Optimal Steady-State Temperature Field in an Experimental Annealing Furnace

The computation of an optimal steady-state operating point in an experimental annealing furnace is considered. In particular, the optimum spatial distribution of electric power supplied to IR-lamps is computed to ensure the temperature uniformity in the specimen fillet. A control-oriented reduced-order model of the steady-state 2D temperature distribution is derived and compared with the full-order model. Saturation functions are used to consider input constraints in a tailored optimization problem. The evaluation of the optimal control input is carried out with the full-order model. Uniqueness of the solution of the optimization problem is investigated numerically. The temperature field in the specimen fillet deviates less than 0.4% of the setpoint value if sufficient heating power is available.