Dynamics of flexible spacecraft: the internal balancing approach towards mathematical model order reduction

Abstract

Mathematical models of the dynamics of spacecraft are needed to carry out numerical simulations, to gain insight into the characteristics of the spacecraft dynamics, and to synthesize control algorithms suitable for online system Identification, estimation, and control. Increases in size and mechanical complexity of spacecraft result in increased complexity of the mathematical models. This results in turn in increased numerical simulation effort, increased difficulties in understanding the characteristics of the dynamics, and increased difficulties in synthesis and implementation of control algorithms. Reduction of the mathematical order of the open loop spacecraft dynamics model - with minimal loss of model accuracy - is therefore of paramount importance. A rather recent approach towards open loop model order reduction is that of Internal Balancing. The given system state is transformed such, that the elements of the new system state display ranking with respect to degree of controllability and degree of observability. The reduced order model is obtained from the state elements with dominant ranking with respect to joint controllability and observability properties. The problem of model order reduction is reviewed. The Internal Balancing approach is developed and commented upon, the algorithms are specialized for the case of spacecraft dynamics in modal form with small modal damping ratios, and numerical applications are described.