2015/05/23 by Mamadou Diagne, Diagne, Mamadou, Nikolaos Bekiaris‐Liberis +3
Chemical Engineering · Engineering · #3D Printing in Biomedical Research #Additive Manufacturing and 3D Printing Technologies #FOS: Mathematics #Injection Molding Process and Properties #Optimization and Control (math.OC) #Rheology and Fluid Dynamics Studies
paper · pdf · doi:10.48550/arxiv.1505.06375
openalex publication_date 2015/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A delay-compensated Bang-Bang control design methodology for the control of\nthe nozzle output flow rate of screw-extruder-based 3D printing processes is\ndeveloped. The presented application has a great potential to move beyond the\nmost commonly used processes such as Fused Deposition Modeling (FDM) and\nSyringe Based Extrusion (SBE), improving the build speed. A geometrical\ndecomposition of the screw extruder in a partially and a fully filled regions\n(PFZ and FFZ) allows to describe the material convection in the extruder\nchamber by a 1D hyperbolic Partial Differential Equation (PDE) coupled with an\nOrdinary Differential Equation (ODE). After solving the hyperbolic PDE by the\nMethod of Characteristics (MC), the coupled PDE-ODE's system is transformed\ninto a nonlinear state-dependent input delay system. The aforementioned delay\nsystem is extended to the nonisothermal case with the consideration of periodic\nfluctuations acting on the material's convection speed, which represent the\neffect of viscosity variations due to temperature changes in the extruder\nchamber, resulting to a nonlinear system with an input delay that\nsimultaneously depends on the state and the time variable. Global Exponential\nStability (GES) of the nonlinear delay-free plant is established under a\npiecewise exponential feedback controller that is designed. By combining the\nnominal, piecewise exponential feedback controller with nonlinear predictor\nfeedback the compensation of the time- and state-dependent input delay of the\nextruder model is achieved. Global Asymptotic Stability (GAS) of the\nclosed-loop system under the Bang-Bang predictor feedback control law is\nestablished when certain conditions, which are easy to verify, related to the\nextruder design and the material properties, as well as to the magnitude and\nfrequency of the materials transport speed variations, are satisfied.\n