Modeling and adaptive open loop control of tunnel kilns

The thermal behaviour of countercurrent tunnel kilns used for instance in the ceramics industry for firing bricks or roofing tiles, can be modelled by a set of partial differential equations more or less complex according to the number of simplification asumptions. A sophisticated model is better for a system analysis but a simplified model allows a less difficult study of the automatic control of the kiln. This is why we first established a model giving temperature profiles through a kiln, knowing the distribution of control actions, and considering a small number of simplification asumptions. Then, we simplified this model by using several techniques such as linearization, functionnal approximation, singular perturbations. In order to solve a temperature profile regulation problem, we have determined an adaptive open loop control, derived from the application of the maximum principle. It consists of computing periodically the control variables from periodical measurements of the kiln temperature profile.