Second Order Algorithm for Time Optimal Control of a Linear System

  • Mark D. Ardema
  • Han-Chang Chou
Part of the ISNM International Series of Numerical Mathematics book series (ISNM, volume 115)


In previous papers, zero-order solutions for time optimal control of singularly perturbed third-order systems have been obtained by the method of matched asymptotic expansions (MAE). The resulting open-loop control laws were founded to give good results, provided the singular perturbation parameter is small. In this paper, we use the MAE method to derive a second-order open-loop controller for a representative third-order system. Numerical simulations show that the second-order controller gives significantly better performance than the zero-order controller.


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  1. [1]
    Cooper, E., Minimizing Power Dissipation in a Disk File Actuator, IEEE Trans. on Magnetics, Vol. 24, No. 3, May 1988.Google Scholar
  2. [2]
    Yastreboff, M., Synthesis of Time-Optimal Control by Time Interval Adjustment, IEEE Trans. Auto. Control, Dec. 1969, pp. 707.Google Scholar
  3. [3]
    Kassam, S.A., Thomas, J.B., and McCrumm, J.D., Implementation of Sub-Optimal Control for a Third-Order System. Comput. Elect. Engng., Vol. 2 1975, pp. 307.zbMATHCrossRefGoogle Scholar
  4. [4]
    Ardema, M.D., An Introduction to Singular Perturbations in Nonlinear Optimal Control, Singular Perturbations in Systems and Control, M.D. Ardema, ed., International Centre for Mechanical Sciences, Courses and Lectures No. 280, 1983.Google Scholar
  5. [5]
    Kokotovic, P.V., Khalil, H.K., and O’Reilly, J.,Singular Perturbation Methods in Control: Analysis and Design, Academic Press, 1986.zbMATHGoogle Scholar
  6. [6]
    Kokotovic, P.V. and Haddad, A.H., Controllability and Time-Optimal Control of Systems with Slow and Fast Modes, IEEE Trans. Auto. Control, Feb. 1975, pp. 111.Google Scholar
  7. [7]
    Ardema, M.D. and Cooper, E., Perturbation Method for Improved Time-Optimal Control of Disk Drives, Lecture Notes in Control and Information Sciences, Vol. 151, J.M. Skowronski et. al. (eds), Springer-Verlag, 1991, pp. 37.Google Scholar
  8. [8]
    Ardema, M.D. and Cooper, E., Singular Perturbation Time-Optimal Controller For Disk Drives, Meeting on Optimal Control, Oberwolfach, Germany, May 1991.Google Scholar
  9. [9]
    Leitmann, G., The Calculus of Variations and Optimal Control, Plenum, 1981.zbMATHGoogle Scholar
  10. [10]
    L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Process. New York: Interscience, 1962.Google Scholar

Copyright information

© Birkhäuser Verlag Basel 1994

Authors and Affiliations

  • Mark D. Ardema
    • 1
  • Han-Chang Chou
    • 1
  1. 1.Department of Mechanical EngineeringSanta Clara UniversitySanta ClaraUSA

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