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Abstract

The development of an LQR-based control algorithm for the Canadian advanced nanospace eXperiment (CanX)-4&5 formation flying nanosatellite mission is described. To facilitate an analytical stability proof of the algorithm, elements of the non-linear and continuous system are linearized and discretized. A suitable state for the system is selected and the algorithm is converted into a discrete linear time-varying system that is very nearly periodic. The stability of the system is then determined by means of discrete Floquet theory. This analysis is applied to the CanX-4&5 algorithm during its primary mission of testing along track orbit formations and projected circular orbit formations. The analysis is also applied to the algorithm while executing a quasi J₂-invariant formation. The results in all cases indicate stability. Finally, for the quasi J₂-invariant formation the control authority of the algorithm is reduced until the stability limit is approached and the minimum Δ V required to maintain the formation is found.

Keywords

stability analysis discrete Floquet theory linear time-varying system formation flying satellites Canadian advanced nanospace eXperiment-4&5

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The stability analysis of a discrete-time control algorithm for the Canadian advanced nanospace eXperiment-4&5 formation flying nanosatellites

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