Complete stability analysis and optimal design for dual-state-feedback delayed resonator

Abstract

We propose a dual-state-feedback delayed resonator (DFDR) by incorporating an additional acceleration-based feedback into the classical DR design. The optimal tuning of its feedback parameters is guided by two objectives: enhancing vibration suppression at a specified target frequency and maintaining overall system stability. First, we extend the Advanced Clustering with Frequency Sweeping (ACFS) methodology from the delay-only domain to the combined delay-gain domain, enabling a rigorous and complete stability analysis where feedback gains and delays interact. Second, we develop the optimal parameter tuning procedure and demonstrate that the proposed DFDR achieves improved stability margins, enhanced robustness to frequency variations, and superior vibration suppression performance compared to the classical DR. These results highlight the practical potential of DFDR as an effective and robust solution for active vibration suppression systems.