Compensation of Time Delay Effect in Semi-active Controlled Suspension Bridges

In order to increase the critical wind speed to avoid galloping of flexible suspension bridges, it is necessary to introduce additional damping. One of the feasible methods of introducing additional damping to suspension bridges is using semi-active tuned mass damper control mechanisms. The time delay in generating the active control action due to the actuator's dynamics is, however, a major practical problem which may destabilize the semi-active controlled structure. In this paper, the effect of the time delay on the stability of a semi-active controlled suspension bridge is investigated. It is shown that when the time delay for the semi-active controlled suspension bridge is considered, the critical wind speed will be less than that determined when the time delay is neglected. The reduction in the critical wind speed due to time delay might cause the suspension bridge to gallop at normal wind speeds. The paper shows how to compensate for the time delay effect in order to ensure the galloping suppression. The time delay compensation is treated by two methods: the first method expresses the delayed control action using a truncated Taylor's series in terms of the current control action and its derivatives; the second method expresses the delayed control action as feedback of the delayed state variables. Both methods are applied on a linear model derived from the actual nonlinear model. The controlled response considering the delay is obtained by applying the designed active control on the actual nonlinear model. The results of both methods of time delay compensation are discussed and compared using a numerical example.