Modeling and feedforward control of filament advancement and retraction in material extrusion additive manufacturing

Material extrusion (MatEx) is the predominant of the available additive manufacturing (AM) methods. High -quality MatEx AM process demands accurate synchronization between motion control and extrusion control. However, the synchronization is challenging due to nonlinearities of the flow inside the nozzle. One of the most common synchronization defects is the inaccuracies at extrusion starts and stops. To address this, material retraction and advancement processes must be applied and controlled accurately. However, feedback extrusion control is limited by the difficulties in sensing the real-time extrusion rate, and existing feedforward (FF) extrusion control methods only rely on models that are developed and identified under continuous extrusion thus do not account for the retraction and advancement processes. Besides, another method that commercial printers commonly employ to address the extrusion problem is to find the optimal printing parameter set through sequential printing tests. However, this method does not generalize well for different materials and extruders, and it could be time and material-consuming. To address these problems in adopting FF control, this paper presents a control-oriented phenomenological model (P-model) that characterizes the extrusion dynamics during the retraction and advancement processes mathematically and a model-based FF control method to compensate the dynamics by altering both the motion and extrusion command. To validate the proposed model, a novel experimental setup (Setup 1) is proposed by retrofitting a MatEx standard printer with a servo motor on its material feeding gear to reveal the extrusion force during the process. The proposed model is validated on Setup 1 by demonstrating an accurate mathematical characterization of the extrusion dynamics and in the meantime revealing the consistency between the extrusion (external) and force (internal) behavior. Additionally, the practicality and effectiveness of the P-model and the P-model-based control method are demonstrated on an unmodified commercial printer (Setup 2). By using Setup 1, the proposed control method demonstrated up to 36.61% and 90.55% reduction in deposition error during advancement and retraction, respectively when compared to a standard FF extrusion control approach. Moreover, up to 39.34% and 35.26% reductions in deposition error during advancement and retractions are observed with the proposed controller when compared to using the standard extrusion profile with a well-tuned retraction and advancement parameters set from a commercial slicer software on Setup 2. Lastly, the potential of the proposed method for enhancing printing accuracy in real-world printing is demonstrated through a practical printing application.