Modelling of the temperature field induced by laser surface irradiation in view of the feedback control theory

Real-time feedback control during laser surface treatment is required to improve stability, reproducibility, efficiency and productivity of the process. Model based controllers are known to outperform controllers based on process identification. In this paper the control problem for laser surface heating (laser transformation hardening) of metals is defined and an architecture for a model based control system is proposed. For the design of model based controllers an analytical dynamical process model, or transfer function, is required. Therefore, analytical expressions for the transient one-dimensional heat conduction, and the corresponding transfer function from laser power to temperature, are derived and analysed for two configurations: a semi-infinite sample and an infinite plate of finite thickness. Observability and controllability of the processes are discussed. For the case of two-dimensional heat conduction in a semi-infinite sample, a first approach to derive a transfer function from laser power and laser beam velocity to temperature is presented.