Adaptive smooth super-twisting sliding mode control of nonlinear systems with unmatched uncertainty

Abstract

This article presents a novel strategy regarding the stabilization control problem for plants with unmatched uncertainties. The methodology is based on Adaptive Smooth Super Twisting Sliding Mode Control. At first, as an initial step, the plant with unmatched uncertainty is transformed into a plant with matched uncertainty. At the second step, the plant with matched uncertainty is decomposed into a unique framework containing the nominal part and some unknown terms (where these unknown terms are computed adaptively). The nominal system is stabilized by using Smooth Super Twisting Sliding Mode Control. The stabilizing controller for the plant with matched uncertainty is designed in a way; it contains some nominal control plus some compensator term. The stability of the said technique is presented impressively. The compensator controller and the adapted laws are derived in such a way that the time derivative of a Lyapunov function becomes strictly negative. The proposed method is tested on a fourth-order plant. The simulation results show the effectiveness and validity of the proposed controller.