Robust control of civil structures with parametric uncertainties through D‐K iteration

Summary Active control is an alternative method to suppress the civil structural vibration, which is more effective than the passive control or strengthening the structural components. The performance of active control is dependent on the control strategy and the accuracy of the structural model. However, there always exist some uncertainties in the model, such as mass, damping and stiffness uncertainties. This paper presents a robust H∞ controller design for civil structures with consideration of the parametric uncertainties. The formulation to extract the parametric uncertainties from the structural model matrices is proposed through the linear fractional transformations approach. The robust H∞ controller design for the civil structures with the parametric uncertainties is achieved through the D-K iteration method. The linear matrix inequality is then used in the H∞ optimization procedure of the D-K iteration. The robustness of the controller is first numerically validated by a four-story building example and then experimentally corroborated by a shaking table test of a two-story frame with one active mass damper. The results show that the robust H∞ controller can consider the parametric uncertainties in the civil structural model and achieve the robust performance. Copyright © 2015 John Wiley & Sons, Ltd.