Symbolic computing tools for nonsmooth dynamics and control

  • C. Teolis
  • H. G. Kwatny
  • M. Mattice
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 247)


In this paper we describe a set of symbolic computing tools for variable structure control system design. The software implements all aspects of a design approach for input-output linearizable systems. It is part of a comprehensive symbolic computing environment for nonlinear and adaptive control system design that has been under continuous development for several years. Current work is focused on plants with nondifferentiable nonlinearities. Some preliminary results are reported.


Control System Design Friction Parameter Variable Structure Control Switching Surface Friction Function 
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.
    Blankenship, G.L., et al., Integrated tools for Modeling and Design of Controlled Nonlinear Systems. IEEE Control Systems, 1995. 15(2): p. 65–79.CrossRefGoogle Scholar
  2. 2.
    Kwatny, H.G. and H. Kim, Variable Structure Regulation of Partially Linearizable Dynamics. Systems & Control Letters, 1990. 15: p. 67–80.zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Kwatny, H.G., Variable Structure Control of AC Drives, in Variable Structure Control for Robotics and Aerospace Applications, K.D. Young, Editor. 1993, Elsevier: Amsterdam.Google Scholar
  4. 4.
    Kwatny, H.G. and J. Berg, Variable Structure Regulation of Power Plant Drum Level, in Systems and Control Theory for Power Systems, J. Chow, R.J. Thomas, and P.V. Kokotovic, Editors. 1995, Springer-Verlag: New York. p. 205–234.Google Scholar
  5. 5.
    Isidori, A., Nonlinear Control Systems. 1989, NY: Springer-Verlag.zbMATHGoogle Scholar
  6. 6.
    Kwatny, H.G. and G.L. Blankenship. Symbolic Tools for Variable Structure Control System Design: The Zero Dynamics. in IFAC Symposium on Robust Control via Variable Structure and Lyapunov Techniques. 1994. Benevento, Italy.Google Scholar
  7. 7.
    Luk'yanov, A.G. and V.I. Utkin, Methods of Reducing Equations of Dynamic Systems to Regular Form. Avtomatica i Telemechanika, 1981(4): p. 5–13.Google Scholar
  8. 8.
    Isidori, A., Nonlinear Control Systems. 3 ed. 1995, London: Springer-Verlag.zbMATHGoogle Scholar
  9. 9.
    Marino, R., High Gain Feedback Non-Linear Control Systems. International Joural of Control, 1985. 42(6): p. 1369–1385.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Utkin, V.I., Sliding Modes and Their Application. 1974 (in Russian) 1978 (in English), Moscow: MIR.Google Scholar
  11. 11.
    Young, K.D. and H.G. Kwatny, Variable Structure Servomechanism and its Application to Overspeed Protection Control. Automatica, 1982. 18(4): p. 385–400.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Slotine, J.J. and S.S. Sastry, Tracking Control of Non-Linear Systems Using Sliding Surfaces, With Application to Robot Manipulators. International Journal of Control, 1983. 38(2): p. 465–492.zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Slotine, J.J.E., Sliding Controller Design for Non-Linear Control Systems. International Journal of Control, 1984. 40(2): p. 421–434.zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Young, K.D., P.V. Kokotovic, and V.I. Utkin, Singular Perturbation Analysis of High Gain Feedback Systems. IEEE Transactions on Automatic Control, 1977. AC-22(6): p. 931–938.CrossRefMathSciNetGoogle Scholar
  15. 15.
    Emelyanov, S.V., S.K. Korovin, and L.V. Levantovsky, A Drift Algorithm in Control of Uncertain Processes. Problems of Control and Information Theory, 1986. 15(6): p. 425–438.MathSciNetGoogle Scholar
  16. 16.
    Kwatny, H.G. and T.L. Siu. Chattering in Variable Structure Feedback Systems. in 10th IFAC World Congress. 1987. Munich.Google Scholar
  17. 17.
    Friedland, B., Advanced Control System Design. 1996, Englewood Cliffs: Prentice hall.zbMATHGoogle Scholar
  18. 18.
    Tao, G. and P.V. Kokotovic, Adaptive Control of Systems with Actuator and Sensor Nonlinearities. 1996, New York: John Wiley and Sons, Inc.zbMATHGoogle Scholar
  19. 19.
    Bennett, W.H., et al., Nonlinear and Adaptive control of Flexible Space Structures. Transactions ASME, Journal of Dynamic Systems, Measurement and Control, 1993. 115(1): p. 86–94.CrossRefGoogle Scholar
  20. 20.
    Bennett, W.H., H.G. Kwatny, and M.J. Baek, Nonlinear Dynamics and Control of Articulated Flexible Spacecraft: Application to SSF/MRMS. AIAA Journal on Guidance, Control and Dynamics, 1994. 17(1): p. 38–47.zbMATHGoogle Scholar
  21. 21.
    Kanellakapoulos, I., P.V. Kokotovic, and A.S. Morse, Systematic design of Adaptive Controllers for Feedback Linearizable Systems. IEEE Transactions on Automatic Control, 1991. AC-36(11): p. 1241–1253.CrossRefGoogle Scholar
  22. 22.
    Freeman, R.A. and P.V. Kokotovic, Design of 'softer’ Robust Nonlinear Control Laws. Automatica, 1993. 29(6): p. 1425–1437.zbMATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    Kwatny, H.G. and C. LaVigna, TSi Dynamics User's Guide, 1994, Techno-Sciences, Inc.: Lanham, MD.Google Scholar
  24. 24.
    Teolis, C., Contract Summary Report: Adaptive Control of Systems with Friction and Backlash,. 1997, Techno-Sciences, Inc.: Lanham.Google Scholar
  25. 25.
    Armstrong-Helouvry, B., Control of Machines with Friction. 1991, Boston: Kluwer Academic Publishers.zbMATHGoogle Scholar
  26. 26.
    Armstrong-Helouvry, B., P. Dupont, and C.C.d. Wit, A survey of models, analysis tools and compensation methods for the control of machines with friction. Automatica, 1994. 30(7): p. 1083–1138.zbMATHCrossRefGoogle Scholar
  27. 27.
    Branch, M.A. and A. Grace, Optimization Toolbox. 1996, Natick, MA: The Mathworks, Inc.Google Scholar

Copyright information

© Springer-Verlag 1999

Authors and Affiliations

  • C. Teolis
    • 1
  • H. G. Kwatny
    • 2
  • M. Mattice
    • 3
  1. 1.Techno-Sciences, IncorporatedLanham
  2. 2.Department of Mechanical Engineering & MechanicsDrexel UniversityPhiladelphia
  3. 3.Advanced Drives and Weapon Stabilization LabU. S. Army ARDECPicatinny Arsenal

Personalised recommendations