## 7 Discussion and Conclusions  
In this study, we propose a new vibration control system that can suppress lateral vibrations of the vibration isolation table. Most studies on active vibration isolation systems so far have been conducted on parallel active systems using air-spring or VCA. These generate force. There are also actuators that generate displacement. A vibration isolation system using these actuators can be expressed as a serial active system such as connecting a linear actuator and a spring-damper in series. As the parallel and serial active system are different system, a suitable control algorithm for each active system is required. However, there are very few studies on vibration isolation systems using serial active systems compared to parallel active systems. Therefore, in this study, a new algorithm for serial active type vibration isolation system was developed. The vibration suppression control system consisting of a support spring damper and an actuator that can accurately control displacement, where the actuator is connected in series with the spring damper. The proposed control algorithm so-called position input and position output (PIPO) was proposed to create active damping. The PIPO control algorithm uses the displacement of the system as an input and outputs the desired displacement of the actuator. In this study, we first attempted to theoretically verify the effectiveness of the single-input and single-output (SISO) PIPO algorithm for a single degree-of-freedom (SDOF) model before experimentation. And the validity of the proposed control algorithm was investigated through simulation. In addition, to investigate the practical applicability of the controller confirmed through simulation, an experiment was conducted with a single-story building model connected to a linear servo motor. The single-input and multi-output (SIMO) PIPO algorithm for the multi-degree-of-freedom (MDOF) system was also proposed in this study. Using the SIMO PIPO algorithm, a numerical simulation was conducted to check the vibration suppression of the two lowest natural modes of the three-degree-of-freedom model with only one displacement sensor. The simulation results show that the proposed SIMO PIPO control algorithm is effective in controlling many modes with a single actuator. In the experiment, a PIPO controller was designed using the Simulink program to control the first and second natural modes of a two-story building model. As a result of the experiment, both the first and second natural modes of the building model were suppressed quickly and reliably. The proposed PIPO control system is particularly effective in controlling the horizontal vibration of the vibration isolation table because the implementation of the actuator connected in series with the air spring. With this control system, vibration suppression of the lateral vibration of the vibration isolation table can be achieved by connecting a simple displacement actuator to a membrane-type air spring in series. The following conclusions were drawn from this study:  
* Air spring and VCA commonly used in vibration isolation tables, is a type of actuator that generates force. These are parallel active type. An actuator that generates displacement, such as a ball-screw mechanism device or a linear motor, can be expressed as a serial active system. However, there are very few studies on vibration isolation systems using serial active systems compared to parallel active systems. * The proposed PIPO control algorithm uses the displacement of the system as an input and outputs the desired displacement of the actuator installed in series with the damper and spring. The proposed configuration of the control system enables us to suppress lateral vibrations of the vibration isolation table accurately. * The stability condition of the proposed PIPO control algorithm is static. Hence, it does not depend on frequency and characteristics of system to be controlled. The stability of the PIPO control system can be easily guaranteed by adjusting only the gain.