Multi-Input Iterative Learning Control for Laser Powder Bed Fusion

Abstract This paper presents an optimization-based iterative learning control (ILC) scheme for multi-input thermal control in LPBF. The control objective is to maintain the maximum and minimum surface temperatures in the melt pool area during the LPBF process within a prescribed range by manipulating the input variables. This objective is formulated as an optimization problem where the upper bound and lower bound temperature errors are to be minimized over the input signals subject to the LPBF system dynamics. To solve this optimization problem, we utilize an ILC algorithm in which the optimal input signals are learned by an adjoint-based gradient descent update. That is, the gradient directions are obtained by feeding the temperature error signal back into the system. Because the gradients are obtained in a data-driven fashion, the algorithm is agnostic to the LPBF system or model of the system. Moreover, the learning algorithm is significantly more computationally efficient than reinforcement learning (RL) or standard numerical optimization techniques which enables us tractably explore control of multiple inputs. Thus, we examine simultaneous control of multiple input variables, namely, the laser power and scan velocity using a simulator of a powder bed layer. Our results show that the optimization-based ILC scheme requires two orders of magnitude less iterations over the system simulator than existing RL control methods demand. Moreover, we find that multiple input control yields a marginal improvement over single-input control with either the power or velocity variable. However, the multi-input control framework produces signals that are less aggressive and are thus more suitable when there are significant constraints on the controller.