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Adaptive Control of Nonsmooth Dynamic Systems pp 49–84Cite as

Deadzone Compensation in Motion Control Systems Using Augmented Multilayer Neural Networks

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Abstract

A novel neural network (NN) structure is given for approximation of piecewise continuous functions of the sort that appear in friction, deadzone, backlash and other motion control actuator nonlinearities. The novel NN consists of neurons having standard sigmoid activation functions, plus some additional neurons having a special class of nonsmooth activation functions termed ‘jump approximation basis functions’. This augmented NN with additional neurons having ‘jump approximation’ activation functions can approximate any piecewise continuous function with discontinuities at a finite number of known points.

A compensation scheme is presented for general nonlinear actuator deadzones of unknown width. The compensator uses two NN, one to estimate the unknown deadzone and another to provide adaptive compensation in the feedforward path. The compensator is an augmented multilayer NN for approximating piecewise continuous functions like the deadzone inverse. Rigorous proofs of closed-loop stability for the deadzone compensator are provided, and yield tuning algorithms for the weights of the two NN. The technique provides a general procedure for using NN to determine the preinverse of an unknown right-invertible function.

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References

  1. R. Barron, Universal approximation bounds for superpositions of a sigmoidal function, IEEE Trans. Inf. Theory, 39, no. 3, 930–945, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  2. R. G. Bartle, The Elements ofReal Analysis, Wiley, New York, 1964.

    Google Scholar 

  3. F.-C. Chen and H. K. Khalil, Adaptive control of nonlinear systems using neural networks, Int. J. Control, 55, no. 6, 1299–1317, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  4. S. Commuri and F. L. Lewis, CMAC neural networks for control of nonlinear dynamical systems: structure, stability and passivity, Proc. IEEE Int. Symp. Intell. Control, Monterey, 1995, 123–129.

    Google Scholar 

  5. M. J. Corless and G. Leitmann, Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems, IEEE Trans. Automat. Control, 26, no. 5, 850–861, 1982.

    MathSciNet  Google Scholar 

  6. J. J. Craig, Adaptive Control of Robot Manipulators, Addison-Wesley, Reading, MA, 1988.

    Google Scholar 

  7. G. Cybenko, Approximation by superpositions of a sigmoidal function, Math. Control Signals, Syst., 2, no. 4, 303–314, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  8. C. A. Desoer and S. M. Shahruz, Stability of dithered nonlinear systems with backlash or hysteresis, Int. J. Control, 43, no. 4, 1045–1060, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  9. B. Friedland, Advanced Control System design, Prentice-Hall, New Jersey, 1996.

    MATH  Google Scholar 

  10. K. Funahashi, “On the approximate realization of continuous mappings by neural networks,” Neural Networks, vol. 2, pp. 183–192, 1989.

    Article  Google Scholar 

  11. J. W. Gilbart and G. C. Winston, Adaptive compensation for an optical tracking telescope, Automatica, 10, 125–131, 1974.

    Article  Google Scholar 

  12. B. Igelnik and Y. H. Pao, Stochastic choice of basis functions in adaptive function approximation and the functional-link net, IEEE Trans. Neural Networks, 6, no. 6, 1320–1329, 1995.

    Article  Google Scholar 

  13. K. Hornik, M. Stinchombe, and H. White, Multilayer feedforward networks are universal approximators, Neural Networks, 2, 359–366, 1989.

    Article  Google Scholar 

  14. J.-Y. Jeon, J.-H. Kim, and K. Koh, Experimental evolutionary programmingbased high-precision control, IEEE Control Syst. Mag., 17, no. 2, 66–74, 1997.

    Article  Google Scholar 

  15. B. S. Kim and A. J. Calise, Nonlinear flight control using neural networks, Journal of Guidance, Control, and Dynamics, 20, no. 1, 1997.

    Google Scholar 

  16. J.-H. Kim, H.-K. Chae, J.-Y. Jeon, S.-W. Lee, Identification and control of systems with friction using accelerated evolutionary programming, IEEE Control Syst. Mag., 16, no. 4, 38–47, 1996.

    Article  Google Scholar 

  17. J.-H. Kim, K.-C. Kim, and E. K. P. Chong, Fuzzy precompensated PD controllers, IEEE Trans. Control Syst. Technol., 2, no. 4, 406–411, 1994.

