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Results on the Robust Observer-based Position Controller for Parallel Kinematic Machines

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Abstract

The problem of state observation and position control by output feedback for a nonlinear three degrees-of-freedom (3-DOF) parallel kinematic machine (PKM) system is considered, based on the limited signal availability (only the moving platform displacement measurements are assumed available). Unknown velocity signals are estimated via a nonlinear robust observer that is designed for the nonlinear system with observable linear dynamics part and bounded nonlinearities and disturbances, and that guarantees global exponential stability of the observation error. A proportional-derivative (PD) controller is designed to solve the position control problem, utilizing the estimated velocity, as well as the gravitation compensation, dynamic friction and external disturbance compensation for the PKM. The closed-loop system is proven to have global asymptotical stability according to the Lyapunov analysis method and LaSalle’s invariance principle. Performance of the resulting observer and controller is illustrated in a simulation study of a 3-DOF PKM. Modifications to the nonlinear observer and control law are discussed, that assure convergence of the position error and state observation error to zero when the upper bounds on the model uncertainties/disturbances are not known a priori.

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References

  1. Azemi A., Yaz, E.E.: Sliding-mode adaptive observer approach to chaotic synchronization. J. Dyn. Syst. Meas. Control 122, 748–765 (2000)

    Article  Google Scholar 

  2. Berghuis, H., Nijmeijer, H.: Global regulation of robots using only position measurements. Syst. Contr. Lett. 21, 289–293 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  3. Dawson, D.M., Qu, Z., Caroll, J.C.: On the state observation and output feedback problems for nonlinear uncertain dynamic systems. Syst. Control. Lett. 18, 217–222 (1992)

    Article  MATH  Google Scholar 

  4. Ge, S.S., Lee, T.H., Harris, C.J.: Adaptive Neural Network Control of Robotic Manipulator. World Scientific, Rover Edge (1998)

    Google Scholar 

  5. Lewis, F.L., Abdallah, C.T., Dawson, D.M.: Control of Robot Manipulators. Macmillan, New York (1993)

    Google Scholar 

  6. Kaneko, K., Horowitz, R.: Repetitive and Adaptive Control of Robot Manipulators with Velocity Estimation. IEEE Trans. Robot. Autom. 13(2), 204–217 (1997)

    Article  Google Scholar 

  7. Kelly, R., Carelli, R.: A class of nonlinear PD-type controllers for robot manipulators. J. Robot. Syst. 13(12), 793–802 (1996)

    Article  MATH  Google Scholar 

  8. Khelfi, M.F., Zasadzinski, M., Rafaralahy, H., Richard, E.: Reduced-order observer-based point-to-point and trajectory controllers for robot manipulators. Control Eng. Pract. 4(7), 991–1000 (1996)

    Article  Google Scholar 

  9. Le, S.H., Song, J.B., Choi, W.C., Hong, D.: Position control of a Stewart platform using inverse dynamics control with approximate dynamics. Mechatronics 13(6), 605–6190 (2003)

    Article  Google Scholar 

  10. Lebret, G., Liu, K., Lewis, F.L.: Dynamic analysis and control of a Stewart platform manipulator. J. Robot. Syst. 10(5), 629–655 (1993)

    Article  MATH  Google Scholar 

  11. Lin, L.C., Tsay, M.U.: Modeling and Control of Micropositioning Systems Using Stewart Platforms. J. Robot. Syst. 17(1), 17–52 (2000)

    Article  MATH  Google Scholar 

  12. Polycarpou, M.M., Ioannou, P.A.: A robust adaptive nonlinear control design. In: Proc. American Control Conf., pp. 1365–1369. San Francisco (1993)

  13. Qi, Z., McInroy, J.E., Jafari, F.: Trajectory Tracking with Parallel Robots Using Low Chattering, Fuzzy Sliding Mode Controller. J. Intell. Robot. Syst. 48(3), 333–356 (2007)

    Article  Google Scholar 

  14. Slotine, J.J., Li, W.: Applied Nonlinear Control. Prentice Hall, Englewood Cliffs (1991)

    MATH  Google Scholar 

  15. Takegaki, M., Arimoto, S.: A new feedback method for dynamic control of manipulators. ASME J. Dyn. Syst. Meas. Control 102, 119–125 (1981)

    Article  Google Scholar 

  16. Walcott, B.L., Corless, M.J., Zak, S.H.: Comparative study of the nonlinear state-observation techniques. Int. J. Control 45(6), 2109–2132 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  17. Wang, J., Ge, S.S., Lee, T.H.: Adaptive NN control of robot manipulator with unknown dynamic friction. In: Proc. of Asian Conference on Robotics and Applications, pp. 160–165. Singapore (2001)

  18. Zhang H., Stefanovic, M.: Nonlinear robust observer-based position controller for the 3-DOF parallel kinematic machine. In: Proc. 3rd IEEE Multi-conference on Systems and Control, pp. 1574–1579. Saint-Petersburg, Russia (2009)

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  1. Department of Electrical and Computer Engineering, University of Wyoming, Laramie, WY, USA

    Margareta Stefanovic & Huijuan Zhang

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  1. Margareta Stefanovic
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  2. Huijuan Zhang
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Correspondence to Margareta Stefanovic.

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Stefanovic, M., Zhang, H. Results on the Robust Observer-based Position Controller for Parallel Kinematic Machines. J Intell Robot Syst 66, 417–428 (2012). https://doi.org/10.1007/s10846-011-9622-0

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  • DOI: https://doi.org/10.1007/s10846-011-9622-0

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