Abstract
We consider the problem of synthesizing simple structured relay controllers as part of a self-oscillatory system with a linear plant. The controller structure is said to be simple if it cannot be simplified since any further simplification that consists in excluding any element from it leads to the impossibility of satisfying all the requirements for the system. It is necessary to ensure the presence of self-oscillations with a given frequency and amplitude in the system and bring its behavior closer to the desired one. A method for solving the problem under consideration is proposed.
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REFERENCES
Tsypkin, Ya.Z., Releinye avtomaticheskie sistemy (Relay Automatic Systems), Moscow: Nauka, 1974.
Faldin, N.V., Relay automatic control systems, in Matematicheskie modeli, dinamicheskie kharakteristiki i analiz sistem avtomaticheskogo upravleniya (Mathematical Models, Dynamic Characteristics, and Analysis of Automatic Control Systems), Pupkov, K.A. and Egupov, N.D., Eds., Moscow: Izd. Mosk. Gos. Univ., 2004.
Boiko, I., Discontinuous Control Systems, Boston: Birkhäuser, 2009.
Boiko, I.M., Kuznetsov, N.V., Mokaev, R.N., and Akimova, E.D., On asymmetric periodic solutions in relay feedback systems, J. Franklin Inst., 2021, vol. 358, no. 1, pp. 363–383.
Popov, E.P. and Pal’tov, I.P., Priblizhennye metody issledovaniya nelineinykh avtomaticheskikh sistem (Approximate Methods for Studying Nonlinear Automatic Systems), Moscow: Fizmatgiz, 1960.
Pervozvanskii, A.A., Kurs teorii avtomaticheskogo upravleniya (A Course in Automatic Control Theory), Moscow: Nauka, 1975.
Leonov, G.A., On the method of harmonic linearization, Autom. Remote Control, 2009, vol. 70, no. 5, pp. 800–810.
Rudnev, S.A. and Faldin, N.V., On the extension of the scope of applicability of the conditions for the stability of relay systems, Izv. Akad. Nauk SSSR. Tekh. Kibern., 1980, no. 5, pp. 193–196.
Faldin, N.V. and Rudnev, S.A., Synthesis of relay systems by the phase locus method, Izv. Vyssh. Uchebn. Zaved. Priborostr., 1982, no. 7, pp. 32–36.
Mozzhechkov, V.A., Design of simple-structure linear controllers, Autom. Remote Control, 2003, vol. 64, no. 1, pp. 23–36.
Gajduk, A.R., Design of control systems from transfer functions, Autom. Remote Control, 1980, vol. 41, no. 1, pp. 6–11.
Gajduk, A.R., On design of control systems with a specified form of exogenous signals, Autom. Remote Control, 1984, vol. 45, no. 6, pp. 692–699.
Gajduk, A.R., Choice of feedbacks in a control system of minimal complexity, Autom. Remote Control, 1990, vol. 51, no. 5, pp. 593–600.
Voevoda, A.A. and Chekhonadskikh, A.V., Optimizing the pole arrangement in a control system with a lower-order controller, Avtometriya, 2009, vol. 4, no. 5, pp. 113–123.
Panovko, Ya.G., Vvedenie v teoriyu mekhanicheskikh kolebanii (Introduction to the Theory of Mechanical Vibrations), Moscow: Nauka, 1971.
Goryachenko, V.D., Elementy teorii kolebanii (Elements of the Theory of Vibrations), Moscow: Vyssh. Shkola, 2001.
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Translated by V. Potapchouck
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Mozzhechkov, V.A. Synthesis of Simple Relay Controllers in Self-Oscillating Control Systems. Autom Remote Control 83, 1393–1403 (2022). https://doi.org/10.1134/S0005117922090041
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DOI: https://doi.org/10.1134/S0005117922090041