Identification And Modal Control Of Id Thermal Field Model Of CZ Process

It is important targets that to ensures low defect rates,impurities and dis-locations in Czochralski(CZ)monocrystalline silicon industry.However,Lumped parameter solutions can no longer satisfy the spatial and temporal variations of distributed parameters characteristics in the process of single crystal control.Therefore,it is more appropriate to use partial differential equations or integral equations with distributed parameter characteristics to describe the variation of physical quantities in complex and large-scale controlled objects.Since the partial differential equation is not applicable to the three-dimensional control system de-scribing the Czochralski single crystal process,this paper finds a one-dimensional thermal path from the crystallization point to the outside in the three-dimensional temperature field on the axial section,which represents the temperature distri-bution in the main working area,this will make the complex three-dimensional control system into a simple one dimensional control system.At the same time,the main mode of the input and output function in the time and space are captured by using KL-SVD method,and the kernel function of the system is identified by the singular value decomposition method,which provides a controlled model for the design of feedback control system.In order to achieve accurate control of the system,the input and output relationship of the multi input and output system is carefully analyzed in this pa-per,and the main variables affecting the temperature gradient in the crystalline domain are determined.In the fourth chapter,a method of diameter control as a subsystem for determining the temperature of crystalline domain is proposed,which indirectly realizes the temperature control of crystallization field.Because the number of sensors in the control process is very limited,it is difficult to ob-tain the precise state of each point.According to the law of heat conduction,a static one dimensional temperature curve is fitted with the set values on several discrete points,and the feedforward and feedback control methods are introduced to reduce the error between the actual value and the set value.Finally,the discrete PI controller is designed to adjust the control parameters,and the actual tem-perature curves reflected by the measured values are controlled to the standard temperature curve and the error between them is in a reasonable range.According to the analysis of the above recognition theory and control scheme,the empirical function obtained by the measured data is used to identify the kernel function of the reduced order one-dimensional control system in a period of time on the MATLAB experimental simulation platform,and the system is successfully used to control the system in the time domain.The simulation results show that the method of modal control can maintain the controlled variables well within the expected error.Moreover,the reduced order one dimensional system has the characteristics of short adjustment time and stable control results,which has a good effect on the control of one dimensional temperature curve.It shows that the one dimensional system simplification method combined with the diameter control subsystem and the modal reduction based on KL-SVD have good performance in the simulation control of the growth process of monocrystalline silicon.