Abstract
We consider the synthesis problem for low order controllers that provide given properties for a linear continuous system under uncertainty in object parameters. The synthesis is done with stability and quality criteria that have a simple dependence on the coefficients of the characteristic polynomial. We give examples of synthesizing controllers with given requirements to transition process quality, performance, and tracking accuracy.
Similar content being viewed by others
References
Kharitonov, V.L., Asymptotic Stability for a Family of Systems of Linear Differential Equations, Differ. Equat., 1978, vol. 14, no. 11, pp. 2086–2088.
Polyak, B.T. and Shcherbakov, P.S., Robastnaya stabil’nost’ i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.
Ackermann, J., Robust Control: The Parameter Space Approach, London: Springer-Verlag, 2002.
Bhattacharyya, S.P., Chapellat, H., and Kell, L.H., Robust Control: The Parametric Approach, Upper Saddle River: Prentice Hall, 1995.
Naslin, P., Polynomes Normaux et Critere Algebrique d’Amortissement, Automatisme, 1963, vol. 8, no. 6, pp. 215–233.
Voronov, V.S., Stability and Quality Parameters for Robust Control Systems, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1995, no. 6, pp. 49–54.
Petrov, B.N., Sokolov, N.I., Lipatov, A.V., et al., Sistemy avtomaticheskogo upravleniya ob”ektami s peremennymi parametrami: inzhenernye metody analiza i sinteza (Automated Control Systems for Object with Variable Parameters; Engineering Methods of Analysis and Synthesis), Moscow: Mashinostroenie, 1986.
Skvortsov, L.M. and Fedosov, B.T., On V.S. Voronov’s Algebraic Criteria for the Stability and Quality of Linear Systems, available at http://model.exponenta.ru/bt/bt00118.html.
Opeiko, O.F., Design of a Linear System Using a Simplified Plant Model, Autom. Remote Control, 2005, vol. 66, no. 1, pp. 24–30.
Manabe, S., Brief Tutorial and Survey of Coefficient Diagram Method, Proc. 4th Asian Control Conf., Singapore, 2002, pp. 1161–1166.
Kiselev, O.N. and Polyak, B.T., Design of Low-Order Controllers by the H8 and Maximal-Robustness Performance Indices, Autom. Remote Control, 1999, vol. 60, no. 3, part 2, pp. 393–402.
Goncharov, V.I., Liepin’sh, A.V., and Rudnitskii, V.A., Synthesis of Low Order Robust Controllers, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 2001, no. 4, pp. 36–43.
Gryazina, E.N., Polyak, B.T., and Tremba, A.A., Design of the Low-order Controllers by the H8 Criterion: A Parametric Approach, Autom. Remote Control, 2007, vol. 68, no. 3, pp. 456–466.
Volgin, L.N., Optimal’noe diskretnoe upravlenie dinamicheskimi sistemami (Optimal Discrete Control for Dynamical Systems), Moscow: Nauka, 1986.
Skvortsov, L.M., Interpolation Method for the Assignment Problem of Dominating Poles in the Synthesis of One-Dimensional Controllers, Izv. Ross. Akad. Nauk, Teor. Sist. Upravlen., 1996, no. 4, pp. 10–13.
Vadutov, O.S., Synthesis of Low Order Controllers with a Given Location of the Closed System Poles, Izv. Tomsk. Polytech. Inst., 2007, vol. 311, no. 5, pp. 14–18.
Pukhov, G.E., Metody analiza i sinteza kvazianalogovykh elektronnykh tsepei (Analysis and Synthesis of Quasianalog Electronic Circuits), Kiev: Naukova Dumka, 1967.
Kozlov, O.S., Kondakov, D.E., Skvortsov, L.M., et al., “Modeling in Technical Devices” Software Suite, available at http://model.exponenta.ru/mvtu/20050615.html.
Kozlov, O.S. and Skvortsov, L.M., Study and Design of Automated Systems with the MVTU Software Suite, Inform. Tekhnol., 2006, no. 8, pp. 9–15.
Francis, B., A Course in H8 Control Theory, Lecture Notes Control Inf. Sci, vol. 88, Berlin: Springer-Verlag, 1987.
Wie, B. and Bernstein, D.S., Benchmark Problems for Robust Control Design, J. Guidance, Control, Dynam., 1992, vol. 15, no. 5, pp. 1057–1059.
Chestnov, V.N., Design of Robust H8-Controllers of Multivariable Systems Based on the Given Stability Degree, Autom. Remote Control, 2007, vol. 68, no. 3, pp. 557–563.
Polyak, B.T. and Shcherbakov, P.S., Hard Problems in Linear Control Theory: Possible Approaches to Solution, Autom. Remote Control, 2005, vol. 66, no. 5, pp. 681–718.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © O.S. Kozlov, L.M. Skvortsov, 2015, published in Avtomatika i Telemekhanika, 2015, No. 9, pp. 102–114.
Rights and permissions
About this article
Cite this article
Kozlov, O.S., Skvortsov, L.M. Synthesis of simple robust controllers. Autom Remote Control 76, 1598–1607 (2015). https://doi.org/10.1134/S0005117915090064
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117915090064