Minimum-time feedforward technique for PID control

This study deals with the determination of the (reference) command input to be applied to a closed-loop control system in order to achieve a minimum-time output transition subject to constraints on both the control variable and the system output. In particular, the authors consider the important practical case of a process described by a first-order-plus-dead-time transfer function with a proportional-integral-derivative feedback controller. The optimal command input is determined by suitably approximating the state variables and the input signal by means of Chebyshev series and by subsequently solving a constrained optimisation problem. Simulation as well as experimental results demonstrate the effectiveness of the methodology.