Control of nonlinear non-minimum phase systems using dynamic sliding mode

Abstract

A newly developed dynamic sliding mode control technique for multiple input systems is shown to be useful in the control of nonlinear, non-minimum phase systems where the zero dynamics have no finite escape time. The system may not be dynamic feedback linearizable. To achieve asymptotic performance, unbounded control may be necessary as determined by the zero dynamics. As long as the growth rate of the zero dynamics is no more than exponential, ultimate bounded performance can be achieved with finite control effort. Lagrange stability analysis of the closed-loop system resulting from the proposed variable structure scheme is performed. Essentially a thin layer is introduced around the sliding surface. Outside the layer, the sliding mode controller is used; inside the layer, the controller is designed to asymptotically (exponentially) stabilize the dynamic compensator. It is shown that there is a trade-off between control performance and control effort. The method is illustrated by the control of the Inverted Double Pendulum which is not dynamic-feedback linearizable and is non-minimum phase and thus constitutes a testing example for the proposed scheme.