Mathematical Methods for Curves and Surfaces

A key factor in developing and assessing any vibration attenuation technique for elastic systems is the measure that quantifies the occurring vibrations. In this paper, we propose a general and instantaneous vibration measure which allows for more subtle methods of localized vibration attenuation techniques. This measure is based on extracting the vibrational part from the conventional tracking error signal using wavelet technique. The paper also provides a method for constructing a wavelet function based on the system impulse response. This wavelet outperforms the existing ones in representing the system behavior while guaranteeing admissibility and providing sufficient smoothness and rate of decay in both time and frequency domains.

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