Mathematical Models of Flexible Spacecraft Dynamics : A Survey of Order Reduction Approaches

Abstract

Increases in size and mechanical complexity of spacecraft result in increased complexity of the mathematical model of the spacecraft dynamics. In turn, this results in increased computational effort, increased difficulties in understanding the characteristics of the spacecraft dynamics, and increased difficulties in designing as well as implementing suitable algorithms for the control of the spacecraft dynamic motions. Reduction of the order (i.e. the complexity) of the mathematical open loop model with minimal loss of model accuracy, is therefore of prime importance. Literature contains descriptions of a large number of approaches towards open loop model order reduction. These have been surveyed from the point of view of usefulness for application to flexible spacecraft dynamics models. Six basic approaches have been identified, involving: (i) parameter optimization, (ii) aggregation, (iii) singular perturbation, (iv) modal dominance, (v) component cost analysis, and (vi) internal balancing, respectively. The latter three approaches appear to be most meaningful, and convenient in applications. The problem of model order reduction is reviewed, and each of the six approaches is discussed. The latter three approaches are applied to the case of a long, flexible beam in space, controlled with two line torquers.