1 process characteristics 过程特征 shen guo-jiang institute of industrial control, zhejiang...
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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
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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
17
A Self-regulating Process
The controlled process is stable. Why ?
Steam
Tsp
Tm
T
RV
RF , Ti
u(t)
Condensate
Process Fluid
TC22
TT22
18
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
20
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.
21
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 :
22
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 :
25
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
11
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
26
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
27
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
28
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)
31
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
32
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
34
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.
35
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
37
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.
38
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)(
)(
39
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
41
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.
42
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.
45
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
47
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
48
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?