Transcript Document

Process Characteristics
过程特征
Shen Guo-jiang
Institute of Industrial Control,
Zhejiang University
1
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 .
2
Example
Psp
Pm
PC
51
F2
PT
51
u
P2
f2
P
P1
f1
F1
For the above pressure control
system, please describe its CV,
SP, MV, DVs, control diagram as
well as control objective.
Variable relations
are as follows:
dP
V
 K1 F1  K 2 F2
dt
F1  KV 1 f1 P1  P
f1 100 u
F2  KV 2 f 2 P  P2
If the P1 is increased suddenly, How the feedback
control maintain the P at its set point.
Problem Discussion



Defined the types of processes: selfregulating 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.
Contents
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Process and Importance of Process
Characteristics
Introduction of Final Control Elements
Types of Processes
Obtaining Characteristics from Process
Dynamics
Obtaining Characteristics from Process
Data
Summary
5
Heat Exchanger
Temperature Control System
Tsp
The extended controlled
process (广义对象) is anything
except the controller.
Steam
u(t)
TC
22
Tm
RV
TT
22
RF , Ti
Process
Fluid
T
Condensate
Tsp
u(t)
Controller
I/P
& valve
Heat
exchanger
Sensor
Transmitter
mA, CO
Tm(t)
mA, TO
Flow
T
mV
6
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
7
Heat Exchanger
Temperature Control System
Tsp
TC
22
u(t)
Process description and
signal flow diagram?
蒸汽
RV
Tm
TT
22
换热器
RF , Ti
工艺
介质
T
凝液
温度控制系统的信号流程图
RF (t), Ti (t)
Tsp
控制器
TC 22
Tm
mA
u(t)
mA
电气
转换器
温度
变换器
p(t)
MPa
气动
控制阀
T(t)
RV (t)
换热器
T/hr
热电偶
mV
TT 22
℃
Pneumatic Control Valves
pc
.......
.......
弹簧
0.02 ~ 0.1MPa
薄膜片
阀杆
密封填料
阀芯
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。
阀体
10
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
11
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
12
变频调速主电路
整流器
D1
D3
滤波器
Tr1
D5
三 a
相
b
电 c
源
逆变器
Tr3
Tr5
a
Ud
D2
D4
b
c
C
D6
Tr4
Tr6
Tr2
IM
0
电机
13
变频器基本组成
主电路
电源
整流器
逆变器
滤波器
AC200-230V
50-60Hz
电动机
DC0 - 10V
DC4 - 20mA
变频器运
行状态信
号输出
IM
直流电源
V/F
转换器
基极驱
动电路
加减速
调节器
函数
发生器
电压
发生器
PWM正弦
波发生器
保护电路
.电压过载
.电流过载等
CPU
相序
切换器
触摸式操作
面板, 包括
.操作按键
.状
手动操作
状态检测
14
Problem Discussion



Defined the types of processes: selfregulating 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.
Types of Processes
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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
16
A Self-regulating Process
Tsp
u(t)
TC
22
Steam
RV
Tm
TT
22
RF , Ti
Process
Fluid
T
Condensate
The controlled process
is stable. Why ?
17
A Non-self-regulating Process
u(t)
Qi
h
LT
41
y(t)
LC
41
ysp
Qo
The controlled process
is unstable. Why ?
18
A Self-regulating
Liquid Level Process
The process is selfregulating. Why ?
y(t)
Qi
h
u(t)
Qo  KA(u(t )) h0  h(t )
Qo
19
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.
20
Modeling Example #1
Qi

Material balance equation：
A
dH
 Qi  Qo
dt
Relationship between flow
and level：

H
Qo
A
Qo  k H
Problem Discussion:
How to build the controlled process
with SimuLink?
dH
A
 Qi  k H
dt
(\Simulink\ LevelProcess01.mdl)
21
Modeling Example #1
Qi
H
Qo
A
A
dH
 Qi  Qo
dt
AsH (s)  Qi (s)  Qo (s)
Qo  k H
Qo (s) 
k
H (s)
2 h0
H (s)
R

Qi ( s) RAs  1
R
2 h0
k
22
Modeling Example #2
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:
Qd
Qi
h1
Q1
A1
Q1  k1 h1 ,
h2
A2
Q2  k2 h2
Q2
Please obtain the process characteristics by dynamic equations,
and build the corresponding Matlab/SimuLink model.
23
Modeling Example #2
 Material balance equation：
dH 1
dH 2
A1
 Qi  Q1 , A2
 Q1  Q2
dt
dt
Qi
H1
 Relationship between flow and level：
Q1
Q1  k1 H1 , Q2  k2 H2
A1
H2
Q2
A2
Simulation ex.: \simulink\
LevelProcess02.mdl
dH1
A1
 Qi  k1 H 1 ,
dt
dH 2
A2
 k1 H 1  k 2 H 2
dt
State equation and linearization ?
24
Modeling Example #2
A1
dH 1
 Qi  Q1 ,
dt
A2
dH 2
 Q1  Q2
dt
A1sH1 (s)  Qi (s)  Q1 (s), A2 sH2 (s)  Q1 (s)  Q2 (s)
Q1  k1 H1 , Q2  k2 H2
Qi
H1
Q1 ( s ) 
R1 
Q1
A1
H1 ( s) 
H2
Q2
R1
Qi ( s)
R1 A1s  1
1
1
H1 ( s ), Q2 ( s ) 
H 2 (s)
R1
R2
2 h10
k1
, R2 
A2 sH 2 (s) 
A2
2 h20
k2
1
Qi (s)  R2 H 2 (s)
R1 A1s  1
H 2 ( s)
R2

