Constrained trajectory planning and actuator design for electromagnetic heating systems

A trajectory planning approach for electromagnetic heating systems is presented capable to optimize the electrical excitation and spatial configuration of the corresponding actuator (e.  g. inductor or electrode). In order to accurately incorporate the electromagnetic and thermal phenomena, a PDE constrained optimization problem is formulated. The optimality conditions are derived in the function space of the original problem formulation following a first optimize then discretize approach to ensure that not only the system dynamics but rather the whole optimality system can be solved by FEM-based simulation software. The major advantage lies in coping with different types of electromagnetic heating systems. Numerical results illustrate the applicability and accuracy of the trajectory planning.