## 1 Introduction  
In the casting industry, the pouring process creates a dangerous working environment, involving high-temperature molten metal. Therefore, automatic pouring systems have been developed and applied to keep workers away from the pouring site [1; 2]. Recently, a tilting-ladle-type automatic pouring system has been developed, which is simple to construct and which allows the molten metal in the ladle to be easily changed [3]. An automatic pouring machine must be able to precisely and quickly pour molten metal into a mold, to ensure the quality of the cast product and to ensure safety in the working environment. However, it is difficult to precisely pour molten metal into the pouring basin of a mold, as the outflow from the ladle can be indirectly controlled by controlling its tilt [4; 5; 6; 7]. Pouring control systems which can be used to precisely pour a liquid by tilting the liquid container have been proposed in previous studies. A mathematical model that represents the pouring process using an automatic pouring system has been derived, and a feed-forward flow rate control system, based on the inverse model, has been developed by the present authors [8]. Furthermore, feed-forward flow rate control has been applied to control the liquid level in the tundish of a strip-caster [9]. The supervisory control of an automatic pouring system with a fan-shaped ladle was proposed, in order to perform multiple tasks: To ensure that the liquid in the pouring basin was maintained at a constant level; that the total quantity of the liquid that was poured into the mold was achieved precisely at the target quantity; and that sloshing of the liquid in the ladle was suppressed [10]; in this approach, flow rate control was achieved using feed-forward control based on the inverse pouring model. The parameters of the inverse pouring model in the feed-forward control have been adaptively tuned, using the on-line model parameters identification method [11]. Additionally, the motion of the liquid container was optimized using a computer fluid dynamics simulation based on the Navier-Stokes model [12; 13]. Recently, the model-based pouring control system was applied to a pouring robot, which was constructed with a parallel mechanism [14]. Other recent pouring control approaches have noted that the falling position and flow rate of the outflow liquid from the ladle can be directly manipulated from a remote location [15]. In the previously-described approaches, various pouring control systems have been proposed with model-based designs, and feed-forward control approaches are employed in most of them. As for pouring control using model-free approaches, various feedback control systems have been proposed to ensure that the liquid volume in the target container can be achieved at the target volume, using a vision system [16; 17]. More recently, the liquid poured from an unknown container, which has a simple and symmetric shape, has been controlled by estimating the geometry of the container shape, using the model learning approach [18; 19]. These approaches are robust with respect to the shape of the source container, and specialize in ensuring that the total liquid volume poured from the source container is achieved precisely at the target volume. However, flow rate control is very important for designing a high-precision automatic pouring machine in the casting field, as the flow rate influences the pouring conditions, including the falling position of the outflow liquid, the liquid level in the target container, and the total outflow. Some pouring control systems have been proposed based on the model-based feedback approach. A real-time flow rate estimation system was developed, using an extended Kalman filter based on the pouring model [20]. Additionally, an un-scented Kalman filter was applied to realize real-time flow rate estimation for a ladle with a complicated shape [21]. To construct a flow rate feedback control system, the present authors developed a flow rate control based on differential flatness [22].