Abstract

This master thesis addresses model-based state estimation and radius regulation for semiconductor crystals grown with the Czochralski process. These crystals are cut into thin slices (wafers), used for the fabrication of electronic micro devices. In industry currently radius control is achieved with PID controllers, not very appropriate for the time-variant, nonlinear Czochralski process. Thus more advanced regulation systems are required; for this purpose a nonlinear state space model, describing the hydro mechanical part of the process, was derived. Based on this model a linear-quadratic regulator (LQR) was designed. Furthermore for the estimation of the hidden state variables two statistical algorithms were compared, namely the Extended Kalman Filter and the Unscented Kalman Filter. These algorithms were found to yield equal statistical performance; furthermore the LQR approach works fine in simulation. So far no experimental closed loop tests were made