Minimum-time feedforward plus PID control using a Chebyshev technique

This paper 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 we 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 optimization problem. Simulation as well as experimental results demonstrate the effectiveness of the methodology.