## 7 Conclusions and Future Works  
In this study, we addressed the manner in which flow rate control based on differential flatness can be applied to a tilting-laddle-type automatic pouring machine, and verified the efficacy of the developed flow rate control through various experiments. The following conclusions can be obtained:  
1. From the viewpoint of practical application, a SISO-nonlinear-type controller design based on differential flatness was applied, to ensure the flow rate control of the automatic pouring machine;
2. while implementing the flow rate control using the feedback control scheme, it was necessary to measure the states of the automatic pouring machine--however, it is difficult to directly measure the states of high-temperature molten metal. Therefore, in this study, the Kalman filter approach was applied for estimating the state variables of the automatic pouring machine;
3. the steady-state and extended Kalman filters were decomposed for simple construction of the state estimate of the automatic pouring machine;
4. in the experiments related to the pouring process without disturbance, both the feed-forward flow rate control based on the inverse pouring model, and the flow rate control based on differential flatness, achieved a flow rate by which the outflow liquid precisely tracked with the reference trajectory: We conclude that the pouring model described in this study could precisely represent the actual pouring process in the automatic pouring machine;
5. in the experiments on a pouring process with disturbance, the tracking performance of the flow rate in the pouring machine could be improved by implementing flow rate control based on differential flatness; and
6. a majority of the tracking errors of the flow rate control based on differential flatness were caused by the estimation errors of the extended Kalman filter. Furthermore, the following recommendations for future work can be obtained:  
1. To obtain high tracking performance, the state estimation approach of the pouring machine should be improved in future studies;
2. in the developed flow rate control, the flow rate of the outflow liquid was indirectly controlled, based on the liquid height at the pouring mouth. If any disturbances were observed in the relation between the flow rate and the liquid height at the pouring mouth, the tracking performance of the flow rate control may have degraded. Further, direct flow rate control must be achieved to construct a high-precision automatic pouring machine; and
3. in practical pouring processes, the characteristics of the pouring material are variable with temperature, the added substance, and so on. Therefore, a control approach with computational intelligence, such that the controller can be adapted autonomously to the pouring environment, should be developed in the future work.  
Conceptualization, Y.N.; Methodology, Y.N.; software, Y.N. and Y.S.; Validation, Y.N. and Y.S.; Formal analysis, Y.N.; Investigation, Y.N.; Resources, Y.N.; Data curation, Y.N.; Writing--original draft preparation, Y.N.; Writing--review and editing, Y.N. and Y.S.; Visualization, Y.N.; Supervision, Y.N.; Project administration, Y.N.; Funding acquisition, Y.N.  
This study was funded by JKA foundation, grant number 2018M-177; and the Adaptable and Seamless Technology Transfer Program through Target-driven R&D, JST, project \"Development of measurement system for pouring process by sensor-fusion\".  
The authors declare no conflict of interest.  
The following abbreviation is used in this manuscript:  
SISO Single input and single output.