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Adaptive chaos synchronization of a mechanical system with disturbances and uncertainties

Pikaso Pal, Vivekananda Mukherjee and Gang Gyoo Jin

Vol. 10 (2022), No. 3, 245–263
Abstract

Centrifugal flywheel governor (CFG) systems are nonautonomous mechanical systems that exhibit chaotic behavior. The nonlinearities in the system equation are responsible for chaos. These systems nullify the damaging effects of changing load torques and, thereby, control the speed of the engine automatically. In this article, a backstepping strategy is integrated with sliding mode controls (SMCs) to synchronize two alike chaotic mechanical devices against model uncertainties and external disturbances. The mechanical systems are considered to have different control initial values. Next, adaptation laws are derived to guesstimate the upper bounds (unknown) of disturbances and uncertainties. The proposed adaptation laws eradicate the necessity to know the bounds. These adaptive laws are incorporated with the backstepping SMC laws, and adaptive backstepping SMC (ABSMC) are proposed. The main aspects of the proposed controller are smooth convergence, fast transients and improved robustness. The Lyapunov stability theorem and Barbalat’s lemma confirm the asymptotic stability of the system. According to simulation results, the control laws converge the synchronization error to the close neighborhood of origin.

Keywords
adaptation rule, backstepping sliding mode control, centrifugal flywheel governor system, chaotic synchronization, master and slave system, Lyapunov stability theorem
Mathematical Subject Classification
Primary: 65P20, 93C15, 93D05
Milestones
Received: 4 November 2021
Revised: 24 February 2022
Accepted: 24 April 2022
Published: 4 December 2022

Communicated by Miguel A. F. Sanjuán
Authors
Pikaso Pal
Department of Electrical Engineering
Indian Institute of Technology
Indian School of Mines
Dhanbad
India
Vivekananda Mukherjee
Department of Electrical Engineering
Indian Institute of Technology
Indian School of Mines
Dhanbad
India
Gang Gyoo Jin
Department of Electrical Power and Control Engineering
Adama Science and Technology University
Adama
Ethiopia