Assessment and Future Directions of Nonlinear Model Predictive ...

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Nonlinear Predictive Control of Irregularly Sampled Data Systems 147Inlet flow(Lt/min)21.510.50.60.55Inlet Temp. (K)500450400Concentration Cb0.50.45Caio(mol/Lt)1.110.90.8sampling instant50 100 150 200 250 300 350 400 450 500sampling instant(a) Manipulated inputs and unmeasureddisturbance0.4Validation dataNOE+NARMA predictions0.350 100 200 300 400 500 600 700 800 900Minor sampling instant(b) NOE+NARMA predictions0.550.60.55C b(mol/l)0.50.45Predicted case−IPrdicted case−IIValidation dataConcentration Cb0.50.450.40.55−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 0.5Deviation in Inlet flow(l/min)0.4Validation dataNOE predictionsC b(mol/l)0.50.450.40.350.350 100 200 300 400 500 600 700 800 900Minor sampling instant(c) NOE predictions0.3−60 −40 −20 0 20 40 60Deviation in Inlet Temp.(K)(d) Steady state plotsFig. 2. Model Validation ResultsTable 1. Model validation statisticsPrediction PPE PEENOE+NARMA 18.5160 12.0682NOE 32.7957 28.7206models with the validation data is presented in Figure(2(b)) and Figure(2(c)),respectively. The results of model validation are also summarized in Table(1). Ifwe compare the PEE values for NOE+NARMA model with that of NOE modeland model predictions presented in Figures (2(b)) and (2(c)), it is clear thatthe NARMA component significantly contributes towards improving the intersamplepredictions. Figure (2(c)) demonstrates that the NOE component of themodel has very good long range prediction capability. Figure (2(d)) representscomparison of the steady state behavior of the plant with identified models forreactor concentration with respect to manipulated variables. As can be observedform this figure, the NOE +NAR models capture the steady state behavior ofthe system over a wide operating range around extremum operating point. Inparticular, the predictions capture the change in the sign of steady state gainreasonably well.
148 M. Srinivasarao, S.C. Patwardhan, and R.D. GudiC b(mol/l)0.560.540.520.50.48ProcessSetpointMeasurements40 60 80 100 120 140Cai (mol/l)1.31.21.110.9Step40 60 80 100 120 140Sampling instantFig. 3. Regulatory responses of multi-rate NMPCC b(mol/Lt)0.50.450.4ProcessSetpointMeasured50 100 150 200 2500.17Level(m)0.160.150.1450 100 150 200 250Sampling instantFig. 4. Servo responses of multi-rate NMPCThe identified NOE+NARMA was further used to formulate an multi-rateNMPC scheme. The NMPC controls reactor level (h) and reactor concentration(C b ) by manipulating inlet flow rate (F i ) and inlet feed temperature (T i ). Ourmain focus here was to asses the regulatory and servo performances of the proposedNMPC scheme. The operating point was chosen as the peak point, whichis a singular point where steady state gain reduces to zero and changes it signacross the peak point. The simulations studies are carried out with predictionhorizon of p = 40,control horizon of q =1,W u = I and W e = diag [ 1 100 ] .Toassess the regulatory performance, we introduce a step jump in the input concentrationat 50 th sampling instant of magnitude 0.15. From Figure 3, it can beobserved that the controller quickly rejects the step jump in (C ai ) and maintainthe concentration at the desired setpoint. The servo performance of the 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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Page 123 and 124: ReferencesModel Predictive Control
Page 125 and 126: 116 F.A.C.C. Fontes, L. Magni, and
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Page 169 and 170: Numerical Methods for Efficient and
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Page 187 and 188: 182 A. Grancharova, T.A. Johansen,
Page 199 and 200: 194 V. Sakizlis et al.presented her
Page 201 and 202: 196 V. Sakizlis et al.linear PWA fu
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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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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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