Chaos in a fractional-order micro-electro-mechanical resonator and its suppression

doi:10.1088/1674-1056/21/10/100505

中国物理B ›› 2012, Vol. 21 ›› Issue (10): 100505-100505.doi: 10.1088/1674-1056/21/10/100505

Chaos in a fractional-order micro-electro-mechanical resonator and its suppression

Mohammad Pourmahmood Aghababa

Electrical Engineering Department, Urmia University of Technology, Urmia, Iran

收稿日期:2012-01-14 修回日期:2012-04-06 出版日期:2012-09-01 发布日期:2012-09-01

Chaos in a fractional-order micro-electro-mechanical resonator and its suppression

Mohammad Pourmahmood Aghababa

Electrical Engineering Department, Urmia University of Technology, Urmia, Iran

Received:2012-01-14 Revised:2012-04-06 Online:2012-09-01 Published:2012-09-01
Contact: Mohammad Pourmahmood Aghababa E-mail:m.p.aghababa@ee.uut.ac.ir; m.pour13@gmail.com

摘要/Abstract

摘要： The present paper investigates the existence of chaos in a non-autonomous fractional-order micro-electro-mechanical resonator system (FOMEMRS). Using the maximal Lyapunov exponent criterion, we show that the FOMEMRS exhibits chaos. Strange attractors of the system are plotted to validate its chaotic behavior. Afterward, a novel fractional finite-time controller is introduced to suppress the chaos of the FOMEMRS with model uncertainties and external disturbances in a given finite time. Using the latest version of the fractional Lyapunov theory, the finite time stability and robustness of the proposed scheme are proved. Finally, we present some computer simulations to illustrate the usefulness and applicability of the proposed method.

关键词: micro-electro-mechanical resonator, chaotic behavior, fractional calculus, fractional finite-time controller

Abstract: The present paper investigates the existence of chaos in a non-autonomous fractional-order micro-electro-mechanical resonator system (FOMEMRS). Using the maximal Lyapunov exponent criterion, we show that the FOMEMRS exhibits chaos. Strange attractors of the system are plotted to validate its chaotic behavior. Afterward, a novel fractional finite-time controller is introduced to suppress the chaos of the FOMEMRS with model uncertainties and external disturbances in a given finite time. Using the latest version of the fractional Lyapunov theory, the finite time stability and robustness of the proposed scheme are proved. Finally, we present some computer simulations to illustrate the usefulness and applicability of the proposed method.

Key words: micro-electro-mechanical resonator, chaotic behavior, fractional calculus, fractional finite-time controller

中图分类号: (Control of chaos, applications of chaos)

05.45.Gg

05.30.Pr (Fractional statistics systems) 85.85.+j (Micro- and nano-electromechanical systems (MEMS/NEMS) and devices) 02.30.Yy (Control theory)

Mohammad Pourmahmood Aghababa. Chaos in a fractional-order micro-electro-mechanical resonator and its suppression[J]. 中国物理B, 2012, 21(10): 100505-100505.

Mohammad Pourmahmood Aghababa. Chaos in a fractional-order micro-electro-mechanical resonator and its suppression[J]. Chin. Phys. B, 2012, 21(10): 100505-100505.

参考文献 33

[1]	Lyshevski S E 2001 MEMS and NEMS: Systems, Devices, and Structures (Boca Raton: CRC Press)
[2]	Lyshevski S E 2003 Energy Conversion Manage 44 667
[3]	Zhu G, Lévine J, Praly L and Peter Y A 2006 J Microelectromech. Syst. 15 1165
[4]	Xie H and Fedder G 2002 Sens. Actuat. A 95 212
[5]	Mestrom R M C, Fey R H B, van Beek J T M, Phan K L and Nijmeijer H 2007 Sens. Actuat. A 142 306
[6]	Younis M I and Nayfeh A H 2003 Nonlinear Dyn. 31 91
[7]	Braghin F, Resta F, Leo E and Spinola G 2007 Sens. Actuat. A 134 98
[8]	Wang Y C, Adams S G, Thorp J S, MacDonald N C, Hartwell P, Bertsch F, et al. 1998 IEEE Trans. Circ. Syst. I 45 1013
[9]	De S K and Aluru N R 2006 J. Microelectromech. Syst. 15 355
[10]	Luo A and Wang F Y 2002 Commun. Nonlinear Sci. Numer. Simul. 7 31
[11]	Chavarette F R, Balthazar J M, Felix J L P and Rafikov M 2009 Commun. Nonlinear Sci. Numer. Simul. 14 1844
[12]	Barry E, De M, Butterfield E, Moehlis J and Turner K 2007 J. Microelectromech. Syst. 16 1314
[13]	Liu S, Davidson A and Lin Q 2004 J. Micromech. Microeng. 14 1064
[14]	Haghighi H H and Markazi A H D 2010 Commun. Nonlinear Sci. Numer. Simul. 15 3091
[15]	Yau H T, Wang C C, Hsieh C T and Cho C C 2011 Comput. Math. Appl. 61 1912
[16]	Podlubny I 1999 Fractional Differential Equations (New York: Academic Press)
[17]	Hilfer R 2001 Applications of Fractional Calculus in Physics (New Jersey: World Scientific)
[18]	Rapaić M R and Jeličić Z D 2010 Nonlinear Dyn. 62 39
[19]	Luo Y, Chen Y Q and Pi Y 2011 Mechatronics 21 204
[20]	Laskin N 2000 Physica A 287 482
[21]	Rivero M, Trujillo J J, Vázquez L and Velasco M P 2011 Appl. Math. Comput. 218 1089
[22]	Cao J, Ma C, Jiang Z and Liu S 2011 Commun. Nonlinear Sci. Numer. Simul. 16 1443
[23]	Petráš I 2009 Nonlinear Dyn. 57 157
[24]	Wu X and Wang H 2010 Nonlinear Dyn. 61 407
[25]	Ge Z M and Jhuang W R 2007 Chaos, Solitons and Fractals 33 270
[26]	Ge Z M and Yi C X 2007 Chaos, Solitons and Fractals 32 42
[27]	Aghababa M P 2012 Commun. Nonlinear Sci. Numer. Simul. 17 2670
[28]	Aghababa M P 2011 Nonlinear Dyn. doi:10.1007/s11071-011-0261-6
[29]	Li Y, Chen Y Q and Podlubny I 2009 Automatica 45 1965
[30]	Rosenstein M T, Collins J J and De Luca C J 1993 Physica D 65 117
[31]	Hardy G H, Littlewood J E and Polya G 1952 Inequalities (Cambridge: Cambridge University Press)
[32]	Utkin V I 1992 Sliding Modes in Control Optimization (Berlin: Springer-Verlag)
[33]	Diethelm K, Ford N J and Freed A D 2002 Nonlinear Dyn. 29 3

