Optimal control of an aluminum casting furnace: Part II. Fuel optimization

In this second of a two-article series, the simplified model of the aluminum casting furnace presented in Part I is used to solve a fuel-optimal control problem. Basically a Lagrange problem with equality and inequality constraints, it is formulated through variational calculus into a two-point boundary-value problem with known initial and final conditions and specified final time. It yields an optimal solution with a time-vary ing fuel flow rate that gives 10.9 pct fuel economy over the conventional nonoptimal constant fuel flow rate. This shows that variational calculus can be used to solve optimal control problems for the aluminum casting furnace and for other similar thermal systems commonly encountered in the metallurgical industry.