Sage Journals: Discover world-class research

Abstract

This article presents the application of multi-input multi-output (MIMO) quantitative feedback theory (QFT) to the control of a single-link flexible manipulator. The manipulator employs an actuation scheme comprised of a DC motor that provides spatially discrete actuation and a surface bonded piezoelectric ceramic that provides spatially distributed actuation. The efficacy of the sequential MIMO QFT methodology for articulating flexible structure control is investigated using the flexible manipulator testbed, with the control system designed to achieve rapid, rest-to-rest positioning of the manipulator tip in the presence of significant parametric and non-parametric structured uncertainty. Numerical simulations and experiments are employed to validate the synthesised control system and the combined discrete-distributed actuation scheme. Conservatisms in the MIMO QFT methodology are identified and partly alleviated using recent theoretical and design improvements.

Keywords

Active vibration control flexible manipulator piezoelectric quantitative feedback theory robust control

Get full access to this article

View all access options for this article.

References

Borghesani, C. , Chait, Y. , and Yaniv, O. , 1994 Quantitative Feedback Theory Toolbox Users Guide, The Math Works Inc., Natick, MA .

Boulet, B. , Francis, B. A. , Hughes, P. C. , and Hong, T. , 2001, “μ-synthesis for a large flexible space structure experimental testbed,” Journal of Guidance, Control, And Dynamics 24(5), 967-977 .

Cannon, R. H. and Schmitz, E. , 1984, “Initial experiments on the end-point control of a flexible one-link robot,” International Journal of Robotics 3(3), 62-75 .

Chait, Y. , Park, M. S. , and Steinbuch, M. , 1994, “Design and implementation of a QFT controller for a compact disc player,” Journal of Systems Engineering 4, 107-117 .

Chang, P. and Jayasuriya, S. , 1995, “An evaluation of several controller methodologies using a rotating flexible beam as a test bed,” ASME Journal of Dynamic Systems, Measurement and Control 117, 360-373 .

Choi, S. B. , Cho, S. , Shin, H. , and Kim, H. , 1999, “Quantitative feedback theory control of a single-link flexible manipulator featuring piezoelectric actuator and sensor,” Smart Material and Structures 8, 338-349 .

Fuller, C. R. , Elliot, S. J. , and Nelson, P. A. , 1996, Active Control of Vibrations, Academic Press, London, UK .

Garcia, E. and Inman, D. J. , 1990, “Advantages of slewing an active structure,” Journal of Intelligent Material Systems and Structures 1, 261-272 .

Garcia, E. and Inman, D. J. , 1991, “Modelling of the slewing control of a flexible structure,” Journal of Guidance, Control and Dynamics 14(4), 736-742 .

10.

Horowitz, L. , 1979, “Quantative Synthesis of uncertain multi input-output feedback system,” International Journal of Control 30(1), 81-106 .

11.

Karkoub, M. , Balas, G. , Tamma, K. , and Donath, M. , 2000, “Robust control of flexible manipulators via μ-synthesis,” Control Engineering Practice 8, 725-734 .

12.

Kerr, M.L., 2004, “Robust control of an articulating flexible structure using MIMO QFT,” Ph.D. Thesis, Department of Mechanical Engineering, The University of Queensland, Australia.

13.

Kerr, M. L. , Asokanthan, S. F. , and Jayasuriya, S. , 2002 “Robust tracking control of a single-link flexible manipulator,” in Proceedings of the 15th IFAC World Congress on Automatic Control, Barcelona, Spain, July 21-26.

14.

Kerr, M. L. , Jayasuriya, S. , and Asokanthan, S. F. , 2003, “Robust stability in sequential MIMO QFT,” in Proceedings of the 2003 American Control Conference, Denver, Colorado, June 4-5.

15.

Kerr, M. L. , Jayasuriya, S. , and Asokanthan, S. F. , 2005, “Robust stability of sequential MIMO QFT designs,” Journal of Dynamic Systems, Measurement and Control 127(2), 250-256 .

16.

Meirovitch, L. , 1997, Principles and Techniques of Vibrations, Prentice Hall, Upper Saddle River, NJ .

17.

Miu, D. K. , 1991, “Physical interpretation of transfer function zeros for simple control systems with mechanical flexibilities,” ASME Journal of Dynamic Systems, Measurement and Control 113, 419-424 .

18.

Mordfin, T.G., 2001, “Component body modelling and controlled articulated flexible multibody dynamics,” Ph.D. Thesis, Department of Mechanical Engineering, Catholic University of America, Washington DC.

19.

Park, M. S. , Chait, Y. , and Steinbuch, M. , 1997, “Inversion-free algorithms for multivariable quantitative feedback theory: An application to robust control of a CD-ROM,” Automatica 33(5), 915-920 .

20.

Piedmonte, M. D. , Meckl, P. H. , Nwokah, O. D. I. , and Franchek, M. A. , 1998, “Multivariable vibration control of a coupled flexible structure using QFT,” International Journal of Control 69(4), 475-498 .

21.

Skogestad, S. and Postlethwaite, I. , 1996, Multivariable Feedback Control-Analysis and Design, Wiley, NewYork .

22.

Sutton, R. P. , Halikias, G. D. , Plummer, A. R. , and Wilson, D. A. , 1999, “Modelling and H∞ control of a single-link flexible manipulator,” Proceedings of the Institute of Mechanical Engineers 123, 85-104 .

23.

Yang, S. M. and Liu, Y. C. , 1995, “Frequency domain control of flexible beams with piezoelectric actuator,” ASME Journal of Dynamic Systems, Measurement and Control 117, 541-546 .

24.

Yaniv, O. , 1992, “Synthesis of uncertain MIMO feedback systems for gain and phase margins at different channel breaking points,” Automatica 28(5), 1017-1020 .

25.

Yaniv, O. , 1999, Quantitative feedback design of linear and nonlinear control systems, Kluwer, Norwell, MA .

26.

Yaniv, O. , and Schwartz, B. , 1991, “Criterion for loop stability in MIMO feedback systems having an uncertain plant,” International Journal of Control 53(3), 527-539 .

QFT Based Robust Control of a Single-Link Flexible Manipulator

Abstract

Keywords

Get full access to this article

References