Data-driven reference shaping for optimal fused filament fabrication

This paper presents a practical methodology for enhancing deposited strand uniformity of fused filament fabrication (FFF) machines, with minimal need for hardware modifications. The approach relies on model-based shaping of the filament feed rate to compensate for strand width variation (under-extrusion and over-extrusion) caused by changes of programmed printing speed. By utilizing sensor data from trial deposition tests, a Multi Input Single Output (MISO) linear dynamic model is identified. Based on this model, a constrained convex optimization problem is formulated to compute optimal filament feed rate profiles that minimize deviations from the desired strand width, incorporating a regularization term to promote smooth solutions. The methodology utilizes well-established tools of linear system identification and quadratic optimization. Its simplicity, generality, and minimal need for hardware modifications make it easily applicable to a wide range of FFF machines, with potential for easy automation and periodic updates. The only additional requirement is the availability of a sensor capable of offline measurement of the strand width after deposition tests. The method, validated through simulations and laboratory experiments, significantly outperforms conventional approaches that compute filament feed rate as simply proportional to the programmed print speed. Experimental results demonstrate that, despite the feedforward nature of the scheme, a substantial reduction in strand width error can be achieved by reshaping the filament feed rate profile, whilst leaving the printing speed unmodified. Specifically, it is observed that the normalized Root Means Square Error (RMSE) of the strand width is highly affected by the smoothing parameter /i, designed to smoothen the reshaped filament feed rate. The normalized error decreases from 100% (in the case of the current non-optimized reference) to 55% for /i = 1, 49% for /i = 10 (the best performance), and 65% for /i = 100 when shaped commands are applied. One limitation of the method is that significant changes in the FFF machine setup require the model to be re-identified.