Nonlinear State Predictor for Czochralski Crystal Diameter Control
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Solution Overview
Problem
Existing control methods for manufacturing single crystal ingots by the Czochralski method face challenges in accurately controlling the diameter and crystallinity, especially during the formation of large-diameter ingots at high speeds, due to unsteadiness and nonlinearity between heater temperature and crystal diameter.
Innovation Solution
A control system that incorporates a nonlinear state predictor and sliding mode control, with time-variant system parameters, to predict future state variables and constrain them within a sliding mode, ensuring accurate control of the ingot diameter and crystallinity by adjusting heater temperature and pulling speed.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If conventional control methods are used for large-diameter single crystal ingot production at high speeds, then productivity is improved, but manufacturing precision deteriorates due to unsteadiness and nonlinearity between heater temperature and crystal diameter
Solution Approach 1:
The patent applies dynamic control by using a nonlinear state predictor that adapts to time-variant system characteristics. The control system continuously updates predictions based on current system state and historical data, allowing the controller to adjust heater temperature dynamically to compensate for changing thermal characteristics during high-speed pulling, thereby maintaining diameter control accuracy despite increased productivity
Solution Approach 2:
The patent changes control parameters by using time-variant system parameters in the nonlinear state predictor. The predictor models the relationship between heater temperature and crystal diameter using parameters that vary over time, capturing the unsteadiness and nonlinearity of the thermal system. This allows accurate prediction of future diameter values and enables precise control even at high pulling speeds
2Device complexity
If conventional control methods are used, then device complexity is reduced, but manufacturing precision deteriorates due to inability to handle time variant system with dead time
Solution Approach 1:
The patent applies preliminary action by using a nonlinear state predictor to forecast future crystal diameter values before they actually occur. The predictor uses current heater temperature, past diameter measurements, and time-variant system parameters to predict the diameter at future time points, accounting for the dead time in the thermal system. This advance prediction enables the controller to take preemptive action to maintain diameter control accuracy
Solution Approach 2:
The patent implements feedback control by comparing predicted future diameter values with target diameter values and using the deviation to adjust heater temperature. The nonlinear state predictor continuously monitors system state and provides feedback signals that drive the control algorithm to correct any diameter deviations, thereby improving manufacturing precision through closed-loop control
3Ease of operation
If existing control methods are used for shoulder portion formation, then ease of operation is maintained, but manufacturing precision deteriorates due to unsteadiness in temperature-diameter relationship
Solution Approach 1:
The patent applies self-service by implementing an autonomous control system that automatically adapts to changing thermal characteristics during shoulder portion formation. The nonlinear state predictor continuously updates its internal model using time-variant parameters and historical data, enabling the system to self-adjust control actions without manual intervention. This maintains ease of operation while improving manufacturing precision through automatic compensation for thermal unsteadiness
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enhances the controllability and crystal product quality of both the shoulder and straight body portions of the single crystal ingot, maintaining temperature gradients and reducing crystal defects.
Implementation Method 1
applying heat to the melt with a heater
Implementation Method 2
applying heat to the melt with a heater
Implementation Method 3
pulling up a single crystal ingot from a melt
Implementation Method 4
pulling up a single crystal ingot from a melt
Data Source
AI summary
A device controls an object in a time variant system with a dead time such as a Czochralski method single crystal production device (CZ equipment). The dead time, time constant, and process gain value of an object (CZ equipment) are set. The process gain preset value has time variant characteristics. An output value and its first-order and second-order time differentiated values serve as the state variable. A nonlinear state predicting unit predicts a state variable value at a future time, based upon the current output value, dead time, time constant, and process gain preset value. A gain scheduled sliding mode control unit performs a gain scheduled sliding mode control operation based upon the state variable value at the future time, an output deviation at the future time, the time constant, and the set value of the process gain at the future time, to determine the manipulated variable of the object.