Qi (s)  R1 A1s  1 R2 A2 s  1
25
Single-Capacitance Processes Ex.1
65
60
Inlet Temp.
Ti (t)
55
Temperature
speepest slope
T (t)
50
45
Outlet Temp.
40
35
30
25
0
5
10
15
20
25
30
Time, min
35
40
45
50
26
Single-Capacitance Processes Ex.2
Inlet Flow
45
Qi
T/hr
40
35
30
H
25
Qo
0
5
10
15
20
25
30
35
40
45
50
25
30
Time, min
35
40
45
50
Liquid Level
10
A
meter
H ( s)
?
Qi ( s)
8
6
4
0
5
10
15
20
27
Single-Capacitance Processes Ex.3
Valve Position
70
60
%
Qi
50
40
h
u(t)
30
0
5
10
15
20
25
30
35
40
45
50
25
30
Time, min
35
40
45
50
Liquid Level
10
Qo
meter
H ( s)
?
u ( s)
8
6
4
0
5
10
15
20
28
Problem Discussion



Defined the types of processes: selfregulating 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.
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).
Output O final  Oinitial
K

Input
I final  Iinitial


Process Time Constant (T)
Process Dead Time (τ)
30
Process Gain Calculation Ex.1
Output
K
Input
O final  Oinitial

I final  I initial
65
60
Inlet Temp.
55
Temperature
speepest slope
50
45
(45  30) Cent

(60  50) Cent
Cent outlet temp.
 1.5
Cent inlet temp.
Outlet Temp.
40
35
30
25
0
5
10
15
20
25
30
Time, min
35
40
45
50
31
Process Gain Calculation Ex.2
Inlet Flow
45
T/hr
40
35
30
25
0
5
10
15
20
25
30
35
40
45
50
Liquid Level
10
meter
8
6
4
0
5
10
15
20
25
30
Time, min
35
40
45
50
Output
K
Input
O final  Oinitial

I final  I initial
(9  5) meter

(40  30) T / hr
meter
 0.4
T / hr
32
Process Gain Calculation Ex.3
Valve Position
70
%
60
50
40
30
0
5
10
15
20
25
30
35
40
45
50
Liquid Level
10
meter
8
6
4
0
5
10
15
20
25
30
Time, min
35
40
45
50
Output
K
Input
O final  Oinitial

I final  I initial
(4  9) meter

(60  40) %
meter
 0.25
%
33
Notes to Process Gain
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

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.
34
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.
Liquid Level
10
9
8
7
9+(4-9)*63.2% = 5.84
meter

6
5
4
T
3
0
5
10
15
20
25
30
Time, min
35
40
45
50
35
Process Dead Time (τ)
Definition
the finite
amount of time
between the
change in input
variable and
when the output
variable starts
to respond.
60
Inlet Temp.
55
50
Cent

Inlet/Outlet Temp.
65
45
Outlet Temp.
40
35
30
25
T
0
5
10
15
20
25
30
Time, min
35
40
45
50
36
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.
37
Mathematical Description of
Single-Capacitance Processes

The transfer function for a firstorder-plus-dead-time (FOPDT)
process is given by
y(s)
K  s

e
u ( s) Ts  1
38
Multi-capacitance Processes Ex.2
Ti (t)
65
Ti(t)
60
55
50
45
0
10
20
30
40
50
0
10
20
30
40
50
0
10
20
30
40
50
0
10
20
30
Time, min
40
50
65
T1(t)
T1(t)
60
55
50
45
T2(t)
65
T2(t)
60
55
50
45
T4(t)
65
T5(t)
60
55
50
T5(t)
45
39
Mathematical Description of
Multi-Capacitance Processes



K
 s
High-Order Model: O ( s ) 
e
I ( s )  n (Ti s  1)
i 1
Second-orderplus-dead-time
Model
O( s )
K

e s
I ( s) (T1s  1)(T2 s  1)
First-order-plusdead-time Model
O( s )
K  s

e
I ( s) Ts  1
40
Characteristics of Real Processes




Most controlled processes are selfregulating 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.
41
Parameters Describing Process
Characteristics

Process Gain (K)
Ratio of the change in output (or responding variable) to the
change in input (or forcing function).
Output O final  Oinitial
K

Input
I final  Iinitial


Process Time Constant (T)
Process Dead Time (τ)
42
Problem Discussion



Defined the types of processes: selfregulating 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.
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.
44
The Step Response Curve
for a Heat Exchanger
Controller Output
65
%
RV
55
50
Tm
45
TT
22
0
10
RF , Ti
20
30
40
50
40
50
Heat Exchanger Outlet Temp.
160
Process
Fluid
T
Condensate
158
156
Cent
Tsp
u(t)
TC
22
60
Steam
154
152
150
148
0
10
20
30
time, min
45
Obtain the Dynamic Terms from
the Step Response Curve
Controller Output
65
%
60
T  1.5  t0.632 O  t0.283 O 
55
?
50
45
0
10
20
30
40
50
Heat Exchanger Outlet Temp.
160
  t0.632 O  T0  T
158
63.2%
Cent
156
154
?
28.3%
152
150
148
T2
T0
0
10
T1
20
30
40
50
time, min
46
Obtain Process Gain from the
Step Response Curve
Controller Output
65
%
60
55
50
45
0
5
10
15
20
25
30
35
40
45
50
Heat Exchanger Outlet Temp.
160
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
158
K
Cent
156
154
152
?
150
148
changein transm itter ' s output, %
changein controller' s output, %
0
5
10
15
20
25
30
time, min
35
40
45
50
47
Summary



Defined the types of processes: selfregulating 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.
48
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?