## 6 Experimental Verification
Therefore, we observe the simulation results in Figure 101-k as actual states in the automatic pouring machine. In the experiments on the pouring process without any disturbance, the liquid height at the pouring mouth and the flow rate of the outflow liquid in each flow rate control were precisely tracked to the reference trajectory. We also conducted experiments on the pouring process with disturbance. The disturbance was applied, as depicted in Figure 11. The controller planned to begin pouring the liquid at a tilt angle of \(\theta_{p}=20\) deg. However, pouring started at a tilt angle of \(\theta_{a}=23.7\) deg in the experiments. The experimental results are depicted in Figure 12, which are presented in the same manner as in the Figure in Figure 10.  
As can be observed from Figure 121,j, the initial increases in the liquid height at the pouring mouth and the flow rate in each flow rate control were delayed by the disturbance. The tracking performances of the reference trajectories were improved by applying the flow rate control based on differential flatness to the automatic pouring machine. In Figure 13, we denote the results of the state estimation of the liquid height at the pouring mouth. These results were obtained in the experiments using a pouring process with disturbance. Figure 12a,b denote the liquid heights at the pouring mouth, obtained by implementing the developed flow rate control based on the differential flatness and the conventional feed-forward flow rate control, respectively. In Figure 13, the blue lines represent the simulation results obtained from the pouring model, which are the same as the graph 12i. The orange lines represent the estimation results obtained using the extended Kalman filter. The broken yellow lines represent the reference trajectories. As can be observed from Figure 13b, the extended Kalman filter caused the estimated trajectory to gradually converge with the actual trajectory. Furthermore, in Figure 13a, the estimated liquid height matches precisely with the reference trajectory. Therefore, majority of the tracking error was caused by the estimation error using the extended Kalman filter. The state estimation of the automatic pouring machine must be improved to more precisely track to a target flow rate in the developed control system. Figure 11: Illustration of the disturbance applied in the experiments, which was caused by a difference between the tilt angles at the beginning of pouring the liquid in the experiments and the controller design. Figure 12: Experimental results of flow rate control to pouring process with disturbance. **(a)** Input signal added to motor of the \(\Theta\)-axis. **(b)** Input signal added to motor of the \(X\)-axis. **(c)** Input signal added to motor of the \(Z\)-axis. **(d)** Angle of tilting ladle on \(\Theta\)-axis. **(e)** Position of ladle on \(X\)-axis. **(f)** Position of ladle on \(Z\)-axis. **(g)** Angular velocity on \(\Theta\)-axis, estimated by steady-state Kalman filter. **(h)** Acceleration on \(Z\)-axis, estimated by steady-state Kalman filter. **(i)** Liquid height at pouring mouth in simulation, using pouring model. **(j)** Flow rate of outflow liquid in simulation, using pouring model. **(k)** Weight of outflow liquid in simulation, using pouring model. **(l)** Weight of outflow liquid, measured by load cell. Figure 13: Comparative results of liquid height at pouring mouth. **(a)** Liquid height in developed flow rate control. **(b)** Liquid height in conventional feed-forward flow rate control.