Robust Stabilization under Mode Truncation and Parameter Variations

This paper addresses the issue of stability robustness under mode truncation and parameter variations with emphasis on Large Space Structure (LSS) models. The recent development of elemental (structured) upper bounds on the perturbation of an asymptotically stable linear system to maintain stability is extended to the problem of LSS control in which both mode truncation (model reduction) as well as parameter variations (uncertainty in modal frequencies, dampings, and mode shape slopes at actuator/sensor locations) are considered as perturbations acting on the control design model. A simple algorithm is proposed to design a robust controller, with vibration suppression as the control objective, for robust stability and acceptable nominal performance under mode truncation and parameter errors. The algorithm is such that it clearly delineates the trade off between the control effort needed for acceptable regulation and the number of modes one needs to control for robust stability.