 | | 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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| M.V. Levskii, "Optimal Control of a Spacecraft Orientation Taking into Account the Energy of Rotation," Mech. Solids. 54 (2), 144-156 (2019) |
| Year |
2019 |
Volume |
54 |
Number |
2 |
Pages |
144-156 |
| DOI |
10.3103/S0025654419030166 |
| Title |
Optimal Control of a Spacecraft Orientation Taking into Account the Energy of Rotation |
| Author(s) |
M.V. Levskii (Maksimov Research Institute of Space Systems, Khrunichev State Research and Production Space Center, Korolev, 141091 Russia, dp940@mail.ru) |
| Abstract |
The problem of optimal control of the reorientation of a spacecraft as a solid body from an
arbitrary initial position into a prescribed final angular position is considered and solved. The construction of an optimal slew control is based on the quaternionic variables and Pontryagin’s maximum
principle. The case is investigated when the minimized functional combines, in a given proportion, the
integral of the kinetic energy of rotation and the duration of the maneuver. On the basis of necessary
optimality conditions, the main properties, laws, and key characteristics (parameters, constants, integrals of motion) of the optimal solution of the control problem, including the maximum kinetic energy
for the optimal motion and the turn time, are determined. It is proved that during the optimal rotation,
the direction of the kinetic moment is constant in the inertial coordinate system. Formalized equations
and expressions for the synthesis of the optimal rotation program are obtained. The optimal solution
corresponds to the strategy “acceleration – rotation by inertia – braking”. An assessment is made of
the influence of the limiting control moment on the character of the optimal motion and on the quality control indicators. It is shown that the accepted optimality criterion guarantees the motion of a
spacecraft with a kinetic rotational energy not exceeding the required value. For dynamically symmetric spacecraft, a complete solution of the reorientation problem in closed form is presented. An example and results of mathematical modeling of the motion of a spacecraft with optimal control are given,
demonstrating the practical feasibility of the method for controlling spacecraft spatial orientation. |
| Keywords |
optimal control, optimality criterion, maximum principle, orientation, quaternion, rotation by inertia |
| Received |
01 February 2018 |
| Link to Fulltext |
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