Implementation of min–max MPC using hinging hyperplanes. Application to a heat exchanger ☆

Abstract Min–max model predictive control (MMMPC) is one of the few control techniques able to cope with modelling errors or uncertainties in an explicit manner. The implementation of MMMPC suffers a large computational burden due to the numerical min–max problem that has to be solved at every sampling time. This fact severely limits the range of processes to which this control structure can be applied. An implementation scheme based on hinging hyperplanes that overcome these problems is presented here. Experimental results obtained when applying the controller to the heat exchanger of a pilot plant are given.

[1]  Manuel Berenguel,et al.  ROBUST ADAPTIVE MODEL PREDICTIVE CONTROL OF A SOLAR PLANT WITH BOUNDED UNCERTAINTIES , 1997 .

[2]  T. Alamo,et al.  Efficient implementation of constrained min-max model predictive control with bounded uncertainties , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[3]  P. Pucar,et al.  On the Hinge-Finding Algorithm for Hinging Hyperplanes , 1998, IEEE Trans. Inf. Theory.

[4]  David W. Clarke,et al.  Generalized predictive control - Part I. The basic algorithm , 1987, Autom..

[5]  Alberto Bemporad,et al.  The explicit linear quadratic regulator for constrained systems , 2003, Autom..

[6]  Eduardo F. Camacho,et al.  On the piecewise linear nature of min-max model predictive control with bounded uncertainties , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[7]  Zhenghong Yu,et al.  Worst-case formulations of model predictive control for systems with bounded parameters , 1997, Autom..

[8]  Manfred Morari,et al.  Robust Model Predictive Control , 1987, 1987 American Control Conference.

[9]  M. Morari,et al.  Robust model predictive control: Piecewise linear explicit solution , 2001, 2001 European Control Conference (ECC).

[10]  Don R. Hush,et al.  Efficient algorithms for function approximation with piecewise linear sigmoidal networks , 1998, IEEE Trans. Neural Networks.

[11]  Leo Breiman,et al.  Hinging hyperplanes for regression, classification, and function approximation , 1993, IEEE Trans. Inf. Theory.

[12]  Wook Hyun Kwon,et al.  An application of min–max generalized predictive control to sintering processes , 1997 .

[13]  Alberto Bemporad,et al.  Min-max control of constrained uncertain discrete-time linear systems , 2003, IEEE Trans. Autom. Control..

[14]  Jay H. Lee,et al.  Dynamically scheduled MPC of nonlinear processes using hinging hyperplane models , 1998 .

[15]  Sandor M. Veres,et al.  Predictive self-tuning control by parameter bounding and worst-case design , 1993, Autom..

[16]  Eduardo Sontag Nonlinear regulation: The piecewise linear approach , 1981 .