Optimal control of an aluminum casting furnace: Part I. The control model
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I.
INTRODUCTION
THE casting furnace is the centerpiece equipment in the fabrication of aluminum. It receives the liquid aluminum from the electrolytic potrooms at a known temperature and must bring it up to a desired final temperature in a given time for metal treatment, alloying, and casting. It consumes large amounts of fuel, and an optimal control of fuel flow is economically justified. The difficulty is in obtaining a control model that is representative of the real process yet is simple enough for control and optimization purposes. The best way to model the casting furnace, or any other industrial process for that matter, is to write a set of equations describing the physics of the process. The model thus obtained, often called the analytic model, may have good representativity without being a convenient tool for control purposes due to its mathematics. For control purposes, a model of the form A = Ax + Bu, linear or nonlinear, is more tractable, especially when the ultimate aim is a real-time on-site control. There are two ways to obtain such a control model. One can obtain the expressions for A and B from the relations describing the real process; a well-known illustration of this approach is the approximation of the parameters and the equations describing the radiative heat
R.T. BUI, Professor, and R. OUELLET, Research Engineer, are with the Department of Applied Science, Universit6 du Qu6bec ~t Chicoutimi, Chicoutimi, PQ, Canada G7H 2B1. Manuscript submitted July 17, 1989. METALLURGICAL TRANSACTIONS B
transfer by a proper selection of simplified parameters. An alternative is the statistical approach making use of either the experimental plant test data tl] or the predicted data coming from an analytic model that has been properly validated previously.[2l This work belongs to the latter case.
II.
THE CASTING FURNACE
Figure 1 gives the cutaway views of the furnace in the axial and transverse directions. The furnace can be seen as made of four main components: the gas in the chamber, the metal, the roof, and the floor. The gas (gaseous fuel and air) comes in through burner (4) and exits through stack duct (3). Liquid metal from crucibles is introduced through siphon (11) up to level (9). The roof (1) and (2) and the floor (6), (7), and (8) are made of steel shell, insulation materials, and refractory linings. At casting time, the furnace is tilted and the metal is poured into the mold through spout (12). This description is taken from a 72-ton furnace in operation at Alcan Smelters and Chemicals Ltd., Jonqui6re, PQ, Canada. Approximate dimensions are 10 m in length, 4 m in width, and 3 m in height. Since the focus of this work is the control model and fuel optimization, only liquid metal heating is considered and no scrap melting is included. Thus, a typical schedule of a batch is composed of the loading of the liquid metal, followed by a 1-hour heating period, and then other preparations, such as stirring, fluxing, alloying, and skimming, before casting takes place. This work VOLUME 21B, JUNE 1990--48
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