Chaos in a fractional-order micro-electro-mechanical resonator and its suppression

Chaos in a fractional-order micro-electro-mechanical resonator and its suppression

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 33

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Abderrahmane Abbes, Adel Ouannas, and Nabil Shawagfeh. An incommensurate fractional discrete macroeconomic system: Bifurcation, chaos, and complexity[J]. 中国物理B, 2023, 32(3): 30203-030203.
[2]	Shaobo He(贺少波), Huihai Wang(王会海), and Kehui Sun(孙克辉). Solutions and memory effect of fractional-order chaotic system: A review[J]. 中国物理B, 2022, 31(6): 60501-060501.
[3]	Wu-Yang Zhu(朱伍洋), Yi-Fei Pu(蒲亦非), Bo Liu(刘博), Bo Yu(余波), and Ji-Liu Zhou(周激流). A mathematical analysis: From memristor to fracmemristor[J]. 中国物理B, 2022, 31(6): 60204-060204.
[4]	Xiang Xu(徐翔), Gangquan Si(司刚全), Zhang Guo(郭璋), and Babajide Oluwatosin Oresanya. Modeling and character analyzing of multiple fractional-order memcapacitors in parallel connection[J]. 中国物理B, 2022, 31(1): 18401-018401.
[5]	Mei Li(李梅), Ruo-Xun Zhang(张若洵), and Shi-Ping Yang(杨世平). Adaptive synchronization of a class of fractional-order complex-valued chaotic neural network with time-delay[J]. 中国物理B, 2021, 30(12): 120503-120503.
[6]	Zong-Li Yang(杨宗立), Dong Liang(梁栋), Da-Wei Ding(丁大为), Yong-Bing Hu(胡永兵), and Hao Li(李浩). Transient transition behaviors of fractional-order simplest chaotic circuit with bi-stable locally-active memristor and its ARM-based implementation[J]. 中国物理B, 2021, 30(12): 120515-120515.
[7]	Adel Ouannas, Amina Aicha Khennaoui, Shaher Momani, Viet-Thanh Pham, Reyad El-Khazali. Hidden attractors in a new fractional-order discrete system: Chaos, complexity, entropy, and control[J]. 中国物理B, 2020, 29(5): 50504-050504.
[8]	何秋燕, 余波, 袁晓. Carlson iterating rational approximation and performance analysis of fractional operator with arbitrary order[J]. 中国物理B, 2017, 26(4): 40202-040202.
[9]	张立民, 孙克辉, 刘文浩, 贺少波. A novel color image encryption scheme using fractional-order hyperchaotic system and DNA sequence operations[J]. 中国物理B, 2017, 26(10): 100504-100504.
[10]	Hossam A. Ghany, Abd-Allah Hyder. Abundant solutions of Wick-type stochastic fractional 2D KdV equations[J]. 中国物理B, 2014, 23(6): 60503-060503.
[11]	Hossam A. Ghany, A. S. Okb El Bab, A. M. Zabel, Abd-Allah Hyder. The fractional coupled KdV equations：Exact solutions and white noise functional approach[J]. 中国物理B, 2013, 22(8): 80501-080501.
[12]	Rajneesh Kumar, Vandana Gupta. Uniqueness, reciprocity theorem, and plane waves in thermoelastic diffusion with fractional order derivative[J]. 中国物理B, 2013, 22(7): 74601-074601.
[13]	王发强, 马西奎. Transfer function modeling and analysis of the open-loop Buck converter using the fractional calculus[J]. 中国物理B, 2013, 22(3): 30506-030506.
[14]	马松华, 方建平, 任清褒, 杨征. Chaotic behaviors of the (2+1)-dimensional generalized Breor–Kaup system[J]. 中国物理B, 2012, 21(5): 50511-050511.
[15]	魏含玉, 夏铁成 . A new generalized fractional Dirac soliton hierarchy and its fractional Hamiltonian structure[J]. 中国物理B, 2012, 21(11): 110203-110203.