Assessment and Future Directions of Nonlinear Model Predictive ...

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Receding-Horizon Estimation and Control of Ball Mill Circuits 4914 Numerical ResultsIn this section, the combined scheme (software sensor + NMPC) is evaluated insimulation, using a typical test run corresponding to a setpoint change. Point1 in Figure 2 (where y =[0.86 0.35] T ) is the initial operating condition, andpoint 2 (with y =[0.90 0.31] T ) represents the target (this point correspondsto a higher product fineness and near maximum product flow rate). The samplingperiod T s = 5 min and the prediction horizon is 80 min (Np = 16). Twomanipulated variable moves are used (Nu = 2) and the weighting matrix Q i ischosen as a constant identity matrix. Amplitude saturations are qCmaxand Reg max = 100. Limits for the rates of change are ∆qCmaxand ∆Reg max = 80. Limits on the mill flow rate are q min=60 tonhour= 15 tonhourtonM = 60hourandqMmax ton=90hour. The observer parameters are defined in Section 3.2.It is first assumed that the process model is accurate and that the measurementsare noise free. Figure 4 shows the controlled and the manipulated variables (solidlines). The performance is satisfactory, the controlled variables reach the setpointafter about 20 min and the steady state is obtained after 70 min. Moreover, constraintsare active in the first 5 min (first sample), as the maximum register displacementand the maximum rate of change of the input flow rate are required.The performance of the control scheme is then tested when measurementsare subject to a noise with a maximum absolute error of 0.02 tonm(around a 5%maximum relative error). The software sensor can efficiently take these stochasticdisturbances into account, and the performance of the control scheme remainsquite satisfactory.Finally, the influence of parametric uncertainties (plant-model mismatch dueto errors at the identification stage) is investigated. A parametric sensitivityanalysis is performed, and Figure 5 shows step responses corresponding to eitheran accurate model or to a −10% error in the fragmentation rate or the transportvelocity. Clearly, fragmentation parameters (which represents material hardness0.920.315w P;30.910.90.890.880.870.86w M;20.310.850 20 40 60 80 1000.3050 20 40 60 80 100100408035Reg (%)60q C(t/h)304025200 20 40 60 80 100time (min)200 20 40 60 80 100time (min)Fig. 4. NMPC and state observer; solid: noise-free measurements, dashed: measurementscorrupted by white noise
492 R. Lepore et al.0.950.9w P;30.850.80.750.70 10 20 30 40 50 60 70 80 90 1000.550.5w M;20.450.40.350.30 10 20 30 40 50 60 70 80 90 100time (min)Fig. 5. Parametric sensitivity - Time evolution of the controlled variables; solid: nominalcase, dashed: mismatch in the fragmentation rate, dotted: mismatch in the transportvelocity0.920.370.910.360.90.35w P;30.890.88w M;20.340.330.870.320.860.310.850 20 40 60 80 1000.30 20 40 60 80 100100458040Reg (%)60q C(t/h)35304025200 20 40 60 80 100time (min)200 20 40 60 80 100time (min)Fig. 6. Plant-model mismatch: solid: without compensation, dotted: with a DMC-likecompensationor grindability) have a larger impact on the model prediction than the materialtransportation parameters.The performance of the control scheme is evaluated when a prediction modelwith erroneous fragmentation rates is used (which is the worst case of plant-modelmismatch). Figure 6 shows results corresponding to −5% errors in the fragmentationrates. Clearly, performance deteriorates and a significant steady-state errorappears. To alleviate this problem, a DMC-like compensation is proposed, whichconsiders the plant-model mismatch as a constant output disturbance ˆd k+i = ˆd kover the prediction horizon. An estimate of the disturbance ˆd k is obtained fromthe process output y k and the observer output, noted ȳ k , as follows:ˆd k = y k − ȳ k (6)
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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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Controlling Distributed Hyperbolic
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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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