    Article  Google Scholar 

  18. J.-H. Kim, J.-H. Park, S.-W. Lee, and E. K. P. Chong, Fuzzy precompensation of PD controllers for systems with deadzones, J. Int. Fuzzy Syst., 1, 125–133, 1993.

    Article  Google Scholar 

  19. J.-H. Kim, J.-H. Park, S.-W. Lee, and E. K. P. Chong, A two-layered fuzzy logic controller for systems with deadzones, IEEE Trans. Industrial Electron., 41, no. 2, 155–162, 1994.

    Google Scholar 

  20. B. Kosko, Neural Networks and Fuzzy Systems, Prentice Hall, New Jersey, 1992.

    MATH  Google Scholar 

  21. S.-W. Lee and J.-H. Kim, Control of systems with deadzones using neuralnetwork based learning control, Proc. IEEE Int. Conf. Neural Networks, 1994, 2535–2538.

    Google Scholar 

  22. F. L. Lewis, C. T. Abdallah, and D. M. Dawson, Control of Robot Manipulators, Macmillan, New York, 1993.

    Google Scholar 

  23. F. L. Lewis, S. Jagannathan, and A. Yesildirek, Neural Network Control of Robot Manipulators and Nonlinear Systems, Taylor and Francis, Philadelphia, PA, 1999.

    Google Scholar 

  24. F. L. Lewis, A. Yesildirek, and K. Liu, Multilayer neural-net robot controller with guaranteed tracking performance, IEEE Trans. Neural Networks, 7, no. 2, 1–11, 1996.

    Article  Google Scholar 

  25. F. L. Lewis, K. Liu, and A. Yesilidrek, Neural net robot controller with guaranteed tracking performance, IEEE Trans. Neural Networks, 6, no. 3, 703–715, 1995.

    Article  Google Scholar 

  26. F. L. Lewis, K. Liu, R. R. Selmic, and Li-Xin Wang, Adaptive fuzzy logic compensation of actuator deadzones, J. Robot. Syst., 14, no. 6, 501–511, 1997.

    Article  MATH  Google Scholar 

  27. F. L. Lewis, Neural network control of robot manipulators, IEEE Expert special track on “Intelligent Control “ Eds. K. Passino and Ü. Özgüner, 64–75, 1996.

    Google Scholar 

  28. W. Li and X. Cheng, Adaptive high-precision control of positioning tables-theory and experiment, IEEE Trans. Control Syst. Technol., 2, no. 3, 265–270, 1994.

    Article  Google Scholar 

  29. K. S. Narendra and A. M. Annaswamy, A new adaptive law for robust adaptation without persistent excitation, IEEE Trans. Automat. Control, 32, no. 2, 134–145, 1987

    Article  MathSciNet  MATH  Google Scholar 

  30. K. S. Narendra, Adaptive Control Using Neural Networks, Neural Networks for Control, 115–142. Eds. W. T. Miller, R. S. Sutton, P. J. Werbos, MIT Press, Cambridge, MA, 1991.

    Google Scholar 

  31. K. S. Narendra and K. Parthasarathy, Identification and control of dynamical systems using neural networks, IEEE Trans. Neural Networks, 1, 4–27, 1990.

    Article  Google Scholar 

  32. J. Park and I. W. Sandberg, Criteria for the approximation of nonlinear systems, IEEE Trans. Circuits Syst., 39, no. 8, 673–676, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  33. J. Park and I. W. Sandberg, Nonlinear approximations using elliptic basis function networks, Circuits, Systems, and Signal Processing, 13, no. 1, 99–113, 1993.

    Article  MathSciNet  Google Scholar 

  34. M. M. Polycarpou, Stable adaptive neural control scheme for nonlinear systems, IEEE Trans. Automat. Control, 41, no. 3, 447–451, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  35. M. M. Polycarpou and P. A. Ioannou, Modeling, identification and stable adaptive control of continuous-time nonlinear dynamical systems using neural networks, Proc. Amer. Control Conf, 1992, 1, 36–40.

    Google Scholar 

  36. D. A. Recker, P. V. Kokotovic, D. Rhode, and J. Winkelman, Adaptive nonlinear control of systems containing a dead-zone, Proc. IEEE Conf. Decis. Control, 1991, 2111–2115.

    Google Scholar 

  37. G. A. Rovithakis and M. A. Christodoulou, Adaptive control of unknown plants using dynamical neural networks, IEEE Trans. Systems, Man, and Cybernetics, 24, no. 3, 400–412, 1994.

