Skip to main content
SpringerLink
Log in

Stick-Slip Friction Compensation Using a General Purpose Neuro-Adaptive Controller with Guaranteed Stability

  • Chapter
Applications of Neural Networks in High Assurance Systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 268))

  • 1244 Accesses

Abstract

A general purpose neuro-adaptive controller, which realizes an indirect-adaptive control strategy, is introduced. The proposed algorithm is based on the use of two Multi-Layer feed-forward Perceptron (MLP) Neural Networks (NNs), which are trained using a momentum back-propagation (MBP) algorithm. One of the MLP NNs is used to identify the process. The other MLP NN is used to generate the control signal based on the data provided by the NN identifier. Training is done on-line to tune the parameters of the neuro-identifier and neuro-controller that provides the control signal. Pre-learning is not required and the structure of the overall system is very simple and straightforward, no additional controller or adaptive signal is needed. Tracking performance is guaranteed via Lyapunov stability analysis, so that both tracking error and neural network weights remain bounded. An interesting fact about the proposed approach is that it does not require a NN being capable of globally reconstructing the nonlinear model.

Several simulation examples are reported to demonstrate the merits of the proposed algorithm. As is shown in the simulations, the developed control algorithm can deal with different types of challenges that might happen in real-time applications, including the change of the reference model and the effect of applied unknown disturbances. The application of the proposed neuro-control algorithm to the adaptive control of electro-mechanical systems subject to stick-slip friction is shown in the last section of this paper. Reported simulations reveal that the proposed algorithm is able to eliminate the effect of this nonlinear phenomenon on the performance of the system.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Dupont, P.E.: Avoiding stick-slip through PD control. IEEE Trans. Automatic Contr. 39, 1094–1097 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  2. Leonard, N.E., Krishnaprasad, P.: Adaptive friction compensation for bi-directional low velocity position tracking. In: Proc. 31st CDC, Tucson, AZ, pp. 267–273 (1992)

    Google Scholar 

  3. Friedland, B., Park, Y.J.: On adaptive friction compensation. IEEE Trans. Automatic Contr. 40, 419–425 (1992)

    MathSciNet  Google Scholar 

  4. Li, W., Cheng, X.: Adaptive high-precision control of positioning tables-Theory and experiments. IEEE Trans. Contr. Syst. Technol. 2, 265–270 (1994)

    Article  Google Scholar 

  5. Tan, K.K., Lim, S.Y., Lee, T.H., Huang, S.N.: Adaptive control of DC permanent magnet linear motor for ultra-precision applications. In: Int. Conf. Mechatronic Tech., Taiwan, R.O.C., pp. 243–246 (1998)

    Google Scholar 

  6. De Wit, C.C., Lischinsky, P.: Adaptive friction compensation with partially known dynamic friction model. Int. J. Adapt. Contr. Sig. Process. 11(1), 65–80 (1997)

    Article  MATH  Google Scholar 

  7. Otten, G., de Vries, T.J.A., van Amerongen, J., Rankers, A.M., Gaal, E.W.: Linear motor motion control using a learning forward controller. IEEE/ASME Trans. Mechatronics 2(3), 179–187 (1997)

    Article  Google Scholar 

  8. Southward, S.C., Radcliffe, C.J., MacCluer, C.R.: Robust nonlinear stick-slip friction compensation. ASME J. Dyn. Syst., Meas., and Contr. 113, 639–645 (1991)

    Article  MATH  Google Scholar 

  9. Lee, S.-W., Kim, J.-H.: Robust adaptive stick-slip friction compensation. IEEE Trans. Industrial Elec. 42(5) (1995)

    Google Scholar 

  10. De Wit, C.C., Olsson, H., Astrom, K., Lischinsky, P.: A new model for control of systems with friction. IEEE Trans. Automatic Contr. 40, 419–425 (1995)

    Article  MATH  Google Scholar 

  11. Panteley, E., Ortega, R., Gafvert, M.: An adaptive friction compensator for global tracking in robot manipulators. Syst. Contr. Lett. 33, 307–313 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  12. Huang, S.N., Tan, K.K., Lee, T.H.: Adaptive friction compensation using neural network approximations. IEEE Trans. Syst., Man and Cyber.-C 30(4), 551–557 (2000)

