 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| B. N. Sokolov, "Guaranteed estimate of the influence of flexible elements on the dynamics of the attitude stabilization of a structure under bang-bang control," Mech. Solids. 40 (3), 1-7 (2005) |
| Year |
2005 |
Volume |
40 |
Number |
3 |
Pages |
1-7 |
| Title |
Guaranteed estimate of the influence of flexible elements on the dynamics of the attitude stabilization of a structure under bang-bang control |
| Author(s) |
B. N. Sokolov (Moscow) |
| Abstract |
The influence of a system of particles on the controlled motion
of a rigid body to be stabilized with respect to a prescribed direction
is investigated. The particles are attached to one another and to the
body by means of linear viscoelastic elements. The motion occurs under
the action of an external disturbance and the control torque the components
of which are directed along the principal axes of inertia of the undeformed
body about its center of mass. The control torque components are bang-bang
functions of time. There is a fixed time delay in the control channel,
which makes arbitrarily frequent switchings of the control functions
impossible. The vibrations arising due to the inertial forces
influence the motion of the rigid body, which should be taken
into account when designing the stabilizing control. We obtain a guaranteed
estimate of the magnitude of the torque caused by the inertial forces
and the amplitudes of the relative vibration of the system of particles
resulting from the control switchings. It is assumed that the kinematic
state of the system of particles is unknown to the controller.
The estimates obtained enable one to utilize the guaranteed
approach to form the control strategy [1-3]. This approach treats
the influence of the system of particles on the motion
of the body as an uncertain external disturbance constrained in
magnitude. This paper is adjacent to the publications of [4-6]
and continues the investigation of the effectiveness of the bang-bang
delayed controllers in the control channel in terms of guaranteed
stabilization [7-10]. The dynamics of a rigid body with elastic and dissipative
elements has been studied in [11] under the assumption that
the natural vibration period and the characteristic damping time
are small as compared with the total characteristic time of motion. |
| References |
| 1. | R. Issacs, Differential Games [Russian translation],
Mir, Moscow, 1967. |
| 2. | A. I. Subbotin and A. G. Chentsov,
Optimization of Guaranty in Control Problems
[in Russian], Nauka, Moscow, 1981. |
| 3. | N. N. Krasovskii,
Control of a Dynamical System: Minimization of the Guaranteed
Result
[in Russian], Nauka, Moscow, 1985. |
| 4. | K. B. Alekseev and G. G. Bebenin,
Control of a Spacecraft
[in Russian], Mashinostroenie, Moscow, 1964. |
| 5. | E. V. Gaushus and N. D. Smol'yaninov,
"Investigation of a bang-bang stabilization system
for a flying vehicle,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 2, pp. 5-13, 1970. |
| 6. | E. V. Gaushus,
Investigation of Dynamical Systems by Using the Point Transformation Method
[in Russian], Nauka, Moscow, 1976. |
| 7. | N. V. Banichuk, I. I. Karpov, D. M. Klimov, et al.,
Mechanics of Large-scale Space Structures
[in Russian], Faktorial, Moscow, 1997. |
| 8. | V. F. Ivanova and B. N. Sokolov,
"Maximal guaranteed accuracy of a bang-bang regulator in a
one-dimensional stabilization problem,"
Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 26-36, 1999. |
| 9. | B. N. Sokolov,
"On the structure of a single-channel controller
providing a guaranteed accuracy with maximum efficiency,"
Izv. AN. MTT [Mechanics of Solids], No. 3, pp. 17-33, 2002. |
| 10. | B. N. Sokolov,
"A single-channel bang-bang controller for guaranteed
stabilization of translational motions of a rigid
body with internal degrees of freedom,"
Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 10-16, 2003. |
| 11. | F. L. Chernousko,
"On the motion of a rigid body with elastic and dissipative elements,"
PMM [Applied Mathematics and Mechanics], Vol. 42, No. 1, pp. 31-42, 1978. |
|
| Received |
14 May 2003 |
| << Previous article | Volume 40, Issue 3 / 2005 | Next article >> |
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