## 1 Introduction  
Vibration isolation is an effective way to reduce vibration transmission from rotary mechanical equipment, as well as an important means of reducing vibration and noise [1]. Double-layered vibration isolation [2], floating raft vibration isolation [3] and other passive vibration isolation methods play an important role in middle- and high-frequency bands. [PERSON] [4] discussed minimizing the effect of external mechanical vibration on hydraulic valves in different military hydraulic drive systems by introducing materials with known stiffness and damping characteristics to reduce the vibration on the valve casing, but such materials fail to meet the requirements for the low-frequency vibration isolation of rotary mechanical equipment. Active vibration isolation effectively suppresses low-frequency vibrations with an additional force source [5]. However, there are problems, such as large energy consumption and unsatisfactory bearing capacity. Active-passive hybrid vibration isolation technology combines the technical advantages of active and passive vibration isolation. Therefore, it has wider application prospects. Currently, further research is still required to achieve an effective combination of active-passive hybrid vibration isolation technology in order to realize a high output force, large bearing capacity, low power consumption and impact resistance [6; 7; 8]. [PERSON] [9] established a magnetic field analytical model of a non-equal-size Halbach array based on the equivalent magnetic charge method and the principle of field strength superposition. This magnetic field analytical model improves the linearity of the output force and reduces the power loss, but it fails to meet the requirements for impact resistance and large bearing capacity. [PERSON] [10] designed a hybrid vibration isolation system combining an active piezo stack-based actuator and passive rubber-based isolator, and it has a compact structure with high reliability, reducing the resonance peak, but the bearing capacity is unsatisfactory. [PERSON] [11] designed a new electromagnetic actuator based on [PERSON]'s normal stress, which improves the low-frequency vibration isolation effect under the static stiffness and realizes the vibration isolation in a wider frequency band by combining the passive vibration isolation device, but the reliability under dynamic working conditions has not been verified. [PERSON] [12], [PERSON] [13] and [PERSON] [14], respectively, proposed a new magnetic circuit topology that integrated the magnetic flux leakage effect, edge effect and nonlinear magnetic permeability, which improved the output force of the actuator but failed to consider power consumption and heat generation. [PERSON] [15] embedded the fluid damping into the electromagnetic actuator, which can effectively isolate tiny vibrations in the range of 5-200 Hz, but it failed to meet the requirements for vibration isolation requiring a large output force. [PERSON] [16] designed a hybrid vibration isolation system combining a magnetorheological semi-active vibration isolator and a piezoelectric stack actuator; meanwhile, the author also designed an active semi-active switch according to the excitation input. The combination of the semi-active piezoelectric actuator and the changeover switch effectively attenuates the full-band vibration, but the output force response is slow, and the displacement of the mover is large, which is not conducive to the stability of the active control. [PERSON] [17] proposed a new electro-hydraulic hybrid vibration isolation system electro-hydrostatic actuator (EHA), which consists of the brushless DC motor and the bidirectional gear pump. EHA, featured in low natural frequency and low power consumption, is applied to the vibration control between helicopter fuselage and rotor. However, the problem of oil leakage occurs and EHA's performance is greatly affected by the temperature, resulting in affected accuracy of control.