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

We extend the recently developed delay-compensated “Bang-Bang” control design methodology for control of the nozzle output flow rate of isothermal screw-extruder-based 3D printing processes to the non-isothermal case, in which, the viscosity of the material that convects in the extruder chamber varies with time, resulting in periodic fluctuations of the material’s transport speed. We model the dynamics of the material convection in the extruder chamber with a nonlinear system with an input delay that simultaneously depends on the state and the time variable to account for the time variations of the transport speed. By combining a nominal, piecewise exponential feedback controller, which achieves global exponential stability in the nominal delay-free case, with nonlinear predictor feedback, the compensation of the time- and state-dependent input delay of the extruder model is achieved. Global asymptotic stability of the closed-loop system under the Bang-Bang predictor feedback 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 material’s transport speed variations, are satisfied. Simulations results are presented to illustrate the effectiveness of the proposed control design.