TY - JOUR

T1 - Averaging technique in the problem of Lorentz attitude stabilization of an Earth-pointing satellite

AU - Aleksandrov, A.Yu.

AU - Tikhonov, A.A.

N1 - Funding Information: The reported study was partially supported by the Russian Foundation for Basic Research , research project No. 19-01-00146-a . Publisher Copyright: © 2020 Elsevier Masson SAS

PY - 2020/9

Y1 - 2020/9

N2 - An Earth-pointing satellite with Lorentz attitude control system is under consideration. The problem of the satellite attitude stabilization in the orbital reference frame in the presence of disturbances and complicated by underactuation is studied. The averaging technique is developed and applied in the problem. A rigorous mathematical justification is proposed, which makes it possible to consider a satellite with unequal moments of inertia and to obtain specific estimates for the control parameters that provide a solution to the problem of satellite attitude stabilization with the use of the Lorentz control torque. The octupole approximation of the Earth's magnetic field is used; the periodic functions of time arise in geomagnetic field induction. With the aid of nonlinear approach to the problem it is proved that Lorentz attitude control system ensures asymptotic stability of the satellite equilibrium under the perturbing action of disturbing torques provided dissipative torque is operating alongside with the restoring one. The proof is based on the Lyapunov direct method and the averaging technique. In the paper, original constructions of nonstationary Lyapunov functions are proposed. These constructions take into account the structure of perturbations acting on the considered system. With the aid of the proposed Lyapunov functions, sufficient conditions for the asymptotic stability of the satellite equilibrium position are derived. These conditions are formulated in terms of explicit inequalities on the control parameters. Thus, a constructive approach to the design of stabilizing controls is formulated.

AB - An Earth-pointing satellite with Lorentz attitude control system is under consideration. The problem of the satellite attitude stabilization in the orbital reference frame in the presence of disturbances and complicated by underactuation is studied. The averaging technique is developed and applied in the problem. A rigorous mathematical justification is proposed, which makes it possible to consider a satellite with unequal moments of inertia and to obtain specific estimates for the control parameters that provide a solution to the problem of satellite attitude stabilization with the use of the Lorentz control torque. The octupole approximation of the Earth's magnetic field is used; the periodic functions of time arise in geomagnetic field induction. With the aid of nonlinear approach to the problem it is proved that Lorentz attitude control system ensures asymptotic stability of the satellite equilibrium under the perturbing action of disturbing torques provided dissipative torque is operating alongside with the restoring one. The proof is based on the Lyapunov direct method and the averaging technique. In the paper, original constructions of nonstationary Lyapunov functions are proposed. These constructions take into account the structure of perturbations acting on the considered system. With the aid of the proposed Lyapunov functions, sufficient conditions for the asymptotic stability of the satellite equilibrium position are derived. These conditions are formulated in terms of explicit inequalities on the control parameters. Thus, a constructive approach to the design of stabilizing controls is formulated.

KW - Satellite

KW - Attitude stabilization

KW - Geomagnetic field

KW - Asymptotic stability

KW - Averaging technique

UR - https://www.sciencedirect.com/science/article/abs/pii/S1270963820306453

UR - http://www.scopus.com/inward/record.url?scp=85086357910&partnerID=8YFLogxK

U2 - 10.1016/j.ast.2020.105963

DO - 10.1016/j.ast.2020.105963

M3 - статья

VL - 104

JO - Aerospace Science and Technology

JF - Aerospace Science and Technology

SN - 1270-9638

M1 - 105963

ER -