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Control of a Solution Copolymerization Reactor using Piecewise Linear Models. Leyla Özkan APACT03 York, UK April 30 th , 2003. Presentation Outline. Motivation MultiModel Predictive Control Formulation Implementation on MMVA Solution Copolymerization Reactor Stability Analysis
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Leyla Özkan
APACT03 York, UK
April 30th , 2003
APACT0330 April, 2003
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Özkan, L. et.al. , Control of a solution copolymerization reactor using multimodel predictive control, Chem. E. Science, 58:12071221, 2003
The resulting LMI problemFeasible
ONLY IF
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(x(k) terminal region)
APACT0330 April, 2003
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Input ConstraintsAPACT0330 April, 2003
Monomer (FB)
Initiator (FI)
Coolant
Solvent (FS)
Coolant
Transfer Agent (FC)
Polymer
Solvent
Unreacted feed
Inhibitor (FZ)
Richards, J. R. et.al. , Feedforward and Feedback Control of a Solution Copolymerization Reactor, AIChE Journal, 35(6):891907, 1989
MMVA Solution Copolymerization ReactorChallenge: Optimization problem involves 200–300 variables
APACT0330 April, 2003
4
OP 2
3.8
Mw/E4 (kg/kmol)
3.6
OP 1
3.4
0
10
20
30
40
50
time (h)
Implementation on MMVA copolymerization reactorAPACT0330 April, 2003
x3
x
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x2
x1
t
Implementation on MMVA (cont’d)APACT0330 April, 2003
Y
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30
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0
10
10
20
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time (h)
time (h)
Implementation on MMVA (cont’d)2 models
4
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3 models
353.4
3.8
T (K)
353.3
4 models
Mw/E4 (kg/kmol)
353.2
3.6
353.1
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Off–spec. (kg)
0.64
27
26
0.62
Open loop 302.4
25
0.6
2 models 134.8
Gpi (kg/h)
0.58
24
3 models 110.1
23
0.56
4 models 109.8
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22
APACT0330 April, 2003
Asymptotically
stable origin
V(x)
Time
Stability AnalysisAPACT0330 April, 2003
components
Continuous
dynamical systems
Logic commands (switches,automata)
Hybrid systems
Hybrid systemsAPACT0330 April, 2003
Branicky, M.S., Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE Trans. Automatic Control, 43(4):475482, 1998.
Multiple Lyapunov FunctionsIf Viis monotonically nonincreasing on(T) then system is stable in the sense of Lyapunov
APACT0330 April, 2003
V1(x)
t0
t1
t2
t3
t4
t5
t6
V2(x)
Multiple Lyapunov FunctionsAPACT0330 April, 2003
Ifx(k) terminal region, the quasi–infinite horizon optimization problem is solvedincluding the contractive constraint. If x(k) terminal regionthe infinite horizon optimization problem is solved. The closed loop system is stable if the feasible solutions of the control strategy defined are implemented in a receding horizon fashion
MultiModel Predictive Control with Stability GuaranteeAPACT0330 April, 2003
terminal region
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MultiModel Predictive Control with Stability GuaranteeAPACT0330 April, 2003
10
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3
10
4
10
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t(h)
MMVA solution copolymerization revisitedAPACT0330 April, 2003
APACT0330 April, 2003