regulating Process

The controlled process is stable. Why ?

Steam

Tsp

Tm

T

RV

RF , Ti

u(t)

Condensate

Process Fluid

TC22

TT22

A Non-self-regulating Process

h

Qi

Qo

ysp

y(t)

u(t)

LC41

LT41

The controlled process is unstable. Why ?

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

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.

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?

(\ProcessModel\ LevelProcess01.mdl)

Relationship between flow and level ：

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

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

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

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

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)

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

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

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

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.

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.

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

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.

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)(

)(

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

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)n

ii

O s K

I s T s

1 2

( )

( ) ( 1)( 1)sO s K

eI s T s T s

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 and slow; Most processes are nonlinear, so the

numerical values of model parameters vary with operating conditions.

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)

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.

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

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

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

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.

For the level controlled process, h2 is selected as its controlled variable, and Qin is the main input of the process. Suppose the sectional area of two tanks are A1 and A2. The rates of outlet flow are assumed to satisfy the following equations:

Problem 2-1

K12A1 A2

h1h2

K2 Q2

Q12

Qin

K1

Q1

,111 hKQ 222 hKQ ,211212 hhKQ

Please obtain the process characteristics by dynamic equations (the ODE equations).