Heat treatment control by polytope methods

This article addresses the problem of thermal quality regulation in a variety of manufacturing processes involving heat treating of a part of 2D geometry by a localized, sequentially moving heat source, and formulates it as a distributed-parameter, feedback control problem of the developed temperature distribution. A numerical simulation of thermal processing is developed and validated experimentally on a plasma-arc system, with infrared temperature measurement on the part surface. The design of a thermal regulator is then based on minimization of the deviation of the measured temperature field from a desired thermal distribution. A robust and efficient constrained optimization algorithm based on the concept of polytopes is employed to define the torch trajectory and heat input distribution. This distributed-parameter control strategy is tested in closed-loop operation both computationally and in the laboratory, during heat treatment of steel plates.