Pole assignment control of nonminimum phase systems: a combined adaptive control-variable structure approach

A combined approach based on both the theory of variable structure control systems and the theory of model reference adaptive control is presented. The resultant control scheme solves a pole assignment control problem in the presence of uncertain nonminimum phase systems and is characterized by a simple first-order fixed compensator placed in parallel to the plant (so that the parallel connection turns out to be a relative-degree-one system with a nonnecessarily Hurwitz numerator), by a set of tunable state variable filters, along with an all-pass filter which prevents any unstable pole-zero cancellation from occurring, as long as the plant numerator is non-Hurwitz. Indeed, the use of discontinuous control actions, together with the introduction of the all-pass filter, guarantees the convergence of the signal playing the role of output error to zero, while all the control signals turn out to be bounded, and the appointed control objective is attained