Active Vibration Suppression of a Flexible Structure Using Sliding Mode Control

  • Itik Mehmet (Erciyes University, Yozgat Engineering and Architecture Faculty, Mechanical Engineering Department) ;
  • Salamci Metin U. (Gazi University, Engineering and Architecture Faculty, Mechanical Engineering Department)
  • 발행 : 2006.08.01

초록

In this paper, sliding mode control (SMC) is designed and applied to an elastic structure to suppress some of its vibration modes. The system is an elastic beam clamped on one end and the designed controller uses only the deflection measurement of the free end. The infinite dimensional mathematical model of the beam is reduced to an ordinary differential equation set to represent the behavior of required modes. Since the states of the finite dimensional model are not physically measurable quantities, an observer is designed to estimate these states by measuring the tip deflection of the beam. The performance of the observer is important because the observed states are used in the SMC design. In this study, by using the output information, an observer is designed and tested to estimate the states of the finite dimensional model of the beam. Then the designed SMC is applied to the experimental beam system which gives satisfactory suppressed vibrations.

키워드

참고문헌

  1. Bailey, T. and Hubbard, J. E., 1985, 'Distributed Piezoelectric-Polymer Active Vibration Control of a Cantilever Beam,' Journal of Guidance, Control and Dynamics, Vol. 8, No.5, pp.605-611 https://doi.org/10.2514/3.20029
  2. Banks, S. P., Salamci, M. U. and Ozgoren, M. K., 1999, 'On the Global Stabilization of Nonlinear Systems via Switching Manifolds,' Turkish Journal of Electrical Engineering & Computer, Elektrik, Vol. 7, No. 1-3, pp. 1-17
  3. Cavallo, A., De Maria, G. and Setola, R., 1999, 'A Stable Manifold Approach for Vibration Reduction of Flexible Systems,' Automatica, Vol. 35, pp. 1689-1696 https://doi.org/10.1016/S0005-1098(99)00068-0
  4. Choi, J. J. and Kim, J. S., 2003, 'Robust Control for Rotational Inverted Pendulums Using Output Feedback Sliding Mode Controller and Disturbance Observer,' KSME International Journal, Vol. 17, No. 10, pp. 1466-1474
  5. Choi, S. B., Cho, S. S. and Park, Y. P., 1999, 'Vibration and Position Tracking Control of Piezoceramic-Based Smart Structures via QFT,' Journal of Dynamic Systems, Measurement and Control, Vol. 121, pp.27-33 https://doi.org/10.1115/1.2802438
  6. DeCado, R. A., Zak, S. H. and Matthews, G. P., 1988, 'Variable Structure Control of Nonlinear Multivariab1e Systems: A Tutorial,' Proceeding of IEEE, Vol. 76, No.3, pp.212-232 https://doi.org/10.1109/5.4400
  7. Dorling, C. M. and Zinober, A. S. I., 1986, 'Two Approaches to Hyperplane Design in Multivariable Structure Control Systems,' International Journal of Control, Vol. 44, pp. 65-82 https://doi.org/10.1080/00207178608933583
  8. Dosch, J., Leo, D. and Inmann, J., 1995, 'Modeling and Control for Vibration Suppression of a Flexible Active Structure,' Journal of Guidance, Control and Dynamics, Vol. 18, pp. 340-346 https://doi.org/10.2514/3.21389
  9. Itik, M., Salamci, M. D., Ulker, F. D. and Yaman, Y., 2005, 'Active Vibration Suppression of a Flexible Beam via Sliding Mode and Hinfinity Control,' to be presented in IEEE Conference on Decision and Control and European Control Conference (CDC-ECC05) to be held in Seville, Spain, on December 12-15
  10. Jean, S., Ahn, H. J. and Han, D. c., 2002, 'Model Validation and Controller Design for Vibration Suppression of Flexible Rotor Using AMB,' KSME International Journal, Vol. 16, No. 12, pp. 1583-1593
  11. Petersen, I. R. and Pota H. R., 2003, 'Minimax LQG Optimal Control of a Flexible System,' Control Engineering Practice, Vol. 11, pp. 1273-1287 https://doi.org/10.1016/S0967-0661(02)00240-X
  12. Salamci, M. U., 1999, 'Two New Switching Surface Design Techniques for Nonlinear Systems with Their Applications to Missile Control,' PhD. Thesis, Middle East Technical University
  13. Salamci, M. U., Ozgoren, M. K. and Banks, S. P., 2000, 'Sliding Mode Control with Optimal Sliding Surfaces for a Missile Autopilot Design,' AIAA Journal of Guidance, Control and Dynamics, Vol. 23, No.4, pp. 719-727 https://doi.org/10.2514/2.4588
  14. Shin, H. C. and Choi, S. B., 2001, 'Position Control of Two Link Flexible Manipulator Featuring Piezoelectric Actuators and Sensors,' Mechatronics, Vol. 11, pp. 707-729 https://doi.org/10.1016/S0957-4158(00)00045-3
  15. Spurgeon, S. K. and Edwards, C., 1998, 'Sliding Mode Control: Theory and Applications,' Taylor & Francis, London
  16. Utkin, V.I. and Yang, K. D., 1978, 'Methods for Constructing Discontinuity Planes in Multidimensional Variable Structure Systems,' Automation and Remote Control, Vol. 39, pp. 1466-1470
  17. Utkin, V. I., 1992, 'Sliding Modes in Control and Optimization,' Springer Verlag, Berlin
  18. Young, K. K. D., (editor), 1993, 'Variable Structure Control for Robotics and Aerospace Applications,' Elsevier, Amsterdam
  19. Young, K. K. D. and Ozguner, U., 1993, 'Frequency Shaping Compensator Design for Sliding Mode,' International Journal of Control, Vol. 57, No.5, pp. 1005-1019 https://doi.org/10.1080/00207179308934427
  20. Zames, G. and Francis, B.A., 1983, 'Feedback Minimax Sensitivity and Optimal Robustness,' IEEE Trans. On Automatic Control, Vol. AC-28, No.5, pp. 585-600 https://doi.org/10.1109/TAC.1983.1103275
  21. Zames, G., 1981, 'Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Seminorms, and Approximate Inverses,' IEEE Trans. On Automatic Control, Vol. AC-26, No.2, pp. 301-320 https://doi.org/10.1109/TAC.1981.1102603
  22. Zinober, A. S. I., (editor), 1990, 'Deterministic Control of Uncertain Systems,' Peter Peregrinus Ltd., London