On Chattering-Free Dynamic Sliding Mode Controller Design

Jeang-Lin Chang

doi:10.1155/2012/564906

Abstract

For a class of linear MIMO uncertain systems, a dynamic sliding mode control algorithm that avoids the chattering problem is proposed in this paper. Without using any differentiator, we develop a modified asymptotically stable second-order sliding mode control law in which the proposed controller can guarantee the finite time convergence to the sliding mode and can show that the system states asymptotically approach to zero. Finally, a numerical example is explained for demonstrating the applicability of the proposed scheme.

Highlights

Sliding mode control (SMC) has been successfully used in controlling many uncertain systems [1, 2]
For a linear MIMO system with the matched disturbance, in this paper we propose a dynamic sliding mode control algorithm in which the proposed procedure can effectively reduce the chattering effect
We propose a dynamic sliding mode control algorithm which can successfully avoid the chattering in the linear MIMO system with the matched disturbance

Summary

Introduction

Sliding mode control (SMC) has been successfully used in controlling many uncertain systems [1, 2]. Since no boundary layer is used in the controller, the advantages of a dynamic sliding mode controller are that chattering reduction is obtained by using an integrator and the property of perfect disturbance rejection is guaranteed. Bartolini et al [11, 12] presented a suboptimal version of the twisting algorithm [15, 16] to cope with the chattering problem This method requires at least the knowledge of the sign of the derivative of the sliding variable. Comparing with the conventional dynamic sliding mode controllers [10,11,12,13,14], the proposed method does not need any observer structure to estimate the derivative of the sliding variable.

Problem Formulation

Dynamic Sliding Mode Controller Design

Numerical Example

Conclusions