Development of Frequency-dependent Optimal Control in Independent Modal Space

Abstract

In this study, a frequency dependent algorithm is proposed in the independent modal space as an improvement to the linear quadratic regulator control algorithm. The passive control parameters such as mass, stiffness and damping of a dynamic system are sensitive to different frequency ratio when subjected to external excitation. Depending upon the sensitivity of these parameters, the algorithm is developed in such a way that the similar response reduction as that of a linear quadratic regulator can be achieved with a significantly smaller gain. The optimal gain is obtained by optimizing the H 2 norm of the transfer function. It is observed from the results that the algorithm works well for high frequency ratio and near resonance regimes. The efficiency of the proposed algorithm is demonstrated by considering a base isolated structure when subjected to a narrow band base excitation. By comparing with the results from linear quadratic regulator control, it is observed that the proposed algorithm is more efficient in terms of displacement response and optimal gain. It is envisioned that the proposed algorithm will be highly useful for response control of base isolated structures.