    Article  Google Scholar 

  13. Baruch, I., Beltran, R.L., Olivares, J.-L., Garrido, R.: A Fuzzy-Neural Multi-Model for Mechanical Systems Identification and Control. In: Monroy, R., Arroyo-Figueroa, G., Sucar, L.E., Sossa, H. (eds.) MICAI 2004. LNCS (LNAI), vol. 2972, pp. 774–783. Springer, Heidelberg (2004)

    Google Scholar 

  14. Suraneni, S., Kar, I.N., Bhatt, R.K.P.: Adaptive stick-slip friction compensation using dynamic fuzzy logic system. In: Proc. TENCON 2003, the conference on convergent Technologies for Asia-Pacific Region, vol. 4, pp. 1470–1474 (2003)

    Google Scholar 

  15. Baruch, I., Garrido, R., Mitev, A., Nenkova, B.: A neural network approach for stick-slip model identification. In: Proc. of the 5th Int. Conf. on Engineering Applications of Neural Networks, EANN 1999, Warsaw, Poland, pp. 183–188 (1999)

    Google Scholar 

  16. Cohen, M.A., Grossberg, S.: Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. on Systems, Man, and Cybernetics 13(5), 815–825 (1993)

    MathSciNet  Google Scholar 

  17. Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proc. of the National Academy of Sciences, USA 79, 2554–2558 (1982)

    Article  MathSciNet  Google Scholar 

  18. Kosko, B.: Structural stability of unsupervised learning in feedback neural networks. IEEE Trans. on Automatic Control 36(7), 785–792 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  19. Guez, A., Protopopsecu, V., Barhen, J.: On the stability, storage capacity and design of non-linear continuos neural networks. IEEE Trans. on Systems, Man, and Cybernetics 18(1), 80–87 (1988)

    Article  Google Scholar 

  20. Kelly, D.G.: Stability in contractive non-linear neural networks. IEEE Trans. on Biomedical Eng. 37(3), 231–242 (1990)

    Article  Google Scholar 

  21. Vidyasagar, M.: Location and stability of the high gain equilibria of non-linear neural networks. IEEE Trans. on Neural Networks 4(4), 660–672 (1993)

    Article  Google Scholar 

  22. Jim, L., Nikiforuk, P.N., Gupta, M.M.: Absolute stability conditions for discrete-time recurrent neural networks. IEEE Trans. on Neural Networks 5(6), 954–964 (1994)

    Article  Google Scholar 

  23. Tzirkel-Hancock, E., Fallside, F.: A stability based neural network control method for a class of non-linear systems. In: Proc. Inter. Joint Conf. on Neural Networks, vol. 2, pp. 1047–1052 (1991)

    Google Scholar 

  24. Lewis, F.L., Yesildirek, A., Liu, K.: Neural net robot controller with guaranteed stability. In: Proc. 3rd Inter. Conf. on Indus. Fuzz. Cont., pp. 103–108 (1993)

    Google Scholar 

  25. Lewis, F.L., Yesildirek, A., Liu, K.: Multilayer neural net robot controller with guaranteed tracking performance. IEEE Trans. on Neural Networks 7(2), 388–399 (1996)

    Article  Google Scholar 

  26. Kwan, C., Lewis, F.L., Dawson, D.M.: Robust neural-network control of rigid-link electrically driven robots. IEEE Trans. on Neural Networks 9(4), 581–588 (1998)

    Article  Google Scholar 

  27. Kuntanapreeda, S., Fullmer, R.R.: A training rule which guaranteed finite region stability for a class of closed-loop neural network control system. IEEE Trans. on Neural Networks 7(3), 629–642 (1996)

    Article  Google Scholar 

  28. Park, S., Park, C.H.: Comments on a training rule which guarantees finite-region stability for a class of closed-loop neural-network control systems. IEEE Trans. on Neural Networks 8(5), 1217–1218 (1997)

