Assessment and Future Directions of Nonlinear Model Predictive ...

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On Disturbance Attenuation of Nonlinear Moving Horizon Control 291flow rate q to the reactor and the heat removal power j Q from the cooling jacketare considered as control inputs, that are assumed to be saturated as3 1 h ≤ q ≤ 35 1 h , −9000kJ h ≤ j Q ≤ 0 kJh . (24)Since the main product of the CSTR is the substance B, we choose z e =(Hx e Eu e ) T with H = diag(0.1, 1, 0.5, 0.1) and E = diag(0.35, 0.35) as performanceoutput. The proposed moving horizon tracking scheme is implementedwith a sampling time of T = 20s, and the tuning parameters in (19) are chosenas r c = 11, q 1 =0.1 andq 2 =1.c A[mol/l]c B[mol/l]ϑ [ o C]2.82.62.42.20 0.2 0.4 0.6 0.8 1 1.21.11.0511141120 0.2 0.4 0.6 0.8 1 1.21100 0.2 0.4 0.6 0.8 1 1.2time[h]DisturbancesOnline γ0.20.10−0.10 0.2 0.4 0.6 0.8 1 1.2Tx Pk ekx ek/r c300200100210 0.2 0.4 0.6 0.8 1 1.200 0.2 0.4 0.6 0.8 1 1.2time[h]Fig. 1. Reference trajectory (left) and disturbances (right,top): normalized inflow concentration( ) and temperature (−·−); profiles of γ(t) and xe(t)T Px e(t)r c(right,middleand bottom)The left plot of Fig. 1 shows a reference trajectory generated by flatnesstechnique [RRZ96], that is consistent with the unperturbed CSTR model andfeasible for control constraints to drive the CSTR from the setpoint of ϑ =110 o C and c B =0.975 mollto the maximal yield point of ϑ = 114.07 o Candc B =1.09 moll. In the presence of disturbances shown in the top right of Fig. 1,the tracking errors are plotted in Fig. 2. As a comparison, we design two fixedH ∞ controllers by solving the following LMI optimization problemmin γ 2 subject to (18) and (19c) (25)γ 2 ,Q=Q T >0,Ywith r c = 11 (denoted as A) and r c = 40 (denoted as B), where the subscript kin (18) is replaced by i with i =1, 2 corresponding to the linearized models ofthe CSTR at the two setpoints. We stress that the control actions injected intothe CSTR will be clipped if the values exceed the bounds given in (24). Thishappens for the fixed controller A during the both disturbances (see the dashedlines in Fig. 3), and for the B during the second disturbance (see the dash-dottedlines in Fig. 3). A clear performance degeneration duo to clipping can be seen inFig. 2. For the suggested moving horizon tracking controller, we summarize the
292 H. Chen et al.c A[mol/l]10−10 0.2 0.4 0.6 0.8 1 1.2c B[mol/l]0−0.2ϑ[ o C]−0.40 0.2 0.4 0.6 0.8 1 1.210.50−0.50 0.2 0.4 0.6 0.8 1 1.2time[h]Fig. 2. Tracking errors for moving horizon controller with r c =11(controllers with r c =11(−−) andr c =40(−·−)) and fixed4030q[h −1 ]201000 0.2 0.4 0.6 0.8 1 1.22000j Q[kJ/h]0−2000−4000−60000 0.2 0.4 0.6 0.8 1 1.2time[h]Fig. 3. Control inputs for moving horizon controller with r c =11( ) and fixedcontrollers with r c =11(−−) andr c =40(−·−)following points: Control constraints are satisfied; it achieves better performanceby avoiding saturation and making the best of the allowable controls; it avoidsactuator saturation by relaxing the performance level and recovers a higher
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Lecture Notesin Control and Informa
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Series Advisory BoardF. Allgöwer,
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ContentsFoundations and History of
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ContentsIXRobustness, Robust Design
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ContentsXIHybrid NMPC Control of a
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Nonlinear Model Predictive Control:
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Hybrid MPC: Open-Minded but Not Eas
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Hybrid MPC: Open-Minded but Not Eas
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22 S.E. Tuna et al.this says that i
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24 S.E. Tuna et al.In particular, f
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26 S.E. Tuna et al.W N (f(x, ¯κ N
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28 S.E. Tuna et al.where ᾱ := max
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30 S.E. Tuna et al.21.521.5µ=51
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32 S.E. Tuna et al.obstacle and gra
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34 S.E. Tuna et al.[19] C. Prieur.
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36 É. Gyurkovics and A.M. Elaiw[8]
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38 É. Gyurkovics and A.M. ElaiwWe
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40 É. Gyurkovics and A.M. ElaiwWe
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Conditions for MPC Based Stabilizat
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A Computationally Efficient Schedul
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The Potential of Interpolation for
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The Potential of Interpolation 65De
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The Potential of Interpolation 67Al
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The Potential of Interpolation 693.
