한剳정밀공학회 2013 년도 추계학술대회논문집 1. Introduction In high precision system, active vibration isolator usually includes horizontal control system to reject the disturbances such as reaction force due to high- speed acceleration motion of stage producing large vibration and reducing machine performance. Horizontal vibration control system can be achieved using electromagnetic planar actuator providing the disturbance rejection characteristics by generating the forces to adjust horizontal damping and stiffness [1]. The horizontal vibration control using the horizontal force to compensate the initial damping is studied thoroughly in [2]. However, there is not much reference of reducing the vibration by adjusting stiffness using force of electromagnetic planar actuator. This paper presents a horizontal vibration isolator using vertical force of an electromagnetic planar actuator. The active horizontal vibration isolator under study consists of two main parts: a passive vibration isolator and an electromagnetic planar actuator. Based on the dynamic model of the active horizontal vibration isolator, the Lyapunov method is applied to control the vertical force of planar actuator to adjust the horizontal stiffness of beam column. Finally, simulations are performed to verify the performance of the horizontal disturbance rejection of the active vibration isolator. 2. Vibration model 2.1 Topology Fig. 1 shows the model of the active horizontal vibration isolator using electromagnetic actuator. The electromagnetic actuator generated the force in horizontal direction to adjust the horizontal damping. In addition, the vertical force by electromagnetic actuator impacted to the horizontal stiffness of the beam columns and reduced the nature frequency of the vibration isolator model. The mathematical model of the planar actuator is similar as [3] and active horizontal vibration isolator is presented in [1]. Fig. 1 Active horizontal vibration isolator model 2.2 Lyapunov controller The horizontal stiffness highly depends on payload. Therefore, the vertical F z is applied in order to adjust the effect of payload and to change the horizontal stiffness of set of beam columns. The dynamic model of the horizontal active vibration using vertical force of planar actuator is derived in Eq. (1). mሷ + cሶ + n b (A 1 – A 2 ௠ ௡  )x = F z A 2 x + ω(t) (1) where m is mass, c is damping coefficient, n b is the total number of beam column, A 1-2 are approximate coefficients of beam column horizontal stiffness. The control force of actuator is derived using Lyapunov method as Eq. (2). 평면 전자기 割동기의 수직력을 이용한 수평방향 제진기 Horizontal vibration isolator using vertical force of an electromagnetic planar actuator 팜민나 1 , 트란띠린 1 , # 안형준 2 M. N. Pham 1 , T. T. Linh 1 , # H. J. Ahn 2 1 숭실대학교 기계공학과 대학원, 2 숭실대학교 기계공학과 Key words : Vibration isolator, electromagnetic planar actuator