    Article  MathSciNet  Google Scholar 

  38. N. Sadegh, A perceptron network for functional identification and control of nonlinear systems, IEEE Trans. Neural Networks, 4, no. 6, 982–988, 1993.

    Article  Google Scholar 

  39. R. M. Sanner and J.-J. E. Slotine, Stable adaptive control and recursive identification using radial gaussian networks, Proc. IEEE Conf. Decis. and Control, Brighton, 1991.

    Google Scholar 

  40. J. R. Schilling, Fundamentals of Robotics Analysis and Control, Prentice Hall, New Jersey.

    Google Scholar 

  41. R. R. Selmic and F. L. Lewis, Neural network approximation of piecewise continuous functions: application to friction compensation, Proc. IEEE Int. Symp. Intell. Control, Istanbul, July 1997.

    Google Scholar 

  42. R. R. Selmic and F. L. Lewis, Neural network approximation of piecewise continuous functions: application to friction compensation, Soft Computing and Intelligent Systems: Theory and Applications, Eds. N. K. Sinha and M. M. Gupta, Academic Press, 1999.

    Google Scholar 

  43. R. R. Selmic and F. L. Lewis, Deadzone compensation in motion control systems using neural networks, IEEE Trans. Automat. Control, 45, no. 4, 602–613, 2000.

    Article  MathSciNet  MATH  Google Scholar 

  44. J.-J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice-Hall, New Jersey, 1991.

    MATH  Google Scholar 

  45. J.-J. E. Slotine and W. Li, Adaptive manipulator control: a case study, IEEE Trans. Automat. Control, 33, no. 11, 995–1003, 1988.

    Article  MATH  Google Scholar 

  46. G. Tao, Adaptive backlash compensation for robot control, Proc. IFAC World Congress, San Francisco, 1996, pp. 307–312.

    Google Scholar 

  47. G. Tao and P. V. Kokotovic, Adaptive control of plants with unknown deadzones, IEEE Trans. Automat. Control, 39, no. 1, 59–68, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  48. G. Tao and P. V. Kokotovic, Adaptive control of systems with unknown output backlash, IEEE Trans. Automat. Control, 40, no. 2, 326–330, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  49. G. Tao and P. V. Kokotovic, Adaptive control of plants with unknown hystereses, IEEE Trans. Automat. Control, 40, no. 2, 200–212, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  50. G. Tao and P. V. Kokotovic, Continuous-time adaptive control of systems with unknown backlash, IEEE Trans. Automat. Control, 40, no. 6, 1083–1087, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  51. G. Tao and P. V. Kokotovic, Discrete-time adaptive control of systems with unknown deadzones, Int. J. Control, 61, no. 1, 1–17, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  52. G. Tao and P. V. Kokotovic, Adaptive Control of Systems With Actuator and Sensor Nonlinearities, John Wiley & Sons, New York, 1996.

    MATH  Google Scholar 

  53. M. Tian and G. Tao, Adaptive control of a class of nonlinear systems with unknown deadzones, Proc. IFAC World Congress, San Francisco, 1996, pp. 209–214.

    Google Scholar 

  54. V. I. Utkin, Sliding modes and their application in variable structure systems, Mir, Moscow, 55–63, 1978.

    MATH  Google Scholar 

  55. L.-X. Wang, Adaptive Fuzzy Systems and Control: Design and Stability Analysis, Prentice-Hall, New Jersey, 1994.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Signalogic, Inc., Dallas, Texas, USA

    Rastko R. Šelmic

  2. Automation and Robotics Research Institute, The University of Texas at Arlington, Fort Worth, Texas, USA

    Frank L. Lewis

Authors
  1. Rastko R. Šelmic
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  2. Frank L. Lewis
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22903, USA

    Gang Tao PhD

  2. Automation and Robotics Research Institute, University of Texas at Arlington, Fort Worth, TX, 76118, USA

    Frank L. Lewis PhD

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© 2001 Springer-Verlag London

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Šelmic, R.R., Lewis, F.L. (2001). Deadzone Compensation in Motion Control Systems Using Augmented Multilayer Neural Networks. In: Tao, G., Lewis, F.L. (eds) Adaptive Control of Nonsmooth Dynamic Systems. Springer, London. https://doi.org/10.1007/978-1-4471-3687-3_3

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  • DOI: https://doi.org/10.1007/978-1-4471-3687-3_3

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-84996-869-0

  • Online ISBN: 978-1-4471-3687-3

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