tuning pid controller institute of industrial control, zhejiang university, hangzhou, p. r. china...
TRANSCRIPT
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Tuning PID Controller
Institute of Industrial Control, Zhejiang University, Hangzhou, P. R.
China
2013/03/27
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Single-loop PID Control System
ysp u(t)
+_
ym(t)
++ y(t)MV
DVs
Disturbance Path
Sensor & Transmitter
Final Control Element
Control Path
PIDController
Extended Controlled Process
(广义对象)
Problem: For an unknown extended controlled process, how to design and tune our PID controller ?
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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 (design and realization ?)
1 1( ) 1
1
dc c
d i
d
T sG s K
T T ssA
The derivative gain Ad = 10.
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Problem Discussion
Explain the function of PID controller for a stable controlled process.
Analyze the effect of PID parameter changes on control performances
How can we realize the industrial PID controller in Simulink ?
PID tuning example (See ../PIDControl /PIDLoop.mdl )
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Contents Selection of PID Controller Types ( PID
控制器类型选择) Tuning of PID Controller Parameters
(控制器参数整定) Flow Control (流量控制) Level Control (液位控制) Reset Windup and Its Prevention (积分
饱和与防止) Summary
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Type Selection of PID Controllers
*1: For some slow processes with long time constants, the derivative action is suggested to use. However, if there exists strong measurement noises, a first-order or average filter should be added.
Please analyze the rule of type selection ?
Controlled Variable
Controller Type
Temperature /
CompositionPID*1
Flow / Pressure
/Liquid-LevelPI
Liquid-Level P
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PID Tuning Concept
Process Characteristics
Controller Kc or PB,
Ti ,Td
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Offline Tuning Based on Process Parameters: K, T,τ
Step 1: switch the controller to manual mode, change the output of controller in step form, and record input/output data of controller.
Step 2: obtain process characteristics: K, T,τ, from the step response data.
Step 3: set the PID parameters Kc, Ti , Td, and switch the controller to automatic mode.
Step 4: increase or decrease the gain Kc until obtaining the satisfactory response.
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0 10 20 30 40 50 60 70 80 90 100
54
56
58
60
62
%
Controller Output
0 10 20 30 40 50 60 70 80 90 10066
68
70
72
74
76
78
80%
Transmitter Output
Simulation of Offline Tuningstep 1: Step Testing
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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0 10 20 30 40 50 60 70 80 90 10066
68
70
72
74
76
78
80
%
min
Transmitter Output
Step 2: Obtain Process Para.
Tt O 632.0
OO ttT 283.0632.05.1
,%
,%final initial
final initial
TO TOTOK
CO CO CO
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Step 3: Obtain Initial PID Para.
(Ziegler-Nichols Method)
Controller Kc Ti Td
P
PI
PID
1 T
K
0.9 T
K
1.2 T
K
3.33
2.0 0.5
Note: the above method was developed for 0 T
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Initial Value
Step 3: Obtain Initial PID Para.
(Lambda Tuning Method)
Controller
Kc Ti Td
P
PI T
PID T τ/2
1 T
K
Note: the above method is not limited by the value of
/T
1 T
K
1 T
K
0
0.2
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0 50 100 15059
59.5
60
60.5
61
61.5
62
62.5
63
Time, min
%
Output of Transmitter
Ziegler-Nichols methodLambda tuning methodset point
Simulation Example #1
K = 1.75
T = 6.5,τ= 3.3 min
For PI Controller,
Z-N tuning: Kc = 1.0, Ti = 11 min
Lambda tuning: Kc = 0.56, Ti = 6.5 min
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0 50 100 150 20059
59.5
60
60.5
61
61.5
62
62.5
63
Time, min
%
Output of Transmitter
Z-N tuningLambda tuningset point
Simulation Example #2
K = 1.75
T = 6.5,τ= 6.3 min
For PI Controller,
Z-N tuning: Kc = 0.53, Ti = 20.8 min
Lambda tuning: Kc = 0.30, Ti = 6.5 min
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Procedure of Online Tuning: Ziegler-Nichols Technique
Step 1: with the controller online (in automatic mode), remove all the reset (Ti = maximum) and derivative (Td = 0) modes. Start with a small Kc value.
Step 2: make a small set point or load change and observe the response of CV.
Step 3: if the response is not continuously oscillatory, increase Kc, or decrease PB, repeat step 2.
Step 4: Repeat step 3 until a continuous oscillatory response is obtained.
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0 10 20 30 40 5058
59
60
61
62
63
64
65
66
Time, min
%
Output of Transmitter
set point
Kc = 0.5 Kc = 1
Kc = 2
Kc = 4
Kc = 3.5 Tu
Ti = 6000 min, Td = 0 min
Example of Online Tuning
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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Online Tuning: Ziegler-Nichols Technique
Controller
Kc Ti Td
P 0.5Kcu
PI 0.45Kcu Tu /1.2
PID 0.65Kcu Tu /2 Tu /8
The gain that gives these continuous oscillations is the ultimate gain ( 临界增益 ), Kcu. The period of the oscillations is called the ultimate period ( 临界周期 ), Tu. the ultimate gain and the ultimate period are the characteristics of the process being tuned. The following formulas are then applied:
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0 20 40 60 80 10059
60
61
62
63
%
Output of Transmitter
0 20 40 60 80 10040
60
80
100
Time, min
%Output of Controller
set point
Inlet temp. drops 5 Cent.
Kcu = 3.4, Tu = 11 min
PID: Kc = 2.2, Ti = 5.5 min, Td = 1.4 min
Online Tuning Result
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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0 10 20 30 40 5058
59
60
61
62
63
64
65
66
Time, min
%
Output of Transmitter
set point
Kc = 0.5 Kc = 1
Kc = 2
Kc = 4
Kc = 3.5 Tu
Ti = 6000 min, Td = 0 min
Limitation of Online Tuning
Process Fluid
Fuel Oil
T(t)
u(t)
y(t) %, TO
%, CO ysp(t)
Ti (t)
TC27
TT27
Furnace
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Auto-tuning Based on Relay Feedback ( 基于继电反馈的参数自整
定 )
PID
Auto
Tune
uyspControlled
Process+ _
yme(t)
Relay
(+)
Here we suppose the process gain > 0
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Relay Feedback Example
)12)(15(
)2exp(0.2
)(
)(
ss
s
sU
sYm
The controlled process can be described as
The amplitude of relay controller is d = ±2.0
PID
Auto
Tune
uyspControlled
Process+ _
yme(t)
Relay
(+)
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Response of Relay Feedback
Oscillation period TU & amplitude AY
(振荡周期与幅度) ?
0 5 10 15 20 25 30 35 40 45 5058.5
59
59.5
60
60.5
61
61.5Ym
0 5 10 15 20 25 30 35 40 45 5047
48
49
50
51
52
53U
min
See the detailed results:
../ PIDLoopAutoTuning.mdl
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The Ultimate Gain ( 临界增益 ) Kcu Calculation
/4da
YCU A
dK 4
0 5 10 15 20 25 30 35 40 45 5047
48
49
50
51
52
53U
min
经 FT 变换可知,控制输出的一次谐波幅度为
而对应的控制器临界增益为
/4d
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Online Z-N Tuning Parameters
Controller
Kc Ti Td
P 0.5Kcu
PI 0.45Kcu Tu /1.2
PID 0.65Kcu Tu /2 Tu /8If we use a PID controller, then we select the following parameters ……
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Closed-loop Response of PID Feedback System
0 20 40 60 80 100 120 140
60
65
70
75
Ym
0 20 40 60 80 100 120 14040
60
80
100U
min
Above auto-tuning method can be applied to other controlled processes ?
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Characteristics of Flow Loops
Fast dynamic response Zero dead time, which results in an infinite
controller gain in every tuning equation Large measurement noise To decrease the change of control valve, a
PI controller is common used with very small proportional action and a large integral action to approximate an integral controller. (Why?)
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0 20 40 60 80 10045
50
55
60
65
%
Output of Transmitter
0 20 40 60 80 1000
20
40
60
Time, min
%
Output of Controller
Kc = 4, Ti =2 minKc = 1, Ti = 0.5 min
Tuning Example of Flow Loops
u(t)
y(t)
% CO
% TOysp(t)
F(t)
FC
See ../PIDControl/FlowLoop.mdl
Please compare the proportional gain with the integral gain
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C201
FIC 102
C301
Product
LT201
LC201
LT301
LC301
FC 201 FC 302
Examples of Level Loops
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Characteristics of Level Loops
Very often levels are integrating processes
There are two types of possible control objectives when the input flow varies: (1) Tight Level Control;(2) Average Level Control
(“ 液位均匀控制” )
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Tight Level Control The objective is to control the level tightly at
set point, and the output flow can be allowed to vary without limitation
If a level process happens to be self-regulated, and it is possible to obtain K, T andτ, the above tuning techniques can be used directly
If a level process is integrating, a PI controller is common used with large proportional action and a very small integral action
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Average Level Control The objective is to smooth the output flow
from the tank, which feeds the downstream unit, the level in the tank must be allowed to “float” between a high and a low level
A P controller is common used in Average Level Control with a small proportional gain
Tuning: the gain should be set to be as small as possible, as long as the level changes between a high and a low level for the expected flow deviation from the average flow.
