Optimal truncated model for vibration control design within a specified bandwidth

The work in this paper is directed at developing correction terms for a truncated structural dynamic model, which includes the effect on the structural response of both low and high frequency unmodelled vibration modes. The proposed model correction approach considers the corrected truncated model that only takes into account resonant modes within the bandwidth of interest and the optimised correction terms. The proposed approach is in contrast to the standard model correction approach that normally utilises a feedthrough correction term, taking into account only the unmodelled high frequency modes, while including all low frequency resonant modes into the truncated model. Thus, when one only interested in controlling vibration associated with a specified bandwidth of interest, the order of the corrected truncated model can be kept sufficiently low since the model does not have to include low and high frequency modes, leading to less complicated control design problems. Such active control within the specified bandwidth can be crucial for control tasks in the vibration minimisation at localised structural regions or in the noise reduction due to some coupled structural-acoustic modes. The procedures for calculating the optimal correction terms which include the lower and higher order mode contributions are outlined for both analytical and experimental models, allowing the procedures to be used for a wide range of theoretical and practical applications.