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Chaos Suppression of an Electrically Actuated Microresonator Based on Fractional-Order Nonsingular Fast Terminal Sliding Mode Control

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  • Jianxin Han
  • Qichang Zhang
  • Wei Wang
  • Gang Jin
  • Houjun Qi
  • Qiu Li

Abstract

This paper focuses on chaos suppression strategy of a microresonator actuated by two symmetrical electrodes. Dynamic behavior of this system under the case where the origin is the only stable equilibrium is investigated first. Numerical simulations reveal that system may exhibit chaotic motion under certain excitation conditions. Then, bifurcation diagrams versus amplitude or frequency of AC excitation are drawn to grasp system dynamics nearby its natural frequency. Results show that the vibration is complex and may exhibit period-doubling bifurcation, chaotic motion, or dynamic pull-in instability. For the suppression of chaos, a novel control algorithm, based on an integer-order nonsingular fast terminal sliding mode and a fractional-order switching law, is proposed. Fractional Lyapunov Stability Theorem is used to guarantee the asymptotic stability of the system. Finally, numerical results with both fractional-order and integer-order control laws show that our proposed control law is effective in controlling chaos with system uncertainties and external disturbances.

Suggested Citation

  • Jianxin Han & Qichang Zhang & Wei Wang & Gang Jin & Houjun Qi & Qiu Li, 2017. "Chaos Suppression of an Electrically Actuated Microresonator Based on Fractional-Order Nonsingular Fast Terminal Sliding Mode Control," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-12, February.
    • Handle: RePEc:hin:jnlmpe:6564316
    DOI: 10.1155/2017/6564316
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    Cited by:

    1. Fawaz W. Alsaade & Mohammed S. Al-zahrani, 2023. "A Novel Fault-Tolerant Super-Twisting Control Technique for Chaos Stabilization in Fractional-Order Arch MEMS Resonators," Mathematics, MDPI, vol. 11(10), pages 1-18, May.

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