MSC2010 34C20
Two-criteria problems for optimal protection of elastic structures from vibration
D. V. Balandin1, E. N. Ezhov2, I. A. Fedotov3
| Annotation | In a multi-objective formulation with criteria such as the maximal deformation of the elastic object to be protected and maximal deformations of the protection devices, a new class of optimal vibration protection problems is considered. The mathematical problem is to find a linear feedback control minimizing the above criteria in Pareto sense. A general approach to solving these problems based on results of modern control theory using linear matrix inequalities technique is presented. A system of linear matrix inequalities for obtaining the desired gain matrix is derived. An example of a solution of two-criteria problem for a multistorey building under seismic disturbances is given. Pareto set on the plane of the criteria is constructed. The <<ideal>> Pareto optimal isolator and optimal isolators of active and passive types are compared as well. It is shown that the <<active>> vibration isolators are not much better than the passive one, but all these isolators are noticeably inferior to the <<ideal>> vibration isolator. |
|---|---|
| Keywords | optimal vibration protection, multi-criteria problem, linear matrix inequalities, Germeyer convolution |
1Dmitry V. Balandin, Professor, Department of Differential Equations and Mathematical and Numerical Analysis, National Research Lobachevsky State University of Nizhny Novgorod (23 Gagarin St., Nizhny Novgorod 603950, Russia), Sc. (Physics and Mathematics), ORCID: https://orcid.org/0000-0001-7727-5924, dbalandin@yandex.ru
2Egor N. Ezhov, Ph.D Student, Department of Differential Equations and Mathematical and Numerical Analysis, National Research Lobachevsky State University of Nizhny Novgorod (23 Gagarin St., Nizhny Novgorod, 603950, Russia), ORCID: https://orcid.org/0000-0001-5434-7075, ezhovegor@gmail.com
3Igor A. Fedotov, CEO Ltd "REHEYA" university spin-off\, (8 bld., 23 Gagarin St., Nizhny Novgorod, 603950, Russia), Ph.D (Physics and Mathematics), ORCID: https://orcid.org/0000-0002-3912-8971, optimal.control@gmail.com
Citation: D. V. Balandin, E. N. Ezhov, I. A. Fedotov, "[Two-criteria problems for optimal protection of elastic structures from vibration]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,20:2 (2018) 215–224 (In Russian)
DOI 10.15507/2079-6900.20.201802.215-224
