Abstract
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.
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This research was supported by the National Natural Science Foundation of China under Grant Nos. 51505170, 51475097 and 51505045, Basic and Frontier Research Program of Chongqing Municipality under Grant Nos. cstc2016jcyjA0584 and cstc2016jcyjA0441), Project of Introduction of Talents of Guizhou University (No. [2017]27) and Key Scientific Research Program of Guizhou Province under Grant No. [2017]3001).
This paper was recommended for publication by Editor LIU Yungang.
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Luo, S., Li, S. & Tajaddodianfar, F. Chaos and Nonlinear Feedback Control of the Arch Micro-Electro-Mechanical System. J Syst Sci Complex 31, 1510–1524 (2018). https://doi.org/10.1007/s11424-018-7234-5
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DOI: https://doi.org/10.1007/s11424-018-7234-5