Abstract
The time optimal deployment of a satellite from a space ship is studied. In order to take the mass and lateral oscillations of the tether into account, a discretized model of the tether is build. Applying Pontryagin’s Maximum Principle a time-optimal deployment from a trivial downhanging configuration close to the space ship to another one farther away is computed. It is found, that the obtained solution displays a difficult switching pattern and during the variation of the initial length different kinds of bifurcations occur, leading to discontinuous variations of the optimal solution candidates.
Highlights
The deployment and retrieval of tethered satellites is an important and difficult operation in space missions.This article is dedicated to Prof
The control input should optimally be applied by tension control, that is by a tension force at the outlet of the tether
Several important goals for the control design have been listed in the review [9], one of which is the reduction of lateral oscillations during the process
Summary
The deployment and retrieval of tethered satellites is an important and difficult operation in space missions. For safety reasons a PD controller, called Kissel’s law, is used commonly during space flights This controller leads to an exponential decay of the lateral oscillations, but takes very long to complete the mission. In order to find out, how much time could be saved theoretically, a time optimal solution was investigated in [8] It turned out, that this solution was by an order of magnitude faster than the conventional strategy, but it used a bang–bang control, which could cause unwanted oscillations in the tether. For a reasonable set of parameters a valid optimal control solution could be obtained This investigation is certainly not intended to provide a control strategy, which should be used in real world applications, but to learn about the typical shape of optimally controlled deployment trajectories. Further the solution family, which is calculated by a continuation algorithm, displays a non-monotonic behaviour, generating multiple candidates for the optimal control strategy
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