Investigation of Instabilities in Detumbling Algorithms

Abstract: Detumbling refers to the act of dampening the angular velocity of the satellite. This operation is of paramount importance since it is virtually impossible to nominally perform any other operation without some degree of attitude control. Common methods used to detumble satellites usually involve magnetic actuation, paired with different types of sensors which are used to provide angular velocity feedback. This paper presents the adverse effects of time-discretization on the stability of two detumbling algorithms. An extensive literature review revealed that both algorithms achieve absolute stability for systems involving continuous feedback and output. However, the physical components involved impose limitations on the maximum frequency of the algorithm, thereby making any such system inconceivable. This asserts the need to perform a discrete-time stability analysis, as it is better suited to reflect on the actual implementation and dynamics of these algorithms. The paper starts with the current theory and views on the stability of these algorithms. The next sections describe the continuous and discrete-time stability analysis performed by the team and the conclusions derived from it. Theoretical investigation led to the discovery of multiple conditions on angular velocity and operating frequencies of the hardware, for which the algorithms were unstable. These results were then verified through various simulations on MATLAB and Python3.6.7. The paper concludes with a discussion on the various instabilities posed by time-discretization and the conditions under which the detumbling algorithm would be infeasible.