On Problems of Time Delay and Sensitivity when Mathematically Modeling the Thermal Operation of a Burning Kiln for the Production of Artificial Graphite

摘要

The effect of the relation between the thermal delay of a container (with a half-finished product and a backfill) and the sensitivity of a control system to the temperature field of the half-finished product for the production of artificial graphite is investigated by mathematical modeling. The effect of the design time step (At) on the results of mathematical modeling is also studied. The modeling results for the delayless control system of a burning kiln are demonstrated to be practically independent of Ax. In the case of the finite sensitivity of the control system, temperature fluctuations, which are generated by the system, penetrate deeply into the container as the thermal delay of the container (thickness of the backfill layer) decreases. However, it is possible to reveal that computationally at small Ax because large time steps give a smoothed pattern with monotonic tendencies corresponding to actuality only at a significant thickness of the backfill layer. It is also determined that the convergence rate of the iteration algorithm in the computation is high enough when Ax is substantially greater or less than the time of modeled periodic processes. If these quantities are of one order of magnitude, the algorithm may be cyclic or the required number of iterations may rise by several orders of magnitude.