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Control of flexible manipulators via singular perturbations and distributed vibration damping

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Dynamics and Control

Abstract

A composite control strategy for a two-link flexible manipulator is analyzed which combines hub actuation with distributed vibration control. The hub actuation is based upon an integral manifold approach in which the system dynamics are approximately linearized to any order of a small parameter E representing stiffness of the robot arms. A polymer film is proposed as a distributed actuator to dampen vibrations due to elasticity in the links. Simulation results are provided which show that the addition of the distributed actuator significantly reduces the displacement and velocity of the first flexible mode in each link compared to hub actuation alone.

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References

  1. Bailey, T. and Hubbard, Jr., J. E., “Distributed piezoelectric-polymer active vibration control of a cantilever beam,”J. Guidance, vol. 8, no. 5, pp. 605–611, 1985.

    Google Scholar 

  2. Barbieri, E., Modelling and control of planar flexible structures with application to an optical-tracking system, Ph.D. Thesis, The Ohio State University, 1988.

  3. Blevins, R. D.,Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold: New York, 1979.

    Google Scholar 

  4. Bhat, B. R. and Wagner, H., “Natural frequencies of a uniform cantilever with a tip slender in the axial direction,”J. Sound and Vibration, vol. 45, no. 2, pp. 304–307, 1976.

    Google Scholar 

  5. Burke, S. E. and Hubbard, Jr., J. E., “Active vibration control of a simply supported beam using a spatially distributed actuator,”IEEE Control Syst Mag., vol. 7, no. 4, pp. 25–30, 1987.

    Google Scholar 

  6. Burke, S. E. and Hubbard, Jr., J. E., “Distributed actuator control design for flexible beams,”Automatica, vol. 24, no. 5, pp. 619–627, 1988.

    Google Scholar 

  7. Chassiakos, A. G. and Bekey, G. A., “On the modelling and control of a flexible manipulator arm by point actuators,”Proc. 25th IEEE Conf. on Decision and Control, Athens, Greece, pp. 1145–1150, 1986.

  8. Collins, S. A., Notestine, R. J., Padilla, C. E., Ramey, M. Schmitz, E., and von Flotow, A. H., “Design, manufacture, and application to space robotics of distributed piezoelectric film sensors,”Proc. of the 31st AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conf., Long Beach, CA, pp. 1899–1906, 1990.

  9. Crawley, E. F. and de Luis, J., “Use of piezoelectric actuators as elements of intelligent structures,”AIAA J., vol. 25, no. 10, pp. 1371–1385, 1987.

    Google Scholar 

  10. De Luca, A. and Siciliano, B., “Trajectory control of a non-linear one-link flexible arm,”Int. J. Control, vol. 50, no. 5, pp. 1699–1715, 1989.

    Google Scholar 

  11. Ding, X., Tarn, T. J. and Bejczy, A. K., “A novel approach to the dynamics and control of flexible robot arms,”Proc. 27th Conf. on Decision and Control, Austin, TX, pp. 52–57, 1987.

  12. Edberg, D. L., “Control of flexible structures by applied thermal gradients,”AIAA J., vol 25, no. 6, pp. 877–883, 1987.

    Google Scholar 

  13. Khorrami, F. and Özgüner, Ü., “Singular perturbation analysis of a distributed parameter model of flexible manipulators,”Proc. 7th Amer. Control Conf., Atlanta, GA, pp. 1704–1709, 1988.

  14. Khorrami, F., “Asymptotic perturbation and Lyapunov stability based approaches for control of flexible and rigid robot manipulators,” Ph.D. Thesis, The Ohio State University, 1988.

  15. Khorrami, F., “Analysis of multii-link flexible manipulators via asymptotic expansions,”Proc. 28th Conf. on Decision and Control, Tampa, FL, pp. 2089–2094, 1989.

  16. Khorrami, F. and Zheng, S., “Vibration control of flexible-link manipulators,”Proc. 9th Amer Control Conf., San Diego, CA, pp. 175–180, 1990.