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Example of Level Control
See ../PIDControl/ LevelLoop.mdl
u(t) % CO
% TOh(t)
Fi(t)
Fo(t)
A
ysp
y(t)LC41
LT41
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Analysis of Average Level Control Systems
Dynamic equation of the controlled process:
where A is the area of the tank.
Suppose
LC
u(t)
y(t)
% CO
% TO
ysp(t)
h(t)
Fi(t)
Fo(t)
A
)()()(
0 tFtFdt
tdhA i
)()(0 tuKtF V
,)()(maxh
thty
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Analysis of Average Level Control Systems (cont.)
For a proportional controller, Gc = - Kc,
+-
+Gc
Fi (s)
-
Fo (s) h(s)ysp
KV
u(s)
sA
1
max
1
h
y(s)
1
1
1)(
)(
max
max
max
sKK
Ah
sAh
KKsAh
KK
sF
sF
VC
VC
VC
i
o
1
11
1
1
)(
)(
max
max
max
sKK
AhKKsAh
KKsAh
sF
sy
VC
VCVCiPlease analyze the above models.
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Ysp
Ym
Y
Uman
SW1
e u
PID Man/Auto
0.2
Kv
10
KT
1
10s
Gp
Fo
Fi
DU
Examples of Average Level Control Systems
Please see ../PIDControl/ AverageLevelLoop.mdl
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Simulation Results of P-type Average Level Control
0 10 20 30 40 50 60 70 80 90 1009
9.5
10
10.5
11
m3/
hr
Fin, Fout
0 10 20 30 40 50 60 70 80 90 10046
48
50
52
54
time, min
%
Ysp, Ym Kc = -0.5
Fin
Kc = -2.0
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Reset Windup Problem
Please see the following simulation example
…/PIDControl/PidLoopwithLimit.mdl
+-
++
d(t)
Controlled Process ym(t)
ysp(t) e(t) uc11C
I
KT s
up
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Simulation Result with Reset Windup in a Single-Loop
System
Discussion:
Which difference exists between reset windup and the open or closed status of the control valve completely ?
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The Principle of Preventing Reset Windup
Principle: remove the reset or integral action if the control output is beyond the normal operation range.
+-
++
d(t)
A Controlled Process ym(t)
ysp(t)KC
++
1
1
sTI
e(t) uc up
maxmax
maxmin
minmin
)(,
)(),(
)(,
)(
utuifu
utuuiftu
utuifu
tu
c
cc
c
p
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0 20 40 60 80 100 120 140 160 180 20055
60
65
70
75
%
Ysp, Ym
0 20 40 60 80 100 120 140 160 180 2000
50
100
150
%
time, min
Uc, Up
Anti-reset Windup Example
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Industrial PID Controller
+-
++
d(t)
A Controlled Process ym(t)
ysp(t)
++
1
1
sTI
1
1
sA
TsT
K
D
D
DC
PID Controller
e(t) uc up
KC+
-
ysp(t)
++
1
1
sTI
Derivative Action First PID Controller
1
1
sA
TsT
D
D
D
e(t) uc up ++
d(t)
A Controlled Process ym(t)
PID1
PID2
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Summary Selection of PID Controller Types Tuning of PID Controller Parameters Tuning of PID Controller for Flow Loops Tight / Average Level Control Reset Windup and Its Prevention
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Problem Discussion For an unknown stable temperature control
system, can you determine PID parameters in Offline and Online tuning methods ?
Please realize the industrial PID controller in Simulink ?
For the fast flow control loop, show me your tuning principle and explain why.
For the AVERAGE level control loop, show me your tuning principle and explain why.
Explain the existing reason of reset windup and show me your prevention schemes
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Exercise 3.1
A controlled process is shown in the Problem 2-1 (p.34) in Automated Continuous Process Control.
(1) calculate its characteristics parameters K, T and τ;
(2) decide on the action of the valve and the controller;
(3) tune your PID controller.
![Page 45: Tuning PID Controller Institute of Industrial Control, Zhejiang University, Hangzhou, P. R. China 2013/03/27](https://reader036.vdocument.in/reader036/viewer/2022062318/5518a0dd550346881f8b4882/html5/thumbnails/45.jpg)
Exercise 3.2
/4da
0 5 10 15 20 25 30 35 40 45 5047
48
49
50
51
52
53U
min
假设 Relay( 继电器法 ) 镇定 PID 参数时,控制器输出如上图所示,信号周期为 Tu, 振幅为 d=2 。证明经傅立叶变换,控制输出的一次谐波幅度为 /4d