This paper presents an experimental investigation on active control of the elastodynamic response of a four-bar (4R) mechanism system using “smart” materials featuring piezoelectric sensor/actuator (S/A) pairs and multivariable optimal control. The experimental 4R mechanism is made such that its coupler link is flexible, its follower link is slightly less flexible and its crank is relatively rigid. Two thin plate-type piezoceramic S/A pairs are bonded to the flanks of the coupler link at the high strain locations corresponding to the first and second vibration modes. Based on the optimal multivariable control theory, a controller which consists of a linear quadratic regulator (LQR) and a Luenberger observer as a state estimator is designed and implemented. The results of the experimental investigation prove that in order to prevent high mode excitations, the controller design should be based on the modes representing vibrations of all components comprising the mechanism system rather than the modes corresponding to the link to which the S/A pairs are bonded. Response amplitude attenuation ratios up to 50 percent are achieved and high mode excitations are prevented.
Issue Section:
Mechanisms and Robotics Papers
1.
Anderson, E. H., Hagood, N. W., and Goodliffe, J. M., 1992, “Self-Sensing Piezoelectric Actuation: Analysis and Application to Controlled Structures,” Proceedings of the 33rd AIAA/ASME/ASC/AHS, Structures, Structural Dynamics and Materials Conference, Dallas, TX., Paper No. 92-2465
2.
Anderson, El. D. O., and Moore, J. B., 1990, Optimal Control, Linear Quadratic Methods, Prentice Hall.
3.
Bailey
T.
Hubbard
J. E.
1985
, “Distributed Piezoelectric-Polymer Active Control of a Cantilever Beam
,” AIAA Journal of Guidance Control and Dynamic
, Vol. 8
, No. 5
, pp. 605
–611
.4.
Balas
M. J.
1987
, “Feedback Control of Flexible Systems
,” IEEE Transaction on Automatic Control
, Vol. AC-23
, No. 4
, pp. 673
–679
.5.
Baz
A.
Poh
S.
1988
, “Performance of An Active Control System with Piezoelectric Actuators
,” Journal of Sound and Vibration
, Vol. 126
, No. 2
, pp. 327
–343
.6.
Choi
S-B.
Cheong
C-C.
Thompson
B. S.
Gandhi
M. V.
1994
, “Vibration Control of Flexible Mechanisms Using Piezoelectric Films
,” Mechanism and Machine Theory
, Vol. 29
, No. 4
, pp. 535
–546
.7.
Cleghorn
W. L.
Fenton
R. G.
Tabarrok
B.
1981
, “Optimal Design of High-Speed Flexible Mechanisms
,” Mechanism and Machine Theory
, Vol. 16
, pp. 339
–406
.8.
Crawley
E. F.
DeLuis
J.
1987
, “Use of Piezoelectric Actuators as Elements of Intelligent Structures
,” American Institute of Aeronautic and Astronautics Journal
, Vol. 2
, No. 10
, pp. 1373
–1385
.9.
Dosch
J. J.
Inman
D. J.
Garcia
E.
1992
, “A Self-Sensing Piezoelectric Actuator for Collocated Control
,” Journal of Intelligent Material Systems and Structures
, Vol. 3
, pp. 166
–185
.10.
Edberg, D. L., Bicos, A. S., and Fechter, J. S., 1991, “On Piezoelectric Energy Conversion for Electronic Passive Damping Enhancement,” Proceedings of Damping 91, San Diego, Paper No. GBA-1.
11.
Fanson, J. L., Blackwood, G. H., and Chu, C-C., 1989, “Active Member Control of Precision Structures,” Proceedings of the 30th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, AIAA Paper 89-1329.
12.
Gandhi, M. V., and Thompson, B. S., 1992, Smart Materials and Structures, Chapman & Hall.
13.
Hagood
N. W.
Chung
W. H.
Flotow
A. V.
1990
, “Modelling of Piezoelectric Actuator Dynamics for Active Structural Control
,” Journal of Intelligent Material Systems and Structures
, Vol. 1
, pp. 327
–354
.14.
Hagood
N. W.
Flotow
A. V.
1991
, “Damping of Structural Vibrations with Piezoelectric Materials and Passive Electrical Networks
,” Journal of Sound and Vibration
, Vol. 146
, No. 2
, pp. 243
–268
.15.
