Advertisement

Automation and Remote Control

, Volume 62, Issue 4, pp 597–606 | Cite as

Minimization of Overshoot in Linear Discrete-Time Systems via Low-Order Controllers

  • O. N. Kiselev
  • B. T. Polyak
Article

Abstract

For the SISO linear discrete-time control systems, a technique of response optimization was proposed. It is based on introducing a performance function which is the upper bound of the maximum of error magnitude. Its minimization leads to a linear programming problem in the controller coefficients. Importantly, a low-order controller can be designed in this manner. Various generalizations of the problem, including the robust variant, were considered.

Keywords

Control System Mechanical Engineer System Theory Programming Problem Performance 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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    Dahleh, M.A. and Pearson, J.B., Minimization of a Regulated Response to a Fixed Input, IEEE Trans. Autom. Control, 1988, vol. 33, no. 10, pp. 924–930.Google Scholar
  2. 2.
    Moore, K.L. and Bhattacharyya, S.P., A Technique for Choosing Zero Locations for Minimal Overshoot, IEEE Trans. Autom. Control, 1990, vol. 35, no. 5, pp. 577–580.Google Scholar
  3. 3.
    Casavola, A. and Mosca, E., Minimization of a Closed-Loop Response to a Fixed Input for SISO Systems, IEEE Trans. Autom. Control, 1997, vol. 42, no. 11, pp. 1581–1587.Google Scholar
  4. 4.
    Hill, R.D. and Halpern, M.E., Minimum Overshoot Design for SISO Discrete-Time Systems, IEEE Trans. Autom. Control, 1992, vol. 38, no. 1, pp. 155–158.Google Scholar
  5. 5.
    Keel, L. and Bhattacharyya, S.P., Robust Stability and Performance with Fixed-Order Controllers, Automatica, 1999, vol. 35, no. 10, pp. 1717–1724.Google Scholar
  6. 6.
    Halpern, M.E. and Polyak, B.T., Optimal Tracking with Fixed-Order Controllers, 39th CDC, Sydney, Australia, 2000, pp. 3908–3913.Google Scholar
  7. 7.
    Blanchini, F. and Sznaier, M., A Convex Optimization Approach to Fixed-Order Controller Design for Disturbance Rejection in SISO Systems, IEEE Trans. Autom. Control, 2000, vol. 45, no. 4, pp. 784–789.Google Scholar
  8. 8.
    Polyak, B.T. and Halpern, M.E., The Use of a New Optimization Criterion for Discrete-Time Feedback Controller Design, 38th CDC, Phoenix, Arizona, 1999, pp. 894–899.Google Scholar
  9. 9.
    Tsypkin, Ya.Z., Teoriya lineinykh impul'snykh sistem (Theory of Linear Pulse Systems), Moscow: Fizmatgiz, 1963.Google Scholar
  10. 10.
    Volgin, L.N., Optimal'noe diskretnoe upravlenie dinamicheskimi sistemami (Optimal Discrete Control of Dynamic Systems), Moscow: Fizmatgiz, 1986.Google Scholar
  11. 11.
    Vishnyakov, A.N. and Polyak, B.T., Design of Low-Order Controllers for Discrete-Time Control Systems under Nonrandom Perturbations, Avtom. Telemekh., 2000, no. 9, pp. 112–119.Google Scholar
  12. 12.
    Zhou, K., Doyle, J.C., and Glover, K., Robust and Optimal Control, Upper Saddle River: Prentice Hall, 1996.Google Scholar
  13. 13.
    Polyak, B.T. and Halpern, M.E., Robust Stability and Design of Linear Discrete-Time SISO Systems under ℓ Uncertainties, IEEE Trans. Autom. Control, 1999, vol. 44, no. 11, pp. 2076–2080.Google Scholar
  14. 14.
    Tsypkin, Ya.Z. and Polyak, B.T., Stability of Difference Linear Equations with Unmodelled Higher Order Terms, J. Differ. Equat. Appl., 1998, vol. 3, no. 5/6, pp. 539–546.Google Scholar

Copyright information

© MAIK “Nauka/Interperiodica” 2001

Authors and Affiliations

  • O. N. Kiselev
    • 1
  • B. T. Polyak
    • 1
  1. 1.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia

Personalised recommendations