The Energy Compensation of the HRG Based on the Double-Frequency Parametric Excitation of the Discrete Electrode

In this study, for energy compensation in the whole-angle control of Hemispherical Resonator Gyro (HRG), the dynamical equation of the resonator, which is excited by parametric excitation of the discrete electrode, is established, the stability conditions are analyzed, and the method of the double-frequency parametric excitation by the discrete electrode is derived. To obtain the optimal parametric excitation of the resonator, the total energy stability of the resonator is simulated for the evolution of the resonator vibration with different excitation parameters and the free precession of the standing wave by the parametric excitation. In addition, the whole-angle control of the HRG is designed, and the energy compensation of parametric excitation is proven by the experiments. The results of the experiments show that the energy compensation of the HRG in the whole-angle control can be realized using discrete electrodes with double-frequency parametric excitation, which significantly improves the dynamic performance of the whole-angle control compared to the force-to-rebalance.

The Influence Region Analysis for the Delayed Resonator Vibration Absorber

This paper presents an influence region analysis for an actively tuned vibration absorber, the Delayed Resonator (DR). DR is shown to respond to tonal excitations with time varying frequencies [1–3]. The vibration suppression is most effective at the point of attachment of the absorber to the primary structure. In this study we show that proper feedback control on the absorber can yield successful vibration suppression at points away from this point of attachment. The form and the size of such “influence region” strongly depend on the structural properties of the absorber and the primary system. There are a number of questions addressed in this paper: a) Stability of vibration absorption, considering that a single absorber is used to suppress oscillations at different locations. b) Possible common operating frequency intervals in which the suppression can be switched from one point on the structure to the others. A three-degree-of-freedom system is taken for as example case. One single DR absorber is demonstrated to suppress the oscillations at one of the three masses at a given time. Instead of an “influence region” a set of “influence points” is introduced. An analysis method is presented to find the common frequency interval in which the DR absorber operates at all three influence points.

A Single-Step Automatic Tuning Algorithm for the Delayed Resonator Vibration Absorber

The delayed resonator (DR) is an active vibration control approach where a passive mass-spring-damper arrangement is converted into an undamped real-time tunable dynamic absorber using partial state feedback with time delay. In the presented work, robustness of the control strategy against fluctuations in the structural parameters of the controlled system is addressed. A single-step automatic tuning algorithm based on on-line parameter identification is developed as a means of increasing robustness against uncertainties and variations in the mechanical properties of the absorber arrangement. The tuning process is completed within the absorber section of the controlled system with no external information from the primary structure. Implementation of the algorithm is demonstrated experimentally on a clamped-clamped flexible beam.