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Vibration control of elastodynamic response of a 3-PRR flexible parallel manipulator using PZT transducers

Published online by Cambridge University Press:  01 September 2008

Xuping Zhang ,
James K. Mills  and
William L. Cleghorn
Xuping Zhang*
Affiliation:
Department of Mechanical and Industrial Engineering, University of Toronto5 King's College Road, Toronto, Ontario, Canada, M5S 3G8
James K. Mills
Affiliation:
Department of Mechanical and Industrial Engineering, University of Toronto5 King's College Road, Toronto, Ontario, Canada, M5S 3G8
William L. Cleghorn
Affiliation:
Department of Mechanical and Industrial Engineering, University of Toronto5 King's College Road, Toronto, Ontario, Canada, M5S 3G8
*
*Corresponding author. E-mail: [email protected]
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Summary

This paper addresses the dynamic simulation and control of structural vibrations of a 3-PRR parallel manipulator with three flexible intermediate links, to which are bonded lead zirconate titanate (PZT) actuators and sensors. Flexible intermediate links are modelled as Euler–Bernoulli beams with pinned-pinned boundary conditions. A PZT actuator controller is designed based on strain rate feedback (SRF) control. Control moments from PZT actuators are transformed to force vectors in modal space and are incorporated in the dynamic model of the manipulator. The dynamic equations are developed based on the assumed mode method for the flexible parallel manipulator with multiple PZT actuator and sensor patches. Numerical simulation is performed and the results indicate that the proposed active vibration control strategy is effective. Spectral analyses of structural vibrations further illustrate that deformations from structural vibration of flexible links are suppressed to a significant extent when the proposed vibration control strategy is employed, while the deflections caused by inertial and coupling forces are not reduced.

Keywords

Flexible manipulatorsParallel manipulatorsAssumed modeStrain rate feedbackPZT Transducers
Type
Article
Information
Robotica , Volume 26 , Issue 5 , September 2008 , pp. 655 - 665
Copyright
Copyright © Cambridge University Press 2008

