A nonlinear reduced order model for estimation and control of vacuum arc remelting of metal alloys

Vacuum arc remelting (VAR) is an industrial metalluraical process widely used throughout the specialty metals industry to cast large alloy ingots. The VAR process is carried out in a vacuum with the aim of melting a large consumable electrode (A in in diameter and 3000 kg in mass and larger) in such a way that that the resulting ingot has improved homogeneity. The VAR control problem consists of adjusting arc current to control electrode melt rate, which also depends on the electrode temperature distribution and adjusting electrode ram speed to control the are gap between the electrode and the ingot. The process is governed by a I dimensional heat conduction partial differential equation with a moving boundary, which leads to an infinite dimensional, nonlinear system. In addition to the process nonlinearity, the inputs and all of the available measurements are corrupted with noise. In order to design a controller and a Kalman based estimator for this process, integral methods are used to derive a set of two coupled nonlinear ordinary differential equations in time, which capture the steady state and transient characteristics of melting in a VAR furnace. The model with the experimentally measured noise is then used to construct an estimator and a controller. The system can be described by two state variables that change in time: thermal boundary. layer and melted length or alternatively electrode gap. The reduced order model compares favorably, to an accurate finite difference model as well as melting data acquired for Ti-6Al-4V. It will be shown how this model can be used to obtain dynamic closed loop melt rate control while simultaneously controlling electrode cap. This controller and estimator were tested on a laboratory furnace at Timet.