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The Potential of Interpolation 71Pr
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The Potential of Interpolation 73Th
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The Potential of Interpolation 75de
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Techniques for Uniting Lyapunov-Bas
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94 M. Lazar et al.Lipschitz continu
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96 M. Lazar et al.let X T ⊆ X den
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98 M. Lazar et al.S 0 {j ∈S|0
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100 M. Lazar et al.Fig. 1. State-sp
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102 M. Lazar et al.[11] Grimm, G.,
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Model Predictive Control for Nonlin
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ReferencesModel Predictive Control
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116 F.A.C.C. Fontes, L. Magni, and
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On the Computation of Robust Contro
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142 M. Srinivasarao, S.C. Patwardha
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Numerical Methods for Efficient and
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L i (s i ,u i ):=Numerical Methods
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182 A. Grancharova, T.A. Johansen,
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194 V. Sakizlis et al.presented her
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196 V. Sakizlis et al.linear PWA fu
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198 V. Sakizlis et al.non-linear sy
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200 V. Sakizlis et al.Remark 1. For
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202 V. Sakizlis et al.One should no
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204 V. Sakizlis et al.g0.050.10.15x
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Interior-Point Algorithms for Nonli
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n p,2 ≤Interior-Point Algorithms
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Hard Constraints for Prioritized Ob
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A Nonlinear Model Predictive Contro
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State Estimation Analysed as Invers
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State Estimation Analysed as Invers
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Minimum-Distance Receding-Horizon S
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New Extended Kalman Filter Algorith
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NLMPC: A Platform for Optimal Contr
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384 K. Naidoo et al.polymer control
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386 K. Naidoo et al.are two key qua
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388 K. Naidoo et al.1. It greatly s
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390 K. Naidoo et al.However, with t
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392 K. Naidoo et al.Fig. 4. Bounded
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394 K. Naidoo et al.1. Maintain pro
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396 K. Naidoo et al.7 Commissioning
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398 K. Naidoo et al.[3] N.M.C. Oliv
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400 R. Franke and J. DoppelhamerImp
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402 R. Franke and J. DoppelhamerFig
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404 R. Franke and J. DoppelhamerFig
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406 R. Franke and J. Doppelhamer[3]
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408 B.A. Foss and T.S. Scheicritica
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410 B.A. Foss and T.S. ScheiFig. 2.
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412 B.A. Foss and T.S. Scheidiscuss
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414 B.A. Foss and T.S. ScheiOther a
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416 B.A. Foss and T.S. ScheiIn the
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Integration of Economical Optimizat
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Controlling Distributed Hyperbolic
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444 K.R. Muske, A.E. Witmer, and R.
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Robust NMPC for a Benchmark Fed-Bat
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Real-Time Implementation of Nonline
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Non-linear Model Predictive Control
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NMPC of the Hashimoto Simulated Mov
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486 R. Lepore et al.In this study,
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488 R. Lepore et al.3 Control Strat
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490 R. Lepore et al.400.80.6|x−x
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492 R. Lepore et al.0.950.9w P;30.8
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Hybrid NMPC Control of a Sugar Hous
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Application of the NEPSAC Nonlinear
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Integrating Fault Diagnosis with No
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524 M. Alamirmin V (x u(·,x),T) un
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526 M. AlamirDefinition 4. The syst
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528 M. Alamir♭V is radially unbou
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530 M. AlamirBut according to the s
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532 M. AlamirFig. 2. Stabilization
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534 M. AlamirFig. 3. Closed loop be
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A New Real-Time Method for Nonlinea
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A Two-Time-Scale Control Scheme for
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566 X.-B. Hu and W.-H. Chen2 Online
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568 X.-B. Hu and W.-H. Chentime alo
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570 X.-B. Hu and W.-H. ChenFig. 3.
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572 X.-B. Hu and W.-H. ChenTable 4.
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574 M. Fujita et al. CameraCameraTa
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576 M. Fujita et al.J(u, t) =∫t+T
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578 M. Fujita et al.ξ 2[rad/s]6420
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580 M. Fujita et al.Acknowledgement
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582 A. Casavola, D. Famularo, and G
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4. c(t) ∈Cfor all t ∈ Z + ;5. T
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608 W.B. Dunbar and S. Desaand sequ
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610 W.B. Dunbar and S. Desademand r
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612 W.B. Dunbar and S. Desabacklog
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614 W.B. Dunbar and S. Desacasescas
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Robust Model Predictive Control for
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630 J.J. Arrieta-Camacho, L.T. Bieg
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Author IndexAlamir, Mazen 523Alamo,
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Lecture Notes in Control and Inform
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