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Chaos Control of an Impact Mechanical Oscillator Based on the OGY Method

Chaos Control of an Impact Mechanical Oscillator Based on the OGY Method

Hassène Gritli, Safya Belghith, Nahla Khraief
Copyright: © 2015 |Pages: 20
ISBN13: 9781466672482|ISBN10: 146667248X|EISBN13: 9781466672499
DOI: 10.4018/978-1-4666-7248-2.ch009
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MLA

Gritli, Hassène, et al. "Chaos Control of an Impact Mechanical Oscillator Based on the OGY Method." Handbook of Research on Advanced Intelligent Control Engineering and Automation, edited by Ahmad Taher Azar and Sundarapandian Vaidyanathan, IGI Global, 2015, pp. 259-278. https://doi.org/10.4018/978-1-4666-7248-2.ch009

APA

Gritli, H., Belghith, S., & Khraief, N. (2015). Chaos Control of an Impact Mechanical Oscillator Based on the OGY Method. In A. Azar & S. Vaidyanathan (Eds.), Handbook of Research on Advanced Intelligent Control Engineering and Automation (pp. 259-278). IGI Global. https://doi.org/10.4018/978-1-4666-7248-2.ch009

Chicago

Gritli, Hassène, Safya Belghith, and Nahla Khraief. "Chaos Control of an Impact Mechanical Oscillator Based on the OGY Method." In Handbook of Research on Advanced Intelligent Control Engineering and Automation, edited by Ahmad Taher Azar and Sundarapandian Vaidyanathan, 259-278. Hershey, PA: IGI Global, 2015. https://doi.org/10.4018/978-1-4666-7248-2.ch009

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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 chiefly on the OGY method. First, an analytical expression of a constrained controlled Poincaré map is derived. Secondly, the linearized controlled Poincaré map around the fixed 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 efficient for the control of chaos for the desired fixed point and for the fixed 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.

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