Dynamic Optimization of a Slab Reheating Furnace With Consistent Approximation of Control Variables

A dynamic optimization method is developed for temperature control of steel slabs in a continuous reheating furnace. The work was stimulated by the need for furnace control concepts that are computationally undemanding, robust, accurate, and capable of non-steady-state operating scenarios, where the properties and the temperature goals of slabs may vary significantly. The proposed hierarchical control structure is based on a continuous-time switched nonlinear model and uses the furnace zone temperatures as intermediate control variables. Consistent approximation is applied to obtain a parametric optimization problem that can be efficiently solved with the quasi-Newton method. Constraints on system states and control variables are considered by penalty terms in the cost function and saturation functions, respectively. The optimization method plans temperature trajectories for both the furnace and the slabs, which may be useful for open-loop control and feedforward branches of two-degrees-of-freedom control structures. The capabilities of the method are demonstrated in an example problem.