 | | 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, "On the structure of a single-channel controller providing a guaranteed accuracy with maximum efficiency," Mech. Solids. 37 (3), 13-27 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
3 |
Pages |
13-27 |
| Title |
On the structure of a single-channel controller providing a guaranteed accuracy with maximum efficiency |
| Author(s) |
B. N. Sokolov (Moscow) |
| Abstract |
A bang-bang controller is synthesized for a single-degree-of-freedom system
modeling, for example, the spacecraft attitude stabilization system operated
by on-off jet engines with a delay of the thrust switch-off. The system is
subject to unknown disturbances that are constrained in absolute value
by a prescribed constant. The control law is formed so as to provide
a prescribed guaranteed accuracy of stabilization with a minimum average
flow rate of the working substance of the controller. By guaranteed accuracy
we understand the accuracy corresponding to the worst disturbance.
To solve this problem, game theory methods [1-3] combined with the
phase plane technique are utilized. From the set of feedback bang-bang
control laws providing the guaranteed stabilization with the prescribed
accuracy starting from some time instant, we select the law corresponding
to the minimum flow rate of the working substance of the control engines.
The solution is given for a certain set of parameters determined by
the specifications of the controller.
A number of efficient bang-bang control laws that can be applied for
the stabilization of motion have been considered in [4-6]. Solutions
of minimax problems of stabilization by means of bang-bang controllers
with a delay in the control switching circuit have been given in [7, 8].
For example, the book [7] presents an approximate solution of the problem
of design of the controller providing a prescribed guaranteed accuracy
with maximum efficiency for the case where the magnitude of the disturbance
is small in comparison with that of the control force. |
| References |
| 1. | R. Isaacs, Differential Games [Russian translation],
Nauka, Moscow, 1967. |
| 2. | A. I. Subbotin and A. G. Chentsov,
Guaranteed Optimization in Control Problems [in Russian],
Nauka, Moscow, 1981. |
| 3. | N. N. Krasovskii, Control of a Dynamical System.
Problem of the Minimum 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,
"Analysis of a bang-bang control system for a flying vehicle,"
Izv. AN SSSR. MTT [Mechanics of Solids], No. 2, pp. 5-13, 1970. |
| 6. | E. V. Gaushus, Analysis of Dynamical Systems by means
of Point Mapping [in Russian], Nauka, Moscow, 1976. |
| 7. | N. V. Banichuk, I. I. Karpov, D. M. Klimov,
A. P. Markeev, B. N. Sokolov, and A. V. Sharanyuk,
Mechanics of Large-Scale Space Structures [in Russian],
Faktorial, Moscow, 1997. |
| 8. | V. F. Ivanova and B. N. Sokolov,
"Maximum guaranteed accuracy of the bang-bang controller
in a one-dimensional stabilization problem,"
Izv. AN. MTT [Mechanics of Solids], No. 2, pp. 26-36, 1999. |
| 9. | E. S. Pyatnitskii, "Decomposition principle in control
of dynamical systems," Doklady AN SSSR, Vol. 300, No. 2,
pp. 300-303, 1988. |
| 10. | F. L. Chernousko, Decomposition and feedback control
in dynamical systems," Izv. AN SSSR. Tekhnicheskaya
Kibernetika, No. 6, pp. 64-82, 1990. |
| 11. | L. S. Pontryagin, V. G. Boltyanskii,
R. V. Gamkrelidze, and E. F. Mishchenko,
Mathematical Theory of Optimal Processes [in Russian],
Nauka, Moscow, 1983. |
|
| Received |
10 April 2000 |
| << Previous article | Volume 37, Issue 3 / 2002 | Next article >> |
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