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

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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.

Original languageEnglish
Article number111735
JournalChaos, Solitons and Fractals
Publication statusPublished - Feb 2022


  • Adaptive backstepping control
  • Analog circuit
  • FO MEMS gyroscope
  • IT2FLS
  • Imprecise reference trajectories

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics


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