## 4 Current Progress of Magnetic Negative Stiffness in QZS Isolators
### QZS-Based Hybrid Magnetic Negative Stiffness Elements
Adjusting the current in the coil enables variation of the electromagnetic stiffness, facilitating online optimization of the system and averting degradation of the damping performance. In comparison to passive vibration isolators, this isolator extends the isolation bandwidth and enhances the isolation performance near the natural frequency of the passive system. In contrast to certain other electromagnetic vibration isolation systems, the present system boasts a more compact structure, increased load capacity, and enhanced efficiency in negative stiffness generation. Nonetheless, given the need for a power source to activate the coil, assessing the power requirements and energy consumption emerges as a crucial consideration when evaluating the system. Despite having the lowest power consumption at the same resonant frequency, the power consumption escalates as the resonant frequency shifts into the lower frequency range. Overall, this electromagnetic vibration isolator design excels in compactness, load capacity, negative stiffness generation efficiency, and vibration isolation performance. However, the power requirements and energy consumption warrant careful consideration. Figure 31: Experimental setup of the proposed HSLDS isolator: (**a**) HSLDS system; (**b**) electromagnetic mechanism, where the green and red arrow represent the magnetization direction and the polarity of current, respectively; (**c**) coil winding and permanent magnet; and (**d**) experimental setup. As shown in Figure 32, [PERSON]'s [62] contribution lies in proposing an electromagnetic-based absolute displacement sensor (ADS) featuring near-linear QZS characteristics. This design employs non-contact electromagnetic QZS rather than mechanical QZS. The design achieves a more compact structure by initially embedding a toroidal permanent magnet in the electromagnetic coil. The non-contact characteristic of the electromagnetic force can lead to a reduced damping factor and extended fatigue life. The electromagnetic stiffness can be adjusted to achieve near linearity within a range, mitigating the impact of the stiffness non-linearity and enhancing the measurement accuracy. The measurement accuracy of this design reaches 0.1 mm at frequencies exceeding 3 Hz. The performance of this ADS system is validated through analysis of its structure and working principle, as well as through numerical simulations and experiments. Through parameter analysis and selection, the paper demonstrates how performance optimization can be achieved by tuning the system parameters. The experimental results demonstrate the effective performance of the proposed ADS system in displacement measurement, with high accuracy and effective vibration isolation, particularly at higher frequencies. Furthermore, the system is capable of operating in harsh environments, including high temperature conditions, while maintaining stable performance. The design achieves greater compactness by embedding toroidal permanent magnets in the electromagnetic coil. The non-contact characteristic of the electromagnetic force can lead to a reduced damping factor and extended fatigue life. The electromagnetic stiffness can be adjusted to achieve near linearity within a certain range, thus mitigating the impact of the stiffness nonlinearity and enhancing the measurement accuracy. The experimental results demonstrate the effective performance of the proposed ADS system in displacement measurement, with a measurement accuracy of up to 0.1 mm for high-frequency applications exceeding 3 Hz.