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Nonlinear feedback synthesis and control of periodic, quasiperiodic, chaotic and hyper-chaotic oscillations in mechanical systems

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Abstract

Self-excited periodic, quasiperiodic and chaotic oscillations have many significant applications in engineering devices and processes. In the present paper, a centralized nonlinear controller is proposed to artificially generate and control self-excited periodic, quasiperiodic, chaotic and hyper-chaotic oscillations of required characteristics in a fully actuated n-DOF spring-mass-damper mechanical system. The analytical relations among the amplitude, frequency and controller parameters for minimum control energy have been obtained using the method of two-time scale. It is shown that the proposed control can generate modal and nonmodal self-excited periodic and quasiperiodic oscillations of desired amplitude and frequency for minimum control energy. The analytical results have been verified numerically with MATLAB SIMULINK. Bifurcation analysis and extensive numerical simulations reveal a region of multistability in the plane of control parameters, where system responses may be periodic, quasiperiodic, chaotic and hyper-chaotic depending on initial conditions. However, it has been shown that the probability of obtaining chaotic and hyper-chaotic oscillations is very high for a wide range of controller parameters. The procedures of controlling the amplitude, frequency and characteristics of chaotic oscillations are also discussed. The results of the present paper are expected to find applications in various macro- and micro-mechanical systems and applications.

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  1. Department of Mechanical Engineering, Indian Institute of Engineering Science and Technology, Shibpur, P.O. Botanic Garden, Howrah, West Bengal, 711103, India

    Prasanjit Kumar Kundu & Shyamal Chatterjee

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  1. Prasanjit Kumar Kundu
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  2. Shyamal Chatterjee
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All authors contributed to the study conception and design. Analysis was performed by PKK. The first draft of the manuscript was written by PKK and SC. All authors read and approved the final manuscript.

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Correspondence to Shyamal Chatterjee.

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Kundu, P.K., Chatterjee, S. Nonlinear feedback synthesis and control of periodic, quasiperiodic, chaotic and hyper-chaotic oscillations in mechanical systems. Nonlinear Dyn 111, 11559–11591 (2023). https://doi.org/10.1007/s11071-023-08402-0

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