Method for Undershoot-Less Control of Non-Minimum Phase Plants Based on Partial Cancellation of the Non-Minimum Phase Zero: Application to Flexible-Link Robots

Abstract

As a well understood classical fact, non- minimum phase zeros of the process located in a feedback connection cannot be cancelled by the corresponding poles of controller since such a cancellation leads to internal instability. This impossibility of cancellation is the source of many limitations in dealing with the feedback control of non-minimum phase processes. The aim of this paper is to study the possibility and usefulness of partial (fractional-order) cancellation of such zeros for undershoot-less control of non-minimum phase processes. In this method first the non-minimum phase zero of the process is cancelled to an arbitrary degree by the proposed pre-compensator and then a classical controller is designed to control the series connection of these two systems. Since plants with multiple non-minimum phase zeros and oscillatory poles are very common in the problems related to robotics, the proposed method is applied to these systems to confirm its effectiveness.