###### Abstract
Passive vibration isolation devices do not consume any energy, making them an environmentally friendly solution. Passive vibration isolation devices have a long lifespan and require little to no maintenance, making them a reliable solution for many applications. However, there are disadvantages of passive vibration isolation devices. Passive vibration isolation devices may not provide the same level of isolation performance as active vibration isolation systems. Passive vibration isolation devices can be affected by changes in temperature,  
Figure 1: Vibration control systems. (**a**) Passive system; (**b**) Semi-active system; (**c**) Parallel active system; (**d**) Serial active system. humidity, and other environmental factors, which can affect their performance over time. Passive vibration isolation devices may not provide effective isolation over a wide range of frequencies, making them less suitable for applications with complex vibration spectra. Passive vibration isolation devices cannot be easily adjusted to accommodate changes in the vibrating source or the sensitive structure, making them less flexible than active vibration isolation systems. Passive systems have predetermined properties that cannot be adjusted while the system is operating. Although passive vibration isolation systems remain an effective solution to a wide range of vibration problems today, there are many applications where passive systems alone cannot satisfy customer requirements. Semi-active systems use a variable damping technique, as shown in Figure 1b. Depending on the states, the variable damper changes their damping coefficient to minimize the displacement. Semi-active vibration isolation systems offer some of the benefits of both passive and active vibration isolation systems. Compared to passive vibration isolation systems, semi-active vibration isolation systems can provide improved isolation performance, especially in the presence of changing or unpredictable vibrations. Semi-active vibration isolation systems can be adjusted to accommodate changes in the vibrating source or the sensitive structure, making them more flexible than passive vibration isolation systems. Semi-active vibration isolation systems consume less energy than active vibration isolation systems, making them a more energy-efficient solution. Compared to active vibration isolation systems, semi-active vibration isolation systems are less expensive, making them a cost-effective solution for many applications. However, there are also disadvantages of using semi-active vibration isolation systems. Semi-active vibration isolation systems are more complex than passive vibration isolation systems, requiring specialized knowledge and technical expertise to design, install, and maintain. The performance of semi-active vibration isolation systems depends on the design of the control algorithms, which can be affected by changes in the environment, sensor noise, and other factors. Semi-active vibration isolation systems require regular maintenance to ensure proper functioning, which can increase their overall cost of ownership. Semi-active vibration isolation systems require a power source, which may not be available in some remote or harsh environments. The most widely used variable damping device is the Magneto-Rheological Fluid (MRF) damper [5; 6; 7; 8], and sky-hook control is the distinctive control algorithm employed by the MRF damper [9]. The sky-hook control is a very simple but effective vibration control algorithm that generates voltage according to the absolute and relative velocities of the main body. However, the sky-hook control algorithm requires the absolute and relative velocities that cannot be measured directly. Active vibration control systems use actuators, sensors, and controllers to directly suppress vibration in the system [10]. Actuators must be able to provide the desired force or displacement to the system, depending on the type of actuator. Sensors are used to detect motion in systems involving acceleration, velocity, or relative displacement.