A multivariable multiobjective predictive controller

Predictive control of MIMO processes is a challenging problem which requires the specification of a large number of tuning parameters (the prediction horizon, the control horizon and the cost weighting factor). In this context, the present paper compares two strategies to design a supervisor of the Multivariable Generalized Predictive Controller (MGPC), based on multiobjective optimization. Thus, the purpose of this work is the automatic adjustment of the MGPC synthesis by simultaneously minimizing a set of closed loop performances (the overshoot and the settling time for each output of the MIMO system). First, we adopt the Weighted Sum Method (WSM), which is an aggregative method combined with a Genetic Algorithm (GA) used to minimize a single criterion generated by the WSM. Second, we use the Non- Dominated Sorting Genetic Algorithm II (NSGA-II) as a Pareto method and we compare the results of both the methods. The performance of the two strategies in the adjustment of multivariable predictive control is illustrated by a simulation example. The simulation results confirm that a multiobjective, Pareto-based GA search yields a better performance than a single objective GA.

[1]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[2]  Christophe Aubrun,et al.  Performance evaluation based fault tolerant control with actuator saturation avoidance , 2011, Int. J. Appl. Math. Comput. Sci..

[3]  Adrian Gambier,et al.  Multi-objective Optimal Control: An Overview , 2007, 2007 IEEE International Conference on Control Applications.

[4]  Michel Kinnaert,et al.  Adaptive generalized predictive controller for MIMO systems , 1989 .

[5]  David W. Clarke,et al.  Generalized Predictive Control - Part II Extensions and interpretations , 1987, Autom..

[6]  Alberto Bemporad,et al.  Multiobjective model predictive control , 2009, Autom..

[7]  Ali Elkamel,et al.  Selection of control structure for distributed model predictive control in the presence of model errors , 2010 .

[8]  A. Farag,et al.  Tuning of a PID controller Using a Multi-objective Optimization Technique Applied to A Neutralization Plant , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[9]  Gary B. Lamont,et al.  Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art , 2000, Evolutionary Computation.

[10]  Michel Kinnaert Generalized predictive control of multivariable linear systems , 1987, 26th IEEE Conference on Decision and Control.

[11]  Zhenyu Yang,et al.  Automatic tuning of PID controller for a 1-D levitation system using a genetic algorithm - a real case study , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.

[12]  E. Camacho,et al.  Generalized Predictive Control , 2007 .

[13]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[14]  Piotr Tatjewski,et al.  Supervisory predictive control and on-line set-point optimization , 2010, Int. J. Appl. Math. Comput. Sci..

[15]  Zengqiang Chen,et al.  Multivariable Decoupling Predictive Control Based on QFT Theory and Application in CSTR Chemical Process , 2006 .

[16]  陈增强,et al.  Multivariable Decoupling Predictive Control Based on QFT Theory and Application in CSTR Chemical Process , 2006 .

[17]  Andrzej Królikowski,et al.  Self-Tuning Generalized Predictive Control With Input Constraints , 2001 .

[18]  Kalyanmoy Deb,et al.  MULTI-OBJECTIVE FUNCTION OPTIMIZATION USING NON-DOMINATED SORTING GENETIC ALGORITHMS , 1994 .

[19]  Lise Getoor,et al.  Learning in Logic , 2010, Encyclopedia of Machine Learning.

[20]  Sirous Shafiei,et al.  Optimal control of distillation column using Non-Dominated Sorting Genetic Algorithm-II , 2011 .

[21]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[22]  Kalyanmoy Deb,et al.  Simulated Binary Crossover for Continuous Search Space , 1995, Complex Syst..

[23]  S. Joe Qin,et al.  A survey of industrial model predictive control technology , 2003 .

[24]  A. Gambier,et al.  MPC and PID control based on Multi-Objective Optimization , 2008, 2008 American Control Conference.

[25]  Mayuresh V. Kothare,et al.  Simultaneous linear and anti-windup controller synthesis using multiobjective convex optimization , 2009, Autom..

[26]  A. Berro,et al.  Optimisation multiobjectif et stratégies d' évolution en environnement dynamique , 2001 .

[27]  Mekki Ksouri,et al.  Application of Fuzzy Logic to the On-Line Adjustment of the Parameters of a Generalized Predictive Controller , 1998, Intell. Autom. Soft Comput..

[28]  Eduardo F. Camacho,et al.  Model predictive control in the process industry , 1995 .