In this paper a distributed parameter model of a slewing beam system with piezoelectric actuators and sensors is considered. The system has a torque motor at a pinned (proximal) end, an endpoint motion sensor at the distal end, and patches of thin piezoelectric laminates attached to its surface. The partial differential equation of motion for this system is transformed to Laplace domain transfer functions after application of the appropriate boundary conditions. Transfer functions relating the various actuator/sensor pairs are developed. The results are shown to reduce to previously known results which are special cases of the system under consideration. Examples and experimental results are presented using a beam experiment at the US Air Force, Frank J. Seller Research Laboratory.

1.
Alberts
T. E.
, and
Colvin
J. A.
, “
Observations on the Nature of Transfer Functions for Control of Piezoelectric Laminates
,”
J. of Intelligent Material Systems & Structures
, Vol.
2
, No.
4
,
1991
, pp.
528
541
.
2.
Alberts, T. E., DuBois, T. V., and Pota, H. R., “Experimental Verification of Multivariable Transfer Functions for a Slewing Piezoelectric Laminate Beam,” Proceedings of the 12th World Congress of the IFAC, Vol. 8, Sydney, Australia, 1993, pp. 515–518.
3.
Bailey
Thomas
, and
Hubbard
James E.
, “
Distributed Piezoelectric-Polymer Active Vibration Control of a Cantilever Beam
,”
J. Guidance, Control and Dynamics
, Vol.
8
, No.
5
,
1993
, pp.
605
611
.
4.
Baz
A.
, and
Poh
S.
, “
Performance of an Active Control System with Piezoelectric Actuators
,”
J. of Sound and Vibrations
, Vol.
126
, No.
2
,
1988
, pp.
327
343
.
5.
Cudney, H. H., “Distributed Structural Control Using Multilayered Piezoelectric Actuators,” PhD thesis, SUNY Buffalo, NY, 1989.
6.
Friedland, B., Control System Design. An Introduction to State-Space Methods, McGraw-Hill, New York, 1986.
7.
Garcia, E., Inman, D., and Dosch, J., “Vibration Suppression Using Smart Structures,” ASME 1991 Winter Meeting, AD-Vol. 24, Smart Structures and Materials, 1991, pp. 167–172.
8.
Lee, C. K., “Piezoelectric Laminates for Torsional and Bending Modal Control: Theory and Experiment,” Ph.D thesis, Cornell University, 1987.
9.
Lee
C-K.
, and
Moon
F. C.
, “
Modal Sensors/Actuators
,”
ASME Journal of Applied Mechanics
, Vol.
57
,
1991
, pp.
434
441
.
10.
Pan, J., Hansen, C. H., and Snyder, S. D., “A Study of the Response of a Simply Supported Beam to Excitation by a Piezoelectric Actuator,” Proceedings of the Conference on Recent Advances in Active Control of Sound and Vibration, VPI & SU, VA, 1991, pp. 39–49.
11.
Crawley
E. F.
, and
Anderson
E. H.
, “
Detailed Models of Piezoelectric Actuation of Beams
,”
J. of Intelligent Material Systems & Structures
, Vol.
1
,
1990
, pp.
4
25
.
12.
Papoulis, A., The Fourier Integral and its Applications, McGraw-Hill, Sydney, 1962.
13.
Pota, H. R., Alberts, T. E., and Petersen, I. R., “H Control of Flexible Slewing Link with Active Control,” N. W. Hagood, ed., Proceedings of the 1993 North American SPIE Conference on Smart Structures and Intelligent Systems, Vol. 1917, Paper #06, Albuquerque, NM, 1993.
14.
Schmitz, E., “Experiments on the End-Point Position Control of A Very Flexible One-Link Manipulator,” PhD thesis, Stanford University, 1985.
15.
Tzou
H. S.
, “
Integrated Distributed Sensing and Active Vibration Suppression of Flexible Manipulators Using Distributed Piezoelectrics
,”
Journal of Robotic Systems
, Vol.
6
, No.
6
,
1989
, pp.
745
767
.
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