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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 Presentation
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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
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.
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
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
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 ?
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:
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?)
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
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
pH Ratio Cascade Control
AC
F2
F1
pHm
pHsp
Base
Acid
u2
FC ×
NeutralizationTube
Advantages & Disadvantages ?
Base
Acid
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
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 ?
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
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.
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
Methods for Compensating Process Nonlinearity
Nonlinear Valves Cascade Control Variable Ratio Control Nonlinear Gain Compensation Nonlinear Transformation Identification + Adaptive
Control