Minimum-time rest-to-rest feedforward action for PID feedback MIMO systems

In this paper we present a methodology for the design of a feedforward control law to be applied to a closed-loop PID-based control system for a multi-input multi-output process in order to achieve a minimum-time rest-to-rest transition of the system from an equilibrium point to another subject to constraints on both the control and process variables. In particular, the proposed approach uses decentralized PID controllers which can be designed by any of the conventional methods, such as, for example, those aiming at rejection of load disturbances. Then, the closed-loop generalized bang-bang command input vector is determined by applying a linear programming approach in order to minimize the rest-to-rest output transitions. Conditions for the constraints for which the problem admits a solution are given. Simulations for a two-inputs two-outputs plant highlight the effectiveness of the approach.