Relative Stability Analysis for Vibration Absorbers With Multiple Delayed Feedback

Abstract

A novel tuning methodology for active vibration absorption is discussed. The underlying proposition is to use partial state feedback with multiple unrelated time delays. The objective of this tuning is to combat excitation forces with multiple frequencies, which are time varying. It is shown that the required control parameters can be evaluated on-line rather rapidly. The system stability aspect however, needs to be resolved a priori to the control actuation. This is the challenge facing this procedure due to the presence of multiple (and mostly “unrelated”) time delays. A new stability assessment methodology, the Directional Stability Chart method, is presented. The outcome of this procedure is used to determine the local stability levels and preferred operating zones in the domain of the multiple excitation frequencies. The method is also expanded to assess the relative stability level of the tuned absorber. Example case is taken from a PZT actuated active absorber. Desirability of the operating points are compared based on the relative stability levels, and the observations are verified by simulations.