Large-displacement Closed-loop Control of Variable Area Electrostatic Actuation for Membrane Reflectors

Abstract

Membrane mirrors may be attractive in some space applications where light weight, deployability, and conformability are desired. This article investigates large-displacement closed-loop control of electrostatically driven mirrors being used in focusing and steering of laser beams. The required transient response characteristics for the membrane response are achieved using a variable area, constant voltage actuation method, which may be advantageous in some applications. Our previous work on variable area control was restricted to membrane deflections not exceeding 1/3 (the available gap size), and assumed that a continuous area variation was available. In this article, the controller design is extended to enable deflections approaching the entire available gap size, which would help to bring down the voltage requirement for a prescribed deflection range. A Lyapunov function-based approach is used here along with a fully nonlinear dynamic model. Although a single-mode lumped parameter model is used, a feedforward technique to compensate for a class of residual modes is investigated in this paper. Also studied in this article is the use of a Lyapunov function-based framework to guide the design of a controller to handle step-wise/discrete area changes. A dynamic observer based on quad-cell beam-position detector measurements and a fully nonlinear plant model is also studied. The article discusses numerical simulation results, which show that the controllers under study are fairly successful at providing closed-loop deflections approaching the full gap size at the required bandwidth.

Keywords

Membrane mirrors electrostatic actuation closed-loop control large-displacement.

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References

Ball Aerospace 2004. "Tip-tilt Mirrors," available at www.ballaerospace.com, September 2005.

Bifano, T. , Boerden, P. and Perreualt, J. 2004. "Micromachined Deformable Mirrors for Dynamic Wavefront Control," In: Gonglewski, J.D, Gruneisen, M.T. and Giles, M.K. (eds), Advanced Wavefront Control: Methods, Devices, and Applications II, Proceedings of SPIE, vol. 5553, pp. 1-15, SPIE , Bellingham, WA.

Bush, K. , German, D. , Klemme, B. , Marrs, A. and Schoen, M. 2004. "Electrostatic Membrane Deformable Mirror Wavefront Control Systems: Design and Analysis," In: Gonglewski, J.D. , Gruneisen, M.T. and Giles, M.K. (eds), Advanced Wavefront Control: Methods, Devices, and Applications II, Proceedings of SPIE , Vol. 5553, pp. 28-38, SPIE, Bellingham, WA.

Carreras, R.A. , Marker, D.K. and Wilkes, J.W. 1998. "Tunable Membrane Mirrors used with Real Time Holography ," In: Artificial Turbulence for Imaging and Wave Propagation , Proceedings of SPIE, Vol. 3432, pp. 120-128, SPIE, Bellingham, WA .

Grade, J.D. , Jerman, H. and Kenny, T.W. 2003. "Design of Large-deflection Electrostatic Actuators ," IEEE J. Microelectromechanical Systems, 12(3):335-343.

Gross, R.P. and Yellin, M. 1977. "The Membrane Mirror as an Adaptive Optic Element ," J. Optical Society of America, 67(3):399-406.

Hui, J.R. , Wu, X. and Warde, C. 2004. "Addressing Large Arrays of Electrostatic Actuators for Adaptive Optics Applications," In: Gonglewski, J.D., Gruneisen, M.T. and Giles, M.K. (eds), Advanced Wavefront Control: Methods, Devices, and Applications II, Proceedings of SPIE, Vol. 5553, pp. 17-27, SPIE, Bellingham, WA.

Korde, U.A. 2008. "Studies on Area-controlled Electrostatic Actuation of Small Membrane Reflectors," J. Intelligent Material Systems and Structures, 19(11):1339-1359.

Lang, J.H. and Staelin, D.H. 1982. "Electrostatically Figured Reflecting Membrane Antennas for Satellites," IEEE Trans. Automatic Control, AC-27(3):666-670.

10.

Maithripala, D.H.S. , Berg, J.M. and Dayawansa, W.P. 2005. "Control of an Electrostatic Micromechanical System using Static and Dynamic Output Feedback," ASME J. Dynamic Systems, Measurement, and Control, 127:443-450.

11.

Marker, D.K. , Wilkes, J.M. , Carreras, R.A. , Rotge, R.H. Jenkins, C.H. and Ash, J.T. 2001. "Fundamentals of Membrane Optics," In: Jenkins, C.H. (ed.) Gossamer Spacecraft: Membrane and Inflatable Structure Technology for Space Applications, AIAA Progress in Astronautics and Aeronautics ( Zarkan, P. : ed.), Vol. 191, pp. 111-201, AIAA , Reston, VA.

12.

Mihora, D.J. and Redmond, P.J. 1980. "Electrostatically Formed Antennas," J. Spacecraft and Rockets, 17(5): 465-473.

13.

Moore, J. , Patrick, B. , Chodimella, S. , Marker, D. and deBlonk, B. 2005. "Meter-class Actively Controlled Membrane Mirror ," In: 5th Mirror Tech Days in Government Conference , Huntsville, AL.

14.

Moore, J. 2006. "Novel Concept Deformable Mirror to Correct Large Amplitude Aberrations," In: 6th Mirror Tech Days in Government Conference, Albuquerque, NM.

15.

Physik Instrumente 2004. "Piezoelectrically Driven Tip/Tilt Platforms," available at www.pi.ws , September 2005.

16.

Rotge, J.R. , Dass, S.C. , Marker, D.K. , Carreras, R.A. , Lutz, B. and Duneman, D. 2000. "Progress Toward Large Aperture Membrane Mirrors ," In: Imaging and Telescopes, Proceedings of SPIE, Vol. 4091, pp. 74-82, SPIE, Bellingham, WA.

17.

Ruggiero, E.J. and Inman, D.J. 2005. "A Comparison between SISO and MIMO Modal Analysis Techniques on a Membrane Mirror Satellite," J. Intelligent Material Systems and Structures, 16(3):273-282.

18.

Seeger, J.I. and Boser, B.E. 2003. "Charge Control of Parallel Plate Electrostatic Actuators and the Tip-in Instability," IEEE J. Microelectromechanical Systems, 12(5):656-671.

19.

SEO Precision, Inc. 2006. "Virtu/FSM Strahl 5 inch," available at www.seoprecision.com/prod01.htm , August 2006.

20.

Shepherd, M.J. , Peterson, G.A. , Cobb, R.G. and Palazotto, A.N. 2006. "Quasi-static Optical Control of In-plane Actuated Deformable Mirror: Experimental Comparison with Finite Element Analysis," In: Proceedings of 47th AIAA/ASME/ ASCE/ASC Structures, Structural Dynamics, and Materials Conf, Newport, RI, AIAA 2006-2231.

21.

Stewart, J.B. , Bifano, T.G. , Cornelissen, S. , Bierden, P. , Levine, B.M. , and Cook, T. 2007. "Design and Development of a 331-segment Tip-tilt-piston Mirror Array for Space-based Adaptive Optics," Sensors and Actuators, A, 138:230-238.

22.

Takami, H. and Iye, M. 1994. "Membrane Deformable Mirror for SUBARU Adaptive Optics ," In: Adaptive Optics in Astronomy, Proceedings of SPIE, Vol. 2201, pp. 762-767, SPIE , Bellingham, WA.

23.

Zhu, G. , Levine, J. , Praly, L. and Peter, Y.-A. 2006. "Flatness-based Control of Electrostatically Actuated MEMS with Application to Adaptive Optics: A Simulation Study," IEEE J. Microelectromechanical Systems, 15(5):1165-1174.