Flatness Control in Strip Rolling via SVD Parameterization
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Solution Overview
Problem
Traditional flatness control methods for multi-actuator cold rolling mills are sensitive to model errors, lead to instability and unnecessary actuator movements, and result in non-independent actuator control, causing operators to switch to manual mode due to decoupling issues and actuator limit violations.
Innovation Solution
The method employs Singular Value Decomposition (SVD) of the mill matrix to parameterize the flatness error profile, using a linear multivariable controller to calculate optimized actuator set-points while ensuring no actuator constraints are violated, thereby achieving robust and stable control.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If traditional flatness control methods are used with multiple actuators, then flatness control capability is improved, but system stability deteriorates due to model errors and actuator limit violations
Solution Approach 1:
The patent transforms the control parameters from direct actuator commands to singular value decomposed components. By changing the parameter representation and using the mill matrix's singular value decomposition, the control system achieves stability while maintaining flatness control capability. The transformation matrix based on singular values decouples the control channels and prevents actuator limit violations.
2Ease of operation
If traditional control methods are used, then actuator control is attempted, but actuator independence deteriorates leading to non-independent control and manual mode switching
Solution Approach 1:
The patent segments the control problem by decomposing the mill matrix into singular value components. This segmentation creates independent control channels through the transformation matrix, allowing each control loop to operate independently without interfering with other actuators. The singular value decomposition naturally separates the coupled actuator controls into independent modes.
3Manufacturing precision
If complex evaluation processes are used for multi-actuator control, then flatness control performance is improved, but calculation complexity increases
Solution Approach 1:
The patent performs preliminary action by pre-calculating and storing the mill matrix and its singular value decomposition. The transformation matrix is computed in advance based on the mill model, so that during actual control operation, only simple matrix multiplications are needed. This preliminary preparation reduces real-time calculation complexity while maintaining high control performance.
Data Source
AI summary
A method and a device for optimization of flatness control in the rolling of a strip using any number of mill stands and actuators. A mill model is used represented by a mill matrix that includes information of the flatness effect of each actuator. Each actuator's flatness effect is translated into a coordinate system having a dimension less than or equal to the number of actuators used. The actual flatness values are monitoring/sampling across the strip. A vector of the flatness error/deviation is computed as the difference between the monitored/sampled strip flatness and a reference flatness vector. The flatness error is converted into a smaller parameterized flatness error vector. A dynamic controller is used to calculate optimized actuator set-points in order to minimize the parameterized flatness error, thereby achieving the desired strip flatness. Also a system for optimization of flatness control in rolling a strip.