 | | 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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| << Previous article | Volume 56, Issue 5 / 2021 | Next article >> |
| Levskii M.V., "Usage of a Combined Criterion of Quality in the Dynamic Problem on Optimal Rotation of a Solid (Spacecraft) with a Constraint Imposed on the Phase Variables," Mech. Solids. 56 (5), 661-683 (2021) |
| Year |
2021 |
Volume |
56 |
Number |
5 |
Pages |
661-683 |
| DOI |
10.3103/S0025654421050149 |
| Title |
Usage of a Combined Criterion of Quality in the Dynamic Problem on Optimal Rotation of a Solid (Spacecraft) with a Constraint Imposed on the Phase Variables |
| Author(s) |
Levskii M.V. (Space System Research and Development Institute, Khrunichev State Research and Production Space Center, Korolev, Moscow oblast, 141091 Russia, levskii1966@mail.ru) |
| Abstract |
Analytical methods are used to solve the dynamic problem on the optimal turn of a solid (for example, a spacecraft) from an arbitrary initial resting position to the required final resting position with limited control (control functions and phase variables are limited). The end time of the maneuver is not fixed. The case of a constraint imposed on the maximum allowable kinetic energy of rotation is considered. For optimization, a combined quality criterion that combines, in a given proportion, the turn time and the integral of the kinetic energy of rotation is used. The construction of the optimal turn control is based on quaternionic variables and the maximum principle. It is shown that during the optimal turn, the moment of forces is parallel to a straight line, motionless in inertial space, and the direction of the kinetic moment of a solid (spacecraft) is constant relative to the inertial coordinate system. The key properties of the optimal solution are formulated in an analytical form. A special control mode has been investigated in detail and the conditions for the existence or impossibility of such a mode have been formulated. Calculated expressions for finding the main characteristics of the control program are given. An example and results of numerical simulation of the motion for a spacecraft as a rigid body under optimal control are given by demonstrating the practical feasibility of the developed control method. For a dynamically symmetric spacecraft, the posed problem of optimal control is comprehensively solved: dependences as explicit functions of time for control variables as well as relations for calculating the parameters of the control law are obtained. The designed control algorithms make it possible to perform turns with limited rotation energy in a minimum time. |
| Keywords |
orientation, quaternion, optimal control, criterion of quality, relay control, maximum principle, boundary value problem |
| Received |
25 July 2020 | Revised |
30 September 2020 | Accepted |
24 December 2020 |
| Link to Fulltext |
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