Robust Interval Adaptive Pole-Placement Controller Based on Variable Structure Systems Theory

In this paper, we present a robust pole placement control scheme that can be used to control a wide class of linear and time invariant systems with unknown parameters, including nonminimum phase systems, using only plant input and output signals. We assume that the unknown plant parameters has known bounds, i.e., the control scheme is designed for an interval plant whose coefficients are closed intervals. The main objective is to locate the closed-loop poles within a region specified by the roots of an interval characteristic polynomial, which is chosen based on performance requirements and whose stability is guaranteed by Kharitonov's Theorem. A Nonlinear Programming (NLP) problem is then constructed to find a closed interval for each controller parameter, i.e., we aim to form an interval control law that meets exactly the pole placement control objective. The unknown plant parameters are estimated on-line by using switching laws based on the Variable Structure Adaptive Pole Placement Control (VS-APPC). This control strategy gives a fast and non-oscillatory transient, smooth control signal and robustness to large model parameter variations, as well as it guarantees that the closed-loop performance requirements are satisfied. To illustrate the properties of the proposed technique, a simulation result is presented for a nonminimum phase plant.