Generalized predictive control tuning by controller matching

Abstract

This paper presents a tuning method for the model predictive control (MPC) based on the transfer function formulation, also known as generalized predictive control (GPC). The aim of the method is to find the tuning parameters of GPC to obtain the same behavior as an arbitrary linear-time-invariant (LTI) controller (favorite controller). The approach consists of two steps. The first step matches GPC gain to that of the favorite controller by equating the respective coefficients of the transfer function of the control law to those of the favorite controller. This step is followed by finding the weighting matrices in the cost function that will result in the GPC gain which is obtained in the first step. This proposed tuning approach does not require either loop-shifting techniques to deal with non-strictly-proper favorite controllers or equal prediction and control horizons as in conventional inverse optimality problems. In this paper, we also extend the method to the feed-forward case, which is seldom considered in standard reverse-engineering tuning methods. The feasibility conditions of the matching of a GPC with a favorite controller are analyzed and the limitation in control space the GPC can span with different tuning settings is shown. The proposed tuning method is demonstrated on a binary distillation column example.