Nonlinear State Estimation in the Czochralski Process

Abstract

The Czochralski process is the only process used commercially for production of monocrystalline silicon for semiconductor and solar cell applications. The process has traditionally been controlled using nested single-loop PID controllers. Advanced model-based control will require the ability to update the model used for control by using the measurements available on-line. This paper presents a study of non-linear state estimation based on a previously developed non-linear dynamical model. Data from actual plant operation are used in the study. Most application studies on state estimation only have on-line, noise corrupted/uncertain measurements available. In this case, the crystal radius as the main process variable, can be measured with much greater accuracy after the crystal is produced. It is therefore possible to assess estimator performance using this more accurate off-line measurement. The experimental results in this work confirm the simulation results from a preceding paper and show that the applied non-linear estimators perform well, with the unscented Kalman filter giving somewhat better results than the extended Kalman filter.