## 3 Materials and Methods
### Transverse Profile Asymmetry Control System for the Reversing Stand of Mill 5000  
The diagram of the control system intended for the compensation of the feed profile deviation is provided in Figure 5. The system provides the alignment of stand strain in the cases when the forces on DS and OS differ. To do this, a zero signal is sent to the RAC controller input which is compared with the actual gap values on the operator and drive sides. On the forces in hydraulic cylinders the setting for gauge differences at the workpiece edges is formed and, correspondingly, the setting for the gaps on DS and OS. This value is calculated by means of the measured force division by the strip elasticity module (Level Modulus). The curve of elasticity module dependence on the force is stored in the form of the table in the file of CAPCS. The difference of forces is divided by the elasticity module on one side of the stand and impacts the position of hydraulic SDs.  
At the output of the RAC controller a setting is established which is sent to SDD position and compensates gauge variation. To eliminate inadmissible gap misalignment, one should set the limitation of the output signal. This is necessary because of the risk of upper and lower roll edge contact at thin feed rolling and significant misalignment. The set limitation is within the range 0.7-2 mm and depends on the rolled profile.  
During the system setting the authors give a rationale for applying a proportional and differential RAC controller which in fact controls the filtered derivative value of the input signal. This controller is selected because such controllers facilitate the control action formation taking into account both the error and the speed of its change. The introduced derivative control speeds up the system response time. This reduces the number of errors in the dynamic mode caused by the shift of screw-down mechanisms.  
The output signal of the (gap) position controller provides for the control of the task on the hydraulic cylinder servo-valve in the range \(\pm\)100% in relation to the zero value. To work out the range at each hydraulic cylinder of screw-down devices (on DS and OS), two servo-valves are installed. They are connected to the head end in parallel and maintain the total range of pressure control in the hydraulic cylinder of \(\pm\)200%. These valves are united  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Rolled Length** & **Feed Axis Deviation from the Rolling Axis (Camber in Figure 4)** \\ \hline
10 m & 25 mm \\
20 m & 35 mm \\
30 m & 58 mm \\
40 m & 70 mm \\
50 m & 90 mm \\ \hline \hline \end{tabular}
\end{table}
Table 1: Permissible camber for Mill 5000.  
Figure 5: Diagram of connection of the RAC controller to the control system for hydraulic SD position.  
into two groups (gr. 1 and gr. 2 in Figure 5). Each group includes one valve, installed on hydraulic cylinders on the sides DS and OS. Depending on the value of the shift signal, received from the output of the position controller, the group. 1 or group. 2 valves are put into operation or the valves of two groups simultaneously. The valve groups are brought into operation by the block \"Distributing tasks into groups\". Such a control algorithm allows maintaining necessary (high) shift speeds as well as increasing the reliability and sustainability of the control.  
More detailed research on the RAC controller operation and the automatic gauge control system (AGCS) is provided in [16; 23].