Stability analysis and controller design for polymer sheet extrusion

Abstract

Dimensional stability of thin extruded polymer sheets is analyzed as a function of draw ratio. It is assumed that the sheet keeps its rectangular cross section between the flat die and the chill roll and the flow is Newtonian. Through the analysis of linearized equations, it is shown that the sheet becomes unstable beyond a critical draw ratio as observed in experimental studies. The nonlinear model of sheet dynamics is then analyzed using the singular perturbation analysis to confirm the existence of a stable limit cycle. A feedback controller is designed to stabilize the sheet dynamics for draw ratios greater than the critical draw ratio. © 2000 Sage Publications, Inc.