Optimal Control of Steel Slab Heating in a Gas Fired Furnace

The problem of optimal slab heating in a gas-fired furnace is formulated and solved by optimal control theory. A performance measure comprising the cost of fuel and of metal lost to scale during the heating period is minimized using a second-order gradient method, while the numerical integration of both the state and costate equations are carried out by a second-order Runge-Kutta method. A terminal constraint on the center plane temperature of the slab is handled using a penalty function approach. Simulation results for different heating periods indicate that economic incentives exist for more efficient furnace operation when compared with conventional inverted-L heating profiles.