Dynamics of flexible spacecraft: an analysis approaches towards mathematical model order reduction

Abstract

Increases in size and mechanical complexity of spacecraft result in increased complexity of the mathematical model which describes the spacecraft dynamics. This results in turn in increased computational effort, in increased difficulties in understanding the characteristics of the spacecraft dynamics, and in increased difficulties in the design as well as the implementation of algorithms suitable for the control of the motion of the spacecraft. Reduction of the mathematical order (i.e., of the mathematical complexity) of the open loop spacecraft dynamics model with minimal loss of model accuracy is therefore paramount importance. Literature contains descriptions of a large number of approach towards open loop model order reduction. These have been analyzed from the point of view of usefulness for application to dynamic models of flexible spacecraft. This report describes five basic approaches that have been identified.These are: (i) parameter optimization, (ii) aggregation, (iii) singular perturbation, (iv) modal dominance, and (v) component cost analysis. The latter two approaches appear to be mosc meaningful and convenient amongst the five. The problem of model order reduction is reviewed. Each of the five approaches mentioned is described and commented upon, related approaches are discussed, and applications are described.