Iterative Self-Learning Control Method for Average Wall Thickness During Seamless Steel Tube Stretching-Reduction

Literature Overview

The paper by Liu Shan and colleagues, published in Iron and Steel (2002, Vol. 37, Issue 4, pp. 29-34), introduces an iterative self-learning control algorithm for the average wall thickness control during the stretching-reduction process of seamless steel tubes. The research was conducted in collaboration between Zhejiang University and Baoshan Iron and Steel Co., Ltd., combining academic control theory with industrial rolling mill practice. The stretching-reduction process is a critical finishing operation in seamless tube production, where the tube is simultaneously stretched (increased in length) and reduced (decreased in wall thickness) through a series of rolling stands. The control of average wall thickness is essential for ensuring dimensional accuracy and product quality.

Technical Background and Control Challenges

The stretching-reduction process involves the coordinated control of multiple rolling stands, each of which imparts a specific reduction ratio to the tube. The average wall thickness of the final product depends on the cumulative reduction across all stands, and any deviation in the rolling conditions of individual stands propagates to the final product. The control challenges are multifaceted:

1. Physical parameter variability: The mechanical properties of the tube material, the roll geometry, and the lubrication conditions all vary from batch to batch and even within a single production run.
2. Modelling uncertainty: The mathematical model relating rolling parameters to wall thickness output is inherently uncertain due to the complex plastic deformation behaviour of the tube during stretching-reduction.
3. Time-varying disturbances: The tube temperature, which affects the flow stress, changes continuously during the rolling process as the tube moves from one stand to the next.

Iterative Self-Learning Control Algorithm

The core of the proposed method is the iterative learning control (ILC) algorithm, which is particularly suited for systems that operate in a repetitive manner. In the stretching-reduction process, each tube passes through the same sequence of rolling stands, and the control parameters for each stand can be adjusted based on the measured deviation between the actual and desired wall thickness of the previous tube.

The algorithm operates as follows:

1. For each tube, the actual wall thickness is measured at the exit of the final stand using an in-line dimensional measurement system.
2. The deviation between the actual and target wall thickness is calculated.
3. The control signal for each stand is updated based on the deviation signal, using a learning gain matrix that determines the magnitude and direction of the correction.
4. The updated control signals are applied to the next tube in the production sequence.

The key innovation is the self-learning aspect: the learning gain matrix is not fixed but is adaptively updated based on the system response. This allows the algorithm to compensate for both the time-varying physical parameters and the modelling errors that would otherwise limit the performance of a conventional feedback control system.

Online Adaptive Adjustment of Stand Speeds

The implementation of the iterative self-learning control involves the online adjustment of the steady-state speed distribution among the rolling stands. In a multi-stand stretching-reduction mill, the speed ratio between adjacent stands determines the tension and the reduction ratio at each stand. By adjusting these speed ratios, the controller can redistribute the reduction among the stands to achieve the target average wall thickness.

The control strategy is:

• The primary control variable is the speed ratio between adjacent stands.
• The secondary control variable is the roll gap setting at each stand.
• The iterative learning algorithm adjusts the speed ratios based on the measured wall thickness deviation, while the roll gap settings are adjusted based on the estimated roll wear and material property changes.

This hierarchical control structure ensures that the fast-acting speed ratio adjustments handle the tube-to-tube variations, while the slower roll gap adjustments compensate for the gradual drift caused by roll wear and material property changes.

Engineering Practice Integration

The algorithm was validated at Baoshan Iron and Steel Co., Ltd., where it was implemented on an industrial stretching-reduction mill. The results demonstrated significant improvements in wall thickness accuracy and consistency. The standard deviation of the average wall thickness was reduced by approximately 30-40% compared to the conventional control method, and the proportion of tubes meeting the dimensional tolerance specification was increased substantially.

For engineers involved in seamless tube production, the key practical considerations are:

• The availability of reliable in-line wall thickness measurement systems is essential for the implementation of the iterative learning control.
• The learning gain matrix must be carefully tuned to ensure stability and convergence, and the tuning process may require several production runs.
• The algorithm should be integrated with the existing process control system to ensure seamless operation and data exchange.

Study Insights and Implications

This paper represents an important contribution to the application of advanced control theory in metallurgical rolling processes. The iterative self-learning control algorithm is particularly well-suited to the stretching-reduction process because of the repetitive nature of the operation and the inherent variability of the physical parameters. The key insight is that by leveraging the historical information from previous tubes, the controller can learn and adapt to the changing conditions of the process, achieving a level of accuracy that would be difficult to attain with conventional feedback control alone.

For the broader field of seamless tube manufacturing, this study demonstrates the value of integrating advanced control algorithms with process engineering knowledge. The success of the algorithm depends not only on the mathematical formulation but also on the accurate modelling of the physical process and the reliable measurement of the process variables. Future work should explore the extension of the iterative learning control to other rolling processes, such as cold drawing and cold rolling, where similar repetitive operations and parameter variabilities exist. The study also highlights the importance of collaboration between academia and industry in solving complex process control problems, as the successful implementation of the algorithm required both theoretical expertise and practical process knowledge.