Email this article 
ON THE NUMERICAL DAMPING OF STRING VIBRATIONS USING SEVERAL STATIONARY ACTUATORS
- Authors: Mikhailov I.E1,2
-
Affiliations:
- Federal Research Center Computer Science and Control, RAS
- Bauman Moscow State Technical University
- Issue: Vol 64, No 9 (2024)
- Pages: 1680-1688
- Section: Partial Differential Equations
- URL: https://rjonco.com/0044-4669/article/view/665193
- DOI: https://doi.org/10.31857/S0044466924090084
- EDN: https://elibrary.ru/WJXWRJ
- ID: 665193
Cite item
Open Access
Access granted
Subscription Access
Abstract
The task is to transfer the string from the initial disturbed state to a state of rest in the shortest possible time. The damping of the string vibrations is carried out using several stationary actuators. The minimized functional is a certain integral. Vibration damping is controlled using a function included in the right part of the hyperbolic equation describing the transverse vibrations of the string and simulating the actions of the actuators. Computational algorithms for solving the problem based on the grid method and the gradient method of finding the minimum of functions of many variables have been developed, and the gradient is calculated using the method of rapid automatic differentiation proposed by Yu. G. Yevtushenko. Examples of calculations of string vibration damping using a different number of actuators are given.
About the authors
I. E Mikhailov
Federal Research Center Computer Science and Control, RAS; Bauman Moscow State Technical University
Email: mikh_igor@mail.ru
Moscow, Russia
References
- Бутковский А.Г. Методы управления системами с распределенными параметрами. М.: Наука, 1975. 366 с.
- Russel D.L. Controllability and stabilization theory for linear partial differential equations // SIAM Rev. 1978. V. 20. № 5. P 639-739.
- Lagness J. Control of wave process with distributed controls supported on a subregion // SIAM J. Control and Optim. 1983. V. 1. № 1. P. 68-85.
- Асланов С.Ж., Михайлов И.Е., Муравей Л.А. Аналитические и численные методы в задаче гашения колебаний струны точечным демпфером // Мехатроника, автоматизация, управление. 2006. № 7. С. 28-35.
- Levinson N. Gap and density theorem // Am. Math. Soc. Colog. Publ. 1940. V. 26.
- Евтушенко Ю.Г. Оптимизация и быстрое автоматическое дифференцирование. М.: ВЦ им. А.А. Дородницына РАН, 2013. 144 с.
Supplementary files
