nonlinear gain compensation ( 对象非线性增益补偿)
DESCRIPTION
Nonlinear Gain Compensation ( 对象非线性增益补偿). Lei Xie Institute of Industrial Control, Zhejiang University, Hangzhou, P. R. China. Problem Discussion for Nonlinearity Gain Compensation. - PowerPoint PPT PresentationTRANSCRIPT
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Nonlinear Gain Compensation( 对象非线性增益补偿 )
Lei XieInstitute of Industrial Control,
Zhejiang University, Hangzhou, P. R. China
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Problem Discussion for Nonlinearity Gain Compensation
(1) which kind of nonlinearity are there in the control loop for a heat exchanger? Give your methods to compensate there nonlinearity.
Steam
Condensate
ProcessStream
T1
T2
RV
RF
T2sp
TC
u (2) analyze why the PH reactor is one of the most difficulty controlled process
& provide improved schemes.
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Heat Exchanger
Process Steady-state Model:
VVFp RHTTRc )( 12
FFp
V
Vp RRc
H
R
TK
12
Plant Gain:
Discussion: How to reduce the nonlinearity of process gain or make the compensated augmented plant become linear.
Steam
Condensate
ProcessStream
T1
T2
RV
RF
T2sp
TC
u
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Compensation Method: Nonlinear Valves
VFVp RRR
TK
112
VV V
fK f
u
TC GV (s) GP (s)
GM (s)
u
+_
++ T2
T2sp
RV
Linear valve (线性阀 )
Equal-percentage valve( 等百分比阀或对数阀 )
V VR f
Vf cu
VV
ff
u
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0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
u
F/F
max
Linear valve
Equal-percentage valve
Characteristics for FC Valves
Linear valve
Vf cu
1
[1 ( 1) ]Vf R uR
Suppose 0 1
1, 1; 30V Vu u
f f RR
Equal-percentage valve
1uVf R 2
VV
fc f
u
How about FO valves ?
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Compensation Method: Cascade Control
TCFC
Condensate
Steam
Process Stream
T2sp
T1
RV
T2
P1
RVsp
RF
FC
FFp
V
Vspp RRc
H
R
TK
12
Plant Gain:
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Compensation Method: Ratio Control
TC
FC×
u
T2T1
Condensate
Process Stream
Steam
T2sp
RVsp
RF
For controller TC, the augmented controlled plant is nearly linear (why?)
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Basic pH ControlAC
F2
F1
pHm
pHsp
Base
Acid
Neutralization Tank
Acid flow, % of Base
for a strong base-strong acid system
Existing problem ?
Base
Acid
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Closed-loop Response for Basic pH Control
Experimental process
(1) pHsp: 6.5↑7.0 at 60 min
(2) F1: 30↓15 L/min at 110 min
(3) pH1: 5↓4.5 at 160 min
(4) pH2: 11↓10.5 at 210 min
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pH Ratio Cascade Control
AC
F2
F1
pHm
pHsp
Base
Acid
u2
FC ×
NeutralizationTube
Advantages & Disadvantages ?
Base
Acid
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Closed-loop Response for pH Ratio Cascade Control
Experimental process
(1) pHsp: 6.5↑7.0 at 60 min
(2) F1: 30↓15 L/min at 110 min
(3) pH1: 5↓4.5 at 160 min
(4) pH2: 11↓10.5 at 210 min
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pH Control with Nonlinear Gain
F2
F1
pHm
pHsp
Base
Acid
F2sp
FC
NeutralizationTube
pHC
PID GFC (s) GP (s)
GM (s)pHm
+_
++pHsp pHF2
spF2
Nonlinear pH Controller
Problem: if the setpoint is not at pH=7.0, which will happen ?
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Closed-loop Response for Nonlinear pH Control
Experimental process
(1) pHsp: 6.5↑7.0 at 60 min
(2) F1: 30↓15 L/min at 110 min
(3) pH1: 5↓4.5 at 160 min
(4) pH2: 11↓10.5 at 210 min
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pH Control with Nonlinear Transformation
D
xsp
xm
PID GFC (s)
GM (s)pHm
+_
pHsppHF2
sp F2 pHNeutralization
Tubef(z)
f(z)
777 1010)(10 pHpHpHfHOHx
Note: x is nearly proportional to acid flow, F2, which results in a linear augmented plant. Besides, x is corresponding to pH. If pH=7, then x = 0; if pH>7, x > 0; and if pH<7, x < 0.
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Closed-loop Response for pH Control
with Nonlinear Transformation
Experimental process
(1) pHsp: 6.5↑7.0 at 60 min
(2) F1: 30↓15 L/min at 110 min
(3) pH1: 5↓4.5 at 160 min
(4) pH2: 11↓10.5 at 210 min
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Methods for Compensating Process Nonlinearity
Nonlinear Valves Cascade Control Variable Ratio Control Nonlinear Gain Compensation Nonlinear Transformation Identification + Adaptive
Control