Control Design Applied to a Micro Electro Mechanical System: MEMS Comb Drive

Article Preview

Abstract:

This paper presents the linear optimal control technique for reducing the chaotic movement of the micro-electro-mechanical Comb Drive system to a small periodic orbit. We analyze the non-linear dynamics in a micro-electro-mechanical Comb Drive and demonstrated that this model has a chaotic behavior. Chaos control problems consist of attempts to stabilize a chaotic system to an equilibrium point, a periodic orbit, or more general, about a given reference trajectory. This technique is applied in analyzes the nonlinear dynamics in an MEMS Comb drive. The simulation results show the identification by linear optimal control is very effective.

You might also be interested in these eBooks

Info:

Periodical:

Advanced Materials Research (Volumes 217-218)

Pages:

33-38

Citation:

Online since:

March 2011

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2011 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

[1] B. Illic, D. Czaplewki, H.G. Craighead, P. Neuzal, C. Campagnolo and C. Batt, Mechanical resonant immunospecific biological detector, Applied Physics Letters, 77, (2000), pp.450-452.

DOI: 10.1063/1.127006

Google Scholar

[2] T.D. Stowe, K. Yasumura, T.W. Kenny, D. Botkin, K. Wago, D. Rugar, Attonewton force detection using silicon cantilevers. Applied Physics Letters, 71, (1997), pp.288-290.

DOI: 10.1063/1.119522

Google Scholar

[3] T. Kenny, Nanometer-scale force sensing with MEMS devices. IEEE Sensors Journal, 1, (2001), pp.148-157.

DOI: 10.1109/jsen.2001.936932

Google Scholar

[4] D. Rugar, C.S. Yannoni, and J.A. Sidles, Mechanical detection of magnetic resonance, Nature, 360, (1992), pp.563-566.

DOI: 10.1038/360563a0

Google Scholar

[5] E. Ott, C. Grebogi, and J.A. Yorque, Controlling Chaos, Phys. Rev. Lett. 66, (1990), p.1196.

Google Scholar

[6] S.C. Sinhá, J.T. Henrichs, and B.A. Ravindra, A General Approach in the Design of active Controllers for Nonlinear Systems Exhibiting Chaos. Int. J. Bifur. Chaos, 10-1, (2000), p.165.

DOI: 10.1142/s0218127400000104

Google Scholar

[7] J. Rhoads, S. Shaw, K. Turner, and R. Baskaran, Tunable MEMS filters that exploit parametric resonance, J. Vib. And Acoust., 127-5, (2004), pp.423-430.

DOI: 10.1115/1.2013301

Google Scholar

[8] J. Rhoads, S. Shaw, K. Tunner, J. Moehlis, B. DeMartini, and W. Zhang, Generalized parametric resonance in electrostatically actuated microelectromechanical oscillators, J. sound and Vib., 296, (2006), pp.797-829.

DOI: 10.1016/j.jsv.2006.03.009

Google Scholar

[9] K. Tuner, S. Miller, P. Harwell, N. MacDonald, S. Strogatz, and S. Adams, Five parametric resonances in a microelectromechanical system, Nature, 396, (1998), pp.149-152.

DOI: 10.1038/24122

Google Scholar

[10] B.E. DeMartini, H.E. Butterfield, J. Moehlis, and K.L. Turner, Prediction and Validation of chaotic behavior in a eletrcostatically actuted Microelectromechanical oscillator., in: Proceeding of the 14th International Conference on Solid-State Sensors, Actuators and Microsystems, Lyon, France, (2007).

DOI: 10.1109/sensor.2007.4300478

Google Scholar

[11] W. Zhang, R., Baskaran, and K. Tunner, Effect of nonlinearity on auto-parametrically amplified resonant MEMS mass sensor, Sens. And Act. A-Phys., 103: 1-2, (2002) pp.139-150.

DOI: 10.1016/s0924-4247(02)00299-6

Google Scholar

[12] W. Zhang, K. Turner, P. Harwell, In: SCREAM'03: A single mask process for high-Q single crystal silicon MEMS., ASME Intnl. Mech Eng. Congr. On Sens, Vienna, Austria, (2004), pp.24-27.

DOI: 10.1115/imece2004-61140

Google Scholar

[13] M. Rafikov and J. M. Balthazar, On control and synchronization in chaotic and hyperchaotic systems. Communications in Nonlinear Science & Numerical Simulation, 13, (2008), pp.1246-1255.

DOI: 10.1016/j.cnsns.2006.12.011

Google Scholar

[14] F.R. Chavarette, J.M. Balthazar, N.J. Peruzzi, and M. Rafikov, On Non-Linear Dynamics and Control Designs Applied to the FitzHugh-Nagumo (FN) Mathematical Model (Ideal and Non-Ideal Cases). International Journal of Nonlinear Sciences and Numerical Simulation, USA, 14, (2009).

DOI: 10.1016/j.cnsns.2007.10.016

Google Scholar

[15] F.R. Chavarette, J.M. Balthazar, and J.L.P. Felix, A Reducing of a Chaotic Movement to a Periodic Orbit, of a Micro -Electro-Mechanical System, by Using an Optimal Linear Control Design. Journal Of Computation And Nonlinear Dynamics, 14, (2009).

DOI: 10.1016/j.cnsns.2008.09.003

Google Scholar

[16] K. Ogata, Engenharia de Controle Moderno. São Paulo: Pearson Prentice Hall, (2003), p.788.

Google Scholar