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

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.