Stable inversion of nonlinear non-minimum phase systems

Abstract

Output tracking control of non-minimum phase systems is a highly challenging problem encountered in the control of flexible manipulators, space structures, and elsewhere. Classical inversion provides exact output tracking but leads to internal instability, while recent nonlinear regulation provides stable asymptotic tracking but admits large transient errors. As a first step to solve this problem, this paper addresses the stable inversion of non-minimum phase nonlinear systems. Using the notions of zero dynamics and stable/unstable manifolds, an invertibility condition is established for a class of systems. A stable but non-causal inverse is obtained offline that can be incorporated into a stabilizing controller for dead-beat output tracking. This inverse contrasts with the causal inverse proposed by Hirschorn where unstable zero dynamics result in unbounded inverse solutions. Our results reduce to those of Hirschorn for minimum phase systems, however. In a numerical example, the stable inverse has achieved much superior tracking performance as compared with that produced using nonlinear regulation.