Generalized predictive control tuning by controller matching

The tuning of state-space model predictive control (MPC) based on reverse engineering has been investigated in literature using the inverse optimality problem ( [1] and [2]). The aim of the inverse optimality is to find the tuning parameters of MPC to obtain the same behavior as an arbitrary linear-time-invariant (LTI) controller (favorite controller). This requires equal control horizon and prediction horizon, and loop-shifting is often used to handle non-strictly-proper favorite controllers. This paper presents a reverse-engineering tuning method for MPC based on transfer function formulation, also known as generalized predictive control (GPC). The feasibility conditions of the matching of a GPC with a favorite controller are investigated. This approach uses a control horizon equal to one and does not require any loop-shifting techniques to deal with non-strictly-proper favorite controllers. The method is applied to a binary distillation column example.