Time- and State-Dependent Input Delay-Compensated Bang-Bang Control of a Screw Extruder for 3D Printing

TL;DR

This paper develops a delay-compensated Bang-Bang control method for screw extruders in 3D printing, addressing nonlinear, state- and time-dependent delays to improve build speed and stability.

Contribution

It introduces a novel control approach that accounts for nonlinear, state- and time-dependent delays in screw extruder models, extending to nonisothermal conditions with viscosity variations.

Findings

Achieves global exponential stability of the delay-free plant.

Ensures global asymptotic stability under specific conditions.

Effectively compensates for nonlinear, state- and time-dependent input delays.

Abstract

A delay-compensated Bang-Bang control design methodology for the control of the nozzle output flow rate of screw-extruder-based 3D printing processes is developed. The presented application has a great potential to move beyond the most commonly used processes such as Fused Deposition Modeling (FDM) and Syringe Based Extrusion (SBE), improving the build speed. 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 hyperbolic PDE by the Method of Characteristics (MC), the coupled PDE-ODE's system is transformed into a nonlinear state-dependent input delay system. The aforementioned delay system is extended to the nonisothermal case with the consideration of periodic fluctuations acting on the material's convection speed, which represent the effect of viscosity variations due to temperature changes in the extruder chamber, resulting to a nonlinear system with an input delay that simultaneously depends on the state and the time variable. Global Exponential Stability (GES) of the nonlinear delay-free plant is established under a piecewise exponential feedback controller that is designed. By combining the nominal, piecewise exponential feedback controller with nonlinear predictor feedback the compensation of the time- and state-dependent input delay of the extruder model is achieved. Global Asymptotic Stability (GAS) of the closed-loop system under the Bang-Bang predictor feedback control law is established when certain conditions, which are easy to verify, related to the extruder design and the material properties, as well as to the magnitude and frequency of the materials transport speed variations, are satisfied.