Multi-objective performance optimisation for model predictive control by goal attainment

Abstract

This article proposes an approach for performance tuning of model predictive control (MPC) using goal-attainment optimisation of the cost function weighting matrices. The approach is developed for three formulations of the control problem: (i) minimal and (ii) non-minimal design based on the same cost function and (iii) a non-minimal MPC approach with an explicit integral-of-error state variable and modified cost function. This approach is based on earlier research into multi-objective optimisation for proportional-integral-plus control systems. Simulation experiments for a 3-input, 3-output Shell heavy oil fractionator model illustrate the feasibility of MPC goal attainment for multivariable decoupling and attainment of a specific output response. For this example, the integral-of-error state variable offers improved design flexibility and hence, when it is combined with the proposed tuning method, yields an improved closed-loop response in comparison to minimal MPC.

Keywords:

• model predictive control
• non-minimal state space
• optimal controller tuning
• decoupling

Acknowledgements

The authors are grateful for the support of the General Michael Arnaoutis Foundation. Preliminary results were presented at UKACC Control 2006 (Exadaktylos, Taylor, and Chotai 2006). The statistical tools and associated estimation algorithms have been assembled as the CAPTAIN toolbox (Taylor et al. 2007) within the MATLAB® software environment and may be downloaded from www.es.lancs.ac.uk/cres/captain.