Research Papers

Adaptive Control for Fractional-Order Micro-Electro-Mechanical Resonator With Nonsymmetric Dead-Zone Input

[+] Author and Article Information
Xiaomin Tian

Key Laboratory of Measurement
and Control of CSE,
School of Automation,
Ministry of Education,
Southeast University,
Nanjing 210096, China
e-mail: tianxiaomin100@163.com

Shumin Fei

Key Laboratory of Measurement
and Control of CSE,
School of Automation,
Ministry of Education,
Southeast University,
Nanjing 210096, China
e-mail: smfei@seu.edu.cn

1Corresponding author.

Manuscript received October 6, 2014; final manuscript received January 3, 2015; published online June 9, 2015. Assoc. Editor: J. A. Tenreiro Machado.

J. Comput. Nonlinear Dynam 10(6), 061022 (Nov 01, 2015) (6 pages) Paper No: CND-14-1238; doi: 10.1115/1.4029604 History: Received October 06, 2014; Revised January 03, 2015; Online June 09, 2015

This paper deals with the adaptive control of fractional-order micro-electro-mechanical resonator system (FOMEMRS) with nonsymmetric dead-zone nonlinear input. The slope parameters of the dead-zone nonlinearity are unmeasured and the parameters of the controlled systems are assumed to be unknown in advance. To deal with these unknown parameters, some fractional versions of parametric update laws are proposed. On the basis of the frequency distributed model of fractional integrator and Lyapunov stability theory, a robust control law is designed to prove the stability of the closed-loop system. The proposed adaptive approach requires only the information of bounds of the dead-zone slopes and treats the time-varying input coefficient as a system uncertainty. Finally, simulation examples are given to verify the robustness and effectiveness of the proposed control scheme.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Mestrom, R. M. C., Fey, R. H. B., van Beek, J. T. M., Phan, K. L., and Nijmeijer, H., 2008, “Modeling the Dynamics of a MEMS Resonator: Simulations and Experiments,” Sens. Actuators, A, 142(1), pp. 306–315. [CrossRef]
Younis, M. I., and Nayfeh, A. H., 2003, “A Study of the Nonlinear Response of a Resonant Microbeam to an Electric Actuation,” Nonlinear Dyn., 31(1), pp. 91–117. [CrossRef]
Braghin, F., Resta, F., Leo, E., and Spinola, G., 2007, “Nonlinear Dynamics of Vibrating MEMS,” Sens. Actuators, A, 134(1), pp. 98–108. [CrossRef]
Barry, E., De, M., Butterfield, E., Moehlis, J., and Turner, K., 2007, “Chaos for a Microelectromechanical Oscillator Governed by the Nonlinear Mathieu Equation,” J. Microelectromech. Syst., 16(6), pp. 1314–1323. [CrossRef]
Chavarette, F. R., Balthazar, J. M., Felix, J. L. P., and Rafikov, M., 2009, “A Reducing of a Chaotic Movement to a Periodic Orbit, of a Micro-Electro-Mechanical System, by Using an Optimal Linear Control Design,” Commun. Nonlinear Sci. Numer. Simul., 14(5), pp. 1844–1853. [CrossRef]
Liu, S., Davidson, A., and Lin, Q., 2004, “Simulation Studies on Nonlinear Dynamics and Chaos in a MEMS Cantilever Control System,” J. Micromech. Microeng., 14(7), pp. 1064–1073. [CrossRef]
Yau, H. T., Wang, C. C., Hsieh, C. T., and Cho, C. C., 2011, “Nonlinear Analysis and Control of the Uncertain Micro-Electro-Mechanical System by Using a Fuzzy Sliding Mode Control Design,” Comput. Math. Appl., 61(8), pp. 1912–1916. [CrossRef]
Aghababa, M. P., 2012, “Chaos in a Fractional-Order Micro-Electro-Mechanical Resonator and Its Suppression,” Chin. Phys. B, 21(10), p. 100505. [CrossRef]
Yang, C. C., and Qu, C. J., 2013, “Adaptive Terminal Sliding Mode Control Subject to Input Nonlinearity for Synchronization of Chaotic Gyros,” Commun. Nonlinear Sci. Numer. Simul., 18(3), pp. 682–691. [CrossRef]
Abooee, A., and Haeri, M., 2013, “Stabilisation of Commensurate Fractional-Order Polytopic Nonlinear Differential Inclusion Subject to Input Nonlinearity and Unknown Disturbances,” IET Control Theory Appl., 7(12), pp. 1624–1633. [CrossRef]
