Sliding Mode Control for Mismatched Uncertain Systems Using an Extended Disturbance Observer

This paper extends a recent result on sliding mode control for general n th order systems with mismatched uncertainties. In this paper, a control is proposed to handle a larger class of mismatched uncertainties by extending the disturbance observer and modifying and generalizing the sliding surface. The practical stability of the overall system is proved and the results are verified by simulation of an illustrative example.

I. Introduction

Sliding mode control (SMC) is an effective and popular control strategy for controlling systems affected by uncertainties and external unmeasurable disturbances and has found several applications in diverse fields [2]. The conventional SMC shows insensitivity to matched uncertainties and disturbances. While for a large class of systems, the uncertainties and disturbances are matched, there are many practical systems for which this is not true [3]. Many practical systems like the permanent magnet synchronous motors [4], [5], roll autopilots for missiles acted upon by external disturbances [6], are affected by unmatched uncertainties. In fact, all systems represented using physical state variables, in which the control is implemented by an actuator in cascade with the plant, are examples of systems with unmatched uncertainties.