(587g) Model Predictive Control and Materials Property Estimation of an Industrial Heat Treating Furnace
The system under consideration is a heat treating furnace, currently in operation at an industrial partner. During heat treatment (austenitization), the metal parts are heated to a very high temperature in an inert atmosphere (i.e., without oxidizing the surface), then rapidly quenched in an oil bath where desired mechanical properties such as ductility, hardness and shear strength are induced. The furnace is operated in a continuous manner. The metal parts travel on a conveyor belt through the furnace, which is heated by ceiling and floor radiant tube burners. For control purposes, the furnace is divided into four temperature zones. Part temperatures, especially the inside part regions, cannot be sensed and controlled directly. Hence, they are indirectly controlled by controlling the zone temperatures.
We develop a two-dimensional physics-based model of the furnace in order to balance computational efficiency with the ability to capture long range radiation interactions. The model provides the exit temperature profiles of the treated steel parts and the energy usage of the furnace by solving conservation equations. As a base case, we adopt a simple linear control strategy, wherein a PI controller controls the temperature of each zones by manipulating the fuel flow rate to the burners of the respective zone. We investigate the energy consumption and part temperature distributions for a batch of forty parts, under the heuristic zone temperature set points suggested by the operators of the plant.
Then, the objective of model predictive control scheme is to control the minimum part temperature at furnace exit by adjusting the zone temperature set points of the PI controller. For this purpose, we develop simplified step response models that capture the dynamics of the system. These models are then used for anticipating future events and optimal control action is taken at each time step based on the simplified model predictions and the actual measured values from the detailed 2D model. Preliminary results show theoretical energy savings of 6.3%, when comparing the MPC operation mode with the aforementioned heuristic case.
Furthermore, we study the metallurgical property changes as a function of temperature and rate of heating. This is essential since changes in operating conditions of upstream heat treating can have ramifications downstream in machining. We model the extent of material transformation from Ferrite to Austenite using the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation  and ensure that there are no untransformed portions of the parts when operating under model predictive control.
 V Viswanathan, R Davies, and J Holbery. Opportunity analysis for recov- ering energy from industrial waste heat and emissions. Pacific Northwest National Laboratory, 2005.
 A Thekdi. Energy efficiency improvement opportunities in process heating for the forging industry. E3M, 2010.
 D Seborg, TF Edgar, and D Mellichamp. Process dynamics & control. John Wiley & Sons, 2004.
 Melvin Avrami. Kinetics of phase change. ii transformation-time relations for random distribution of nuclei. The Journal of Chemical Physics, 8(2):212â?? 224, 1940.