Handling stiction with variable structure control

  • Cem Hatipoğlu
  • Ümit Özgüner
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 247)


When the control system falls in a class obeying non-Lipschitzian (or “non-smooth”) dynamics, the conventional nonlinear theory can not be readily applied. Among the common non-smooth nonlinearities are those which are discontinuous in the state variables. Existence of such inherent right hand side discontinuities may induce undesirable stiction while hardening the control task during reference tracking. In this work, we analyze the “stiction” phenomenon in depth using analogies from the sliding mode control theory and propose a multi layer variable structure reference tracking controller for a class of systems in their companion forms. Results for an interesting physical example is provided to clarify the concepts.


Control Input Reference Signal Slide Mode Control State Space Representation Variable Structure Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    B.H. Armstrong, “A survey of models, analysis tools and compensation methods for the control of machines with friction”, Automatica, 30(9), 1994, pp. 1083–1138.zbMATHCrossRefGoogle Scholar
  2. 2.
    B.H. Armstrong and B. Amin, “PID control in the presence of static friction: a comparison of algebraic and describing function analysis”, Automatica, vol. 32, no. 5, 1996, pp. 679–692.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    M. Artin, Algebra, Prentice Hall, New Jersey, NY, 1991.Google Scholar
  4. 4.
    C. Canudas de Wit, H. Olson, K.J. Astrom and P. Lischinsky, “A New Model for Control of Systems with Friction”, IEEE Transactions on Automatic Control, vol. 40, No. 3, March 1995.Google Scholar
  5. 5.
    P.E. Dupont and E.P. Dunlap, “Friction modeling and PD compensation at very low velocities”, Journal of Dynamic Systems, Measurement and Control, vol. 117, no. 1, 1995, pp. 8–14.Google Scholar
  6. 6.
    P.E. Dupont, “The effect of friction on the forward dynamics problem”, The Int. Jour. of Robotics Research, vol. 12, no. 2, 1993, pp. 164–179.CrossRefMathSciNetGoogle Scholar
  7. 7.
    S. Drakunov, D. Hanchin, W. C. Su, Ü. Özgüner, “Nonlinear control of a rod-less pneumatic servo-actuator or sliding modes vs coulomb friction”, Automatica, Vol 33, No 7, 1997, pp. 1401–1406.zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    A.F. Filippov, “Differential equations with discontinuous right hand side”, American Mathematical Society Translations, vol 42, 1964, pp. 199–231.Google Scholar
  9. 9.
    M. Fliess, “Generalized controller canonical forms for linear and nonlinear dynamics”, Trans. Aut. Control, AC-35(9), 1990, pp. 994–1001.CrossRefMathSciNetGoogle Scholar
  10. 10.
    M. Fliess, H. Sira-Ramirez, “A module theoretic approach to sliding mode control in linear systems”, Proc. of the 32nd CDC, San Antonio, TX, 1993, pp. 2465–2470.Google Scholar
  11. 11.
    M. Fliess, M. Hazewinkel, Eds., Algebraic and Geometric Methods in Nonlinear Control Theory, Dordrecht, The Netherlands: Riedel, 1986.zbMATHGoogle Scholar
  12. 12.
    H. Fortell, “A generalized normal form and its applications to sliding mode control”, Proc. of the 34th CDC, New Orleans, LA, 1995, pp. 13–18.Google Scholar
  13. 13.
    B. Friedland and Y.J. Park, “On adaptive friction compensation”, IEEE Trans. on Automatic Control, vol. 37, no. 10, 1992, pp. 1609–1611.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    D.A. Haessig and B. Friedland, “On the modeling and simulation of friction”, Journal of Dynamic Systems, Measurement and Control, vol. 113, no. 3, 1992, pp. 354–362.CrossRefGoogle Scholar
  15. 15.
    İ. Haskara, Ü. Özgüner, V.I. Utkin, “On variable structure observers”, Proc. VSS’ 96, Tokyo, Japan, 1996, pp. 193–198.Google Scholar
  16. 16.
    C. Hatipoğlu, “Variable Structure Control of Continuous Time Systems Involving Non-smooth Nonlinearities”, Dissertation, The Ohio State University, Department of Electrical Engineering, 1998.Google Scholar
  17. 17.
    A. Isidori, Nonlinear Control Systems, Springer-Verlag, second edition, 1989.Google Scholar
  18. 18.
    B.E. Karnopp, “Computer simulation of slip-stick friction in mechanical dynamic systems”, ASME Jour. of Dynamic Systems, Measurement and Control, vol. 107, no. 1, 1985, pp. 100–103.CrossRefGoogle Scholar
  19. 19.
    H.K. Khalil, Nonlinear Systems, MacMillan Publishing Company, 1992.Google Scholar
  20. 20.
    H. Sira-Ramirez, “On the dynamical sliding mode control of nonlinear systems”, Int. Journal of Control, 57(5), 1993, pp. 1039–1061.zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    S. Sankaranarayanan and F. Khorrami, “Adaptive Variable Structure Control and Applications to Frequency Compensation”, preprint.Google Scholar
  22. 22.
    S.C. Southward, C.J. Radcliffe, C.R. MacCluer, “Robust nonlinear stick-slip friction compensation”, ASME JDMSC, Vol 113, 1991, pp. 639–645.zbMATHGoogle Scholar
  23. 23.
    S. Tafazoli, C.W. de Silva and P.D. Lawrence, “Tracking control of an electrohydraulic manipulator in the presence of friction”, IEEE Trans. on Control Systems Technology, Vol 6, No 3, pp. 401–411, May 1998.CrossRefGoogle Scholar
  24. 24.
    V.I. Utkin, Sliding Modes in Control Optimization, Springer-Verlag, 1992.Google Scholar
  25. 25.
    K.D. Young “Discontinuous control of sliding base isolated structures under earthquakes”, Proc. of IMACS/SICE Int. Symp. on Robotics, Mechatronics and Manufacturing Systems, Kobe Japan, 1992, pp.375–380.Google Scholar

Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • Cem Hatipoğlu
    • 1
  • Ümit Özgüner
    • 2
  1. 1.AlliedSignal TBSElyriaUSA
  2. 2.The Ohio State UniversityColumbusUSA

Personalised recommendations