The Method of Exponential Differential Inequality in the Estimation of Solutions of Nonlinear Systems in the Vicinity of the Zero of the State Space

I, Melnikov Gennady; Melnikov, Vitaly G.; Dudarenko, Natalia; Talapov, V.V.

doi:10.1007/978-3-030-62062-2_20

Cited by 2 publications

(1 citation statement)

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“…The permanent stability of the AES direct equilibrium position under the perturbing action of the gravitational torque was proved with the use of numerical analysis of the roots of the characteristic polynomial. The analytical proof of the asymptotic stability of the AES direct equilibrium position was presented in [9] where nonlinear analysis of the differential equations of motion was performed on the basis of the Lyapunov direct method [10]- [13] and on the special approach to constructing Lyapunov functions [14], [15].…”

Section: Introductionmentioning

confidence: 99%

Monoaxial Electrodynamic Stabilization of an Artificial Earth Satellite in the Orbital Coordinate System via Control With Distributed Delay

Aleksandrov

Тихонов

2021

IEEE Access

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An artificial Earth satellite (AES) with three different principal central moments of inertia is under consideration. The AES moves along a Keplerian circular equatorial near-Earth orbit. The AES is equipped with electrodynamic attitude control system that simultaneously generates Lorentz and magnetic control torques. The possibility of using an electrodynamic attitude control system for monoaxial attitude stabilization of AES in the orbital coordinate system is analyzed. The development of the concept of electrodynamic attitude control, including the use of a restoring torque with a distributed delay (integral term), is proposed. The conditions are found under which the electromagnetic attitude control system with distributed delay solves the problem of AES monoaxial stabilization in the presence of the disturbing gravitational torque. In a nonlinear formulation, sufficient conditions for the asymptotic stability of the AES equilibrium position are obtained. A theorem on the asymptotic stability of the AES programmed attitude motion is proved. The effectiveness of the constructed attitude control with a distributed delay is confirmed by numerical modeling.

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Section: Introductionmentioning

confidence: 99%