Stochastic linearization for control of hysteretic structures using H∞ algorithm

This paper presents a robust static output feedback H-infinity algorithm for control of hysteretic civil engineering structures subjected to earthquake ground motions. Hysteretic structures present a problem for control design and algorithm development due to changes in the structural parameters during large seismic events. The conventional approach that has been employed in the past is to linearize the structure at the initial equilibrium state, thus ignoring the hysteretic characteristics of the structure when computing the gain matrices. This paper extends the H-infinity algorithm, which has been developed previously for linear structures, to nonlinear structures using a newly developed procedure that uses stochastic equivalent linearization. In this procedure, the Hysteretic parameters are linearized assuming the ground motion to be a filtered white noise using the Kanai-Tajimi power spectral density. The effectiveness of this procedure over the conventional approach is demonstrated by simulation results of a hysteretic single-degree-of-freedom structure subjected to earthquake ground motion. This study also shows the effectiveness of using static output feedback for controlling hysteretic structures. For this case, the control effectiveness is not lost when the measurement of the hysteretic variable is ignored.