Effect of Time Delay on the Stability of Flexible Structures with Rate Feedback Control

Abstract

Time delays can be introduced inadvertently into flexible spacecraft control loops by (for example) computer processing delays. The effects of such time delays on the performance, or even the stability, of such closed-loop control systems are especially important for lightly damped vibratory systems. This paper focuses on the time-delayed rate feedback control of a lightly damped single-degree-of-freedom harmonic oscillator. Even though this situation is relatively simple, it possesses many interesting characteristics and must be treated carefully. Root loci are analyzed to provide a basis for stability conditions, and stability boundaries are plotted, correcting the results derived many years ago by Bellman and Cooke. It is briefly explained how to extend these results for one structural mode to an arbitrary number of structural modes, that is, to a complete spacecraft.