Two-stage optimization of multi-channel delayed feedforward-feedback control for an active quasi-zero-stiffness vibration isolation system

Although time-delay coupling poses a major challenge to high-performance control in active quasi-zero-stiffness (QZS) vibration isolation systems, the involved delays can be exploited as tunable parameters for control optimization. To exploit this potential, this study develops a multi-channel delayed feedforward-feedback (MCDFF) control strategy for active QZS isolation, in which four delayed displacement-velocity channels are independently tuned to shape both stability and isolation performance. First, analytical frequency-sweeping and numerical-iteration procedures are introduced to evaluate delay robustness and stability margin, respectively. Second, a two-stage optimization framework is established, in which feedback tuning first secures stability and feedforward tuning then refines the desired isolation performance. Third, two joint optimization schemes are developed to balance anti-resonance attenuation with resonance suppression and transient performance. Experimental results demonstrate that the optimized MCDFF strategy outperforms the representative baselines. Compared with the QZS-only system, it achieves displacement transmissibility reductions of 81.55% under a 3  Hz single-frequency excitation, 65.92% at 2  Hz and 81.23% at 4  Hz under dual-frequency excitation, and 58.72% over the 2–12  Hz broadband range. Furthermore, the proposed strategy experimentally reduces the initial isolation frequency to below 0.5  Hz, demonstrating its potential for ultra-low-frequency isolation.