IEEE TRANSACTIONS ONINDUSTRY APPLICATIONS, VOL. 36, NO. 3, MAY/JUNE 2000 861 Stabilization of the Molten Steel Level in the Mold of a Continuous Casting Machine by Means of Vacuum Miguel A. Barron, Ricardo Aguilar, and Jesus González Abstract—A two-input two-output model-based controller to stabilize the molten steel level in the mold and the tundish in a one-strand continuous casting machine is developed; to stabilize the mold level, the pressure in the vacuum chamber of the tundish is employed as control input, while to stabilize the tundish level, the position of the slide-gate valve of the ladle is utilized as control input. Numerical simulations show the good dynamic perfor- mance of the proposed controller, corroborating the viability of the vacuum technique to regulate the level of molten steel in the mold. Index Terms—Continuous casting, control, mold level, molten steel, tundish level, vacuum. NOMENCLATURE Cross-sectional area of the ladle (m ). Cross-sectional area of the tundish (m ). Flow area of the tundish nozzle (m ). Cross-sectional area of the mold (m ). Discharge coefficient of the ladle nozzle . Discharge coefficient of the tundish nozzle . Diameter of the ladle nozzle (m). Diameter of the tundish nozzle (m). Gravity constant (m s ). Steel level of the ladle (m). Steel level of the tundish (m). Set point of the tundish level (m). Steel level of the mold (m). Set point of the mold level (m). Control gain of the tundish level control loop (s ). Control gain of the mold level control loop (s ). Pressure at the vacuum chamber (MPa) Atmospheric pressure (MPa). Outlet flow rate from the ladle (m s ). Inlet flow rate into the tundish (m s ). Outlet flow rate from the tundish (m s ). Outlet flow rate from the mold (m s ). Paper PID 99–21, presented at the 1999 Industry Applications Society Annual Meeting, Phoenix, AZ, October 3–7, and approved for publication in the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Metal Industry Committee of the IEEE Industry Applications Society. Manuscript submitted for review October 8, 1999 and released for publication December 10, 1999. M. A. Barron is with the Departamento de Materiales, Universidad Autónoma Metropolitana-Azcapotzalco, 07300 Mexico City, Mexico (e-mail: bmma@hp9000a1.uam.mx). R. Aguilar is with the Departamento de Energía, Universidad Autónoma Metropolitana-Azcapotzalco, 07300 Mexico City, Mexico (e-mail: raguilar@hp9000a1.uam.mx). J. González is with the Departamento de Sistemas, Universidad Autónoma Metropolitana-Azcapotzalco, 07300 Mexico City, Mexico (e-mail: gtji@hp9000a1.uam.mx). Publisher Item Identifier S 0093-9994(00)03164-9. Fig. 1. Continuous casting machine. Position of the slide-gate valve (m). Time (s). Casting speed (m s ). Density of the molten steel (kg m ). I. INTRODUCTION C ONTROL of the mold level in a continuous casting ma- chine is an important task from operating, metallurgical, and quality points of view. Operationally, the mold level must be kept constant in order to avoid molten steel overflows, mold emptying, or strand breakouts which will cause significant eco- nomic losses. From a metallurgical perspective, it is important to stabilize the mold level in order to avoid slag entrapments, steel oxidizing, and alloying segregation. From a quality point of view, the mold level must be kept constant in order to get the product free of internal and surface cracks [1]. Many authors have reported control of the mold level with a great variety of control techniques, which range from conventional proportional–integral–derivative (PID) to artificial intelligence [2]–[6]; however, all of these techniques employ traditional devices such as stopper-rods as control inputs to handle the flow of molten steel. The main drawback of stopper-rods is the instability in the flow of metal due to oxide deposition and eroding. Recently, a vacuum technique to handle the flow of molten steel has been proposed [7] which is lacking from the aforementioned drawback given that it employs a reduced air pressure above the molten steel in the tundish (Fig. 1) in order to regulate the inlet flow to the mold; additional potential benefits from this technique are improved surface quality due to improved mold level performance, improved steel cleanliness due to enhanced inclusion flotation in the tundish, and improved flow patterns in the mold [7]. Besides oxidizing 0093–9994/00$10.00 © 2000 IEEE