| Автор | Llibre, Jaume |
| Автор | Ponce, Enrique |
| Дата выпуска | 1996 |
| dc.description | The describing function method (used normally as a first approximation to study the existence and the stability of periodic orbits) is used here to analyze the dependence of periodic orbits on the parameters of autonomous systems. The method can be applied to a large class of nonlinear systems but, for simplicity, attention here is paid to a class of single-input, single-output control systems with a piecewise linear character- istic function. A first approach to the bifurcation diagram associated with the periodic orbits of such systems, called a first harmonic bifurcation diagram' is obtained for two and three dimensions. This diagram in two dimensions describes all the qualitative behaviour of such systems. Although this is not the case in three dimensions, the information contained in the corresponding first harmonic bifurcation diagram is of great value. It shows much of the complexity of the periodic structure that can be found in such three-dimensional systems; in fact, part of the first harmonic bifurcation diagram coincides with the actual bifurcation diagram |
| Формат | application.pdf |
| Издатель | Journals Oxford Ltd |
| Копирайт | Copyright Taylor and Francis Group, LLC |
| Название | Global first harmonic bifurcation diagram for odd piecewise linear control systems |
| Тип | research-article |
| DOI | 10.1080/02681119608806216 |
| Electronic ISSN | 1465-3389 |
| Print ISSN | 0268-1110 |
| Журнал | Dynamics and Stability of Systems |
| Том | 11 |
| Первая страница | 49 |
| Последняя страница | 88 |
| Аффилиация | Llibre, Jaume; Departament de Matemàtiques, Universitat Autònoma de Barcelona |
| Аффилиация | Ponce, Enrique; Departament de Matemática Aplicada II, E.S. de Ingenieros |
| Выпуск | 1 |
| Библиографическая ссылка | Aizerman, M. A. 1963. Theory of Automatic Control, Oxford: Pergamon. |
| Библиографическая ссылка | Allwright, D, J. 1977. Harmonic balance and the Hopf bifurcation theorem Maths. Proceedings at the Cambridge Phil Society, 82: 453–467. |
| Библиографическая ссылка | Alvarez, J., Suarez, R. and Alvarez, J. 1993. Planar linear systems with single saturated feedback. Systems and Control Letters, 20: 319–326. |
| Библиографическая ссылка | Arneodo, A., Coullet, P. and Tresser, C. 1981. Possible new strange attractors with spiral structure. communications in Mathematical physics, 79: 573–579. |
| Библиографическая ссылка | Atherton, D. P. 1982. Nonlinear Control Engineering (Describing Function Analysis and Design), Reinhold, New York: Van Nostrand. 2nd edn |
| Библиографическая ссылка | Barnett, S. and Cameron, R. G. 1985. Introduction to Mathematical Control Theory, Oxford: Clarendon Press. |
| Библиографическая ссылка | Bogolyubov, N. N. and Krylov, N. M. 1934. Applications of New Nonlinear Mechanics Methods to the Investigation of Working of Synchronous Generators, Moscow, Russian: OMTI. |
| Библиографическая ссылка | Chen, C. T. 1934. Linear System Theory and Design, Winston: Holt Rinehart. |
| Библиографическая ссылка | Freire, R, Rodriguez-Luis, A. J., Gamero, E. and Ponce, E. 1993. A case study for homoclinic chaos in an autonomous electronic circuit. Physica D, 62: 230–253. |
| Библиографическая ссылка | Gantmakher, F. R. 1990. The Theory of Matrices, New york: Chelsca publishing. 2nd edn |
| Библиографическая ссылка | Genesio, R. and Tesi, A. 1992. Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems. Automatica, 28: 531–548. |
| Библиографическая ссылка | Gibson, J. E. 1963. Nonlinear Automatic Control, New York: McGraw-Hill. |
| Библиографическая ссылка | Glover, J. N. 1989. Hopf bifurcations at infinity. Nonlinear Analysis, 13: 1393–1398. |
| Библиографическая ссылка | Goldfarb, L. C. 1947,1956. On Some nonlinear phenomena in regulatory system. Automatika i Telemekanika, Edited by: Oldenburger, U. 349–383. New York: Macmillan. Translation (1956) Frequency Response |
| Библиографическая ссылка | Huseyin, K. 1986. “Multiple parameter stability theory and its applications”. In Oxford Engineering Series 18, Oxford: Clarendon Press. |
| Библиографическая ссылка | Khalil, H, K. 1992. Nonlinear Systems, New York: Macmillan. |
| Библиографическая ссылка | Kochenburger, R. 1950. Frequency response method for analysis of a relay servomechanism. Transactions of the AIEE, 69: 270–283. |
| Библиографическая ссылка | Krenz, G. S. and Miller, R. K. 1979. Qualitative analysis of oscillation. IEEE Transactions on Circuits and Systems CAS-26, : 235–254. |
| Библиографическая ссылка | llibre, J. and Sotomayor, J. 1996. Phase portraits of planar nonlinear control systems. Nonlinear Analysis, Theory, Methods and Applications, in press |
| Библиографическая ссылка | Mees, A. I. 1981. Dynamics of Feedback Systems, New York: Wiley. |
| Библиографическая ссылка | Mees, A. I. and Chua, L. O. 1979. The Hopf bifurcation theorem and its applications to nonlinear oscillations in circuits and systems. IEEE Transactions on Circuits and Systems CAS-26, : 235–254. |
| Библиографическая ссылка | Moila, J. L., Desages, A. and Romagnoli, J. 1991. Degenerate Hopf bifurcations via feedback system theory:higher-order harmonic balance. Chemical Engineering Science, 46: 1475–1490. |
| Библиографическая ссылка | Ogorzalek, M. J. 1986. Some observations on chaotic motion in single loop feedback systems. IEEE Proceedings of 25th Conference on Decision and Control, Athens, 46: 588–589. |
| Библиографическая ссылка | Sparrow, C. T. 1981. Chaos in a three-dimensional single loop feedback system with a piecewise linear feedback function. Journal of Mathematical Analytic Applications, 83: 275–291. |
| Библиографическая ссылка | Suarez, R., Alvarez, J. and Alvarez, J. Stability regions of closed loop linear systems with saturated linear feedback. Preprint |
| Библиографическая ссылка | Vidyasagar, M. 1993. Nonlinear Systems Analysis, Englewood Cliffs, NJ: Prentice-Hall. |
