KL-SVD Based One-Dimensional Modal Control Combining with Diameter Control Subsystem as State Estimator in Czochralski Process

Czochralski(CZ) monocrystalline silicon industrial control processes are nonlinear distribution parameter systems(DPS). It is extraordinary difficult to solve this problem because of complex spatio-temporal coupling and infinitedimensional properties. In this paper, a one-dimensional(1D) thermal path from axial crystallization point to outside is chosen on the axisymmetric plane of three dimensional(3D) temperature field, which indicates thermo flow in the main working region. K-L decomposition and singular value decomposition( SVD) means are popular used to capture dominant modes of spatio-temporal for reduced order one-dimensional model and identify an unknown distributed parameter system, which provides convenient basis to design feedback controller. However, due to working conditions, the number of sensors are limited, it is difficult to obtain more state judgment error, so that diameter control subsystem as state estimator to judge whether temperature profile is reasonable. This method has better accuracy than lumped parameter system(LPS).