Long-Term Libration Dynamics and Stability Analysis of Electrodynamic Tethers in Spacecraft Deorbit

Zhong, Rui; Zhu, Zheng H.

doi:10.1061/(asce)as.1943-5525.0000310

Cited by 24 publications

(11 citation statements)

References 20 publications

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“…The target altitude for the deorbit operation is 250 km. Based on the findings from previous studies [27], three representative orbits for EDT systems are considered: namely, the equatorial, 57 deg inclined, and polar orbits, respectively. An electron emitter is assumed at each end to improve the deorbit efficiency of the EDT system, especially in highly inclined orbits.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…In LEO, the last perturbation is generally orders of magnitude smaller than the others and can be safely ignored in the current study [31]. It is worth pointing out here that the geodetic altitude, instead of geocentric altitude, should be used to calculate the atmospheric and plasma densities (in the following subsection) in order to account for the Earth's oblateness [27].…”

Section: B Environmental Perturbation Forcesmentioning

confidence: 99%

“…Kawamoto et al developed a simple on/off current control strategy based on the feedback of tether libration angles only [22], where the current was switched off when the libration angles exceeded preset thresholds, and vice versa. Zhong and Zhu simplified the current on/off control strategy by the feedback of the out-of-plane angle only [27], where the in-plane libration could be bounded effectively through the nonlinear modal coupling between the in-plane and out-of-plane libration modes. The simplified on/off control was later optimized by the same authors with a piecewise optimal control law to regulate the current on/off to enable a fast and stable spacecraft deorbit for practical implementation [28].…”

Section: Introductionmentioning

confidence: 99%

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Libration Control of Bare Electrodynamic Tethers Considering Elastic–Thermal–Electrical Coupling

Zhu

Cain

et al. 2016

Journal of Guidance, Control, and Dynamics

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The paper investigates the elastic, thermal, and electrical coupling effects on the dynamics and libration stability of flexible bare electrodynamic tethers in the end-of-mission satellite deorbit. A high-fidelity model is developed by considering transverse and longitudinal dynamics and libration dynamics of the tether and environmental effects with the latest models for atmospheric and plasma density, as well as Earth gravity and magnetic fields. The long-term orbital and libration dynamics of the tether are analyzed by a nodal position finite element method and symplectic time integration. Orbital motion limited theory is used to model the electron collection by bare electrodynamic tethers, whereas a Fowler-Nordheim equation is used for a Spindt array cathode. The thermal effect and its coupling with the dynamics of electrodynamic tethers are investigated parametrically. It is found that the thermal effect significantly affects the stability of electrodynamic tethers, which must be considered in the stability control. Two practical and effective electrical current on/off control strategies are developed based on the libration energy and libration angles. Although the libration energy control is found to be more stable and efficient than the libration angle control, the latter is more appealing for practical applications due to its simplicity and low computational effort. NomenclatureA t , A s = cross section or stress area of tether and projected drag area of satellite, m 2 B g = vector of Earth magnetic field strength in the global frame, T c m = specific heat of tether material, J · kg · K −1 d = tether diameter, m e E = eccentricity of electrodynamic tether orbital plane H 0 = Hamiltonian of tethered system in equilibrium configuration, J I t = electrical current at electron emitter device, A L, L = total and characteristic length of tether, m L e0 L e = unstretched length (instant length) of tether element, m M yaw , M in , M out = components of electrodynamic torque in system orbital frame, N · m n orb = orbital mean motion, rad · s −1 Q = thermal flux, W · m 2 R e = electrical resistance in tether, Ω R, S, W = unit vector of orbital frame of tethered system T, T 0 = instant and initial temperature, K t = time t, n, b = unit vectors of the local frame of tether element V cc = potential bias at the cathodic end C with respect to the ambient plasma, V X, Y, Z = components of position vector in global geocentric inertial frame, m Z T = impedance of emitter device, Ω α, _ α = pitch angle and pitch angular velocity of virtual tether, rad α p , _ α p = periodic solution of pitch angle, rad; and angular velocity of virtual tether, rad · s −1 α s ∕ε = ratio of absorptivity to emissivity of the tether β, _ β = roll angle, rad; and angular velocity of virtual tether, rad · s −1 θ, θ 0 = north latitude and colatitude, rad λ = east longitude, rad μ g = gravitational constant of Earth, m 3 s −2 ρ a ,ρ t = atmospheric density and material density of tether, kg · m −3 σ = electrical conductivity of tether material, Ω −1...

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: B Environmental Perturbation Forcesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Libration Control of Bare Electrodynamic Tethers Considering Elastic–Thermal–Electrical Coupling

Zhu

Cain

et al. 2016

Journal of Guidance, Control, and Dynamics

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“…A field emitter array is used as a cathode to expel electrons into the ambient plasma to complete the electric circuit [8,22]. The emitter is installed on the main satellite and sub-satellite in order to improve the efficiency of the EDT system in highly inclined orbits, where the electrical polarity reverses in one orbit [19,22]. The tether is spatially discretized by the nodal position finite element method, where the nodal positions, as opposed to the displacements in the conventional finite element method, are used as state variables.…”

Section: Multiphysics Formulation Of Flexible Electrodynamic Tether Smentioning

confidence: 99%

“…For instance, the optimization methods have generally been applied to solve the non-dimensional OML equations of the rigid tether model [13]. Subsequently, the flexible tether model of the EDT system was developed; however, the empirical formulas [19] and the OML equations based on the rigid tether model are still used [7,9,18]. The dynamic equations of the flexible tether model and OML equations are roughly combined together.…”

Section: Introductionmentioning

confidence: 99%

Parameter influence on electron collection efficiency of a bare electrodynamic tether

Zhu

2017

Sci. China Inf. Sci.

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This study develops a coupled multiphysics finite element method for the dynamic analysis of a bare flexible electrodynamic tether. Contrary to the existing methods, the new method discretizes and solves the orbital motion limited equation and the dynamic equation of an elastic flexible tether simultaneously. First, the new method is verified via comparison with the existing methods in a straight tether situation. Second, the number of tether elements, tether bending deformation, and two design parameters at the cathodic end affecting the electrical current are investigated. It is determined that the tether bending deformation and the two parameters i.e., the impedance Z T and Φ PW have a significant impact on the electron collection efficiency of an electrodynamic tether system. The results indicate that the proposed method should be applied in the refined mission analysis.

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Study of Dynamic Stability and Control of Electrodynamic Tether for a Larger Spacecraft Reboost

2021

Lecture Notes in Electrical Engineering

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Long-Term Libration Dynamics and Stability Analysis of Electrodynamic Tethers in Spacecraft Deorbit

Cited by 24 publications

References 20 publications

Libration Control of Bare Electrodynamic Tethers Considering Elastic–Thermal–Electrical Coupling

Libration Control of Bare Electrodynamic Tethers Considering Elastic–Thermal–Electrical Coupling

Parameter influence on electron collection efficiency of a bare electrodynamic tether

Study of Dynamic Stability and Control of Electrodynamic Tether for a Larger Spacecraft Reboost

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