    Article  Google Scholar 

  29. Sadegh, N.: A perceptron network for functional identification and control of non-linear systems. IEEE Trans. on Neural Networks 4(6), 982–988 (1993)

    Article  Google Scholar 

  30. Polycarpou, M.M.: Stable adaptive neural control scheme for non-linear systems. IEEE Trans. Auto. Control 41(3), 447–451 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  31. Chen, F.-C., Khalil, H.K.: Adaptive control of non-linear systems using neural networks. Int. J. Control 55, 1299–1317 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  32. Chen, F.-C., Khalil, H.K.: Adaptive control of a class of Non-linear Discrete-Time Systems Using Neural Networks. IEEE Trans. Auto. Control 40(5), 791–801 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  33. Chen, F.-C., Liu, C.-C.: Adaptively controlling non-linear continuous-time systems using multilayer neural networks. IEEE Trans. Auto. Control 39(6), 1306–1310 (1994)

    Article  MATH  Google Scholar 

  34. Fabri, S., Kadirkamanathan, V.: Dynamic structure neural networks for stable adaptive control of non-linear systems. IEEE Trans. on Neural Networks 7(5), 1151–1167 (1996)

    Article  Google Scholar 

  35. Sun, F., Sun, Z., Woo, P.-Y.: Stable neural-network-based adaptive control for sampled-data non-linear systems. IEEE Trans. on Neural Networks 9(5), 956–968 (1998)

    Article  Google Scholar 

  36. Jagannathan, S., Lewis, F.L.: Multilayer discrete-time neural-net controller with guaranteed performance. IEEE Trans. on Neural Networks 7(1), 107–130 (1996)

    Article  Google Scholar 

  37. Jagannathan, S., Lewis, F.L., Pasravanu, O.: Discrete-time model reference adaptive control of nonlinear dynamical systems using neural networks. Int. J. Contr. 64(2), 217–239 (1996)

    Article  MATH  Google Scholar 

  38. Suykens, J.A.K., Vandewalle, J.: Global asymptotic stability for multilayer recurrent neural networks with application to modelling and control. In: Proc. Inter. Conf. on Neural Network., vol. 2, pp. 1065–1069 (1995)

    Google Scholar 

  39. Narendra, K.S., Parthasarathy, K.: Identification and control of dynamical systems using neural networks. IEEE Trans. on Neural Net. 1(1), 4–27 (1990)

    Article  Google Scholar 

  40. Mehrabian, A.R., Menhaj, M.B.: A real-time neuro-adaptive controller with guaranteed stability. Applied Soft Comput. J. 8(1), 530–542 (2008)

    Article  Google Scholar 

  41. Hagan, M.T., Menhaj, M.: Training feedforward networks with the Marquardt algorithm. IEEE Trans. on Neural Net. 5(6), 989–993 (1994)

    Article  Google Scholar 

  42. Sinha, N.K., Rao, G.P.: Identification of Continuous-time Systems: Methodology and Computer Implementation. Kluwer Academic, Dordrecht (1991)

    MATH  Google Scholar 

  43. Hornik, K.M., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Net. 2(5), 359–366 (1989)

    Article  Google Scholar 

  44. Hagan, M., Demuth, H., Beale, M.: Neural Network Design. PWS Publishing, Boston (1996)

    Google Scholar 

Download references

Authors
  1. Ali Reza Mehrabian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mohammad Bagher Menhaj
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. RIACS/USRA, NASA Ames Research Center, M/S 269-3, 94035, Moffett Field, CA, USA

    Johann Schumann

  2. Motorola Autonomic Networking Labs, 1301 East Algonquin Road, 60193, Schaumburg, IL, USA

    Yan Liu

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Mehrabian, A.R., Menhaj, M.B. (2010). Stick-Slip Friction Compensation Using a General Purpose Neuro-Adaptive Controller with Guaranteed Stability. In: Schumann, J., Liu, Y. (eds) Applications of Neural Networks in High Assurance Systems. Studies in Computational Intelligence, vol 268. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10690-3_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-10690-3_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-10689-7

  • Online ISBN: 978-3-642-10690-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation