Stability robustness and performance optimization of a semi-active/active hybrid quasi-zero-stiffness isolator with multiple-delayed feedback

This paper presents a novel semi-active/active hybrid quasi-zero-stiffness (SAH-QZS) isolator with multiple-delayed feedback for enhanced low-frequency vibration suppression. The key contributions of this work are threefold. First, the integration of multiple-delayed feedback into the SAH-QZS structure improves overall isolation efficiency and provides superior flexibility in parameter tuning compared with single-delayed feedback. Second, a comprehensive stability analysis framework is developed based on the resultant theory, frequency-sweeping algorithm, and hybrid spectral-delay sweeping method. This framework enables the precise evaluation of stability robustness against multiple-delay uncertainties and is applicable to systems with any number of delays. Third, four optimization algorithms are formulated within a unified framework, allowing the adaptive tuning of delayed control parameters to achieve fast transient response, targeted frequency suppression, multi-frequency suppression, or broadband isolation. In the 5 Hz experimental case, the optimized multiple-delayed feedback with semi-active control achieves the best isolation performance, reducing the transmissibility by 71.55 % and 62.67 % compared with the semi-active and single-delayed configurations, respectively.