Model-free Multi-Objective Iterative Learning Control for Selective Laser Melting

Abstract

This paper presents a model-free iterative learning control (ILC) scheme for multi-objective temperature control in Selective Laser Melting (SLM). The goal is to ensure that while temperature distribution in the selected region is sufficient to cause melting and fusion, the meltpool is not overheated. We first formulate this goal as an optimization problem with the power profile as the decision variable and the cost function to be minimized being the sum of two unidirectional error terms (for upper and lower temperature bounds, respectively). Given the difficulty in analytically modeling the temperature-laser power relationship in SLM for gradient computations as in standard ILC, we solve the minimization problem using a model-free ILC scheme. In this scheme, the control input that minimizes the cost function is learned through a data-driven gradient descent update that uses the process itself to compute the gradient direction. The gradient descent algorithm proposed here accounts for the time-varying behavior of the SLM thermal dynamics because of the scan path. This is accomplished by feeding the temperature output error, reversed in time, through the process itself with a reversed scan path direction. For validation, this multi-objective gradient-based ILC algorithm is implemented on a three-phase high-fidelity simulation of the SLM process. The results demonstrate the algorithm’s ability to drive the temperature distribution to within a prescribed range in scenarios where standard (single-objective constant gain) ILC fails.