from 01.01.1990 to 01.01.2021
Sankt-Peterburg, Russian Federation
UDK 60 Прикладные науки. Общие вопросы
A method for controlling dynamic chaos is proposed by introducing state feedback and changing the spectrum of Lyapunov characteristic parameters of a closed system to achieve the desired result - the transition from chaotic mode to regular motion. The solution of this problem is considered on the example of stabilization of a mechanical tachometer. The parameters of the controller in the feed-back circuit are determined by the method of modal con-trol synthesis.
suppression of chaotic Lyapunov characteristic parame-ters, mechanical tachometer, vibrations
1. Kosarev, B.A. Ustranenie otkloneniy napryazheniya i chastoty, podavlenie haoticheskih kolebaniy v elektrotehnicheskoy sisteme / B.A. Kosarev, V.K. Fedorov // Omskiy nauchnyy vestnik. - 2019. - № 6. - S. 52-57.
2. Andrievskiy, B.R. Metody podavleniya nelineynyh kolebaniy v astaticheskih sistemah avtopilotirovaniya letatel'nyh apparatov / B.R. Andrievskiy, N.V. Kuznecov, G.A. Leonov // Izvestiya RAN. Teoriya i sistemy upravleniya. - 2017. - № 3. - S. 118-134.
3. Magnickiy, N.A. O prirode haoticheskoy dinamiki v avtonomnyh nelineynyh sistemah differencial'nyh uravneniy / N.A. Magnickiy // Sistemnyy analiz i informacionnye tehnologii. - 2017. - №3 (69). - S. 65-72.
4. Andrievskiy, B.R. Upravlenie haosom: metody i prilozheniya. II. Prilozheniya / B.R. Andrievskiy, A.L. Fradkov // Avtomatika i telemehanika. - 2004. - № 4. - S. 3-34.
5. Ott, E. Controlling chaos / E. Ott, C. Grebogi, G. Yorke // Phys. Rev. Lett. - 1990. - V. 64, № 11. - Pp. 1196-1199.
6. Pyragas, K. Continuous control of chaos by self-controlling feedback / K. Pyragas // Phys. Lett. A. - 1992. - V. 170, № 6. - P. 421-428.
7. Luongo, A. Advances in stability, bifurcations and nonlinear vibrations in mechanical systems / A. Luongo, M.J. Leamy // Nonlinear Dinamics. - 2021. - Vol. 103, № 4. - Pp. 2993-2995.
8. Petrov, L.F. Nelineynaya dinamika mehanicheskih sistem: ot asimptoticheskih metodov k determinirovannomu haosu / L.F. Petrov // Trudy MFTI. - 2017. - T. 9, № 3. - S. 41-50.
9. Kuznecov, S.P. O nekotoryh prostyh primerah mehanicheskih sistem s giperbolicheskim haosom / S.P. Kuznecov, V.P. Kruglov // Trudy matematicheskogo instituta im. V.A. Steklova. - 2017. - T. 297. - S. 232-259.
10. Steingrube, S. Self-organized adaptation of simple neural circuit enables complex robot behavior / S. Steingrube, M. Timme, P. Manoonpong // Nature Phys. - 2010. - Vol. 6, № 3. - Pp. 224-230
11. Kucherova, V.Yu. Primenenie metoda AKAR dlya resheniya zadachi stabilizacii sostoyaniya ravnovesiya tipovyh nelineynyh sistem / V.Yu. Kucherova, V.N. Pet'kov, P.F. Artamonova // Fundamental'nye issledovaniya. - 2016. - № 5. - S.264-268.
12. Seyfullauv, R.E. Analiz diskretno-nepreryvnyh nelineynyh mnogosvyaznyh sistem na osnove lineynyh matrichnyh neravenstv / R.E. Seyfullauv, A.L. Fradkov // Avtomatika i telemehanika. - 2015. - № 6. - S. 57-74.
13. Budnik, S.V. Upravlenie haoticheskoy dinamikoy nelineynyh sistem / S.V. Budnik, V.N. Shashihin // Sistemnyy analiz v proektirovanii i upravlenii : sbornik trudov XXIII Mezhdunarodnoy nauchno-prakticheskoy konferencii. - Sankt-Peterburg, 2019. - S. 12-19.
14. Ge, Z.-M. Non-linear dynamics and control of chaos for a tachometer / Z.-M. Ge, J.S. Shiue // J. Sound Vibr. - 2002. - V. 253. - Pp. 1231-1242.
15. Grobman, D. Gomeomorfizm sistem differencial'nyh uravneniy / D. Grobman // DAN SSSR. - 1959. - T. 128, № 5. - S. 880-881.
16. Omorov, R.O. Metod topologicheskoy grubosti dinamicheskih sistem / R.O. Omorov // Materialovedenie. -2017. - № 4(24). - S. 77-83.
17. Shashihin, V.N. Upravlenie krupnomasshtabnymi dinamicheskimi sistemami / V.N. Shashihin, S.V. Budnik. -SPb. : Izd-vo Politehpress, 2020. - 308 s.
