Stochastic response analysis, order reduction, and output feedback controllers for flexible spacecraft

Real disturbances and real sensors have finite bandwidths. The first objective of this paper is to incorporate this finiteness in the "open-loop modal cost analysis" as applied to a flexible spacecraft. Analysis based on residue calculus shows that among other factors, significance of a mode depends on the power spectral density of disturbances and the response spectral density of sensors at the modal frequency. The second objective of this article is to compare performances of an optimal and a suboptimal output feedback controller, the latter based on "minimum error excitation" of Kosut. Both the performances are found to be nearly the same, leading us to favor the latter technique because it entails only linear computations. Our final objective is to detect an instability due to truncated modes by representing them as a multiplicative and an additive perturbation in a nominal transfer function. In an example problem we find that this procedure leads to a narrow range of permissible controller gains, and that it labels a wrong mode as a cause of instability. A free beam is used to illustrate the analysis in this work.

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