Tunable Nonlinear-Function-Based Estimators for Mismatched Disturbances and Performance Analysis

In this article, based on the concept of an equivalent-input-disturbance (EID), a tunable nonlinear-function-based estimator is developed for fast and efficient control of unknown and mismatched disturbances of a tracking control system, and the control performances are analyzed. A great superiority over the conventional EID estimators is that the gain is varying and tunable with respect to an intermediate disturbance-rejection performance indicator. First, the control task is divided into the control of reference-tracking and disturbance-rejection, and the corresponding control mechanisms are clarified. For the disturbance-rejection control, explanation of the intermediate performance indicator is provided and a tunable nonlinear-function-based EID estimator is constructed. Then, the tunability condition for the varying gain of the developed EID estimator is given. A relation between control performances and control parameters is clarified a theoretical analysis. An input-to-state stability condition is derived for the closed-loop control system. Finally, comparisons with other methods through simulations and experiments demonstrate fast disturbance-rejection response, weak noise impact, and strong robustness of the developed method.

I. Introduction

Unknown disturbances and/or uncertainties are inevitable in engineering practice, which reduce the control precision and even may destroy the stability of control systems [1]. How to suppress the influence on control systems has been receiving lots of attention [2].