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Minimization of basic quality indices in linear discrete systems

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Abstract

A method of synthesis of controllers for one-dimensional linear discrete control systems is put forward, which optimizes a transition function relative to basic quality indices such as the overshoot or the settling time. This method rests on the conditions of the finite duration of a transient process, which determines the convexity of objective functions by the parameters of a controller and systematically enables reducing the optimization problems to the standard algorithm of linear programming.

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REFERENCES

  1. Aaron, N.R. and Segers, R.G., A Necessary and Suficient Condition for a Bounded Nondecreasing Step Response, IRE Trans. Circuit Theory, 1958, vol. 5, pp. 226–227.

    Google Scholar 

  2. Dahleh, M.A. and Pearson, J.B., Minimization of a Regulated Response to a Fixed Input, IEEE Trans. Automat. Control, 1988, vol. 33, no.10, pp. 924–930.

    Google Scholar 

  3. Moore, K.L. and Bhattacharyya, S.P., A Technique for Choosing Zero Locations for Minimal Overshoot, IEEE Trans. Automat. Control, 1990, vol. 35, no.5, pp. 577–580.

    Google Scholar 

  4. Izmailov, R.N., Lower Estimates of Overshoot in Stable Linear Links with a Rational Transfer Function, Avtom. Telemekh., 1991, no. 6, pp. 28–33.

    Google Scholar 

  5. Casavola, A. and Mosca, E., Minimization of a Closed-Loop Response to a Fixed Input for SISO Systems, IEEE Trans. Automat. Control, 1997, vol. 42, no.11, pp. 1581–1587.

    Google Scholar 

  6. Hill, R.D. and Halpern, M.E., Minimum Overshoot Design for SISO Discrete-Time Systems, IEEE Trans. Automat. Control, 1992, vol. 38, no.1, pp. 155–158.

    Google Scholar 

  7. Kiselev, O.N. and Polyak, B.T., Minimization of Overshoot in Linear Discrete Systems by Regulators of the Low Order, Avtom. Telemekh., 2001, no. 4, pp. 98–108.

  8. Filimonov, A.B. and Filimonov, N.B., To a Problem of the Dynamic Quality of Linear Stationary Control Systems. Analytical Methods of Synthesis of Controllers, in Mezhvuz. Nauch. Sb., Saratov, 1981, pp. 94–106.

  9. Mita, T. and Yoshida, H., Undershooting Pgenomenon and Its Control in Linear Multivariable Servo-mechanisms, IEEE Trans. Automat. Control, 1990, vol. 35, no.5, pp. 578–580.

    Google Scholar 

  10. Philips, S.F. and Seborg, D.E., Conditions that Guarantee no Overshoot for Linear Systems, Int. J. Control, 1988, vol. 47, no.4, pp. 1043–1059.

    Google Scholar 

  11. Jayasuriya, S. and Song, J., On the Synthesis of Compensators for Nonovershooting Step Response, J. Dynam. Syst., Measure, Control, 1996, vol. 118, no.4, pp. 753–763.

    Google Scholar 

  12. Darbha, S. and Bhattacharyya, S.P., Controller Synthesis for Sign-Invariant Impulse Response, IEEE Trans. Automat. Control, 2002, vol. 47, no.8, pp. 1346–1351.

    Google Scholar 

  13. Leon, B.A. and Salazar, F.J., Discrete-Time Systems with Monotonic Step Responses and Complex Conjugate Poles and Zeros, IEEE Trans. Automat. Control, 2002, vol. 47, no.12, pp. 2098–2101.

    Google Scholar 

  14. Darbha, S. and Bhattacharyya, S.P., On the Synthesis of Controllers for a Nonovershooting Step Response, IEEE Trans. Automat. Control, 2003, vol. 48, no.5, pp. 797–799.

    Google Scholar 

  15. Marden, M., Geometry of Polynomials, Providence: AMS, 1966.

    Google Scholar 

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Translated from Avtomatika i Telemekhanika, No. 3, 2005, pp. 65–73.

Original Russian Text Copyright © 2005 by Kiselev.

Deceased.

This paper was recommended for publication by B.T. Polyak, a member of the Editorial Boarb

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Kiselev, O.N. Minimization of basic quality indices in linear discrete systems. Autom Remote Control 66, 398–405 (2005). https://doi.org/10.1007/s10513-005-0069-2

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  • DOI: https://doi.org/10.1007/s10513-005-0069-2

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