Motion control of a bridge crane with a load by finding its acceleration
DOI:
https://doi.org/10.21638/11701/spbu01.2020.115Abstract
A possible approach to controlling a bridge crane motion while moving cargo is considered. Two different methods for finding the controlling acceleration that providing vibration damping of the cargo being carried are suggested. The first of these methods is based on applying classical Pontryagin maximum principle. The second method, using generalised Gauss principle, is based on modern researches in nonholonomic mechanics. The new method relies on the results of applying the classical one and can be used as independent approach for solving various problems of control.
Keywords:
Pontryagin maximum principle, generalised Gauss principle, optimal control, vibrations damping
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Понтрягин Л. С., Болтянский В. Г., Гамкрелидзе Р. В., Мищенко Е. Ф. Математическая теория оптимальных процессов. М.: Наука, 1983.
Поляхов Н. Н., Зегжда С. А., Юшков М. П. Обобщение принципа Гаусса на случай неголономных систем высших порядков // Доклады Академии наук СССР. 1983. Т. 269, № 6. С. 1328–1330.
Зегжда С. А., Солтаханов Ш. Х., Юшков М. П. Неголономная механика: теория и приложения. М.: Физматлит, 2009.
Поляхов Н. Н., Зегжда С. А., Юшков М. П. Теоретическая механика. М.: Высшая школа, 2000.
Shugailo T. S., Yushkov M. P. Motion control of gantry crane with container // The Eighth Polyakhov’s Reading: Proceedings of the International Scientific Conference on Mechanics. 2018. Vol. 1959. Art. no. 030021. https://doi.org/10.1063/1.5034576
Зегжда С. А., Шатров Е. А., Юшков М. П. Новый подход к нахождению управления, переводящего систему из одного фазового состояния в другое // Вестн. С.-Петерб. ун-та. Математика. Механика. Астрономия. 2016. Т. 3. Вып. 2. C. 284–292. https://doi.org/10.21638/11701/spbu01.2016.212
Зегжда С. А., Шатров Е. А., Юшков М. П. Гашение колебаний тележки с двойным маятником с помощью управления ее ускорением // Вестн. С.-Петерб. ун-та. Математика. Механика. Астрономия. 2016. Т. 3. Вып. 4. C. 683–688. https://doi.org/10.21638/11701/spbu01.2016.418
Черноусько Ф. Л., Акуленко Л. Д., Соколов Б. Н. Управление колебаниями. М.: Наука, 1980.
Зегжда С. А., Солтаханов Ш. Х., Юшков М. П. Уравнения движения неголономных систем и вариационные принципы механики. Новый класс задач управления. М.: Физматлит, 2005.
Zegzhda S. A., Yushkov M. P., Soltakhanov Sh. Kh., Naumova N. V., Shugailo T. S. A novel approach to suppression of oscillations // ZAMM Zeitschrift f¨ur angewandte Mathematik und Mechanik.
Vol. 98, no. 5. P. 781–788.
References
Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mishchenko E. F., The mathematical theory of optimal processes (Interscience Publishers John Wiley and Sons Inc., New York; London, 1962).
Polyakhov N. N., Zegzhda S. A., Yushkov M. P., “Generalization of the Gauss principle to the case of non-holonomic high-order systems”, Doklady AN SSSR 269(6), 1328–1330 (1983).
Zegzhda S. A., Soltakhanov Sh. Kh., Yushkov M. P., Nonholonomic mechanics: theory and application (Fizmatlit Publ., Moscow, 2009). (In Russian)
Polyakhov N. N., Zegzhda S. A., Yushkov M. P., Theoretical mechanics (Vysshaya shkola Publ., Moscow, 2000). (In Russian)
Shugailo T. S., Yushkov M. P., “Motion control of gantry crane with container”, The Eighth Polyakhov’s Reading: Proceedings of the International Scientific Conference on Mechanics 1959, 030021 (2018). https://doi.org/10.1063/1.5034576
Zegzhda S. A., Shatrov E. A., Yushkov M. P., “A new approach to finding the control that transports a system from one phase state to another”, Vestnik St. Petersburg University: Mathematics 49(2), 183–190 (2016). https://doi.org/10.3103/S106345411602014X
Zegzhda S. A., Shatrov E. A., Yushkov M. P., “Suppression of oscillation of a trolley with a double pendulum by means of control of its acceleration”, Vestnik of Saint Petersburg University. athematics. Mechanics. Astronomy 61(4), 683–688 (2016). https://doi.org/10.21638/11701/spbu01.2016.418 (In Russian)
Chernousko F. L., Akulenko D., Sokolov B. N., Control of oscillations (Nauka Publ., Moscow, 1980). (In Russian)
Zegzhda S. A., Soltakhanov Sh. Kh., Yushkov M. P., Mechanics of non-holonomic systems. A New Class of control systems (Springer-Verlag, Berlin, 2009).
Zegzhda S. A., Yushkov M. P., Soltakhanov Sh. Kh., Naumova N. V., Shugailo T. S., “A novel approach to suppression of oscillations”, ZAMM Zeitschrift f¨ur angewandte Mathematik und Mechanik 98(5), 781–788 (2018). https://doi.org/10.1002/zamm.201700005
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Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.
