Model-based trajectory planning, optimization, and open-loop control of a continuous slab reheating furnace

A temperature control method is developed for reheating steel slabs in an industrial furnace. The work was motivated by the need for mathematically simple furnace control schemes that feature accuracy, robustness, applicability to online control, and capabilities of non-steady-state operating scenarios, where the temperature goals and other properties of the slabs may vary considerably. The proposed hierarchical control concept computes desired heat inputs for each individual slab based on a discrete-time nonlinear model. Then, a quadratic program is solved to plan reference trajectories of furnace temperatures which optimally realize the desired heat inputs into the slabs. The iterative algorithm accounts for constraints on system inputs as well as states and may be used for open-loop control or as a feedforward branch in two-degrees-of-freedom control structures. The feasibility and the limitations of the approach are demonstrated by means of an example problem.