Estimating optimal open-loop controls for industrial batch heating plant

Abstract

A mathematical model of a gas-fired heater is used to estimate fuel input trajectories that minimize fuel consumption. The model has distributed parameters and an active surface temperature constraint. Optimal control theory is used to establish a two-point boundary value problem that is solved by a combination of shooting and relaxation. The shooting algorithm is an extension of the algorithm previously reported by the same authors [3]. The relaxation algorithm is based on a method for inverting a sparse band diagonal matrix. The calculations confirm that as the time available to warm a batch plant increases so the amount of fuel necessary for the task decreases.