Assessment and Future Directions of Nonlinear Model Predictive ...

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Nonlinear Predictive Control of Irregularly Sampled Data Systems 145for k l ≤ k
146 M. Srinivasarao, S.C. Patwardhan, and R.D. Gudican be used to achieve satisfactory servo and regulatory control at the optimumoperating point of the system. The performance of the identified models isevaluated using the following statistical criterion a)Percentage Prediction Error( PPE) and b)Percentage Estimation Error (PEE) (Srinivasarao et al. ([6])). ThePPE values are computed with using multi-rate measurements while the PEEvalues are computed using noise free fast rate outputs of the process (at minorsampling instants) obtained from simulations. The PEE values are indicative ofinter-sample prediction ability of the models while the PPE quantify long rangeprediction capability of the models.The system under consideration consists of a CSTR in which a reversibleexothermic reaction A ⇋ B is carried out. The model equations and the nominalparameters used in the simulation can be found in Li and Biegler ([5]). Thissystem exhibits input multiplicity and change in the sign of steady state gain inthe operating region. The controlled variables are reactor level (L) andreactorconcentration (C b ) while inlet flow rate (F ) and feed inlet temperature (T i )areused as manipulated variables. In the present work, reactor level was assumed tobe regularly sampled measurement at the base sampling interval (T =0.1 min.)where as the output concentration (C b ) in the CSTR was assumed to be sampledat irregular sampling intervals varying between 5 to 15 times that of basesampling interval. Also, the manipulated input moves were computed at the fastrate after every 0.1 min. interval. The inlet feed stream contains only A and itsconcentration C ai was assumed to fluctuate according to a stochastic process.The concentration fluctuations were generated by subjecting a discrete unitygain first order filter (with pole at 0.95) to a zero mean white noise sequence ofstandard deviation 0.02. Note that C ai (k) was assumed to be a piecewise constantfunction during simulations. In addition, it was assumed that manipulatedinputs are subject to unknown fluctuations. These fluctuations in the inlet flowrate and the feed inlet temperature were generated by subjecting discrete unitygain filters (with poles at 0.85) to zero mean white noise sequences with covariance2.5X10 −3 and 10.24, respectively. It was further assumed that concentrationand temperature measurements are corrupted with measurement noise, which isa zero mean Gaussian white noise signal with standard deviations equal to 0.007and 0.4, respectively. Multi-level Pseudo Random Signals (MPRS), with standarddeviations of 0.275 m 3 /s and 19.766 K and switching times of 0.3 and 0.5min, were generated by modifying the PRBS generated using ”idinput” functionin system identification tool box of MATLAB. These MPRS signals were usedto introduce simultaneous perturbations in the inlet flow rate (F in ) and inlettemperature ( T i ), respectively. The inputs used to generate the validation dataset and the unmeasured disturbance introduced in input concentration are givenin figure (2(a)).Model identification was carried out using data generated for 800 minutes.The number of filters n ij is chosen as n ij = 2 with respect to all the inputarguments to the state dynamics in NOE as well as NAR components of themodel. The resulting state vector has 6 states in the combined NOE + NARMAmodel. The comparison of predictions generated by NOE+NARMA and NOE
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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 101 and 102: 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 157 and 158: Nonlinear Model Predictive Control:
Page 169 and 170: Numerical Methods for Efficient and
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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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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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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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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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