## 3 Results  
The proposed method in Figure 12 is experimentally evaluated. For the efficient tracking control, the PD controller is used as the feedback controller \(\left(C\!\left(z^{-1}\right)\right)\) in Figure 12. Since the integral action can amplify the sensor noise and degrade the stability of the closed-loop, the proportional integral derivative (PID) controller is not used. The feedback controller follows the flowrate command (\(r(k)\)) of 100, 150, and 400 cc/min, respectively. The experimental results of the measured flowrate output in the steady state are shown in Figure 13 and Table 3. The Figure 13a-c shows the experimentally measured flowrate outputs of 100, 150, and 400 cc/min, respectively. As shown in Figure 13, the blue line is the measured output of the open-loop system (Open-loop), the green line is the closed-loop system only using the PD controller (PD), and the red line is the closed-loop system using the compensation lookup table-based feedforward controller and the PD controller (Lookup).  
As shown in Figure 13a-c, the open-loop control system showed that the root mean square (RMS) values of the steady-state error were 3.9604, 7.1526, and 27.2863, respectively. In the closed-loop system only using the PD controller, the RMS errors between the flowrate command and the measured output were 2.3493, 3.6986, and 8.0320, respectively. The two control systems could not effectively remove the periodic disturbances. On the other hand, in the case of the proposed control method, the RMS values of tracking error were 0.7275, 1.1953, and 1.6392, respectively. The RMS values of the proposed method are much less than the RMS values of the open-loop system and the PD controller. In the case of the open-loop control system and the PD controller, the flow feedback at the steady state did not reach the flow command in the biased form. On the other hand, the proposed controller compensated the flowrate dependent value in the compensation lookup table as the feedforward type, so that the biased characteristics at the steady state were improved remarkably. Non-biased flow feedback that follows the flowrate command precisely in the painting process is essential. If the flow feedback does not reach the flowrate command sufficiently, there may be a lack of coating. In contrast, defects such as sagging may occur if the flow feedback is higher than the flowrate command. The experimental results show that the proposed controller can reduce the steady-state error significantly for the low-frequency flowrate commands, as well as for the high-frequency flowrate commands compared to the open-loop control system.  
From the experimental results, the proposed control method can reduce the fluctuation amplitude, which is the minimum peak to the maximum peak difference in the steady-state error. The compensation lookup table-based feedforward controller showed that the mean values of fluctuation amplitude were 1.8790, 2.1891, and 3.3696, respectively, when the flowrate commands were 100 cc/min, 150 cc/min, and 400 cc/min. In the closed-loop system only using the PD controller, the mean values of fluctuation amplitude were 3.3110, 3.3740, and 3.5198.  
In the low-speed flowrate command, the fluctuation amplitude of the proposed controller is low, whereas the fluctuation amplitude is as high as much as the conventional PD controller at high-speed flowrate command. The influence of the flowrate dependent compensation value is relatively greater than in the rotational angle-dependent compensation value at a high-speed flow rate command. Therefore, there is a limitation to remove periodic disturbances at high-speed flowrate commands effectively. However, the proposed controller can be effectively used because most of the flowrate commands are operated in the low-speed range of 100 to 150 cc/min in the painting process.