TECHNICAL MECHANICS
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UDC 531.3

Technical mechanics, 2019, 4, 59 - 73

PROGRAM CONTROL OF THE RETRIEVAL OF A SPACE TETHERED SYSTEM WITH THE RECOVERY OF ITS ORIGINAL VERTICAL ORIENTATION

DOI: https://doi.org/10.15407/itm2019.04.059

Zakrzhevskii A. E.

Zakrzhevskii A. E.
Space Research Institute of the National Academy of Sciences of Ukraine and the State Space Agency of Ukraine

      This study is concerned with a space tethered system of two bodies connected with an elastic massless tether. The objective of this study is to extend a new feed-forward control method of the deployment of space tethered systems in the orbit plane with their alignment to the local vertical at the deployment end to the tether retrieval with specific terminal conditions. This allows one to construct the feed-forward control of the tether length or tension in order to provide the required change of the angular momentum of the tethered system under the influence of the gravitational moment. The novelty also lies in a new approach to creation of the control of underactuated mechanical systems, in which the number of control channels is less than the number of degrees of freedom. Here, it is proposed to impose a pitch constraint on motion of the system, which will reduce the number of degrees of freedom, thus allowing one to implement a specified motion regime by controlling the system only in the remaining degrees of freedom. The character of the constraint imposed on the admissible time variation of the pitch angle is governed by the requirements imposed on the motion regime to be executed. This paper considers the retrieval of a tethered system initially aligned to the local vertical to a specified length. The tethered system must be aligned again to the local vertical, and its longitudinal oscillations must be absent. Taking into account all the requirements for the retrieval regime, one can construct an admissible law of time variation of the pitch angle described by an eighth-order power series. For a tethered system with specified parameter values, a numerical investigation was conducted for studying the effect of the retrieval duration and the law of time variation of the pitch angle on the length of the retrieved tethered system and its behavior during the retrieval mode. To demonstrate the practical simplicity of the proposed approach, a numerical example is given where tether retrieval is simulated numerically by integrating a Cauchy problem for Hill–Clohessy–Wiltshire equations. The analysis of results is illustrated by graphs. At the beginning of the paper, the state of the art in the problem under consideration is overviewed.
     

tethered system, retrieval, control, length variation, vertical position, deformation, space tethered system

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DOI: https://doi.org/10.15407/itm2019.04.059

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