Low-Dimensional Non-Linear Luenberger Observer for Thermal Distribution of Wafer in Rapid Thermal Processing Process

A low-dimensional non-linear observer is developed in this paper for the estimation of the thermal distribution in a rapid thermal processing (RTP) process. Based on the reduced model obtained from Galerkin's method, a low-dimensional non-linear Luenberger observer is designed to re-construct the thermal distribution from the output data of the point temperature sensors. Test results in a RTP system show fast convergence speed and small estimated errors of the proposed observer.