Tethered Satellite Flexible Tether Parameter Sensitivity

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Tethered Satellite Flexible Tether Parameter
Sensitivity

• James B. Dabney
• University of Houston Clear Lake
• April 27, 2001

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Overview

• TSS overview
• TSS Applications
• Dynamics formulation
• Example trajectories
• Sensitivity formulation
• Sensitivity results
• Conclusions

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TSS Overview
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Applications

• Electrodynamic power generation
• Upper atmosphere research
• Artificial gravity
• Deorbit energy exchange
• Space station resupply

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Dynamics Overview

• Gravity gradient
• Force magnitude for 1000 lb satellite
• Short tether (1000s of feet) ounces
• Long tether (100,000 ft) few pounds
• Libration
• Length oscillation
• Requires continuous tension

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Coordinate System
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Assumptions

• Platform mass gtgt satellite mass
• Platform in circular Keplerian orbit
• Tether is long damped spring
• Spring constant k
• Damping coefficient c
• In-plane motion only

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Equations of Motion

• Kinetic energy
• Potential energy
• Damping
• Lagranges equation

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Equations of Motion, cont.

• In-plane libration dynamics
• Length dynamics

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Parameters
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Trajectory Near Equilibrium
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Large Amplitude Trajectory
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Sensitivity Costate Equations

• Sensitivity
• Sensitivity dynamics (costate equation) for
  time-invariant parameters
• Jacobian along nominal trajectory
• Partial derivative of nominal function with
  respect to k-th parameter

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Tether Costate Equations
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Simulink Model
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Sensitivity to Spring Constant
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Sensitivity to Damping Coefficient
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Conclusions

• Libration not sensitive to flexibility or damping
• Length oscillations
• Very sensitive to flexibility variations
• Slightly sensitive to damping variations
• Length control must be designed to be robust to
  flexibility uncertainty