Roohi, M., Aghababa, M. P., and Haghighi, A. R., “Switching Adaptive Controllers to Control Fractional-Order Complex Systems With Unknown Structure and Input Nonlinearities,” Complexity (to be published).
Aghababa, M. P., and Hashtarkhani, B., “Synchronization of Unknown Uncertain Chaotic Systems Via Adaptive Control Method,” J. Comput. Nonlinear Dyn.137(5), p. 051004 [CrossRef].
Trigeassou, J. C., Maamri, N., Sabatier, J., and Oustaloup, A., 2011, “A Lyapunov Approach to the Stability of Fractional Differential Equations,” Signal Process., 91(3), pp. 437–445. [CrossRef]
Yu, J., Hu, C., Jiang, H. J., and Fan, X. L., 2014, “Projective Synchronization for Fractional Neural Networks,” Neural Networks, 49, pp. 87–95. [CrossRef] [PubMed]
Haghighi, H. H., and Markazi, A. H. D., 2010, “Chaos Prediction and Control in MEMS Resonators,” Commun. Nonlinear Sci. Numer. Simul., 15(10), pp. 3091–3099. [CrossRef]
Trigeassou, J. C., Maamri, N., Sabatier, J., and Oustaloup, A., 2012, “State Variables and Transients of Fractional Order Differential Systems,” Comput. Math. Appl., 64(10), pp. 3117–3140. [CrossRef]
Trigeassou, J. C., Maamri, N., Sabatier, J., and Oustaloup, A., 2012, “Transients of Fractional-Order Integrator and Derivatives,” Signal Image Video Process., 6(3), pp. 359–372. [CrossRef]
Trigeassou, J. C., and Maamri, N., 2011, “Initial Conditions and Initialization of Linear Fractional Differential Equations,” Signal Process., 91(3), pp. 427–436. [CrossRef]
Yuan, J., Shi, B., and Ji, W. Q., 2013, “Adaptive Sliding Mode Control of a Novel Class of Fractional Chaotic Systems,” Adv. Math. Phys., 2013, p. 576709.
Zhang, R. X., and Yang, S. P., 2012, “Robust Chaos Synchronization of Fractional-Order Chaotic Systems With Unknown Parameters and Uncertain Perturbations,” Nonlinear Dyn., 69(3), pp. 983–992. [CrossRef]
Chen, L. P., Qu, J. F., Chai, Y., Wu, R. C., and Qi, G. Y., 2013, “Synchronization of a Class of Fractional-Order Chaotic Neural Networks,” Entropy, 15(8), pp. 3265–3276. [CrossRef]
Wei, Q., Wang, X. Y., and Hu, X. P., “Feedback Chaotic Synchronization of a Complex Chaotic System With Disturbances,” J. Vib. Control (to be published).
Chen, D. Y., Liu, Y. X., Ma, X. Y., and Zhang, R. F., 2012, “Control of a Class of Fractional-Order Chaotic Systems Via Sliding Mode,” Nonlinear Dyn., 67(1), pp. 893–901. [CrossRef]
Sabatier, J., Agrawal, O. P., and Machado, J., 2007, Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer-Verlag, Berlin, Germany.
Sabatier, J., Farges, C., and Oustaloup, A., 2014, “On Fractional Systems State Space Description,” J. Vib. Control, 20(7), pp. 1076–1084. [CrossRef]
Sabatier, J., Farges, C., Merveillaut, M., and Feneteau, L., 2012, “On Observability and Pseudo State Estimation of Fractional Order Systems,” Eur. J. Control, 18(3), pp. 260–271. [CrossRef]
Hu, Q. L., Ma, G. F., and Xie, L. H., 2008, “Robust and Adaptive Variable Structure Output Feedback Control of Uncertain Systems With Input Nonlinearity,” Automatica, 44(2), pp. 552–559. [CrossRef]
Noroozi, N., Roopaei, M., Karimaghaee, P., and Safavi, A. A., 2010, “Simple Adaptive Variable Structure Control for Unknown Chaotic Systems,” Commun. Nonlinear Sci. Numer. Simul., 15(3), pp. 707–727. [CrossRef]
Liu, L. P., Pu, J. X., Song, X. N., Fu, Z. M., and Wang, X. H., 2014, “Adaptive Sliding Mode Control of Uncertain Chaotic Systems With Input Nonlinearity,” Nonlinear Dyn., 76(4), pp. 1857–1865. [CrossRef]


Grahic Jump Location
Fig. 1

A schematic picture of MEMRS

Grahic Jump Location
Fig. 2

The strange attractors of system (7) with different q: (a) q = 54, (b) q = 0.7, (c) q = 0.8, and (d) q = 0.9

Grahic Jump Location
Fig. 3

Nonsymmetric dead-zone nonlinearity

Grahic Jump Location
Fig. 4

The state trajectories of system (8) with q = 0.54

Grahic Jump Location
Fig. 5

The time evolutions of estimated parameters in system (8)

Grahic Jump Location
Fig. 6

The state trajectories of system (8) with different q: (a) q = 0.7, (b) q = 0.8, and (c) q = 0.9




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In