A stable model predictive control for integrating processes

This paper proposes a stable model predictive control for systems with stable and integrating poles. The method presented here extends the method of [Rodrigues, M. A., & Odloak, D. (2003a). An infinite horizon model predictive control for stable and integrating processes. Computers and Chemical Engineering, 27, 1113-1128] to provide nominal stability for a set of process conditions, which is larger than in previous methods. The main effort is to eliminate the conflict between the constraints in the system inputs, which are usually included in the MPC, and the constraints created by zeroing the integrating modes of the system at the end of the control horizon. This problem has hindered the practical application of nominally stable infinite horizon MPC in industry. The improved controller is obtained through a modified control objective that includes additional decision variables to increase the set of feasible solutions to the control problem. The hard constraints associated with the integrating modes are softened and the resulting control problem is feasible to a much larger class of unknown disturbances and set point changes. Two methods are proposed to obtain stability: by imposing the contraction of the norm of the vector of slack variables associated with the integrating modes and by separating the control problem in two sub-problems. The methods are illustrated with the application of the proposed approach to two integrating examples of the literature.