In this paper we will present a model for an array of microcantilevers that are used in Atomic Force Microscopy and nano-scale manufacturing. The microcantilevers are connected to each other through a common base, and are individually actuated. The sensors are also integrated on each microcantilever. We consider the problem of controlling a tightly packed array of identical microcantilevers that are dynamically coupled. This system is an example of a spatially-invariant system with a distributed array of sensors and actuators. We exploit the spatial invariance of the problem to design optimal ℋ2 controllers for this array. An analytic expression for the optimal controller is derived in the transformed domain, and estimates of the coupling range of the controller is obtained.

Issue Section:
Technical Papers
Topics:
Microcantilevers, Optimal control, Control equipment, Sensors, Actuators, Atomic force microscopy, Design, Manufacturing, Nanoscale phenomena
1.
M. Ashhab, M. Salapaka, M. Dahleh, and I. Mezic, 1997, “Control of Chaos in Atomic Force Microscopes,” Proceedings of the American Control Conference, Albuquerque, NM, pp. 196–202, June.
2.
M. Ashhab, M. Salapaka, M. Daleh, and I. Mezic´, 1997, “Melnikov-based Dynamical Analysis of Microcantilevers in Scanning Probe Microscopy,” UCSB Technical Report.
3.
E. W. Kamen, 1985, “Stabilization of Linear Spatially-Distributed Continuous-Time and Discrete-Time Systems,” Multidimensional Systems Theory, Chap. 4. N. K. Bose, ed., D. Reidel Publishing Company.
4.
B. Bamieh, F. Paganini, and M. A. Dahleh, 1998, “Optimal Control of Distributed Actuator and Sensor Arrays,” to appear in Proc. SPIE 5’th Ann. Intl. Symp. on Smart Structures and Materials, San Diego, Mar.
5.
B. Bamieh, 1997, “The Structure of Optimal Controllers of Spatially-Invariant Distributed Parameter Systems,” Proc. 36’th IEEE Conference on Decision and Control, San Diego, CA, Dec.
6.
B. Bamieh, F. Paganini, and M. A. Dahleh, 1998, “Distributed Control of Spatially Invariant Systems,” submitted to the IEEE Trans. Automatic Control, May.
7.
Binnig
G.
,
Quate
C. F.
, and
Gerber
C.
,
1986
, “
Atomic Force Microscope
,”
Physical Review Letters
, Vol.
56
, No.
9
, pp.
930
–
933
.
8.
Dror Sarid, 1994, Scanning Force Microscopy, Oxford University Press, New York.
9.
Jacob N. Israelachvili, 1985, Intermolecular and Surface Forces, Academic Press.
10.
Minne
S. C.
,
Manalis
S. R.
, and
Quate
C, F.
,
1995
, “
Parallel Atomic Force Microscopy Using Cantilevers with Integrated Piezoresistive Sensors and Integrated Piezoelectric Actuators
,”
Appl. Phys. Lett.
, Vol.
67
(
25
), pp.
3918
–
3920
, Dec.
11.
Minne
S. C.
,
Manalis
S. R.
,
Atalar
A.
, and
Quale
C. F.
,
1996
, “
Independent Parallel Lithography Using the Atomic Force Microscope
,”
J. Vac. Sci. Technology
, Vol. B.
14
(
4
), pp.
2456
–
2461
, July.
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