Assessment and Future Directions of Nonlinear Model Predictive ...

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482 A. Küpper and S. Engellτ [min]Q De[ml/min]Q Re[ml/min]Q Ra[ml/min]Pur Ex[%]Prod. [−]15105manipulated variable00 50 100 150 200 250 3001510500 50 100 150 200 250 30010500 50 100 150 200 250 30010500 50 100 150 200 250 30010.500 50 100 150 200 250 30010095constraintconstraint requirement900 50 100 150 200 250 300Period NumberFig. 4. Simulation of the predictive controller; manipulated variables and constraintsprocess converges to a stationary operating point. The optimizer converges tothe optimum within one sampling time, and hence, can be applied in real-time.5 ConclusionAn online model-based optimization and parameter estimation scheme for theHashimoto Simulated Moving Bed process has been presented. The approachhas the advantage that the process is automatically operated at its economicoptimum while the purity and productivity requirements and plant limitationsare fulfilled. In future research, the application to a pilot-plant is planned.AcknowledgementWe would like to thank Larry Biegler for a fruitful discussion about how to avoidzero gradient information for a SQP solver. This investigation was supported bythe Deutsche Forschungsgemeinschaft (DFG) under grant DFG En 152/34. Thissupport is gratefully acknowledged.References[1] Hashimoto, K., Adachi, S., Noujima, H. and Ueda, Y., “A New Process CombiningAdsorption and Enzyme Reaction for Producing Higher-Fructose Syrup”,Biotechnology and Bioengineering, Vol. 25, pp. 2371-2393, (1983).
NMPC of the Hashimoto Simulated Moving Bed Process 483[2] Hashimoto, K., Adachi, S. and Shirai, Y., “Development of a new bioreactors of asimulated moving-bed type”, in Ganetsos G. & Barker P. (eds.), Preparative andProduction Scale Chromatography, Marcel Dekker, New-York, pp. 395-417, (1993).[3] Engell, S. and Toumi, A., “Optimization and Control of Chromatography”, Computersand Chemical Engineering, Vol. 29, pp. 1243-1252, (2005).[4] Toumi, A., Diehl, M., Engell, S., Bock, H. G. and Schlöder, J., “Finite horizonoptimizing of control advanced SMB chromatographic processes”, IFAC WorldCongress, Fr-M06-TO/2, (2005).[5] Erdem, G., Abel, S., Morari, M. and Mazzotti, M., “Automatic control of simulatedbeds”, Ind. and Eng. Chem. Res., Vol. 43, No. 2, pp. 405-421, (2004).[6] Erdem, G., Abel, S., Morari, M. and Mazzotti, M., “Automatic Control of simulatedmoving beds-II: Nonlinear Iso-therms”, Ind. and Eng. Chem. Res., Vol. 43,No. 14, pp. 3895-3907, (2004).[7] Toumi, A. and Engell, S., “Optimal operation and control of a reactive simulatedmoving bed process”, in Allgöwer, F. & Gao, F. (eds.), 7 th IFAC InternationalSymposium on Advanced Control of Chemical Processes, Hongkong, pp. 243-248,(2004).[8] Toumi, A. and Engell, S., “Optimization-based control of a reactive simulatedmoving bed process for glucose isomerization”, Chemical Engineering Science,Vol. 59, pp. 3777-3792, (2004).[9] Gu, T., “Mathematical Modelling and Scale Up of Liquid Chromatography”,Springer Verlag, New York, (1995).[10] Küpper, A. and Engell, S., “Parameter and State Estimation in ChromatographicSMB Processes with Individual Columns and Nonlinear Adsorption Isotherms”,to be presented at IFAC ADCHEM, (2006).[11] Borren, T., Fricke, J. and Schmidt-Traub, H., “Reactive liquid chromatography”,in Schmidt-Traub, H. & Górak, A. (eds.), Process Intensification by IntegratedReaction and Separation Operation, in preparation, Springer Verlag, Berlin (2006).[12] Chung, S. and Wen, C., “Longitudinal diffusion of liquid flowing through fixedand fluidized beds”, AIChE Journal, Vol. 14, pp. 875-866, (1968).
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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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Robustness and Robust Design of MPC
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MPC for Stochastic SystemsMark Cann
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y i (k) =∑n um=1MPC for Stochasti
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MPC for Stochastic Systems 259we ha
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MPC for Stochastic Systems 261form
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MPC for Stochastic Systems 263( )κ
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MPC for Stochastic Systems 265Fig.
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MPC for Stochastic Systems 267⎡
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NMPC for Complex Stochastic Systems
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284 H. Chen et al.of the moving hor
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286 H. Chen et al.Hence, at each sa
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288 H. Chen et al.control inputs in
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290 H. Chen et al.Corollary 1. The
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292 H. Chen et al.c A[mol/l]10−10
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294 H. Chen et al.[CSA97] H.Chen,C.
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296 L. Xie, P. Li, and G. Woznyand
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298 L. Xie, P. Li, and G. WoznyDeta
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300 L. Xie, P. Li, and G. Wozny3.2
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302 L. Xie, P. Li, and G. WoznyFig.
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304 L. Xie, P. Li, and G. Wozny[3]
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306 H. Arellano-Garcia et al.applic
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308 H. Arellano-Garcia et al.Fig. 1
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310 H. Arellano-Garcia et al.RECIPE
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312 H. Arellano-Garcia et al.optimi
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314 H. Arellano-Garcia et al.The re
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Interval Arithmetic in Robust Nonli
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Optimal Online Control of Dynamical
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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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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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