 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| B. N. Sokolov, "Taking into account the influence of elastic elements of a free structure on the accuracy of its stabilization under a bang-bang control," Mech. Solids. 43 (6), 843-849 (2008) |
| Year |
2008 |
Volume |
43 |
Number |
6 |
Pages |
843-849 |
| DOI |
10.3103/S0025654408060022 |
| Title |
Taking into account the influence of elastic elements of a free structure on the accuracy of its stabilization under a bang-bang control |
| Author(s) |
B. N. Sokolov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia) |
| Abstract |
We consider the problem of stabilization with respect to a prescribed position for the translational motion of a rigid body with interior material points connected with each other and with the exterior body by linear viscoelastic constraints. The motion occurs under the action of a constant exterior perturbation and a bang-bang control force that are directed along the line of motion. We assume that the bang-bang force control channel has a fixed delay, so that arbitrarily frequent switchings are impossible. We suggest a positional control ensuring the solution of this problem. We estimate the amplitude of the rigid body vibrations about the center of mass of the entire structure and the accuracy of stabilization of the prescribed position of the rigid body depending on the mechanical characteristics of the system and the control force magnitude. We also consider the problem of maximizing the stabilization accuracy depending on the control parameters. By way of example, we consider the controlled motion of a two-mass oscillatory system. This work is closely related to [1-3] and continues the studies of the guaranteed optimal bang-bang controllers with delay in the control channel [4-9]. The dynamics of a rigid body with elastic and dissipative elements was studied in [10] under the assumption that the period of natural vibrations and their decay time are small compared with the characteristic time of motion. |
| Received |
13 January 2006 |
| Link to Fulltext |
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