  17. Kokotović, P. V., Khalil, H. K. and O'Reilly, J.,Singular Perturbation Methods in Control: Analysis and Design. Academic Press: London, 1986.

    Google Scholar 

  18. Kotnik, P. T., Yurkovich, S. and Özgüner, Ü., “Acceleration feedback for control of a flexible manipulator arm,”J. Robotic Syst., vol. 5, no. 3, pp. 181–196, 1988.

    Google Scholar 

  19. Leissa, A. W., “Closed form exact solutions for the steady state vibrations of continuous systems subjected to distributed exciting forces,”J. Sound and Vibration, vol 134, pp. 435–453, 1989.

    Google Scholar 

  20. Nicosia, S., Tomei, P. and Tomambè, A., “Nonlinear control and observation algorithms for a single-link flexible robot arm,”Int. J. Control, vol 49, pp. 827–840, 1989.

    Google Scholar 

  21. Oakley, C. M. and Cannon, Jr., R. H., “End-point control of a two-link manipulator with a very flexible forearm: issues and experiments,”Proc. 8th Amer. Control Conf., Pittsburgh, PA, pp. 1381–1388, 1989.

  22. Schoenwald, D. A., Özgüner, Ü. and Chan, H., “An analysis of distributed vibration control of flexible manipulators using integral manifolds,”Proc. 28th Conf. on Decision and Control, Tampa, FL, pp. 2095–2100, 1989.

  23. Schoenwald, D. A. and Özgüner, Ü., “On combining slewing and vibration control in flexible manipulators via singular perturbations,”Proc. 29th Conf. on Decision and Control, Honolulu, HI, 1990.

  24. Siciliano, B., Book, W. J. and De Maria, G. “An integral manifold approach to control of a one link flexible arm,”Proc. 25th IEEE Conf. on Decision and Control, Athens, Greece, pp. 1131–1134, 1986a.

  25. Siciliano, B., Calise, A. J. and Jonnalagadda, V. R. P., “Optimal output fast feedback in two-time scale control of flexible arms,”Proc. 25th IEEE Conf. on Decision and Control, Athens, Greece, pp. 1400–1403, 1986b.

  26. Siciliano, B. and Book, W. J., “A singular perturbation approach to control of lightweight flexible manipulators,”Int. J. Robotics Research, vol 7, no. 4, pp. 79–90, 1988.

    Google Scholar 

  27. Sobolev, V. A., “Integral manifolds and decomposition of singularly perturbed systems,”Syst. Control Lett., vol. 5, pp. 1169–1179, 1984.

    Google Scholar 

  28. Spong, M. W., Khorasani, K. and Kokotović, P. V., “An integral manifold approach to the feedback control of flexible joint robots,”IEEE J. Robotics and Automation, vol. RA-3, no. 4, pp. 291–300, 1987.

    Google Scholar 

  29. Tadikonda, S. and Baruh, H., “Pointwise-optimal control of robotic manipulators,”ASME J. Dynamic Syst., Measurement, and Control, vol. 110, no. 6, pp. 210–213, 1988.

    Google Scholar 

  30. Vincent, T. L., Lin, Y. C. and Joshi, S. P., “Controlling a flexible plate to mimic a rigid one,”Control and Dynamic Systems: Advances in Control Mechanics, vol. 35, no. 2, (Ed: C. T. Leondes), Academic Press: New York, pp. 87–135, 1990.

    Google Scholar 

  31. Young, K. D. and Özgüner, Ü., “Frequency shaped variable structure control,”Proc. 9th Amer. Control Conf., San Diego, CA, pp. 181–185, 1990.

  32. Yurkovich, S., Tzes, A. P. and Hillsley, K. L., “Controlling coupled flexible links rotating in the horizontal plane,”Proc. 9th Amer. Control Conf., San Diego, CA, pp. 362–367, 1990.

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Editor: T. Vincent

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Schoenwald, D.A., Özgüner, Ü. Control of flexible manipulators via singular perturbations and distributed vibration damping. Dynamics and Control 6, 5–32 (1996). https://doi.org/10.1007/BF02169459

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  • DOI: https://doi.org/10.1007/BF02169459

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