Dynamic optimization of low-pressure carburizing furnaces

This paper presents the modelling and dynamic optimization of low pressure carburizing of steel. A cyclic hybrid model alternating two modes, i.e. the two stages of the process, boost and diffusion stages, is proposed. Each mode is characterized by a set of ordinary differential equations and its corresponding transition conditions and transition functions. The subsequent dynamic optimization problem is formulated and it aims to minimize the production of toxic compounds. The decision variables selected are the operating conditions, i.e. the lengths of boost and diffusion stages as well as the inlet flowrate of carburizing gas. Equality and inequality constraints are added on the state variables to ensure the quality of the treated steel parts. The resulting optimization problem of infinite dimension is transformed into a finite-dimension problem by means of the control vector parameterization approach and solved using a gradient-based method, i.e. sequential quadratic programming method. The solution algorithm is tested on an example and the optimal profiles yield satisfactory results.