Synchronization of ball and beam systems with neural compensation

Regular Papers Control Theory

Abstract

Ball and beam system is one of the most popular and important laboratory models for teaching control system. It is a big challenge to synchronize ball and beam systems. There are two problems for ball and beam synchronized control: 1) many laboratories use simple controllers such as PD control, and theory analysis is based on linear models, 2) nonlinear controllers for ball and beam system have good theory results, but they are seldom used in real applications. In this paper we first use PD control with nonlinear exact compensation for the cross-coupling synchronization. Then a RBF neural network is applied to approximate the nonlinear compensator. The synchronization control can be in parallel and serial forms. The stability of the synchronization is discussed. Real experiments are applied to test our theory results.

Keywords

Mechanical systems neural control stability synchronization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    C. F. Andreev, D. Auckly, S. Gosavi, L. Kapitanski, A. Kelkar, and W. White, “Matching, linear systems, and the ball and beam,” Automatica, vol. 38, pp. 2147–2152, 2002.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    I. Blekhman, P. S. Landa, and M. G. Rosenblum, “Synchronization and chaotization in interacting dynamical systems,” ASME Appl Mech. Rev., vol. 48, pp. 733–752, 1997.CrossRefGoogle Scholar
  3. [3]
    Y. C. Chu and J. Huang, “A neural-network method for the nonlinear servomechanism problem,” IEEE Trans. Neural Networks, vol. 10, no. 6, pp. 1412–1423, 1999.CrossRefGoogle Scholar
  4. [4]
    G. Cybenko, “Approximation by superposition of sigmoidal activation function,” Math. Control, Sig Syst, vol. 2, pp. 303–314, 1989.MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    P. H. Eaton, D. V. Prokhorov, and D. C. Wunsch II, “Neurocontroller alternatives for fuzzy ball-andbeam systems with nonuniform nonlinear friction,” IEEE Trans. Neural Networks, vol. 11, no. 2, pp. 423–435, 2000.CrossRefGoogle Scholar
  6. [6]
    L. Feng, Y. Koren, and J. Borenstein, “Crosscoupling motion controller for mobile robots,” IEEE Control Syst. Mag., vol. 13, pp. 35–43, 1993.CrossRefGoogle Scholar
  7. [7]
    F. Gordillo, F. Gómez-Estern, R. Ortega, and J. Aracil, “On the ball and beam problem: regulation with guaranteed transient performance and tracking periodic orbits,” International Symposium on Mathematical Theory of Networks and Systems, University of Notre Dame, 2002.Google Scholar
  8. [8]
    J. Hauser, S. Sastry, and P. Kokotovic, “Nonlinear control via approximate input-output linearization: ball and beam example,” IEEE Trans. on Automatic Control, vol. 37, no. 3, pp. 392–398, 1992.CrossRefMathSciNetGoogle Scholar
  9. [9]
    S. Haykin, Neural Networks-A comprehensive Foundation, Macmillan College Publ. Co., New York, 1994.MATHGoogle Scholar
  10. [10]
    R. M. Hirschorn, “Incremental sliding mode control of the ball and beam,” IEEE Trans. on Automatic Control, vol. 47, no. 10, pp. 1696–1700, 2002.CrossRefMathSciNetGoogle Scholar
  11. [11]
    C. C. Ker, C. E. Lin, and R. T. Wang, “A ball and beam tracking and balance control using magnetic suspension actuators,” International Journal of Control, vol. 80, no. 5, pp. 695–705, 2007.MATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    Y. Koren, “Cross-coupled biaxial computer controls for manufacturing systems,” ASME J. Dynam. Syst., Meas. Control, vol. 102, pp. 265–272, 1980.MATHCrossRefGoogle Scholar
  13. [13]
    P. K. Kulkarni and K. Srinivasan, “Cross-coupled control of biaxial feed drive servomechanisms,” ASME J. Dynam. Syst., Meas. Control, vol. 112, no. 2, 1990.Google Scholar
  14. [14]
    H. C. Lee and G. J. Jeon, “A neuro-controller for synchronization of two motion axes,” Int. J. Intell. Syst., vol. 13, pp. 571–586, 1998.CrossRefMathSciNetGoogle Scholar
  15. [15]
    R. Ortega, M. W. Spong, F. Gómez-Estern, and G. Blankenstein, “Stabilization of a class of underactuated mechanical systems via interconnection and damping assignment,” IEEE Trans. on Automatic Control, vol. 47, no. 8, pp. 1218–1233, 2002.CrossRefGoogle Scholar
  16. [16]
    Ball and Beam-Experiment and Solution, Quanser Consulting, 1991.Google Scholar
  17. [17]
    A. Rodriguez-Angeles and H. Nijmeijer, “Mutual synchronization of robots via estimated state feedback: a cooperative approach,” IEEE Trans. on Control Systems Technology, vol. 12, no. 4, pp. 542–554, 2004.CrossRefGoogle Scholar
  18. [18]
    A. Rodriguez and H. Nijmeijer, Synchronization of Mechanical Systems, World Scientific Publishing Co., Singapore, 2003.MATHGoogle Scholar
  19. [19]
    E. D. Sontag and Y. Wang, “On characterization of the input-to-state stability property,” System & Control Letters, vol. 24, pp. 351–359, 1995.MATHCrossRefMathSciNetGoogle Scholar
  20. [20]
    D. Sun and J. Mills, “Adaptive synchronized control for coordination of two robot manipulators,” Proc. IEEE Int. Conf. Robotics and Automation, Washington, pp. 976–981, 2002.Google Scholar
  21. [21]
    M. Tomizuha, J. S. Hu, and T. C. Chiu, “Synchronization of two motion control axes under adaptive feedforward control,” ASME J. Dynam. Syst., Meas. Control, vol. 114, no. 6, pp. 196–203, 1992.CrossRefGoogle Scholar
  22. [22]
    L. X. Wang, “Stable and optimal fuzzy control of linear systems,” IEEE Trans. on Fuzzy Systems, vol. 6, no. 1, pp. 137–143, 1998.CrossRefGoogle Scholar
  23. [23]
    W. Yu, “Multiple recurrent neural networks for stable adaptive control,” Neurocomputing, vol. 70, no. 1, pp. 430–444, 2006.CrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Departamento de ComputaciónCINVESTAV-IPNMexico D.F.Mexico
  2. 2.Departamento de Control AutomáticoCINVESTAV-IPNMexico D.F.Mexico

Personalised recommendations