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Dead-Time Compensation ( 纯滞后补偿 )
Lei Xie
Institute of Industrial Control, Zhejiang University, Hangzhou, P. R.
China
Contents Introduction Smith Predictor for Dead-Time
Compensation Improved Smith Predictor Simulation Examples Summary
Problem Discussion(1) For the controlled processes, configure your Simulink model & compare their results.
(2) Can you provide some compensation approaches for processes with variable & notable dead-time ?
Process Models:
;14
0.2)( 2s
p es
sG −
+= .
14
0.2)( 8s
p es
sG −
+=
Conventional PID Control Systems
Process Models:
;14
0.2)( 2s
p es
sG −
+= .
14
0.2)( 8s
p es
sG −
+=
Question： Use Ziegler-Nichols or Lambda tuning method to obtain PID parameters and compare their values.
Please see the SimuLink model …SISODelayPlant / PIDLoop.mdl
0 20 40 60 80 100 120 140 160 180 20058
60
62
64
66
68
70
72
74
76
78Output of Transmitter
Time, min
%
setpointZiegler-Nichols TuningLambda Tuning
Simulation Example #1
For PID Controller,
Z-N tuning: Kc = 1.2, Ti = 4 min, Td = 1 min
Lambda tuning:
Kc = 0.83, Ti = 4 min , Td = 1 min
;14
0.2)( 2s
p es
sG −
+=
0 20 40 60 80 100 120 140 160 180 20058
60
62
64
66
68
70
72
74
76
78
80
Time, min
%
Output of Transmitter
set pointZ-N tuningLambda tuning, Td = 1 minLambda tuning, Td = 4 min
Simulation Example #2
For PID Controller,
Z-N tuning: Kc = 0.3, Ti = 16 min, Td = 4 min
Lambda tuning:
Kc = 0.2, Ti = 4 min , Td = 1 min
82.0( ) ;
4 1s
pG s es
−=+
Smith’s Idea (1957)
Kpgp (s)+ _
+
Gc(s) +
D (s)
R (s) Y (s)se τ−
Process
Kpgp (s)+ _
+
Gc(s) +
D (s)
R (s) Y (s)se τ−
Process
Basic Smith Predictor
Kpgp (s)+ _
+
Gc(s)+
D (s)
R (s) Y (s)se τ−
ProcessU(s)
Km gm (s) sme τ−
+
_
Smith Predictor
Y 2(s)Y 1(s) +
+
Smith Predictor #2
+ _
+
Gc(s)+
D (s)
R (s) Y (s)
+_
U (s)s
pppesgK τ−)(
)(sgK mm
+
+
smm
mesgK τ−)(
Please see the SimuLink model …SISODelayPlant / PID_Smith.mdl
0 20 40 60 80 100 120 140 160 180 20058
60
62
64
66
68
70
72
74
76
78
80
Time, min
%
Output of Transmitter
set pointPID with Smith compensatorSimple PID
Results of Basic Smith Predictor with an Accurate Model
Simple PID:
Kc = 0.2, Ti = 4 min , Td = 1 min
PID + Smith:Kc = 2, Ti = 4 min , Td = 1 min
8
( ) ( )
2.0;
4 1
m p
s
G s G s
es
−
=
=+
0 20 40 60 80 100 120 140 160 180 20055
60
65
70
75
80
85
Time, min
%
Output of Transmitter
set pointPID + SmithSimple PID
Results of Basic Smith Predictor with an Inaccurate Model
Simple PID:
Kc = 0.2, Ti = 4 min , Td = 1 min
PID + Smith:Kc = 2, Ti = 4 min , Td = 1 min
8
6
2.0( ) ;
4 12.0
( )4 1
sm
sp
G s es
G s es
−
−
=+
=+
Improved Smith Predictor
+ _
+
Gc(s)+
D (s)
R (s) Y (s)
+_
U (s) spp
pesgK τ−)(
)(sgK mm
+
+
smm
mesgK τ−)(
Gf(s)
1
1)(
+=
sTsG
ffPrediction Error Filter：
0 20 40 60 80 100 120 140 160 180 20058
60
62
64
66
68
70
72
74
76
78
80
Time, min
%
Output of Transmitter
set pointPID + Smith with Gm =GpPID + Smith with Gm <> GpSimple PID
Results of Improved Smith Predictor with an Inaccurate Model
PID + Smith:Kc = 2, Ti = 4 min , Td = 1 min
8
6
2.0( ) ;
4 12.0
( ) ;4 1
1( )
4 1
sm
sp
f
G s es
G s es
G ss
−
−
=+
=+
=+
Summary The principle of Smith predictor for dead-
time compensation Improved Smith predictor for a controlled
process with an inaccurate model Comparison of the Simple PID and the PID
with a Smith predictor
Next Topic: Coupling of Multivariable Systems and Decoupling
Concept of Relative Gains Calculation of Relative Gain Matrix Rule of CVs and MVs Pairing Linear Decoupler from Block Diagrams Nonlinear Decoupler from Basic Principles Application Examples
Problem Discussion for Next Topic
For the two-input-two-input controlled system, design your control schemes.
Suppose that
;,21
221121 FF
FCFCCFFF
++=+=
;12
,14
1,
1
5.0 5
+=
+=
+=
−
s
e
C
A
sC
C
sF
F smm
%.40%,60,25,75 210
20
1 ==== CCFF
Initial states:
