A study of the application of the phase-locked loop (PLL) to modal control of mechanical structures is performed. An analog PLL circuit is used to control the vibration of a cantilevered beam with piezoelectric sensors and actuators. By using the PLL controller, strain rate feedback is provided within a narrow and distinct frequency range about the fourth mode of the beam. The controller ignores all other modes and does not affect the phase outside of the frequency range. The PLL controller provides a simple, inexpensive, and effective method to control an individual structural mode or set of modes without causing spillover.

1.
Balas
M. J.
,
1978
, “
Active Control of Flexible Systems
,”
Journal of Optimization Theory and Applications
, Vol.
25
, No.
3
, pp.
415
437
.
2.
Balas, M. J., and Ouyang, J. J., 1986, “Self-Tuning Adaptive Controller Using On-Line Frequency Locked Loops,” Proceedings of the Twentieth Asilomar Conference on Signals, Systems & Computers, Pacific Grove, California, November 10–12, pp. 681–685.
3.
Balas, M. J., Quan, R., Davidson, R., and Das, B., 1988, “Low-Order Control of Large Aerospace Structures Using Residual Mode Filters,” Proceedings of the American Control Conference.
4.
Best, R. E., 1984, Phase-Locked Loops Theory, Design, and Application, McGraw-Hill Book Company, New York.
5.
Davidson, R. A., 1990, “Compensation Controller-Structure Interaction Using Adaptive Residual Mode Filters,” Dissertation, University of Colorado, Boulder, Colorado.
6.
de Bellescize
H.
,
1932
, “
La Reception Synchrone
,”
Onde Electrique
, Vol.
11
, pp.
230
240
.
7.
EXAR Corporation, 1992, EXAR Datahook, AN-11, AN-40, AN-41.
8.
Gardner, F. M., 1979, Phaselock Techniques, John Wiley & Sons, New York.
9.
Lee
C. K.
, and
Moon
F. C.
,
1990
, “
Modal Sensors/Actuators
,”
ASME Journal of Applied Mechanics
, Vol.
57
, pp.
434
441
.
10.
Meirovitch
L.
, and
Baruh
H.
,
1982
, “
Control of Self-Adjoint Distributed Parameter Systems
,”
Journal of Guidance, Control, and Dynamics
, Vol.
5
, No.
1
, pp.
60
66
.
11.
Meirovitch
L.
, and
Baruh
H.
,
1983
, “
On the Problem of Observation Spillover in Self-Adjoint Distributed Parameter Systems
,”
Journal of Optimization Theory and Application
,’ Vol.
39
, No.
2
, pp.
269
291
.
12.
Meirovitch
L.
, and
Baruh
H.
,
1984
, “
Nonlinear Natural Control of an Experimental Beam
,”
Journal of Guidance, Control, and Dynamics.
, Vol.
7
, No.
4
, pp.
437
442
.
13.
Meirovitch
L.
, and
Baruh
H.
,
1985
, “
Implementation of Modal Filters for Control of Structures
,”
Journal of Guidance, Control, and Dynamics
, Vol.
8
, No.
6
, pp.
707
716
.
14.
Oz
H.
, and
Meirovitch
L.
,
1983
, “
Stochastic Independent Modal-Space Control of Distributed Parameter Systems
,”
Journal of Optimization Theory and Applications
, Vol.
40
, No.
1
, pp.
121
154
.
15.
Shelley, S. J., Freudinger, L. C., Allemang, R. J., 1992, “Development of an On-Line Parameter Estimation System Using the Discrete Modal Filter,” Proceedings of the 10th International Modal Analysis Conference (IMAC), San Diego, California, February 3–8, pp. 173–183.
16.
Shelley, S. J., Freudinger, L. C., Allemang, R. J., Zhang, Q., 1991, “Implementation of a Modal Filter on a Five Meter Truss Structure,” Proceedings of the 9th International Modal Analysis Conference (IMAC), Florence, Italy, April, pp. 1036–1044.
17.
Signetics Corporation, 1977, Signetics Analog Data Manual, pp. 809–860.
18.
Tzou, H. S., and Zhong, J. P., 1991, “Sensor Mechanics of Distributed Shell Convolving Sensors Applied to Flexible Rings,” Proceedings of the 13th Biennial Conference on Mechanical Vibration and Noise presented at the 1991 ASME Design Technical Conferences, Miami, Florida, September 22–5, pp. 67–74.
19.
Zhang, Q., Allemang, R. J., and Brown, D. L., 1990, “Modal Filter: Concept and Applications,” Proceedings of the 8th International Modal Analysis Conference (IMAC), Orlando, Florida, January, pp. 487–496.
This content is only available via PDF.
You do not currently have access to this content.