Inverse feedforward control with output polynomial smoothing

A method of polynomial smoothing is presented for the inverse feedforward control of continuous-time, linear, nonminimum-phase SISO (single-input single-output) systems. Starting from an arbitrarily given output signal, a smoothing procedure is devised to obtain a delayed smoothed output for which stable input-output inversion can be applied. This procedure requires to solve a polynomial interpolating problem whose solution is given by a polynomial parameterized by the smoothing time parameter. Detailed expressions of the deduced inverse input are provided. The minimization of the smoothing time is also pursued in order to reduce the delay in the smoothed output. Examples highlight the proposed method. The aim of the presented approach is to achieve high-performances in a variety of possible control applications such as, e.g., those in process automation and mechatronics.