Email this article On the Prevention of Vibrations in the Problem of the Time-Optimal Control of a System with Two Degrees of Freedom
- Authors: Selyutskiy Y.D.1, Formalskii A.M.1
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Affiliations:
- Institute of Mechanics, Lomonosov Moscow State University, 119991, Moscow, Russia
- Issue: No 6 (2023)
- Pages: 81-92
- Section: ОПТИМАЛЬНОЕ УПРАВЛЕНИЕ
- URL: https://journals.rcsi.science/0002-3388/article/view/148136
- DOI: https://doi.org/10.31857/S0002338823060094
- EDN: https://elibrary.ru/HIHGMD
- ID: 148136
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Abstract
We study a mechanical system with two degrees of freedom, consisting of two absolutely rigid bodies (material points) connected to each other by a weightless rectilinear viscoelastic rod that can be stretched or compressed. The bodies can move translationally along a fixed straight line. A control force limited in absolute value is applied to one of them, whose vector is directed along the rod. A continuous piecewise-linear control in time, which transfers the system from one equilibrium position to another in a length of time close to the minimum possible time, is constructed. In the absence of viscosity, with the constructed quasi time-optimal control, unwanted vibrations of the bodies are not excited either during the transition process or when it ends. In contrast to the time-optimal relay control, the constructed continuous control is also robust with respect to the uncertainty of the design parameters.
About the authors
Yu. D. Selyutskiy
Institute of Mechanics, Lomonosov Moscow State University, 119991, Moscow, Russia
Email: seliutski@imec.msu.ru
Россия, Москва
A. M. Formalskii
Institute of Mechanics, Lomonosov Moscow State University, 119991, Moscow, Russia
Author for correspondence.
Email: formal@imec.msu.ru
Россия, Москва
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