Second Order Algorithm for Time Optimal Control of a Linear System
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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- Cooper, E., Minimizing Power Dissipation in a Disk File Actuator, IEEE Trans. on Magnetics, Vol. 24, No. 3, May 1988.Google Scholar
- Yastreboff, M., Synthesis of Time-Optimal Control by Time Interval Adjustment, IEEE Trans. Auto. Control, Dec. 1969, pp. 707.Google Scholar
- 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
- 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
- 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
- Ardema, M.D. and Cooper, E., Singular Perturbation Time-Optimal Controller For Disk Drives, Meeting on Optimal Control, Oberwolfach, Germany, May 1991.Google Scholar
- 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