Frequency-dependent optimal control in independent modal space for seismic response control of structures

Abstract

In this study, a frequency-dependent algorithm is proposed in independent modal space as an improvement to the linear quadratic Gaussian (LQG) control algorithm. The passive control parameters such as mass, stiffness and damping of a dynamic system are sensitive to different frequency ratios when subjected to external excitation. Depending upon the sensitivity of these parameters, the algorithm is developed in such a way that a response reduction similar to that of an LQG algorithm can be achieved with a significantly smaller control force. An effective gain is obtained by optimizing the H2 norm of the transfer function. It is observed from the results that the algorithm works well for high frequency ratio and near resonance regimes. Thus, a combination of the LQG and the proposed algorithms is considered as a modified LQG control algorithm, where the effectiveness of both algorithms is utilized. The efficiency of the modified LQG control algorithm is demonstrated by considering a base-isolated structure when subjected to earthquake base excitations. By comparing with the results it is observed that the modified LQG control algorithm is more efficient in terms of response reduction with a much lower control force as compared to the LQG control algorithm. It is envisioned that the modified LQG control algorithm will be highly useful for response control of base-isolated structures.