STABILITY AND PERFORMANCE OF FEEDBACK-CONTROL SYSTEMS WITH TIME DELAYS

This paper investigates the time delay effects on the stability and pe rformance of active feedback control systems for engineering structure s. A computer algorithm is developed for stability analysis of a SDOF system with unequal delay time pair in the velocity and displacement f eedback loops. It is found that there may exist multiple stable region s in the plane of the time delay pair, which contain time delays great er 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 w ith multiple stable regions, the boundaries between the stable and uns table regions in the plane of the time delay pair are explicitly obtai ned. The delay time pairs that forms these boundaries are called the c ritical delay time pairs at which the steady-state response becomes un bounded. The conclusions are valid for both large and small delay time s. For any system with multiple stable regions, preliminary guidelines obtained from an explicit formula are given to find the desirable del ay time pair(s). When used, these desirable delay time pair(s) not onl y stabilize an unstable system with inherent time delays, but also sig nificantly reduce the system response and control force. For any syste m 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 syste ms subjected to both harmonic and real earthquake ground motion excita tions. (C) 1997 Published by Elsevier Science Ltd.