Stability of Active‐Tendon Structural Control with Time Delay

In this paper, both analytical and numerical studies of the stability of single‐degree‐of‐freedom systems with active tendon control are presented. In the studies, only an autonomous systems is considered. Prior experimental and analytical work in the area of structural control has shown that time delays are a primary cause of ineffectiveness and instability of the controlled system. Therefore, the very important effect of time delays (including on‐line computation time delay and actuator build‐up time delay) on the control force is taken into account. This is done by using a differential difference equation, or the so‐called retarded functional differential equation. Based on the concept of Liapunov stability and the method of D‐subdivision, the stable and unstable regions are determined analytically. Using numerical simulations, the accuracy of the analytical solutions are verified.