 | | 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, "A single-channel bang-bang controller for guaranteed stabilization of translational motions of a rigid body with internal degrees of freedom," Mech. Solids. 38 (1), 7-12 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
1 |
Pages |
7-12 |
| Title |
A single-channel bang-bang controller for guaranteed stabilization of translational motions of a rigid body with internal degrees of freedom |
| Author(s) |
B. N. Sokolov (Moscow) |
| Abstract |
The problem of stabilization of a rigid body with internal
particles (point masses) about a prescribed fixed position
is considered. The particles are connected to one another
and to the carrier body by means of linear spring-and-dashpot elements. The body moves translationally along a straight line
under the action of a constant disturbance force and a bang-bang
control force, both these forces being directed along the line
of motion. It is assumed that the controller does not have
information about the kinematic state of the internal particles
and that there is a fixed delay in the control channel and, hence,
arbitrarily frequent switchings of the control are not allowed.
To solve this problem, we utilize the game approach [1-3].
In accordance with this approach, the influence of the internal
system of particles on the motion of the carrier body is treated
as the action of an external disturbance force which is unknown
in advance but is bounded in absolute value. Estimates are obtained
for the magnitude of this disturbance, as well as for the amplitudes
of vibrations of the particles appearing under the action of inertial
forces as a result of a switching of the bang-bang control. A guaranteed
attainable estimate is obtained for the accuracy of stabilization
of the prescribed position of the body, depending on the mechanical
parameters of the system and the magnitude of the control force.
As an example, the controlled motion of a two-mass vibrating system is
considered. This paper is closely related to those of [4-6] and continues
investigations of guaranteed optimal linear controllers with delay
in the control channel [7-9]. The dynamics of a rigid body with
elastic and dissipative members has been investigated in [10]
with the assumption that the period of free vibrations and the
time of their damping are small in comparison with
the characteristic time of motion of the entire system. |
| References |
| 1. | R. Issacs, Differential Games [Russian translation],
Mir, Moscow, 1967. |
| 2. | A. I. Subbotin and A. G. Chentsov, Optimization
of Guarantee in Control Problems
[in Russian], Nauka, Moscow, 1981. |
| 3. | N. N. Krasovskii, Control of a Dynamical System:
Guaranteed Result Minimization Problem
[in Russian], Nauka, Moscow, 1985. |
| 4. | K. B. Alekseev and G. G. Bebenin, Control of a Flying
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. No. 2, pp. 5-13, 1970. |
| 6. | E. V. Gaushus, Investigation of Dynamical Systems
by 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,
"Maximum guaranteed accuracy of a bang-bang controller
in a one-dimensional stabilization problem,"
Izv. AN. MTT. No. 2, pp. 26-36, 1999. |
| 9. | B. N. Sokolov, "On the structure of a bang-bang
controller possessing the maximum-efficiency behavior for
a guaranteed accuracy,"
Izv. AN. MTT. No. 3, pp. 17-33, 2002. |
| 10. | 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. 34-42, 1978. |
|
| Received |
24 April 2001 |
| << Previous article | Volume 38, Issue 1 / 2003 | Next article >> |
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