STABILIZATION ELECTRODYNAMIC SPACE TETHERS

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Tethers Unlimited, Inc.Stabilization of Electrodynamic Tetherspoints was assumed. The feedback control wasperformed once every 10 seconds. Furthermore,to prevent the possible development of shortwavelengthoscillations that can be driven byrapid cycling of the tether current, we limitedthe rate of change of the tether current to 100mA/min. Note also that in these simulations,the tether was modeled as having no longitudinaldamping.Test Case: GLAST Deorbit For testing the controlalgorithm, we chose to utilize a test case involvingthe end-of-mission deorbit of theGLAST spacecraft. The GLAST spacecraft isplanned to be a 3360 kg (drymass) space telescopethat will be placed in a 550 km circular orbit at 28.5°inclination. Deorbit of this spacecraft should representa relatively challenging scenario, because atether system can generate larger currents in deorbitmode than in boost mode, leading to faster instabilitygrowth, and because the tethered system willpass though the range of altitudes where magneticfield and ionospheric density are greatest. Thetether system modeled was a Terminator Tether device with a 10 km long, 15 kg tether constructed ofaluminum wire, with a 15 kg endmass containingthe tether deployer and the control electronics.In PlaneLibration Angle (°)In PlaneLibration Angle (°)In PlaneLibration Angle (°)In PlaneLibration Angle (°)In-Plane Libration Angle40No Feedback200-20-400 2 4 640200-20-400 2 4 640200-20-400 2 4 640200-20Tether Configuration Feedback OnlyIn-Plane LibrationFeedback OnlyTether Configuration andIn-Plane Libration Feedback-400 2 4 6Time (days)OscillationEnergy (J)OscillationEnergy (J)OscillationEnergy (J)OscillationEnergy (J)100050000 2 4 6100050010005001000500Oscillation EnergyNo FeedbackTether Configuration Feedback Only00 2 4 6In-Plane LibrationFeedback Only00 2 4 6Tether Configuration andIn-Plane Libration Feedback00 2 4 6Time (days)Figure 3. Comparison of simulation results for deorbit of a 3360 kg GLAST spacecraft by a TerminatorTether device with a 15 kg, 10 km tether and a 15 kg endmass, with no feedback, tether configurationfeedback, in-plane libration feedback, and both tether configuration and in-plane libration feedback.2
Tethers Unlimited, Inc.Stabilization of Electrodynamic TethersResultsTether Configuration Feedback: Figure 3 comparesresults for the tether in-plane libration angle andthe total kinetic energy in the tether oscillationsfor simulations with and without the feedbackcontrol. The top two traces show that, with nofeedback control, the in-plane libration growsrapidly, exceeding the critical angle of 45°within three days. Simulations using only thetether configuration feedback demonstrated thatit performed very well for stabilizing the transverseand skip-rope modes, but it did not preventa slow growth of the in-plane libration.Conversely, use of the in-plane feedback only,shown in the third pair of traces, stabilizes thelibration mode, but excites the higher ordermodes. To address this, we combined the tetherconfiguration feedback with the in-plane librationfeedback by simply superimposing themodulation gains. The bottom pair of tracesshow that this combination is very successful at stabilizingboth the libration and the transverse oscillationinstabilities.Endmass Acceleration Feedback: Figure 4 shows acomparison of simulation results with no feedback,with only the endmass acceleration feedback, andwith both endmass acceleration and in-plane librationfeedback. The results indicate that when thismethod is used by itself, the tether system successfullydamps the transverse and skip-rope oscillations,but the in-plane librations still grow to instability.By superimposing this endmass accelerationbasedmodulation with current modulation basedupon the in-plane libration angle, however, we wereable to stabilize both the in-plane librations and thehigher-order modes for durations in excess of 30days.Figure 4. Simulation results for deorbit of the 3360 kg GLAST spacecraft using a Terminator Tether witha 15 kg, 10 km long tether and a 15 kg endmass, with and without feedback based on the endmass acceleration.1
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STABILIZATION ELECTRODYNAMIC SPACE TETHERS

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