DMSO concentration estimation from a diffusion model of PAN-based carbon fibers

The on-line estimation of the DMSO (Dimethyl Sulphoxide) concentration of PAN-based carbon fibers is of significance to monitoring the quality of carbon fibers during production. In wet-spinning process, large amount of solvent (DMSO) diffuses from the interior of the coagulating fiber into the bath, and large amount of water diffuses in the reverse direction. This process can be modeled by a diffusion partial differential equation (PDE). The diffusion happens uniformly in all directions of the cross section in a cylindrical fiber, so the diffusion model in disk can be simplified to a 1-D PDE along the radial direction. An observer is developed by following backstepping method, which only requires to measure the gradient of the boundary concentration. We prove the designed observer can converge exponentially to the actual system in the norms of L
²
and H
¹
by the Lyapunov method. The observer error convergence is also illustrated by numerical simulation results.