Verification procedure for on-orbit controllers for the MIT Middeck Active Control Experiment

A perturbation expansion on the structural generalized eigenvalue problem is performed which provides a means by which a finite element model and identified frequency and mode shape information can be converted to mass and stiffness matrix perturbations required to match the identified system. For a modified structure, similar to the original, the mass and stiffness matrix perturbations are assumed constant, and are used in a second perturbation expansion to generate predictions of frequency and mode shape perturbations for the modified structure. The stochastic nature of the structure and identification procedure enable first and second order statistics of the frequency and mode shape perturbations to be generated. These are used in a mixed-μ analysis which provides a measure of the stability of the system in feedback with controllers. The mixed-μ analysis is used to determined critical uncertain parameters which can be emphasized in robust control design