Optimal control of a nonlinear induction heating system using a proper orthogonal decomposition based reduced order model

This paper considers the problem of obtaining control inputs for induction heating processes involving nonlinearities and nontrivial geometries. The considered system falls within the much broader class of multiphysics or coupled, distributed parameter systems that are well known for the challenges they pose towards modeling, simulation and control. The approach is based on the versatile finite element method (FEM) widely popular in industry for modeling of such systems. The large dynamic model obtained through FEM is reduced using proper orthogonal decomposition (POD) technique, applicable to nonlinear systems, while preserving the input-output characteristics almost exactly. In the present work, using the reduced model, an optimal control input current for the induction heating system is obtained, for transferring the temperature profile over an axi-symmetric work piece from any initial temperature profile to any other desired temperature profile. The reduced model enables application and numerical implementation of established optimal control techniques based on Hamilton-Jacobi-Bellman theory for the system. Further, although the controller is developed using the reduced model, it is shown to perform perfectly well when used with the original unreduced model as well. Results of the numerical implementation are presented to evaluate the overall proposed approach. (C) 2012 Elsevier Ltd. All rights reserved.