## 3 Materials and Methods
### Analysis of Oscillograph Records at Design Setting of the RAC Controller  
Figure 6 gives the oscillograph records showing changes in gauge and coordinates of hydraulic SDs on DS and OS registered at the rolling in the passages with roll gap misalignment control. Window 1 gives the curves of setting \(h_{0}\) and an actual gauge \(h\) of the feed at stand output. Window 2 shows rolling forces on the sides (\(F_{\text{DS}}\) and \(F_{\text{OS}}\)) which change in the rolling process. Windows 3 and 5 show output signals of the RAC controller \(U_{\text{RAC}}\) and the gauge controller \(U_{\text{AGC}}\), window 4 shows values of roll gaps \(S_{\text{DS}}\) and \(S_{\text{OS}}\). The dimensions on the axes in windows 1, 3-5 are given in mm, the rolling forces dimensions in the second window in kN.  
The present oscillograph records demonstrate the operation of the RAC controller at design setting: it has a control action on the SDs with a larger force. Thus, in the first passage (interval \(t_{1}\)-\(t_{2}\)) it \"clamps\" feed on OS. The gap \(S_{\text{OS}}\) (window 4) is reduced while the force \(F_{\text{DS}}\) (window 2) and the size of the gap \(S_{\text{DS}}\) on the opposite side remain virtually constant. In the second passage (interval \(t_{3}\)-\(t_{4}\)) one can observe the opposite: the gap \(S_{\text{DS}}\) decreases while the action on \(S_{\text{OS}}\) is not so intensive. The misalignment \(\Delta S\) at the end of passages is 2.5 mm, the force difference on the passages \(F_{\text{OS-DS}}\) = 10,000 kN, and at the end  
Figure 6: Oscillograph record at design setting of the RAC controller.  
of the first passage \(F_{\text{OS}}>F_{\text{DS}}\). This ratio is the opposite at the end of the second passage. Such non-uniform distribution of control actions makes the response slower and reduces the efficiency of roll gap alignment. A large imbalance of forces in both passages results in the limitation on the RAC controller (window 3). As a result, in the second passage the emergency roll opening occurs (pointed by an arrow). This leads to the rejection of the workpiece being rolled and production losses.  
In compliance with the design solution, in the structure in Figure 5 a proportional RAC controller is applied. However, the operation reveals its drawback: unsatisfactory control response. This causes continuous rolling force imbalance, which is confirmed by the oscillograph records in Figure 6.  
Obviously, simultaneous formation of control actions on the position controllers of both SDs with opposite signs is more efficient. However, gain factors should be the same. The distribution of drive signals must be conducted with the coefficients 0.5. These conditions are necessary for providing the equality of statistical errors of the SD position control on OS and DS at the absence of a signal at the RAC controller output. Such a signal setting is shown in the diagram, Figure 5.  
In connection with the aforementioned the authors revealed the need to develop a control method for controlling the position of both SDs and changing the RAC controller settings. The solution of these objectives is considered below after presenting the developed method of controlling the transverse asymmetry of the gauge profile, based upon the principle of control action redistribution.