Tuning MPC for desired closed-loop performance for MIMO systems

Model Predictive Control (MPC) is widely used in the process industries. It is an optimization-based approach, where several tuning parameters such as the penalty matrices in the cost function and the prediction and control horizons must be chosen. Tuning such parameters can be challenging as they are related to the closed-loop performance in a complex manner. This problem becomes even more complicated when tuning MPC controllers for MIMO systems. This paper addresses this problem and presents a systematic approach to determine MPC tuning parameters for MIMO systems based on a specification of the desired behaviour of the loop for small changes where the MPC controller acts as a linear controller. In this manner, the robustness of the closed loop to model mismatch can be taken into account systematically using results from robust linear control theory. The approach involves solving sequentially two semidefinite programming problems (convex optimization problems), one of which is formulated in the frequency-domain. A key feature of our approach is that the tuning parameters are determined such that in the unconstrained case they guarantee a nominal robust closed-loop performance. The approach is tested on two process control examples.