On the practical implementation of feedforward control signals given in polynomial form

A Chebyshev optimization approach can be employed effectively for the determination of the (reference) command input to be applied to a feedback PID control system in order to achieve a minimum-time output transition subject to constraints on both the control variable and the system output. The resulting command input function is given in polynomial form, for which a practical implementation can be difficult. In this paper we propose a method for the determination of a stable low-order filter whose step response approximates the open-loop command signal so that a standard two degree-of-freedom controller results. Simulation examples show that the technique is effective and yields a stable transfer function which can be easily implemented into a DCS control system.