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Synthesis of a hybrid control algorithm for chaotifying mechanical systems

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  • Dhobale, Swapnil Mahadev
  • Chatterjee, Shyamal

Abstract

This paper presents a novel hybrid control algorithm for inducing chaos in a limit cycle oscillator by chaotically varying suitable parameters within the chosen bounds. A discrete chaotic map governs the parameter variation at the predetermined Poincaré section. A cubic polynomial mapping is used to obtain the continuous variation between two consecutive crossings at the Poincaré section. A resonant controller with acceleration feedback is designed to implement the proposed control algorithm in a mechanical system with a single degree of freedom. This controller generates a limit cycle at the desired frequency and amplitude. The next step involves using a modified Pomeau-Manneville (PM) map to achieve the chaotification of the limit cycle, which yields a flat Fast Fourier Transform (FFT) of the response within a given bandwidth. The proposed control strategy not only chaotifies the system but also regulates desired response characteristics, such as amplitude, frequency band, chaoticity and power spectral distributions. This is believed to be the first attempt to control the desired characteristics of chaotic response in the case of continuous-time systems. Experiments with an electromagnetic actuator validate the simulation results.

Suggested Citation

  • Dhobale, Swapnil Mahadev & Chatterjee, Shyamal, 2024. "Synthesis of a hybrid control algorithm for chaotifying mechanical systems," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    • Handle: RePEc:eee:chsofr:v:189:y:2024:i:p1:s0960077924012220
    DOI: 10.1016/j.chaos.2024.115670
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    References listed on IDEAS

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    1. Chen, Qingfei & Hong, Yiguang & Chen, Guanrong, 2006. "Chaotic behaviors and toroidal/spherical attractors generated by discontinuous dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 293-302.
    2. Zhang, Jing & Xu, Daolin & Zhou, Jiaxi & Li, Yingli, 2012. "Chaotification of vibration isolation floating raft system via nonlinear time-delay feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1255-1265.
    3. Rogers, Alan & Shorten, Robert & Heffernan, Daniel M., 2008. "A novel matrix approach for controlling the invariant densities of chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 161-175.
    4. Asiain, Erick & Garrido, Rubén, 2021. "Anti-Chaos control of a servo system using nonlinear model reference adaptive control," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    5. Lazaros Moysis & Ioannis Kafetzis & Murilo S. Baptista & Christos Volos, 2022. "Chaotification of One-Dimensional Maps Based on Remainder Operator Addition," Mathematics, MDPI, vol. 10(15), pages 1-26, August.
    6. Zhou, Jiaxi & Xu, Daolin & Zhang, Jing & Liu, Chunrong, 2012. "Spectrum optimization-based chaotification using time-delay feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 815-824.
    7. Jing Zhang & Tao Tang & Wenhua Fang, 2020. "Line Spectrum Chaotification on QZS Systems with Time-Delay Control," Complexity, Hindawi, vol. 2020, pages 1-14, May.
    8. Krylosova, D.A. & Seleznev, E.P. & Stankevich, N.V., 2020. "Dynamics of non-autonomous oscillator with a controlled phase and frequency of external forcing," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    9. Abimael Salcedo & Joaquin Alvarez, 2018. "Oscillations in First-Order, Continuous-Time Systems via Time-Delay Feedback," Complexity, Hindawi, vol. 2018, pages 1-14, October.
    10. Yassen, M.T., 2005. "Controlling chaos and synchronization for new chaotic system using linear feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 913-920.
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