Complete Stability Analysis and Optimization of the Extended Delayed Resonator With Virtual Natural Frequency Adjustment

The delayed resonator (DR) is known for its ideal vibration suppression and simple control logic, but its operable frequency range is also known limited due to stability issues and practical hardware constraints. To extend the limited operable frequency range, we inject an additional nondelayed control term into the feedback loop of the classic DR such that the equivalent natural frequency of the DR can be real-time tuned, so the creation of DR with virtual natural frequency adjustment (DRV). Besides, we take the difference between the adjustable natural frequency of the DRV and the excitation frequency as a control parameter to further enhance the vibration suppression leading to optionally tuned parameters for a given excitation. For this, we start with the complete stability analyses of the DRV and the associated coupled system following independent and purely analytical approaches, and the obtained nonconservative stability maps reveal DRV's greatly extended operable frequency range. Given the optional tuned parameters, an optimization procedure aiming for a faster transient process and stronger robustness is proposed to determine the optimal parameter composition. Finally, three numerical case studies are prepared to demonstrate the benefits of the DRV compared with the classic DR. In addition to extending the operable frequency range of the classic DR, this work simplifies the stability analysis of the existing DR investigations and provides a guideline for the tuned control parameter design if they are optional.