## 1 Introduction  
A painting system using a six-axis articulated robot has been developed to paint complex-shaped objects uniformly and efficiently. Particularly, the automobile painting process requires high quality, and methods of spraying paint quickly and precisely have been developed. For the precise fluid transfer, the fluid gear pump is widely used. As shown in Figure 1, the fluid gear pump operates to control the flowrate using the electronic actuator and the rotational gear. The fluid gear pump has repetitive disturbances, such as flow ripples, that decrease the precision of the fluid transfer. To compensate for the repetitive disturbances, previous studies have suggested a  
Figure 1: Fluid gear pump mechanism. mathematical model of the repetitive flow ripples. The characteristics of the flow ripple are expressed by the theoretical method according to the number of gear teeth [1]. The characteristics of the trapped volume between the gear teeth, which cause the flow ripple, can be calculated by a geometric formula [2]. To express the fluctuation of the flowrate as a mathematical model, a flowrate formula uses an analytical method that considers the shape of the fluid gear pump [3]. A numerical method has been proposed for analyzing the kinematic flow ripple of a fluid gear pump, which allows more precise mathematical modeling than conventional analytical methods [4; 5; 6]. The zero phase error tracking controller (ZPETC) and the repetitive controller based on the internal model principle have been applied to various applications for the repetitive disturbance rejection [7; 8]. The repetitive controller is very effective in servo systems with repetitive disturbances [9]. For more stable control in systems with periodic disturbances, the repetitive controller can be combined with a low-pass filter [10]. The discrete wavelet transform-based repetitive controller minimizes the memory used in the repetitive controller and minimizes the tracking error [11]. To track the desired trajectory while eliminating repetitive disturbances, the repetitive controller can be plugged into a conventional controller such as a proportional-derivative (PD) controller. This plug-in repetitive controller has been applied to the pulse-width modulation (PWM) rectifier and has shown effective performance [12]. The repetitive controller with a disturbance observer can effectively compensate for the disturbances with non-repetitive frequency components [13]. Previous studies have proposed control methods to eliminate system disturbances, and the disturbance observer and the repetitive controller are representative examples [7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17]. To eliminate multiple disturbances as well as single disturbances, a composite hierarchical anti-disturbance control was proposed [18]. Active disturbance rejection control was proposed in order to compensate for disturbances that are difficult to model, by automatically updating the parameters of the controller [19]. Many disturbance rejection methods have been developed, but repetitive controllers can effectively remove periodic disturbances [20; 21]. As an example of the implementation of repetitive control, repetitive disturbances are effectively removed for servo systems such as optical disk drives and hard disk drives [22; 23]. In addition, a repetitive controller applied to the rotor of a wind turbine minimized periodic wind disturbance [24]. For the precise flowrate control of the fluid gear pump-based painting system used in automotive painting processes, this study attempts to eliminate various periods of disturbance for a wide range of flowrate commands. The disturbances in various periods can be expressed by the rotational speed and rotation angle of the motor, relative to the flowrate command. Therefore, a lookup table-based controller can be designed to effectively compensate for periodic disturbances.