Flatness Control Tuning via Singular Value Decomposition
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Solution Overview
Problem
In mills with singular mill matrices, classical control approaches lead to actuator movements that do not affect strip flatness, causing unwanted behavior and actuator saturation due to linear dependence among flatness responses, making it difficult to achieve uniform strip flatness during rolling.
Innovation Solution
The method involves obtaining equivalent movement ranges for each actuator, scaling the mill matrix based on these ranges, and performing singular value decomposition to focus control efforts on actuator positions that influence flatness, thereby avoiding non-influential combinations and improving control performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If classical control approach with one control loop per actuator is used, then control simplicity is maintained, but actuator movements occur that do not affect strip flatness due to singular mill matrix
Solution Approach 1:
The patent transforms the control parameters by using singular value decomposition to change from actuator position commands to singular value-based control signals. This parameter transformation eliminates the null space movements that occur in classical control, ensuring all actuator movements contribute to flatness control while maintaining system simplicity.
Solution Approach 2:
The patent replaces the classical mechanical control approach with a mathematical transformation approach using singular value decomposition. Instead of directly controlling each actuator independently, the system uses matrix decomposition to transform control signals, substituting the mechanical control logic with a mathematical framework that inherently handles the singular mill matrix issue.
2Adaptability or versatility
If actuator position combinations are allowed to move freely to correct flatness errors, then flatness control flexibility is improved, but actuator saturation and wear increase due to movements in null space
Solution Approach 1:
The patent extracts and eliminates the null space component from the control signal by using singular value decomposition. The decomposition separates the control space into effective directions (non-zero singular values) and null space directions (zero singular values), and the control algorithm only activates actuators in the effective directions, taking out the harmful null space movements that cause saturation and wear.
Solution Approach 2:
The patent converts the harmful singular mill matrix property into a benefit by using the singular value decomposition structure. The zero singular values that indicate null space movements are utilized to identify and eliminate redundant actuator combinations, transforming the problematic linear dependence into a useful constraint that prevents actuator saturation while maintaining control flexibility.
3Reliability
If mill matrix is scaled based on equivalent movement ranges, then control robustness is improved, but computational complexity increases due to additional scaling steps
Solution Approach 1:
The patent performs preliminary scaling of the mill matrix based on equivalent movement ranges before performing singular value decomposition. This pre-processing step normalizes the matrix to account for different actuator movement capabilities, improving the robustness of the subsequent decomposition and control. The scaling is done once during setup rather than continuously during operation.
Solution Approach 2:
The scaled mill matrix serves multiple functions: it accounts for different actuator movement ranges, improves numerical stability of the singular value decomposition, and provides a more accurate representation of the actual control authority of each actuator. This single scaling operation enables better control robustness across various operating conditions without requiring separate compensation mechanisms.
Data Source
AI summary
A method for tuning flatness control for rolling a strip in a mill including rolls controllable by means of a plurality of actuators, which mill is modeled by means of a mill matrix. The method includes: a) obtaining an equivalent movement range for each actuator, b) determining a scaled mill matrix by scaling the mill matrix based on the equivalent movement ranges, and c) obtaining a singular value decomposition of the scaled mill matrix for providing flatness control of the strip by means of the actuators. A computer program and a control system for carrying out the above method are also presented herein.