Thermodynamic Modeling and Control of Screw Extruder for 3D Printing

Abstract

This paper proposes a thermodynamic modeling and a control design of screw extrusion-based 3D printing of thermoplastic materials. The model describes the time evolution of the temperature profile of an extruded polymer by means of a partial differential equation (PDE) defined on the time-varying domain. The time evolution of the spatial domain is governed by an ordinary differential equation (ODE) that reflects the dynamics of the position of the phase change interface between polymer granules and molten polymer. Steady-state profile of the distributed temperature along the extruder is obtained when the desired setpoint for the interface position is prescribed. We develop a PDE backstepping state-feedback control law to stabilize the temperature dynamics at the spatially distributed steady-state considering a cooling mechanism at the boundary inlet as an actuator. For some given screw speeds that correspond to slow and fast operating modes, numerical simulations are conducted to prove the performance of the proposed controller. The convergence of the interface position to the desired setpoint is achieved under physically reasonable temperature profiles.