Estimating optimal open-loop controls for industrial batch heating plant

• Published in: Proceedings of the Institution of Mechanical Engineers. Part C, Journal of mechanical engineering science Vol. 214; no. 8; pp. 1079 - 1097
• Main Authors: Ford, J, Griffiths, A J, Brandon, J A
• Format: Journal Article
• Language: English
• Published: London, England SAGE Publications 01.01.2000; Mechanical Engineering Publications; SAGE PUBLICATIONS, INC
• Subjects: Algorithms; Applied sciences; Boundary value problems; Computer science; control theory; systems; Control theory. Systems; Devices using thermal energy; Distributed parameter control systems; Energy; Energy. Thermal use of fuels; Exact sciences and technology; Fuel economy; Furnaces; Gas heating; Mathematical models; Maximum principle; Modelling and identification; Optimal control systems; Process control. Computer integrated manufacturing; distributed parameters; Pontryagin; relaxation; shooting; optimal control; furnace modelling; active state constraints; two-point boundary value problem; steel reheating; fuel minimization; Shooting; Process control; Pontryagin principle; Fuel consumption; Metallurgical furnace; Modeling; Band matrix; Boundary value problem; Diagonal matrix; Two point boundary value problem; Optimal control; Batch process; Open loop; Relaxation method; Distributed parameter system
• ISSN: 0954-4062; 2041-2983
• DOI: 10.1243/0954406001523533

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.