Chaos Suppression of an Electrically Actuated Microresonator Based on Fractional-Order Nonsingular Fast Terminal Sliding Mode Control
作者： Jianxin Han , Qichang Zhang , Wei Wang , Gang Jin , Houjun Qi
DOI: 10.1155/2017/6564316
关键词: Engineering 、 Vibration 、 Control of chaos 、 Lyapunov stability 、 Control theory 、 Exponential stability 、 Terminal sliding mode 、 Bifurcation 、 Synchronization of chaos 、 Chaotic
摘要: This paper focuses on chaos suppression strategy of a microresonator actuated by two symmetrical electrodes. Dynamic behavior this system under the case where origin is only stable equilibrium investigated first. Numerical simulations reveal that may exhibit chaotic motion certain excitation conditions. Then, bifurcation diagrams versus amplitude or frequency AC are drawn to grasp dynamics nearby its natural frequency. Results show vibration complex and period-doubling bifurcation, motion, dynamic pull-in instability. For chaos, novel control algorithm, based an integer-order nonsingular fast terminal sliding mode fractional-order switching law, proposed. Fractional Lyapunov Stability Theorem used guarantee asymptotic stability system. Finally, numerical results with both laws our proposed law effective in controlling uncertainties external disturbances.
hindawi.com
core.ac.uk参考文章(38)
Kohei Yamasue, Takashi Hikihara, Control of microcantilevers in dynamic force microscopy using time delayed feedback Review of Scientific Instruments. ,vol. 77, pp. 053703- ,(2006) , 10.1063/1.2200747
Sara Dadras, Hamid Reza Momeni, Control of a fractional-order economical system via sliding mode Physica A: Statistical Mechanics and its Applications. ,vol. 389, pp. 2434- 2442 ,(2010) , 10.1016/J.PHYSA.2010.02.025
R.M.C. Mestrom, R.H.B. Fey, J.T.M. van Beek, K.L. Phan, H. Nijmeijer, Modelling the dynamics of a MEMS resonator : simulations and experiments Sensors and Actuators A-physical. ,vol. 142, pp. 306- 315 ,(2008) , 10.1016/J.SNA.2007.04.025
Mohammad Pourmahmood Aghababa, A fractional-order controller for vibration suppression of uncertain structures ISA Transactions. ,vol. 52, pp. 881- 887 ,(2013) , 10.1016/J.ISATRA.2013.07.010
Hossein S. Haghighi, Amir H.D. Markazi, Chaos prediction and control in MEMS resonators Communications in Nonlinear Science and Numerical Simulation. ,vol. 15, pp. 3091- 3099 ,(2010) , 10.1016/J.CNSNS.2009.10.002
Albert C.J. Luo, F.Y. Wang, Chaotic motion in a micro-electro–mechanical system with non-linearity from capacitors Communications in Nonlinear Science and Numerical Simulation. ,vol. 7, pp. 31- 49 ,(2002) , 10.1016/S1007-5704(02)00005-9
Mohammad Pourmahmood Aghababa, A switching fractional calculus-based controller for normal non-linear dynamical systems Nonlinear Dynamics. ,vol. 75, pp. 577- 588 ,(2014) , 10.1007/S11071-013-1087-1
Yan Li, YangQuan Chen, Igor Podlubny, Technical communique: Mittag-Leffler stability of fractional order nonlinear dynamic systems Automatica. ,vol. 45, pp. 1965- 1969 ,(2009) , 10.1016/J.AUTOMATICA.2009.04.003
Fábio Roberto Chavarette, José Manoel Balthazar, Jorge LP Felix, Marat Rafikov, None, A reducing of a chaotic movement to a periodic orbit, of a micro-electro-mechanical system, by using an optimal linear control design Communications in Nonlinear Science and Numerical Simulation. ,vol. 14, pp. 1844- 1853 ,(2009) , 10.1016/J.CNSNS.2008.09.003
Shuiqing Hu, Arvind Raman, Chaos in atomic force microscopy. Physical Review Letters. ,vol. 96, pp. 036107- ,(2006) , 10.1103/PHYSREVLETT.96.036107