Analysis of a Linear System for Variable-thrust Control in the Terminal Phase of Rendezvous

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National Aeronautics and Space Administration, 1961 - Linear systems - 43 pages
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A linear system for applying thrust to a ferry vehicle in the 3 terminal phase of rendezvous with a satellite is analyzed. This system requires that the ferry thrust vector per unit mass be variable and equal to a suitable linear combination of the measured position and velocity vectors of the ferry relative to the satellite. The variations of the ferry position, speed, acceleration, and mass ratio are examined for several combinations of the initial conditions and two basic control parameters analogous to the undamped natural frequency and the fraction of critical damping. Upon making a desirable selection of one control parameter and requiring minimum fuel expenditure for given terminal-phase initial conditions, a simplified analysis in one dimension practically fixes the choice of the remaining control parameter. The system can be implemented by an automatic controller or by a pilot.

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