259 Copyright © 2015, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Chapter 9 DOI: 10.4018/978-1-4666-7248-2.ch009 ABSTRACT This chapter deals with the control of chaos exhibited in the behavior of a one-degree-of-freedom impact mechanical oscillator with a single rigid constraint. The mathematical model of such impact oscillator is represented by an impulsive hybrid linear non-autonomous dynamics. The proposed control approach is based chiefy on the OGY method. First, an analytical expression of a constrained controlled Poincaré map is derived. Secondly, the linearized controlled Poincaré map around the fxed point of the constrained map is determined. Relying on the linearized map, a state feedback controller is designed. It is shown that the proposed control strategy is efcient for the control of chaos for the desired fxed point and for the fxed parameter. It is shown also that, by changing the system parameter, the behavior of the impact mechanical oscillator changes radically. Thus, the drawback of the developed OGY control method is revealed and some remedies are given. 1. INTRODUCTION Chaos is defined as a strange phenomenon with erratic appearance and which arises in deterministic continuous or discrete nonlinear systems. The chaos paradigm provides a better understanding of the inherent properties of natural systems. A chaotic system is a nonlinear dynamic system and its response has certain characteristics: Chaos Control of an Impact Mechanical Oscillator Based on the OGY Method Hassène Gritli Institut Supérieur des Etudes Technologiques de Kélibia, Tunisia Safya Belghith Ecole Nationale d’Ingénieurs de Tunis, Tunisia Nahla Khraief Ecole Supérieure de Technologie et d’Informatique, Tunisia