###### Abstract
The controller calculates the required external force or displacement using control algorithms and sends a signal to control the actuator. The controller can be either an analog circuit or a digital controller. Depending on the position of the actuator, there are two types of active control. Figure 1c shows an actuator installed parallel to the damper and spring, whereas Figure 1d shows an actuator installed in series with the damper and spring. Popular actuators used to transmit force to the vibration isolation model shown in Figure 1c are air springs [11; 12; 13; 14; 15; 16; 17], and voice-coil actuators (VCA) [18; 19; 20]. The air springs are actually pneumatic actuators, so that they can support static loads while providing dynamic force. Air springs are commonly used in the suspension systems of vehicles, such as cars, trucks, buses, and trains, to provide a smooth and comfortable ride. They are used in place of traditional mechanical springs to provide improved ride quality, adjustability, and load-carrying capabilities. Air springs are also used in a wide range of industrial equipment, including machine tools, packaging machines, and conveyor systems, to isolate vibration and reduce shock transmission. Overall, air springs are versatile and flexible components that can be used in a wide range of applications to provide improved vibration isolation and shock absorption. A voice-coil actuator is a type of electromagnetic actuator that is commonly used in vibration control systems. It consists of a coil of wire that is placed within a magnetic field, and when a current is passed through the coil, a force is generated that can be used to control the position of an object. In vibration control systems, voice-coil actuators are used in active vibration isolation systems to control the motion of a sensitive structure, such as a delicate instrument or optical system. The actuator is attached to the sensitive structure, and its motion is actively controlled in response to incoming vibrations, effectively isolating the structure from the vibrating source. The effectiveness of the vibration control system depends on the accuracy of the control algorithm and the responsiveness of the voice-coil actuator. Voice-coil actuators are fast and highly responsive, making them a popular choice for many active vibration control applications. When a VCA is used with an air spring, the air spring supports only the static load, whereas the VCA provides the dynamic force. Both pneumatic actuators and VCAs require a command voltage to generate force. In the case of a pneumatic actuator, the command voltage controls the opening of the servo valve to adjust the force, and in the case of a VCA, the command voltage is converted into current through a power amplifier to generate the electro-magnetic force. In comparison to the VCA, it seems difficult to produce accurate control force by using the pneumatic actuator because of nonlinearity. Most active vibration control is performed in the form of Figure 1c, in which actuators capable of generating force are connected in parallel. Compared to the parallel active isolation system in Figure 1c, not much research has been carried out on the serial active isolation system in Figure 1d. A control algorithm must be developed according to the type of sensor and actuator. The Positive Position Feedback (PPF) controller can be used when using position sensors and force-producing actuators [21]. The PPF controller has been widely used for structures equipped with piezoelectric sensors and actuators attached to structures [22; 23; 24]. However, accelerometers are the most widely used sensors for vibration measurement that actually measure absolute acceleration. The so-called Virtual Tuned Mass Damper (VTMD) control was developed to utilize an accelerometer as a sensor, and use an inertial actuator [25]. In applying the VTMD control, the displacement of the inertial actuator should be accurately controlled.