Strip Flatness Control via Singular Value Decomposition
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Mills with singular mill matrices face challenges in achieving uniform flatness control due to actuator position combinations that do not affect the strip's flatness, leading to unwanted actuator movements and potential saturation, which can result in reduced control performance and increased wear.
Innovation Solution
A method that utilizes singular value decomposition to determine an adjusted flatness error by weighting actuator position combinations based on their flatness effect, allowing only those combinations that influence the flatness to be used for control, thereby avoiding movements in the null space and optimizing actuator positioning.
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 saturation and wear increase due to movements in the null space of the mill matrix
Solution Approach 1:
The invention transforms the control problem from physical actuator space to singular value space by changing the parameter representation. The flatness error is projected onto the singular vectors of the mill matrix, and control is applied in this transformed space where the null space is naturally eliminated. This parameter transformation resolves the contradiction by maintaining control simplicity while avoiding actuator saturation.
Solution Approach 2:
The singular value decomposition acts as an intermediary transformation that mediates between the flatness error and the actuator commands. By introducing this mathematical intermediary, the control system can achieve reliable actuator operation without directly confronting the null space problem in the original actuator space.
2Adaptability or versatility
If all actuator position combinations are allowed, then control flexibility is maximized, but flatness control performance deteriorates due to combinations that do not affect the strip's flatness
Solution Approach 1:
The invention extracts and eliminates the null space components from the control problem. By projecting the flatness error onto the singular vectors and applying control only in the directions that affect flatness, the harmful actuator combinations are taken out of the control loop, leaving only the beneficial control actions.
Solution Approach 2:
The control flexibility is maintained in the singular value space where each singular value corresponds to a meaningful flatness direction. The parameter transformation ensures that control actions are applied only where they produce the desired flatness effect, eliminating wasted control authority.
3Adaptability or versatility
If actuator movements in the null space occur, then control freedom is preserved, but control performance reduces and actuator wear increases
Solution Approach 1:
The invention converts the harmful null space movements into a benefit by using the singular value decomposition to identify and eliminate them. The mathematical transformation reveals the structure of the control problem, allowing the system to operate only in the beneficial directions while naturally avoiding the harmful null space movements.
Data Source
AI summary
A method of providing flatness control for rolling a strip in a mill including a plurality of rolls controllable by actuators. The method includes the steps of: receiving flatness measurement data pertaining to a flatness of the strip; determining a flatness error as a difference between a reference flatness of the strip and the flatness measurement data; determining an adjusted flatness error based on the flatness error and weights for actuator position combinations which provide a flatness effect below a threshold value; and utilizing the adjusted flatness error for the control units to control the actuators to thereby control the flatness of the strip. A computer program product and a control system for carrying out the above method are also presented herein.