Hwang
W-S.
Park
H. C.
Hawang
W.
1993
, “Vibration Control of a Laminated Plate with Piezoelectric Sensor/Actuator: Finite Element Formulation and Modal Analysis
,” Journal of Intelligent Material Systems and Structures
, Vol. 4
, pp. 317
–329
.16.
Inman, D. J., 1994, Engineering Vibration, Prentice Hall.
17.
Khan
M. R.
Thornton
W. A.
Willmert
K. D.
1978
, “Optimality Criterion Techniques Applied to Mechanism Design
,” ASME JOURNAL OF MECHANICAL DESIGN
, Vol. 101
, pp. 319
–327
.18.
Liao
C. Y.
Sung
C. K.
1991
, “Vibration Suppression of Flexible Linkage Mechanisms Using Piezoelectric Sensors and Actuators
,” Journal of Intelligent Material Systems and Structures
, Vol. 2
, pp. 177
–197
.19.
Oliver
J. H.
Wysocki
D. A.
Thompson
B. S.
1985
, “The Synthesis of Flexible Linkages by Balancing the Tracer Point Quasi-Static Deflections using Microprocessor and Advanced Material Technologies
,” Mechanism and Machine Theory
, Vol. 20
, No. 2
, pp. 471
–482
.20.
Preiswerk
M.
Venkatesh
A.
1994
, “An Analysis of Vibration Control Using Piezoceramic in planar flexible-likage mechanisms
,” Journal of Smart Materials and Structures
, Vol. 3
, pp. 190
–200
.21.
Sannah, M., 1995, “Active Control of Elastodynamic Vibrations of A Four-Bar Mechanism System with A Smart Coupler Link Using Optimal Multivariable Control: Simulation And Experimental Implementation,” Ph.D. dissertation, Tennessee Technological University.
22.
Sannah, M., Smaili, A., and Lahdhiri, T., 1995, “Digital Optimal Multivariable Control of a Smart Structure Featuring Piezoelectric Sensors and Actuators,” Proceedings of the ASME 15 Biennial Conference on Mechanical Vibrations and Noise, Boston, MA.
23.
Smaili, A. A., Sannah, M., and Kopparapu, M., 1994, “Elastodynamic Response of Mechanism Systems including Compliance of their Drive and Load Shafts,” Journal of Robotics and Mechanism (to appear).
24.
Soong, K., Sunappan, D., and Thompson, B. S., 1987, “The Elastodynamic Response of a Class of Intelligent Machinery-Part I: Theory, Part II: Computational an Experimental Results,” Advanced Topics in Vibrations, DE- Vol. 8, The 1987 ASME Design Technology Conference, Boston, MA, Sep. 27–30, pp. 147–160.
25.
Sung
C. K.
Chen
Y. C.
1991
, “Vibration Control of the Elastodynamic Response of High Speed Flexible Linkage Mechanisms
,” ASME Journal of Vibration and Acoustics
, Vol. 113
, pp. 14
–21
.26.
Sung, C-C, Varadan, V. V., Bao, X-Q., and Varadan, V. K., 1990, “Active Control of Torsional Vibration Using Piezoceramic Sensors and Actuators,” Proceedings of the 30th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, pp. 2317–2322.
27.
Thompson
B. S.
Sung
C. K.
1985
, “The Design of Robot and Intelligent Manipulators Using Modern Composite Material
,” Mechanism and Machine Theory
, Vol. 20
, pp. 471
–482
.28.
Thompson, B. S., and Tao, X., 1994, “A note on the Experimentally-Determine Elastodynamically Response of a Slider-Crank Mechanism Featuring a Macro-scopically-Smart Connecting-Rod with Ceramic Piezoelectric actuators and Strain Gage Sensors,” Machine Elements and Machine Dynamics DE-71, The 1994 ASME Design Technical Conference, 23rd Biennial Mechanisms Conference, Minneapolis, Minnesota, Sep. 11–14, pp. 63–69.
29.
Varadan, V. K., Hong, S-Y., and Varadan, V. V., 1990, “Piezoelectric Sensors and Actuators for Active Damping using Digital Control,” Ultrasonic Symposium, pp. 1211–1214.
This content is only available via PDF.
Copyright © 1998
by The American Society of Mechanical Engineers
You do not currently have access to this content.
