Delayed Resonator With Distributed Delay in Acceleration Feedback-Design and Experimental Verification

The main results of this paper are design, analysis, and experimental verification of a delayed resonator with a distributed-time-delay acceleration feedback. Analogously to the classical delayed resonator, the novel resonator is applied to suppress vibrations of a mechanical system. The theoretical part of this paper includes control parameter design and analysis of their ranges. Next, dynamical properties of the resonator are analyzed including the derivation of a complete stability picture for the combined resonator with the single-degree-of-freedom mechanical system. For the stability analysis, spectral methods are applied including the method of cluster treatment of characteristic roots. Utilizing the distributed delay instead of the lumped delay on the acceleration feedback, both the resonator and the overall system dynamics are converted from neutral to more convenient retarded character. Another positive aspect of the distributed delay is that it acts like a moving average filter on the acceleration measurements. Furthermore, we perform a computational analysis of spectral properties using a numerical root-finding QPmR algorithm. All these stability findings are also verified experimentally on a laboratory setup designed and implemented for this purpose.