Modelling the dynamics and control design for Czochralski, Liquid Encapsulated Czochralski and Floating Zone processes

Here we consider the problem of mathematical modelling of crystallization processes from the melt by Czochralski, Liquid Encapsulated Czochralski and Floating Zone methods based on linearization of three conservation laws: the heat, mass and the growth angle constancy is reviewed in depth. Special attention is given to the problem of the dynamical analysis of these processes in open and closed states and to the synthesis of the digital control of crystal diameter for the weight technique. The main problems discussed involve the determination of the parameters required for calculating such control systems together with the use of the multichannel parametric PID regulator involving the state variable observer concept. In addition briefly considered are the problems of digital filtering of the measurement noise based on multidimentional Kalman filters and the determination of mechanical stability limits for static menisci.