抄録
Due to the nonlinearity of thermal constants such as specific heat, difference equations are used mostly to predict the heating temperature of slabs in the furnace. The difference equation approach entails time sharing, and thus vast amount of recursive computation is required to perform the calculation of heating temperature of slabs by means of difference equation. As a result, the difference equation approach has a defect in long computation time. This drawback becomes a great obstacle when the difference equation approach is used in the application of on-line predictive control of heating temperature of slabs in the furnace.
Instead of the difference equation approach, the authors proposed a fast algorithm for the prediction calculation of heating temperature. The algorithm uses analytical solution but is recursive in nature and takes into account the nonlinearity of thermal constants.
Analytical solution is represented by a sum of infinite series. For the practical use of predictive computation, the infinite series must be approximated by a finite series. There is a trade-off between the speed of computation and the accuracy of result. To retain the fastness of computation, dimension of the finite series must be low as possible. For the accuracy, higher dimension is desired. As such, the dimension of the approximate finite series must be of minimum, while guaranteeing the required accuracy.
In this paper, a simple but useful relationship is derived which relates the finite series approximation of the heat conduction equation and its computational accuracy. A criterion on the dimensional reduction is also proposed. The criterion proposed is applied to the prediction calculation of heating temperature of a billet in a continuous furnace. Calculated temperature is compared to the measured temperature of the billet. It is assured that the fast calculation algorithm and the criterion on order reduction proposed in this paper are of practical use.
