Systematic MPC tuning with direct response shaping: Parameterization and Inverse optimization-based Tuning Approach (PITA)

The automatic tuning of the weighting parameters in model predictive control (MPC) requires a systematic strategy to shape the state and input responses to become close to the user’s specifications. In this paper, based on the system-level parameterization of controllers, the system response under MPC is considered as the optimized response matrix under the tuning parameters, and hence an inverse optimization formulation is proposed to seek the tuning under which the desired response is close to being optimal. This results in a two-phase procedure, both formulated as quadratic programming (QP) or linear programming (LP) problems. First, the user specifications are interpreted as “reference” responses or hard constraints, under which the closest realizable response is found. Then, by fitting the realizable response to optimality conditions, the inversely optimal MPC parameters are determined with minimum residuals. The proposed automatic MPC tuning approach is generic and efficient, whose practical performance is demonstrated by applications on single-loop and process unit-level models.