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References

1.Winfrey, R. C., “Elastic link mechanism dynamics,” ASME J. Eng. Ind. 93, 268–272 (1971).CrossRefGoogle Scholar
2.Sunada, W. and Dubowsky, S., “The application of the finite element methods to the dynamic analysis of flexible spatial and co-planar linkage systems,” ASME J. Mech. Des. 103 (3), 643–651 (1981).Google Scholar
3.Book, W. J., “Recursive Lagrangian dynamics of fexible manipulator arms,” Int. J. Robot Res. 3 (3), 87–101 (1984).CrossRefGoogle Scholar
4.Asada, H., Ma, Z.-D. and Tokumaru, H., “Inverse dynamics of flexible robot arms: Modeling and computation for trajectory control,” ASME. J. Dyn. Syst. Meas. Control 112, 177–185 (1990).CrossRefGoogle Scholar
5.Shabana, A. A., “Flexible multibody dynamics: review of past and recent developments,” Multibody Syst. Dyn. 1, 189–222 (1997).Google Scholar
6.Giovagnoni, M., “Dynamics of Flexible Closed-chain Manipulator,” ASME Design Technical Conference 69-2, Scottsdale, Arizona, USA (1992) pp. 483–490.Google Scholar
7.Lee, J. D. and Geng, Z., “Dynamic model of a flexible Stewart platform,” Comput. Struct. 48 (3), 367–374 (1993).Google Scholar
8.Zhou, Z., Xi, J. and Mechefske, C. K., “Modeling of a fully flexible 3PRS manipulator for vibration analsysis,” J Mech. Des. 128, 403–412 (2006).Google Scholar
9.Wang, X., and Mills, J. K., “FEM dynamic model for active vibration control of flexible linkages and its application to a planar parallel manipulator,” Appl Acous. 66, 1151–1161 (2005).Google Scholar
10.Xuping, Zhang, Mills, J K. and Cleghorn, W. L., “Dynamic modeling and experimental validation of a 3-PRR parallel manipulator with flexible intermediate link,” J. Intell. Robot. Syst. 50, 323–340 (2007).Google Scholar
11.Zhang, X. M., Shen, Y. W., Liu, H. Z. and Cao, W. Q., “Optimal design of flexible mechanisms with frequency constraints,” Mech. Mach. Theory 30 (1), 131–139 (1995).CrossRefGoogle Scholar
12.Cleghorn, W. L., Fenton, F. G. and Tabarrok, B., “Optimal design of high-speed flexible mechanisms,” Mech. Mach. Theory 16, 339–406 (1981).Google Scholar
13.El-Dannah, E. H. and Farghaly, S. H., “Vibratory response of a sandwich link in a high-speed mechanism,” Mech. Mach. Theory 28, 447–457 (1993).CrossRefGoogle Scholar
14.Sisemore, C., Smaili, A. and Houghton, R., “Passive damping of flexible mechanism systems: Experimental and finite element investigations,” In: The 10th World Congress on the Theory of Machines and Mechanisms, Oulu, Finland (Jun. 20–24, 1999), vol. 5, pp. 2140–2145.Google Scholar
15.Ghazavi, A., Gardanine, F. and Chalhout, N. G., “Dynamic analysis of a composite material flexible robot arm,” Comput. Struct. 49, 315–325 (1993).Google Scholar
16.Sung, C. K. and Thompson, B. S., “Material selection: An important parameter in the design of high-speed linkages,” Mech. Mach. Theory 19, 389–396 (1984).CrossRefGoogle Scholar
17.Ulbrich, H. and Stein, H. V., “A combined feedforward-feedback control strategy for improving the dynamics of a flexible mechanism,” Multibody Syst. Dyn. Theory 7, 229–248 (2002).Google Scholar
18.Singer, N. C. and Seering, W. P., “Using a Causal Shaping Techniques to Reduce Robot Vibrations”, Proceedings of IEEE International Conference on Robotics and Automation, Philadelphia (1988) pp. 1434–1439.Google Scholar
19.Siciliano, B. and Book, W., “A singular perturbation approach to control of lightweight flexible manipulators”, Int. J. Robot. Res. 7 (4), 79–90 (1988).CrossRefGoogle Scholar
20.Asokanthan, S. F. and Gu, M., “Distributed Control of Flexible Structure: Theory and Experiment,” Proceedings of Asia-Pacific Control Conference, Brooklyn, New York, USA (1995) pp. 539–553.Google Scholar
21.Bailey, T. and Hubbard, J. J., “Distributed piezoelectric-polymer active vibration control of a cantilever beam,” J. Guid. Control Dyn. 9 (5), 605–611 (1985).CrossRefGoogle Scholar
22.Li, Z. and Bainum, P. M., “Vibration control of flexible spacecraft integrating a momentum exchange controller and a distributed piezoelectric actuator,” J. Sound Vib. 177 (4), 539–553 (1994).Google Scholar
23.Choi, S. B. and Shin, H. C., “A hybrid actuator scheme for robust position control of a flexible single-link manipulator,” J. Robot. Syst. 13 (6), 359–370 (1996).3.0.CO;2-O>CrossRefGoogle Scholar
24.Crawley, E. F. and Luis, D., “Use of piezoelectric actuators as elements of intelligent structures,” AIAA J. 25 (10), 1373–1385 (1987).CrossRefGoogle Scholar
25.Khorrami, F., Zeinoun, I. and Tome, E., “Experimental Results on Active Control of Flexible-link Manipulators with Embedded Piezoceramics,” Proceedings of IEEE International Conference Robotics and Automation, Atlanta, GA, USA (1993) pp. 222–227.Google Scholar
26.Song, G., Schmidt, S. P. and Agrawal, B. N., “Active vibration suppression of a flexible structure using smart material and modular control patch,” Proc. Inst. Mech. Eng. 214, 217–229 (2000).Google Scholar
27.Sung, C. K. and Chen, Y. C., “Vibration control of the elastodynamic response of high-speed flexible linkage mechanisms,” ASME J. Vib. Acoust. 113 (1), 14–21 (1991).Google Scholar
28.Sun, D., Mills, J. K., Shan, J. and Tso, S.K., “A PZT actuator control of a single-link flexible manipulator based on linear velocity feedback and actuator placement,” Mechatronics 14, 381–401 (2004).Google Scholar
29. “Solve initial value problems for ordinary differential equations (ODEs),” MATLAB Function Reference, The Math Works, Inc. 1994-2005.Google Scholar
30.Staicu, S., Zhang, D. and Rugescu, R., “Dynamic modelling of 3-DOF parallel manipulator using recursive matrix relations,” Robotica 24, 125–130 (2006).Google Scholar
31.Kang, B., Yeung, B. and Mills, J. K., “Two-time scale controller design for a high speed planar parallel manipulator with structural flexibility,” Robotica 20, 519–528 (2002).CrossRefGoogle Scholar
32.Meirovitch, L. and Baruh, H., “Optimal control of damped flexible gyroscopic systems,” J. Guid. Control 4, 157–163, (1981).CrossRefGoogle Scholar
33.Baz, A. and Poh, S., “Performance of an active control system with piezoelectric actuators,” J. Sound Vib. 126 (2), 327–343 (1988).CrossRefGoogle Scholar
34.Singh, S. P., Pruthi, H. S. and Agarwal, V. P., “Efficient modal control strategies for active control of vibrations,” J. Sound Vib. 262, 563–575 (2003).CrossRefGoogle Scholar
35. Product Catalogue, Sensor Technology Ltd., Collingwood, Ontario, Canada, 2007.Google Scholar
36.Gosselin, C. M., Lemieux, S. and Merlet, J.-P.,”A New Architecture of Planar Three-Degree of Freedom Parallel Manipulator,” Proceedings of the IEEE International Conference on Robotics and Automation, Minneapolis, Minnesota, (1996) pp. 3738–3743.Google Scholar
37.Yan, X. J. and Yam, L. H., “Optimal design of number and locations of actuators in active vibration control of a space truss,” Smart Mater. Stuct. 11, 496–593 (2002).CrossRefGoogle Scholar
38.Abdullah, M. M., “Optimal locations and gains of feedback controllers at discrete locations,” AIAA J. 36 (11), pp. 2109–2116 (1998).CrossRefGoogle Scholar