Variable structure approach to the pole assignment control of non-minimum phase systems

Abstract

In this paper, a possible merge between the theory of variable structure control systems and that of model reference adaptive control is presented with reference to a pole assignment control problem in the presence of uncertain non-minimum phase systems affected by bounded disturbances. The control scheme proposed is characterized by a simple first-order fixed compensator introduced in parallel to the plant, so that the parallel connection turns out to be a relative-degree-one system with a not necessarily Hurwitz numerator, by a set of tunable state variable filters, along with an all-pass filter which allows us to avoid any unstable pole-zero cancellation in the presence of a non-Hurwitz plant numerator. By applying discontinuous control actions with an all-pass filter, it is possible to force a signal, which plays the role of output error, to zero, keeping the amplitude of all the control signals bounded, and solving a pole assignment problem. The main novelty of this work consists in the analysis of the case in which a bounded disturbance affects the plant behaviour. The rejection of the disturbance is proved by using Filippov's solution concept, after showing that the equivalent bounded control continuous system which describes the behaviour of the plant on the sliding manifold is unique.