Multivariable MPC design based on a frequency response approximation approach

This paper presents an improvement to the MPC tuning approach presented in [1]. The drawbacks of the former approach are discussed and a new tuning approach is proposed to overcome them. The primary aim is to treat linear MPC as a classical controller design problem and to use the tools of linear control theory for determining the tuning parameters. MPC tuning is performed for a desired open-loop frequency response which results from an achievable closed-loop performance determined using the Youla parameterization technique. The tuning approach is performed in two steps and both resulting minimization problems are convex optimization problems. The approach is tested on a challenging example.

[1]  J. Maciejowski,et al.  Tuning MPC using H ∞ loop shaping , 2000 .

[2]  Sebastian Engell,et al.  Comparison of Multivariable and Decentralized Control of a CSTR by Convex Optimization , 1996 .

[3]  Richard H. Middleton,et al.  Modification of Model Predictive Control to Reduce Cross-Coupling , 2008 .

[4]  Fernando Tadeo,et al.  Multiobjective optimization for automatic tuning of robust Model Based Predictive Controllers , 2008 .

[5]  Sebastian Engell,et al.  Optimization-based design of reactive distillation columns using a memetic algorithm , 2011, Comput. Chem. Eng..

[6]  M. Soroush,et al.  Model predictive controller tuning via eigenvalue placement , 2008, 2008 American Control Conference.

[7]  Basil Kouvaritakis,et al.  Multivariable Nyquist self-tuning: a general approach , 1989 .

[8]  James B. Rawlings,et al.  Constrained linear quadratic regulation , 1998, IEEE Trans. Autom. Control..

[9]  Riccardo Scattolini,et al.  Constrained receding-horizon predictive control , 1991 .

[10]  M. Volker,et al.  Multiobjective controllability assessment by finite dimensional approximation , 2005, Proceedings of the 2005, American Control Conference, 2005..

[11]  E. Zafiriou,et al.  Frequency domain design of robustly stable constrained model predictive controllers , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[12]  X. Qin,et al.  Decoupling design of multivariable generalised predictive control , 1994 .

[13]  Stephen P. Boyd,et al.  Linear controller design: limits of performance , 1991 .

[14]  D. Cooper,et al.  A Tuning Strategy for Unconstrained SISO Model Predictive Control , 1997 .

[15]  Hsiao-Ping Huang,et al.  Multivariable Control with Generalized Decoupling for Disturbance Rejection , 2009 .

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

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

[18]  S. L. Shah,et al.  Frequency response characteristics of MIMO GPC , 1992 .

[19]  Xi Yu.  New Approach to Designing Constrained Predictive Controllers , 2005 .

[20]  Jing Ou,et al.  CV damping versus MV suppression for MPC tuning , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[21]  Jorge Otávio Trierweiler,et al.  RPN tuning strategy for model predictive control , 2003 .

[22]  Sebastian Engell,et al.  Tuning MPC for desired closed-loop performance for MIMO systems , 2011, Proceedings of the 2011 American Control Conference.

[23]  Sirish L. Shah,et al.  Analysis and tuning of adaptive generalized predictive control , 1991 .

[24]  Guy A. Dumont,et al.  Two-dimensional frequency response analysis and insights for weight selection in cross-directional model predictive control , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

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

[26]  S. Engell,et al.  Tuning MPC for desired closed-loop performance for SISO systems , 2010, 18th Mediterranean Conference on Control and Automation, MED'10.

[27]  Yugeng Xi,et al.  Some GPC stability results , 1998 .