A hybrid active–passive control strategy of zero-stiffness vibration isolation integrated with energy harvesting

In this paper, we propose a new hybrid active–passive absolute-zero-stiffness vibration isolator (HAZSVI) that achieves long-stroke, full-band vibration isolation under large-displacement excitations with minimal power demand. The key innovation is a feedforward–feedback hybrid control (FFHC) framework that flattens the static restoring force of a quad-stable magnetic negative-stiffness mechanism (MNSM) to establish a practical AZS condition, while reserving feedback control solely for disturbance rejection and uncertainty compensation. The MNSM is modeled using the filament method and validated by finite-element simulations, enabling systematic tuning of air–gap parameters to realize a quad-stable force–displacement relation with seven equilibrium points and an extended quasi-zero-stiffness (QZS) region in a compact configuration. A high-order nonlinear dynamic model and incremental harmonic balance analysis further reveal the regime transition of the quad-stable response and explain the loss of isolation robustness in purely passive operation under large displacements. Experiments demonstrate that the proposed HAZSVI system eliminates resonance amplification and maintains robust full-band isolation, with transmissibility consistently suppressed below − 10 dB even at a base-excitation amplitude of 4.5 mm. Owing to the static compensation mechanism, the control effort remains low, and the maximum average power consumption of the fuzzy PID-based FFHC is only 0.77 W and 1.67 W under 3 mm and 4.5 mm excitations, respectively. A metric-based benchmarking against representative isolators further confirms the superior scalability of the proposed architecture toward compact, high-load, and large-stroke isolation scenarios. The proposed framework redefines multi-stability as a static resource that can be actively reshaped, offering both theoretical insight and engineering feasibility for energy- and weight-constrained precision platforms.