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Dynamic analysis, circuit realization and accelerated adaptive backstepping control of the FO MEMS gyroscope

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  • Luo, Shaohua
  • Yang, Guanci
  • Li, Junyang
  • Ouakad, Hassen M.

Abstract

In this paper, an accelerated adaptive backstepping control problem is investigated for the fractional-order (FO) Micro-electro-mechanical system (MEMS) gyroscope. Its dynamical behaviors are studied through effective tools such as phase diagrams, time histories, Lyapunov exponent, 0-1 test and bifurcation diagram. And its equivalent analog circuits producing regular behaviors as well as complex ones are constructed to further reveal nonlinear dynamics especially chaotic oscillations. In the controller design, the Fourier series and the interval type-2 fuzzy logic system (IT2FLS) are utilized to reconstruct imprecise reference trajectories, and unknown functions are approximated through the IT2FLS with adaptive laws. The speed function is constructed to improve the transient response performance of the FO MEMS gyroscope, and a tracking differentiator (TD) is introduced to solve the problem of ‘explosion of complexity’. Then, an accelerated adaptive backstepping controller integrating the IT2FLS, speed function and TD into the technical framework of backstepping is proposed here. The stability analysis proves that all signals of the closed-loop FO MEMS gyroscope are asymptotically uniformly bounded. Finally, the effectiveness of the proposed control scheme is verified by abundant results.

Suggested Citation

  • Luo, Shaohua & Yang, Guanci & Li, Junyang & Ouakad, Hassen M., 2022. "Dynamic analysis, circuit realization and accelerated adaptive backstepping control of the FO MEMS gyroscope," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    • Handle: RePEc:eee:chsofr:v:155:y:2022:i:c:s0960077921010894
    DOI: 10.1016/j.chaos.2021.111735
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    References listed on IDEAS

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    1. Cui, Li & Lu, Ming & Ou, Qingli & Duan, Hao & Luo, Wenhui, 2020. "Analysis and Circuit Implementation of Fractional Order Multi-wing Hidden Attractors," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    2. Gusso, André & Viana, Ricardo L. & Mathias, Amanda C. & Caldas, Iberê L., 2019. "Nonlinear dynamics and chaos in micro/nanoelectromechanical beam resonators actuated by two-sided electrodes," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 6-16.
    3. Anand, Pallov & Sharma, Bharat Bhushan, 2020. "Simplified synchronizability scheme for a class of nonlinear systems connected in chain configuration using contraction," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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    Cited by:

    1. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Alquhayz, Hani & Abdalla, Manal Z.M. & Alhagyan, Mohammed & Gargouri, Ameni & Shoaib, Muhammad, 2023. "Design of intelligent hybrid NAR-GRNN paradigm for fractional order VDP chaotic system in cardiac pacemaker with relaxation oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    2. Li, Fengyun & Luo, Shaohua & Yang, Guanci & Ouakad, Hassen M., 2023. "Dynamical analysis and accelerated adaptive backstepping funnel control for dual-mass MEMS gyroscope under event trigger," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

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