Assessment and Future Directions of Nonlinear Model Predictive ...

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Putting Nonlinear Model Predictive Controlinto UseBjarne A. Foss 1 and Tor S. Schei 21 Department of Engineering Cybernetics, Norwegian University of Science andTechnology, Trondheim, NorwayBjarne.Foss@itk.ntnu.no2 Cybernetica AS, NorwayTor.S.Schei@cybernetica.noSummary. We will in this paper highlight our experience with NMPC. In our contextNMPC shall mean the use of a nonlinear mechanistic model, state estimation, and thesolution of an online constrained nonlinear optimisation problem. Our reference baseis a number of applications of NMPC in a variety of processes.We discuss the use of mechanistic models in NMPC applications and in particularthe merits and drawbacks of applying such models in online applications. Further, wefocus on state estimation, and the use of Kalman filters and moving horizon estimation.Finally, we consider the design of the optimization problem itself and implementationissues.1 IntroductionNonlinear model predictive control (NMPC) opens for the use of MPC in moredemanding applications than has normally been the case for linear MPC. In particularNMPC lends itself to nonlinear systems which exhibit large variations inoperating conditions and which are critically dependent on the use of a dynamicnonlinear model to gain sufficient performance. A nice overview of NMPC canbe found in [9].NMPC is not a well defined term in the sense that NMPC may be used forcontrollers ranging from a slight variation of linear MPC to the online solutionof a constrained nonlinear optimisation problem. One example of a slight modificationto account for nonlinearities is the use of multiple linear models in sucha way that the current working point defines which model should be active ata given time instant. Hence, the QP-problem frequently encountered in linearMPC will change as the active model changes. In our context NMPC shall meanthe use of a nonlinear mechanistic model, state estimation, and the solution ofan online constrained nonlinear optimisation problem.The scope of this paper is to pinpoint critical issues when applying NMPC bydrawing on our experience within the process industries since 2000. To ensure asound level of credibility we first present our most important application areasand accompanying control challenges in some detail. Thereafter we address fourR. Findeisen et al. (Eds.): Assessment and Future Directions, LNCIS 358, pp. 407–417, 2007.springerlink.com c○ Springer-Verlag Berlin Heidelberg 2007
408 B.A. Foss and T.S. Scheicritical areas: modelling, state estimation, formulation of the control problemitself and implementation issues. The paper ends with some conclusions.2 Reference BaseThe reference base contains a number of industrial applications of NMPC in avariety of processes. Some examples are:• A system for optimization of suspension PVC polymerization processes hasbeen implemented on two large (140 m3) autoclaves located at Hydro Polymers’plant in Porsgrunn, Norway. The system is characterized as follows: Itcontains a rather detailed nonlinear model of the polymerization reactor. Thereactor model includes reaction kinetics, thermodynamic calculations for thefour-phase suspension process, quality parameters and energy balances forthe suspension and cooling systems. The application optimizes the temperaturereference trajectory and the amount of initiators charged to the reactorin order to initiate the polymerization process. The optimization is based onan economic criterion which includes the batch time as well as cost of initiators.The process is highly exothermic, and the purpose of the optimizationis to minimize the batch time without exceeding available cooling capacityand without using an inhibitor to slow down the polymerization process.The optimization is performed once for each batch cycle, and the temperatureprofile, which consists of approximately 80 ”straight line segments”, isoptimised for the entire batch under a number of constraints imposed by thequality specifications of the various PVC products. Based on logged data afew model parameters are estimated as functions of conversion. The systemis implemented using Cybernetica’s NMPC and batch optimisation platform.• Three NMPC applications for stabilization and quality control of the Borealispolypropolyne plant in Schwechat, Austria have been developed and implementedin cooperation with Borealis’ personnel. The implementations arebased on nonlinear first-principles models of the polyolefine plant (includingthree different polymerization reactors), and on Borealis in-house system formodel predictive control (BorAPC). The system is characterized as follows:The three MPC applications comprise a multivariable control system with alltogether 11 control inputs and 19 controlled outputs. The nonlinear modelconsists of 77 states which are estimated on-line together with a few modelparameters.• NMPC of a base-catalyzed phenol-formaldehyde batch polymerization processhas been implemented. The system is based on a rigorous model ofthe polymerization reactor. The system is implemented at Dynea’s plant inSpringfield, Oregon, USA. The model for this condensation polymerizationprocess includes reaction kinetics, thermodynamics, population balances forfunctional groups and energy balance for the reactor and cooling system.Safety is an important issue and one driving force for implementing NMPC.
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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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Robust NMPC for a Benchmark Fed-Bat
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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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Distributed Model Predictive Contro
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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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