Stability Improved of GPC Controller in Unstable Non-minimum Phase LTI Systems and Applied to Control Stewart Platform System

Three methods are discussed for stabilizing Linear Predictive Controller: Infinite Horizon Control (based on Optimal Control), Finite Horizon Control with end-point constraint, and in the third approach, at first the process is stabilized and then controller is designed. In this paper, a new method based on Finite Horizon Control with end-point constraint is proposed; it enables us to control some processes with repetitive unstable pole (Minimum or Non-minimum phase) that can’t be stabilized with existing methods. In these processes, step response has a variety range and the dynamic matrix for long prediction horizon is singular and then existing method fails to have a stable process. We modify the cost function of GPC Controller by adding terms to penalize error variations as well error and adjust these parameters. We have examined the method described for a practical system (Stewart Platform) with 6 unstable poles and 5 unstable zeros.