Design and Stability Analysis of Delayed Resonator With Acceleration Feedback

This paper deals with the problem of active vibration suppression using the concept of delayed resonator with acceleration feedback. A complete dynamics analysis of the resonator and its coupling with a single degree of freedom mechanical system are performed. It is shown that due to presence of a delay in the derivative feedback, the dynamics of the resonator itself, as well as the dynamics of its coupling with the system are of neutral character. Subsequently, the spectral approach is used to obtain the stability boundaries in the space of the resonator parameters. Both, analytical and numerical methods are employed in the analysis. As the contributions, we display a methodology to determine the resonator parameters in order to guarantee desirable functioning of the resonator and to provide safe stability margins. An example is included to demonstrate these analytical results.