Distributed Temperature Control in Laser-Based Manufacturing

Temperature control is essential for regulating material properties in laser-based manufacturing.  Motion and power of the scanning laser affect local temperature evolution, which in turn determines the a posteriori microstructure. This paper addresses the problem of adjusting the laser speed and power to achieve the desired values of key process parameters: cooling rate and melt pool size. The dynamics of a scanning laser system is modeled by a one-dimensional heat conduction equation, with laser power as the heat input and heat dissipation to the ambient. Since the model is one dimensional, length and size are essentially the same. We pose the problem as a regulation problem in the (moving) laser frame.  The first step is to obtain the steady-state temperature distribution and the corresponding input based on the desired cooling rate and melt pool size.  The controller adjusts the input around the steady state feedforward based on the deviation of the measured temperature field from the steady-state distribution.  We show that with suitably defined outputs, the system is strictly passive from the laser motion and power. To avoid over-reliance on the model, the steady-state laser speed and power are adaptively updated, resulting in an integral-like update law for the feedforward.  Moreover, the heat transfer coefficient to the ambient may be uncertain, and can also be adaptively updated.  The final form of the control law combines passive error temperature field feedback with adaptive feedforward and parameter estimation.  The closed-loop asymptotical stability is shown using the Lyapunov arguments and the controller performance is demonstrated in a simulation.