State-dependent input delay-compensated Bang-Bang control: Application to 3D printing based on screw-extruder

In this paper a delay-compensated Bang-Bang control law for the stabilization of the nozzle output flow rate of an isothermal screw-extruder-based 3D printing process is designed. The presented application has a great potential to move beyond the common 3D printing processes such as Fused Deposition Modeling (FDM) and Syringe Based Extrusion (SBE), improving the build speed and the print precision. A geometrical decomposition of the screw extruder in a partially and a fully filled regions (PFZ and FFZ) allows to describe the material convection in the extruder chamber by a 1D hyperbolic Partial Differential Equation (PDE) coupled with an Ordinary Differential Equation (ODE). After solving the hypercolic PDE by the Method of Characteristics (MC), the coupled PDE-ODE system is transformed into a nonlinear state-dependent input delay system. The Global Exponential Stability (GES) of the nonlinear free-delay plant is established with a piecewise exponential feedback control law. Combining the “Bang-Bang”-like controller with a nonlinear predictor feedback control law, the Global Asymptotic Stability (GAS) of the plant with respect to any setpoint in the physical domain is ensured.