Abstract: The optimal control problem for the viscoelastic melt
spinning process has not been reported yet in the literature. In this
study, an optimal control problem for a mathematical model of a
viscoelastic melt spinning process is considered. Maxwell-Oldroyd
model is used to describe the rheology of the polymeric material, the
fiber is made of. The extrusion velocity of the polymer at the spinneret
as well as the velocity and the temperature of the quench air and the
fiber length serve as control variables. A constrained optimization
problem is derived and the first–order optimality system is set up
to obtain the adjoint equations. Numerical solutions are carried out
using a steepest descent algorithm. A computer program in MATLAB
is developed for simulations.