Robust Stabilization for a Class of Uncertain Nonlinear Systems via a Novel Hybrid Control Applicable to Mechanical Systems

Yeong-Jeu Sun

doi:10.1155/2014/952342

Abstract

An important consideration in control system design is that of model uncertainty. Besides, systems with mixed uncertainties, chaotic vibrations, and input nonlinearities are not easily stabilized and traditional control schemes for linear systems are not always effective. Therefore, in this paper, we will solve two problems, first searching a novel hybrid control methodology to achieve the practical stabilization for uncertain systems with mixed uncertainties and second calculating the guaranteed exponential convergence rate with the convergence radius. The applicability of the main results is demonstrated by a tracking controller design for a class of uncertain nonlinear mass-damper-spring systems with mixed uncertainties, chaotic vibrations, and input nonlinearities.

Highlights

Robustness issues in control theory play an important role because each model of a real process has inherent uncertainties that have to be taken into account in any controller design
Uncertain input nonlinearity inevitably exists in dynamic control systems [9]
Attention has been focused on various uncertain input nonlinearities common in uncertain systems, such as deadzones, relays, saturation, hysteresis, and others; see, for instance [6, 13,14,15,16,17] and the references cited therein

Summary

Introduction

Robustness issues in control theory play an important role because each model of a real process has inherent uncertainties that have to be taken into account in any controller design Such uncertainties may be due to measurement error, simplified models of natural laws, neglected dynamics, or inevitably uncertain model. In [8], based on the time-domain approach with differential inequality, a feedback control has been proposed to accomplish generalized exponential synchronization for a pair of mechanical systems with uncertainties. A tracking control has been proposed in [9] to realize the generalized projective synchronization in practical type for the uncertain horizontal platform systems with parameter mismatching, external excitation, and input nonlinearity via the differential inequality approach. Our objective is to design a novel hybrid control such that the practical stabilization for a class of uncertain nonlinear systems with input nonlinearities can be achieved.

Problem Formulation and Main Results

Numerical Simulations

Conclusions