Stability and Performance of Feedback Control Systems with Time Delays

摘要

This paper investigates the time delay effects on the stability and performance of active feedback control systems for engineering structures. A computer algorithm is developed for stability analysis of a SDOF system with unequal delay time pair in the velocity and displacement feedback loops. It is found that there may exist multiple stable regions in the plane of the time delay pair, which contain time delays greater than the maximum allowable values obtained by previous studies. The size, shape and location of these stable and unstable regions depend on the system parameters and the feedback control gains. For systems with multiple stable regions, the boundaries between the stable and unstable regions in the plane of the time delay pair are explicitly obtained. The delay time pairs that forms these boundaries are called the critical delay time pairs at which the steady-state response becomes unbounded. The conclusions are valid for both large and small delay times. For any system with multiple stable regions, preliminary guidelines obtained from an explicit formula are given to find the desirable delay time pair(s). When used, these desirable delay time pair(s) not only stabilize an unstable system with inherent time delays, but also significantly reduce the system response and control force. For any system with multiple stable regions, these desirable delay time pair(s) are above the maximum allowable delay times obtained by previous studies. Numerical results, for both steady-state and transient analysis, are given to investigate the performance of delayed feedback control systems subjected to both harmonic and real earthquake ground motion excitations.