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Adaptive fractional fuzzy sliding mode control of microgyroscope based on backstepping design

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  • Xiao Liang
  • Juntao Fei

Abstract

In this paper, a robust sliding mode control (SMC) based on backstepping technique is studied for a microgyroscope in the presence of unknown model uncertainties and external disturbances using adaptive fuzzy compensator and fractional calculus. At first, the dynamic of microgyroscope is transformed into analogically cascade system to guarantee the application of backstepping design. Then a novel fractional differential sliding surface is proposed which integrates the capacities of the fractional calculus and SMC. In order to reduce the chattering in SMC, a fuzzy logical system is utilized to approximate the external disturbances. In addition, fractional order adaptive laws are derived to estimate the damping and stiffness coefficients and angular velocity online based on Lyapunov stability theory which also guarantees the stability of the closed loop system. Finally, simulation results signify the robustness and effectiveness of the proposed control schemes and the comparison of root mean square error under different fractional orders and integer order are given to demonstrate the better performance of proposed controller.

Suggested Citation

  • Xiao Liang & Juntao Fei, 2019. "Adaptive fractional fuzzy sliding mode control of microgyroscope based on backstepping design," PLOS ONE, Public Library of Science, vol. 14(6), pages 1-21, June.
    • Handle: RePEc:plo:pone00:0218425
    DOI: 10.1371/journal.pone.0218425
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    References listed on IDEAS

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    1. Cheng Liu & Guowei Cai & Jiwei Gao & Deyou Yang, 2017. "Design of Nonlinear Robust Damping Controller for Power Oscillations Suppressing Based on Backstepping-Fractional Order Sliding Mode," Energies, MDPI, vol. 10(5), pages 1-23, May.
    2. Atangana, Abdon & Gómez-Aguilar, J.F., 2017. "Hyperchaotic behaviour obtained via a nonlocal operator with exponential decay and Mittag-Leffler laws," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 285-294.
    3. Park, Sungsu & Horowitz, Roberto & Tan, Chin-woo, 2002. "Digital Implementation of Adaptive Control Algorithms for MEMS Gyroscopes," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt4708b2sj, Institute of Transportation Studies, UC Berkeley.
    4. Park, Sungsu & Horowitz, Roberto & Tan, Chin-woo, 2002. "Adaptive Control for MEMS Gyroscopes," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt8r78v641, Institute of Transportation Studies, UC Berkeley.
    5. Atangana, Abdon, 2018. "Non validity of index law in fractional calculus: A fractional differential operator with Markovian and non-Markovian properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 688-706.
    6. Juntao Fei & Xiao Liang, 2018. "Adaptive Backstepping Fuzzy Neural Network Fractional-Order Control of Microgyroscope Using a Nonsingular Terminal Sliding Mode Controller," Complexity, Hindawi, vol. 2018, pages 1-12, September.
    7. Park, Park & Horowitz, Roberto & Tan, Chin-woo, 2002. "Adaptive Control for Conventional Modes of Operation of MEMS Gyroscopes," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt83v0r9m1, Institute of Transportation Studies, UC Berkeley.
    8. Zhilin Feng & Juntao Fei, 2018. "Design and analysis of adaptive Super-Twisting sliding mode control for a microgyroscope," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-18, January.
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