Repetitive control of non-minimum phase systems along B-spline trajectories

In this paper, a novel repetitive control scheme is presented and discussed, based on the so called B-spline filters. This type of dynamic filters are able to provide a Bspline trajectory if they are fed with the sequence of proper control points that define the trajectory itself. Therefore, they are ideal tools for generating online the reference signal with the prescribed level of smoothness for driving dynamic systems, e.g. with a feedforward compensator. In particular, the so-called Continuous Zero Phase Error Tracking Controller (ZPETC) can be used for tracking control of non-minimum phase systems but because of its open-loop nature cannot guarantee robustness with respect to modelling errors and exogenous disturbances. For this reason, ZPETC and trajectory generator have been embedded in a repetitive control scheme that allows to nullify interpolation errors even in non-ideal conditions, provided that the desired reference trajectory and the disturbances are periodic. The asymptotic stability of the overall control scheme has been proved and its performances have been demonstrated by considering a well-known non-minimum phase plant, i.e. a flexible link arm.

I. Introduction

Quite often, in industrial applications, the given tasks present a cyclic or repetitive nature; this means that, from a control perspective, the plant is required to track a periodic exogenous signal whose cycle time is supposed to be known in advance. When cyclic motions are considered, the Repetitive Control (RC) approach represents a quite standard and effective solution to achieve asymptotic perfect tracking, being able to cancel tracking errors over repetitions by learning from previous iterations, [1]–[3].