%0 Journal Article
%T Dynamic Sliding Mode Control Design Based on an Integral Manifold for Nonlinear Uncertain Systems
%A Qudrat Khan
%A Aamer Iqbal Bhatti
%A Antonella Ferrara
%J Journal of Nonlinear Dynamics
%D 2014
%R 10.1155/2014/489364
%X An output feedback sliding mode control law design relying on an integral manifold is proposed in this work. The considered class of nonlinear systems is assumed to be affected by both matched and unmatched uncertainties. The use of the integral sliding manifold allows one to subdivide the control design procedure into two steps. First a linear control component is designed by pole placement and then a discontinuous control component is added so as to cope with the uncertainty presence. In conventional sliding mode the control variable suffers from high frequency oscillations due to the discontinuous control component. However, in the present proposal, the designed control law is applied to the actual system after passing through a chain of integrators. As a consequence, the control input actually fed into the system is continuous, which is a positive feature in terms of chattering attenuation. By applying the proposed controller, the system output is regulated to zero even in the presence of the uncertainties. In the paper, the proposed control law is theoretically analyzed and its performances are demonstrated in simulation. 1. Introduction Output feedback sliding mode control techniques proved themselves to be the good candidate for systems where only output is measurable and its derivatives can be estimated accurately. Linear systems or systems which could be easily lineralized are addressed in Edwards and Spurgeon [1]. Nonlinear systems with measurable outputs are for instance dealt with via Dynamic Sliding Mode Control (DSMC) ([2¨C4], where the original system is replaced with a differential input-output form often called Fliess Controllable Canonical form or Local generalized controllable canonical (LGCC) form, by using some nonlinear transformation. Asymptotic stabilization of LGCC forms by means of DSMC provided satisfactory results. Traditionally, this control methodology based on the sliding mode control (SMC) theory [5] refers to the case of uncertain systems with matched uncertainties (see, [1] for a definition of this class of uncertainties). However, there are many systems affected by uncertainties which do not satisfy the matching condition. To solve this problem, various methods have been proposed in the literature (see, e.g., [6¨C11]). These papers of Scararat, Swaroop, and Ferrara relied on a backstepping based SMC design to relax the matching conditions. Nonlinear systems often do not remain robust against uncertainties even of matched nature in the so-called reaching phase. Therefore, an approach capable of eliminating this phase in
%U http://www.hindawi.com/journals/jndy/2014/489364/