Optimal Attitude Control of an Accompanying Satellite Orbiting around the Space Station

Paper number

IAC-07-C1.I.03

Author

Prof. Pavel M. Trivailo, RMIT University, Australia, Australia

Coauthor

Dr. Fang Wang, China Academy of Space Technology (CAST), China

Coauthor

Dr. Honghua Zhang, Beijing Institute of Control Engineering, China

Year

2007

Abstract

This paper deals with the optimal control of an accompanying satellite orbiting around the space station in the presence of sinusoidal disturbances. The concept of accompanying satellites (AS) around the space station (SS) is introduced. Both the AS and the SS are modeled as rigid bodies with the reference coordinate frames described for the AS pointing to the SS. There are many functions for the AS of the SS such as navigation, relaying communication data and inspecting the SS. Since all of these functions require attitude control of the AS, it is necessary to study the optimal control for the AS rotating around the SS.

	Untill now there have been many studies about the optimal control of satellites. However, all of them did not consider the case when the satellite is underactuated, i.e., actuators in one or two dimensions are failed, though the fact is that the AS has a probability of disabled (or damaged or malfunctioned) actuators during its running period. Hence it is also necessary to study the problem when AS is underactuated, which is the novelty of the paper. Without loss of generality, the underactuated axis is assumed to be the third axis of the AS.

	The purpose of this paper can be stated as designing an optimal control law so that the underactuated AS can achieve suitable attitude in accordance with the expected thrust direction before orbit maneuvering, and then attain reorientation towards the desired direction (e.g., the SS) after the orbit maneuvering with the least thrust. Based on this purpose, the paper first defines the reference coordinate, frames for the AS pointing to the SS according to different missions. Then by using unit quaternion, the full set of nonlinear equations of motion is derived. These equations are solved numerically using direct transcription method to obtain optimal solution for the underactuated satellite. The direct method seeks to transform the continuous optimal control problem into a discrete mathematical programming problem, which in turn is solved using a non-linear programming algorithm. By discretizing the state and control variables at a series of nodes, the integration of the dynamical equations of motion is not required. The state equations are enforced as constraints by using interpolating polynomials and an implicit integration scheme is used in each discrete segment, which ensures fast computational times. The Chebyshev-pseudospectral method, due to its ease of implementation, high accuracy and fast computation times, was chosen as the direct optimization method to be employed to solve the problem.
The analytical and simulation results show that the proposed control law is effective in the case of failed actuators. 

Further research in this area is discussed. It involves cases when the AS has flexible attachments; the AS is under disturbances; and the inertia matrix is unknown or poorly known, of which the controller for the underactuated AS will become more complicated.

Abstract document

IAC-07-C1.I.03.pdf

Manuscript document

IAC-07-C1.I.03.pdf (🔒 authorized access only).

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