Control of an Electrostatic Microelectromechanical System Using Static and Dynamic Output Feedback
Authors
D. H. S. Maithripala, Jordan M. Berg, W. P. Dayawansa
Abstract
This paper examines control strategies for electrostatically actuated microelectromechanical systems (MEMS), with the goals of using feasible measurements to eliminate the pull-in bifurcation, robustly stabilize any desired operating point in the capacitive gap, decrease settling time, and reduce overshoot. We show that input-output linearization, passivity-based design, and the theory of port-controlled Hamiltonian systems lead naturally to static output feedback of device charge. This formalizes and extends previously reported results from the MEMS literature. Further analysis suggests that significantly improving transient behavior in lightly damped MEMS requires dynamic estimation of electrode velocity. We implement output-feedback control using a reduced-order nonlinear observer. Simulations predict greatly improved transient behavior, and large reductions in control voltage.
Citation
- Journal: Journal of Dynamic Systems, Measurement, and Control
- Year: 2005
- Volume: 127
- Issue: 3
- Pages: 443–450
- Publisher: ASME International
- DOI: 10.1115/1.1985443
BibTeX
@article{Maithripala_2004,
title={{Control of an Electrostatic Microelectromechanical System Using Static and Dynamic Output Feedback}},
volume={127},
ISSN={1528-9028},
DOI={10.1115/1.1985443},
number={3},
journal={Journal of Dynamic Systems, Measurement, and Control},
publisher={ASME International},
author={Maithripala, D. H. S. and Berg, Jordan M. and Dayawansa, W. P.},
year={2004},
pages={443--450}
}
References
- Kovacs, Micromachined Transducers Sourcebook
- Nathanson, H. C., Newell, W. E., Wickstrom, R. A. & Davis, J. R. The resonant gate transistor. IEEE Trans. Electron Devices 14, 117–133 (1967) – 10.1109/t-ed.1967.15912
- Chan, E. K. & Dutton, R. W. Electrostatic micromechanical actuator with extended range of travel. J. Microelectromech. Syst. 9, 321–328 (2000) – 10.1109/84.870058
- Chu, Analysis of Closed-Loop Control of Paralle-Plate Electrostatic MicroGrippers. Proc. of IEEE Int. Conf. Robotics and Automation
- Seeger, Stabilization of Electrostatically Actuated Mechanical Devices. Proceedings of the Ninth International Conference on Solid-State Sensors and Actuators (Transducers ’97)
- Senturia, S. D. Microsystem Design. (Springer US, 2001). doi:10.1007/b117574 – 10.1007/b117574
- Nemirovsky, Y. & Bochobza-Degani, O. A methodology and model for the pull-in parameters of electrostatic actuators. J. Microelectromech. Syst. 10, 601–615 (2001) – 10.1109/84.967384
- Pelesko, J. A. & Triolo, A. A. Journal of Engineering Mathematics 41, 345–366 (2001) – 10.1023/a:1012292311304
- Bloom, The Grating Light Valve: Revolutionizing Display Technology. Projection Displays III Symposium, SPIE Proceedings
- McCarthy, B., Adams, G. G., McGruer, N. E. & Potter, D. A dynamic model, including contact bounce, of an electrostatically actuated microswitch. J. Microelectromech. Syst. 11, 276–283 (2002) – 10.1109/jmems.2002.1007406
- Chu, P. B., Shi-Sheng Lee & Sangtae Park. MEMS: the path to large optical crossconnects. IEEE Commun. Mag. 40, 80–87 (2002) – 10.1109/35.989762
- Chung, S.-W. & Kim, Y.-K. Design and fabrication of 10×10 micro-spatial light modulator array for phase and amplitude modulation. Sensors and Actuators A: Physical 78, 63–70 (1999) – 10.1016/s0924-4247(99)00205-8
- Comtois, J., Michalicek, A., Cowan, W. & Butler, J. Surface-micromachined polysilicon MOEMS for adaptive optics. Sensors and Actuators A: Physical 78, 54–62 (1999) – 10.1016/s0924-4247(99)00204-6
- Florence, J. M. & Gale, R. O. Coherent optical correlator using a deformable mirror device spatial light modulator in the Fourier plane. Appl. Opt. 27, 2091 (1988) – 10.1364/ao.27.002091
- Extracting and analyzing gases. Membrane Technology 2002, 12–13 (2002) – 10.1016/s0958-2118(02)08032-1
- Maithripala, Capacitive Stabilizatipon of an Electrostatic Actuator: An Output Feedback Viewpoint. Proceedings of the 2003 American Control Conference, 4–6 June
