Research Of Applying UKF In Crystal Diameter Control Of Czochralski Process

Unscented Transformation (UT) is an algorithm based on statistical principles by precisely estimating the posterior probability distribution of the non-linear process, which was presented for solving the problem of nonlinear system. Unscented Kalman filter (UKF), which is a combination of UT and Kalman filter, can be widely applied in signal processing, state estimation and filtering in non-linear systems, and performs pretty well. This dissertation deeply analyzed a complex Czochralski crystal growth process, aiming at improving the control precision of monocrystal silicon diameter.In control engineering, state feedback control performs better than output feedback control. As for the controlled object with strong nonlinearity, UKF based on UT has a better performance in state estimation than traditional Extended Kalman filter (EKF), when its state variables are strongly random. This dissertation designed and implement a UKF in crystal diameter control of Czochralski process to estimate meniscus height in the triple point, which can highly increase control precision if considered as a feedback state variable, and also play a positive role in adjusting the thermal field temperature. Although there is a very complicated relationship between varying variables and the crystal diameter in the dynamic model of crystallization, and also heavy measurement noise, UKF which was designed and implemented in this dissertation figured out all these problems. The result of experiment in last chapter shows that UKF performs better than EKF in nonlinear systems, and some derivative UKF forms were also introduced in this dissertation. In addition, through comparison estimation results of different UKF forms, the principle of the sigma points’selection are presented.