Approximate Input-Output Feedback Linearization of Non-Minimum Phase System using Vanishing Perturbation Theory

Abstract

The inverse of a non-minimum-phase system being unstable, standard input-output feedback linearization is not effective to control such systems. In this chapter is a presentation of a new tracking control method for the nonlinear non-minimum-phase system. Indeed, the main idea here is to dismiss a part of system dynamics in order to make the approximate system input-state feedback linearizable. The neglected part is then considered as a perturbation part that vanishes at the origin. Finally, a linear controller is designed to control the approximate system. Stability is analyzed using the vanishing perturbation theory. The efficacy and usage of the proposed approach is evaluated in an illustrative inverted cart-pendulum example.