Sensitivity Analysis of the Laser Power Control System to Measurement Noise in SLS 3D Printers

TL;DR

The paper investigates how temperature measurement uncertainty affects a model-based laser power control system for SLS 3D printers, focusing on the distribution of steady-state tracking error $E_{ss}$ and laser power $P_t^m$. It compares traditional Monte Carlo simulation with an uncertainty-tracked Laplace architecture to quantify this impact, using Wasserstein distance and runtime as performance metrics. Key findings show that measurement uncertainty can shift the tracking error by up to ±$2.5$°C relative to the nominal, and that the Laplace method achieves similar accuracy to Monte Carlo with orders-of-magnitude faster runtimes (e.g., ~17× to ~71× faster, depending on uncertainty type). The results support using fast uncertainty quantification, like Laplace, for real-time sensitivity analysis and robust PID tuning in SLS laser power control.

Abstract

Uniform temperature distribution in Selective Laser Sintering (SLS) is essential for producing durable 3D prints. Achieving uniformity requires a laser power control system that minimises deviation of the printing temperatures from the target temperature. Because the estimate of the actual process temperature is an input to the laser power control, uncertainty in the estimate of the actual temperature can lead to fluctuations in laser power that affect the thermal performance of the SLS. This article investigates the sensitivity of a laser power control system to temperature measurement uncertainty. This article evaluates the effectiveness of two methods for quantifying the effect of input uncertainty on a SLS laser power control system: a recent innovation in uncertainty-tracked architecture and traditional Monte Carlo simulation. We show that recent advances in computer architecture for arithmatic on probability distributions make it possible for the first time, to perform control system uncertainty analysis with latencies under 30 ms, while achieving the same level of uncertainty analysis as Monte Carlo methods with latencies that are two orders of magnitude slower.

Figures (13)

• Figure 1: Illustration depicting the main components and signal flow of the SLS 3D printer. The printer moves the laser beam generated by a laser diode system across the printing bed to track the laser scanning path during the sintering process.
• Figure 2: Block diagram of a laser power control system in an SLS 3D printer. The controller generates the laser power $P_t^{m}$ to minimise the tracking error $E_t^{l}$, which is the difference between the desired temperature $T^{*}$ and the measured temperature $T_t^{l}$. The measured temperature is the sum of the output temperature $T_t^{m}$ and a random value of the measurement uncertainty. The primary objective of the controller is to ensure a consistent temperature distribution during the sintering. Temperature measured by the thermal camera can be affected by uncertainty arising from measurement noise and sensor quantization errors. This uncertainty is subsequently transmitted through the controller, leading to fluctuations in laser power. As a result, it can substantially alter the thermal distribution throughout the sintering process.
• Figure 3: A thermographic measurement using an FLIR camera captures radiation emitted by the object, as well as radiation reflected from the object's surface originating from the surroundings, and radiation passing through the atmosphere.
• Figure 4: Distribution of the calibrated temperature in the presence of uncertainty in the calibrated parameters. The uncertainty in the calibration parameters alone leads to an uncertainty in the calibrated temperature distributed between 400 K and 480 K.
• Figure 5: Experimental setup for measuring the temperatures of the printing bed during the sintering process. We use MLX90640 IR thermal camera with field of view 24$\times$32 integrated into an FPGA board.