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Robust Gain Scheduling for Smart-Structures in Parallel Robots

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Robotic Systems for Handling and Assembly

Part of the book series: Springer Tracts in Advanced Robotics ((STAR,volume 67))

Abstract

Smart-structures offer the potential to increase the productivity of parallel robots by reducing disturbing vibrations caused by high dynamic loads. In parallel robots the vibration behavior of the structure is position dependent. A single robust controller is not able to gain satisfying control performance within the entire workspace. Hence, vibration behavior is linearized at several operating points and robust controllers are designed. Controllers can be smoothly switched by gain-scheduling. A stability proof for fast varying scheduling parameters based on the Small-Gain Theorem is developed. Experimental data from Triglide, a four degree of freedom (DOF) parallel robot of the Collaborative Research Center 562, validate the presented concepts.

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References

  1. Book, W.J.: Controlled motion in an elastic world. Journal of Dynamic Systems, Measurement, and Control 115(2B), 252–261 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  2. Adams, R.J., Apkarian, P., Chrétien, J.-P.: Robust control approaches for a two-link flexible manipulator. In: 3rd International Conference on Dynamics and Control of Structures in Space, pp. 101–116 (1996)

    Google Scholar 

  3. Karkoub, M., Yigit, A.S.: Vibration control of a four-bar mechanism with a flexible coupler link. Journal of Sound and Vibration 222(2), 171–189 (1999)

    Article  Google Scholar 

  4. Anderson, E.H., Leo, D.J., Holcomb, M.D.: Ultraquiet platform for active vibration isolation. In: Chopra, I. (ed.) Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 2717, pp. 436–451 (1996)

    Google Scholar 

  5. Joshi, A., Kim, W.-J.: Modeling and multivariable control design methodologies for hexapod-based satellite vibration isolation. Journal of Dynamic Systems, Measurement, and Control 127(4), 700–704 (2005)

    Article  Google Scholar 

  6. Wang, X., Mills, J.: A fem model for active vibration control of flexible linkages. In: Proc. of IEEE International Conference on Robotics and Automation (ICRA), vol. 5, pp. 1050–4729 (2004) ISSN 1050-4729

    Google Scholar 

  7. Wang, X., Mills, J.K.: Active control of configuration-dependent linkage vibration with application to a planar parallel platform. In: IEEE International Conference on Robotics and Automation (ICRA), pp. 4327–4332 (2005)

    Google Scholar 

  8. Wang, X.: Dynamic Modeling, Experimental Identification, and Active Vibration Control Design of a Smart Parallel Manipulator. Ph.D. thesis, Department of Mechanical and Industrial Engineering, University of Toronto, Toronto (2005)

    Google Scholar 

  9. Zhang, X., Mills, J., Cleghorn, W.: Dynamic modeling and experimental validation of a 3-prr parallel manipulator with flexible intermediate links. Journal of Intelligent and Robotic Systems 50(4), 323–340 (2007)

    Article  MATH  Google Scholar 

  10. Zhou, K., Doyle, J., Glover, K.: Robust and Optimal Control. Prentice-Hall, Englewood Cliffs (1996)

    MATH  Google Scholar 

  11. Algermissen, S., Rose, M., Keimer, R., Monner, H.P., Breitbach, E.: Automated synthesis of robust controllers for smart-structure applications in parallel robots. In: Proc. of AIAA/ASME/AHS Adaptive Structures Conference, Honolulu, USA (2007)

    Google Scholar 

  12. Algermissen, S., Rose, M., Keimer, R., Monner, H.P., Sinapius, M.: Vibration control for smart parallel robots using robust gain-scheduling. In: Borgmann, H. (ed.) ACTUATOR - International Conference on New Actuators, pp. 429–432. Hanseatische Veranstaltungs GmbH, Bremen (2008)

    Google Scholar 

  13. Algermissen, S., Rose, M., Keimer, R., Sinapius, M.: Robust gain-scheduling for smart-structures in parallel robots. In: 16th Annual International Symposium on Smart Structures and Materials, San Diego, CA, USA (2009)

    Google Scholar 

  14. Safonov, M.G.: Imaginary-axis zeros in multivariable hinf optimal control. In: Curtain, R.F. (ed.) Proc. NATO Advanced Research Workshop on Modeling, Robustness and Sensitivity Reduction in Control Systems, Modelling, Robustness and Sensitivity Reduction in Control Systems, pp. 71–81. Springer, Berlin (1987)

    Google Scholar 

  15. Schütz, D., Budde, C., Raatz, A., Hesselbach, J.: Parallel Kinematic Structures of SFB 562. In: Schütz, D., Wahl, F.M. (eds.) Robotic Systems for Handling and Assembly - Modelling. STAR, vol. 67, pp. 109–124. Springer, Heidelberg (2010)

    Google Scholar 

  16. Leith, D.J., Leithead, W.E.: Survey of gain-scheduling analysis and design. International Journal of Control 73(11), 1001–1025 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  17. Rugh, W.J., Shamma, J.S.: Research on gain scheduling. Automatica 36(10), 1401–1425 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  18. Packard, A.: Gain scheduling via linear fractional transformations. Systems & Control Letters 22(2), 79–92 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  19. Braatz, R.D., Morari, M.: On the stability of systems with mixed time-varying parameters. Journal of Robust and Nonlinear Control 7, 105–112 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  20. Paganini, F.: Robust stability under mixed time-varying, time-invariant and parametric uncertainty. Automatica 32(10), 1381–1392 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  21. Shamma, J.S.: Robust stability with time-varying structured uncertainty. IEEE Transactions on Automatic Control 39(4), 714–724 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  22. Teng, J.: Robust Stability and Performance Analysis with Time-Varying Perturbations. Master’s thesis, UC Berkeley, Berkeley, USA (1991)

    Google Scholar 

  23. Shamma, J.S., Athans, M.: Gain scheduling: potential hazards and possible remedies. IEEE Control Systems Magazine 12(3), 101–107 (1992) ISSN 0272-1708

    Article  Google Scholar 

  24. Lu, W.-M., Zhou, K., Doyle, J.: Stabilization of linear systems with structured perturbations. Technical Report CIT-CDS 93-014, California Institute of Technology, Pasadena, CA, USA (1993)

    Google Scholar 

  25. Packard, A., Doyle, J.: The complex structured singular value. Automatica 29(1), 71–109 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  26. Dullerud, G.E., Paganini, F.G.: A course in robust control theory: a convex approach. Springer, New York (1999)

    Google Scholar 

  27. Keimer, R., Sinapius, M.: Design and Implementation of Adaptronic Robot Components. In: Schütz, D., Wahl, F.M. (eds.) Robotic Systems for Handling and Assembly - Modelling. STAR, vol. 67, pp. 413–427. Springer, Heidelberg (2010)

    Google Scholar 

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Algermissen, S., Sinapius, M. (2010). Robust Gain Scheduling for Smart-Structures in Parallel Robots. In: Schütz, D., Wahl, F.M. (eds) Robotic Systems for Handling and Assembly. Springer Tracts in Advanced Robotics, vol 67. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16785-0_10

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  • DOI: https://doi.org/10.1007/978-3-642-16785-0_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16784-3

  • Online ISBN: 978-3-642-16785-0

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