A Hybrid Active-Passive Isolation System Based on Quasi-Zero Stiffness Isolators for Broadband Vibration Control of Continuous Flexible Structures

The application of quasi-zero stiffness (QZS) isolators to continuous flexible structures is often restricted by the inherent conflict between low-frequency resonance suppression and high-frequency isolation performance. This study addresses this limitation by proposing a hybrid active-passive isolation system embedded within a two-stage plate structure that integrates magnetic negative-stiffness mechanisms with voice coil motors. A coupled nonlinear dynamic model is derived via the Lagrange equations to capture the complex interaction between rigid-body modes and elastic structural responses. To mitigate the stiffening effects and control spillover associated with high-gain linear controllers, a centralized nonlinear PID (NPID) control strategy is developed. By employing state-dependent gain scheduling, the controller naturally provides high damping for large-amplitude resonances and transitions to a low-impedance state for high-frequency micro-vibrations, effectively decoupling resonance suppression from the isolation bandwidth. Numerical and experimental results demonstrate that the hybrid system reduces the resonant transmissibility by approximately 18.5 dB compared to a purely passive design. Additionally, the NPID strategy maintains a transmissibility below -5 dB across the 10-100 Hz range, outperforming linear PID controllers and confirming its suitability for broadband isolation in complex flexible environments.