Journal of Systems Science and Complexity

, Volume 31, Issue 6, pp 1510–1524 | Cite as

Chaos and Nonlinear Feedback Control of the Arch Micro-Electro-Mechanical System

  • Shaohua Luo
  • Shaobo LiEmail author
  • Farid Tajaddodianfar


This paper addresses a nonlinear feedback control problem for the chaotic arch microelectro- mechanical system with unknown parameters, immeasurable states and partial state-constraint subjected to the distributed electrostatic actuation. To reflect inherent properties and design controller, the phase diagrams, bifurcation diagram and Poincare section are presented to investigate the nonlinear dynamics. The authors employ a symmetric barrier Lyapunov function to prevent violation of constraint when the arch micro-electro-mechanical system faces some limits. An RBF neural network system integrating with an update law is adopted to estimate unknown function with arbitrarily small error. To eliminate chaotic oscillation, a neuro-adaptive backstepping control scheme fused with an extended state tracking differentiator and an observer is constructed to lower requirements on measured states and precise system model. Besides, introducing an extended state tracking differentiator avoids repeated derivative for the virtual control signal associated with conventional backstepping. Finally, simulation results are presented to illustrate feasibility of the proposed scheme.


Arch micro-electro-mechanical system chaos suppression Neuro-adaptive backstepping nonlinear feedback control uncertainty 


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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Shaohua Luo
    • 1
    • 2
  • Shaobo Li
    • 1
    • 2
    Email author
  • Farid Tajaddodianfar
    • 3
  1. 1.Key Laboratory of Advanced Manufacturing Technology, Ministry of EducationGuizhou UniversityGuiyangChina
  2. 2.School of Mechanical EngineeringGuizhou UniversityGuiyangChina
  3. 3.Department of Mechanical Engineering, Erik Jonsson School of Engineering and Computer ScienceThe University of Texas at DallasRichardsonUSA

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