Time delayH_∞control of structures under earthquake loading

Abstract

In this paper, an H ∞ control algorithm is developed to reduce the earthquake response of structures with consideration of control force execution time delay. To achieve optimal control performance and assure control system stability, the strategy to select two control parameters γ and α is extensively investigated. It was found that the decrease of γ or increase of α results in significant reduction of structural responses. To obtain the same control results, a larger α has to be selected for stiff structures than for flexible structures. In addition, in active control of a real structure, control force execution time delay cannot be avoided. Relatively small delay times not only can render the control ineffective, but also may cause system instability. In this paper, explicit formulas for the maximum allowable delay time and critical control parameters are derived for the design of a stable H ∞ control system. Some solutions are also proposed to lengthen the maximum allowable delay time.

H ∞ drift control of time-delayed seismic structures

“…It shows that the LQR control is a special case of the proposed H ∞ control (Lin et al, 2006(Lin et al, , 2007.…”

“…According to Lin et al (2007), for a SDOF controlled structure, the upper bound of α corresponding to infi nite delay time, called α td , satisfi es the following equation …”

“…In theory, for a stable controlled system, a lower bound of γ, γ stb , exists. For a lightly-damped (or say control needed) structure, γ stb takes the form (Lin et al, 2007) γ ξ ξ α stb = + − …”

“…When the control parameter γ is specifi ed, it implies that the sum of the fi rst interstory drift response and actuator stroke should be limited to a level lower than γ. It has been proved (Lin et al, 2006(Lin et al, , 2007 that under this constraint, the balance between the reduction of interstory drifts and the limitation of the actuator stroke x n (t)…”

“…In recent years, the authors have extensively investigated the time delay effect on the control performance of H ∞ control system for multiple DOF structures (Lin et al, 2006(Lin et al, , 2007. It was found that all controlled modal damping ratios decrease as α decreases or t d or γ increases.…”