- Maithripala, An Energy Based Method for Stabilization of an Electrostatic Actuator. Proceedings of the IMECE
- Nadal-Guardia, R., Dehe, A., Aigner, R. & Castaner, L. M. Current drive methods to extend the range of travel of electrostatic microactuators beyond the voltage pull-in point. J. Microelectromech. Syst. 11, 255–263 (2002) – 10.1109/jmems.2002.1007404
- Seeger, Dynamics and Control of Parallel-Plate Actuators Beyond the Electrostatic Instability. Proceedings of the Tenth International Conference on Solid-State Sensors and Actuators (Transducers ’99)
- Seeger, J. I. & Boser, B. E. Charge control of parallel-plate, electrostatic actuators and the tip-in instability. J. Microelectromech. Syst. 12, 656–671 (2003) – 10.1109/jmems.2003.818455
- Kyynäräinen, J. M., Oja, A. S. & Seppä, H. Analog Integrated Circuits and Signal Processing 29, 61–70 (2001) – 10.1023/a:1011230330035
- Larnaudie, Analytical Simulation of a 1D Single Crystal Silicon Electrostatic Micromirror. Proceedings of the Second International Conference on Modelling and Simulation of Microsystems, Semiconductors, Sensors and Actuators
- Wang, P. K. C. FEEDBACK CONTROL OF VIBRATIONS IN A MICROMACHINED CANTILEVER BEAM WITH ELECTROSTATIC ACTUATORS. Journal of Sound and Vibration 213, 537–550 (1998) – 10.1006/jsvi.1998.1525
- Maithripala, Nano-Precision Control of Micromirrors Using Output Feedback. Proceedings of the CDC
- Pelesko, J. A. Mathematical Modeling of Electrostatic MEMS with Tailored Dielectric Properties. SIAM J. Appl. Math. 62, 888–908 (2002) – 10.1137/s0036139900381079
- Toshiyoshi, H., Mita, M. & Fujita, H. A MEMS piggyback actuator for hard-disk drives. J. Microelectromech. Syst. 11, 648–654 (2002) – 10.1109/jmems.2002.805054
- Krener, Feedback Linearization. Mathematical Control Theory
- Byrnes, C. I., Isidori, A. & Willems, J. C. Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems. IEEE Trans. Automat. Contr. 36, 1228–1240 (1991) – 10.1109/9.100932
- Sepulchre, R., Janković, M. & Kokotović, P. V. Constructive Nonlinear Control. Communications and Control Engineering (Springer London, 1997). doi:10.1007/978-1-4471-0967-9 – 10.1007/978-1-4471-0967-9
- Van der Schaft, L2-Gain and Passivity Techniques in Nonlinear Control
- Kelkar, A. G., Joshi, S. M. & Alberts, T. E. Passivity-based control of nonlinear flexible multibody systems. IEEE Trans. Automat. Contr. 40, 910–914 (1995) – 10.1109/9.384228
- Isidori, Nonlinear Control Systems
- Wonham, Linear Multivariable Control: A Geometric Approach
- Sane, Application of Sliding Mode Control to Electrostatically Actuated Two-Axis Gimbaled Micromirrors. Proceedings of the American Control Conference, Denver, CO
- Ayela, F., Bret, J. L., Chaussy, J., Fournier, T. & Ménégaz, E. A two-axis micromachined silicon actuator with micrometer range electrostatic actuation and picometer sensitive capacitive detection. Review of Scientific Instruments 71, 2211–2218 (2000) – 10.1063/1.1150608
- Dayawansa, W. P. & Martin, C. F. Dynamical systems which undergo switching. IEEE Trans. Automat. Contr. 44, 751–760 (1999) – 10.1109/9.754812
- Ortega, Putting Energy Back in Control. IEEE Control Syst. Mag.
- Maithripala, D. H. S., Berg, J. M. & Dayawansa, W. P. Nonlinear dynamic output feedback stabilization of electrostatically actuated MEMS. 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475) vol. 1 61–66 – 10.1109/cdc.2003.1272536
- Ortega, R., Loría, A., Nicklasson, P. J. & Sira-Ramírez, H. Passivity-Based Control of Euler-Lagrange Systems. Communications and Control Engineering (Springer London, 1998). doi:10.1007/978-1-4471-3603-3 – 10.1007/978-1-4471-3603-3
- Bloch, A. M., Dong Eui Chang, Leonard, N. E. & Marsden, J. E. Controlled Lagrangians and the stabilization of mechanical systems. II. Potential shaping. IEEE Trans. Automat. Contr. 46, 1556–1571 (2001) – 10.1109/9.956051
- Teel, Uniting Local and Global Controllers for the Caltech Fucted Fan. Proceedings, of the American Control Conference, Albuquerque, NM, June 4–6
- Yee, PZT Actuated Micromirror for Fine-Tracking Mechanism of High-Density Optical Data Storage. Sens. Actuators