Electrostatic microactuators are used extensively in MEMS sensors, RF switches, and microfluidic pumps. Due to high bandwidth operation, however, reduction of residual vibration using feedback control is diffcult to implement. This paper designs, proves stability, and simulates a feedforward repetitive controller for an electrostatic microbridge. Squeeze film damping ensures boundedness of the distributed transverse displacement. Offline processing using repetitive control algorithm updates a waveform generator’s parameters based on measured response to reduce errors between the desired and actual displacement distribution. Simulations show a 36% reduction in midspan overshoot.

1.
Hung
E. S.
and
Senturia
S. D.
,
1999
, “
Generating Efficient Dynamical Models for Microelectromechanical Systems from a Few Finite-Element Simulation Runs
.”
IEEE Journal of Microelectromechanical Systems
,
8
, pp.
280
289
.
2.
Pamidighantam
S.
,
Puers
R.
,
Baert
K.
, and
Tilmans
H. A. C.
,
2002
, “
Pull-in Voltage Analysis of Electrostatically Actuated Beam Structures with Fixed-fixed and Fixed-free End Conditions
.”
Journal of Micromech. Microeng
,
12
, pp.
458
464
.
3.
Lam, T. and Darling, R. B., 2001, “Physical Modeling of MEMS Cantilever Beams and the Measurement of Stiction Force.” Proc. of Int. Conf. Modeling and Simulation of Microsystems, NanoTech 2001, 1, pp. 418–421.
4.
Collenz
A.
,
Bona
F. De
,
Gugliotta
A.
, and
Soma
A.
,
2004
, “
Large Deflections of Microbeams Under Electrostatic Loads
.”
Journal of Micromech. Microeng
,
14
, pp.
365
373
.
5.
Liu
A. Q.
,
Zhang
X. M.
,
Lu
C.
, and
Liu
Z. S.
,
2003
, “
Optical and Mechanical Models for a Variable Optical Attenuator Using a Micromirror Drawbridge
.”
Journal of Micromech. Microeng
,
13
, pp.
400
411
.
6.
Lyshevski, S.E., 2002, MEMS and NEMS, Systems, Devices, and Structures, CRC Press, Washington, DC.
7.
Pelesko, J.A. and Bernstein, D.H., 2003, Modeling MEMS and NEMS, Chapman & Hall/CRC, Washington, DC.
8.
Krylov
S.
and
Maimon
R.
,
2004
, “
Pull-in Dynamics of an Elastic Beam Actuated by Continuously Distributed Electrostatic Force
.”
Journal of Vibration and Acoustics
,
126
, pp.
332
342
.
9.
Rahn, C.D., 2001, Mechatronic Control of Distributed Vibration and Noise, Springer.
10.
Zhao, H. and Rahn, C., 2004, “On the Boundedness of Damped Strings and Beams with Boundary and Distributed Inputs.” The 43rd IEEE Conference on Decision and Control, Atlantis, Paradise Island, Bahamas.
11.
Bamieh
B.
,
Paganini
F.
, and
Dahleh
M. A.
,
2002
, “
Distributed Control of Spatially Invariant Systems
.”
IEEE Transactions on Automatic Control
,
47
, pp.
1091
1107
.
12.
Balogh
A.
,
Liu
W. J.
, and
Krstic
M.
,
2001
, “
Stability Enhancement by Boundary Control in 2-D Channel Flow
,”
IEEE Transactions on Automatic Control
,
46
, pp.
1696
1711
.
13.
Senouci Bereksi, G., 2002, “Implementation of a Nonlinear Control Law for the Magnetostrictive Beam Vibrations by an Amplifier of Current to Current.” Proc. of Int. Conf. Modeling and Simulation of Microsystems, NanoTech 2002, 1, pp. 275–278.
14.
Hillerstro¨m
G.
,
1996
, “
Adaptive Suppression of Vibrations – A Repetitive Control Approach
.”
IEEE Transactions on Control Systems Technology
,
4
(
1
), pp.
72
78
.
15.
Dixon
W. E.
,
Zergeroglu
E.
,
Dawson
D. M.
, and
Costic
B. T.
,
2002
, “
Repetitive Learning Control: A Lyapunov-Based Approach
.”
IEEE Transactions on Systems, Man, and Cybernetics – Part B: Cybernetics
,
32
(
4
), pp.
538
545
.
16.
Zhao, H. and Rahn, C., 2005, “Iterative Learning Velocity and Tension Control for Axially Moving Materials.” ASME International 20th Biennial Conference on Mechanical Vibration and Noise, Long Beach, California.
17.
Senturia, S.D., 2001, Microsystem Design, Kluwer Academic Publishers, Massachusetts.
This content is only available via PDF.
You do not currently have access to this content.