## 3 Design of Adaptive PLC Control System
### Determination of Working Parameters of Control System  
Determination of initial cutter parameters:  
(1) Working parameters of cutter-speed, transverse speed, feed  
The soil quality parameters and target yield are determined according to the working environment and working effect before the cutter works, and the most basic parameters (yield, soil quality parameter, cutter type) can be obtained [11; 12; 13; 14]. On the basis of these parameters, taking the two-dimensional cutting theory as the principle [12] calculating the working parameters, the PLC control center can calculate all the other working parameters according to the calculation formula. The formula is as follows:  
Calculation formula of cutter speed:  
\[n=60U_{c}/\pi D_{m}\left(\mathrm{r}/\min\right) \tag{1}\]  
In Equation (1): \(D_{m}\) is the average diameter of the cutter head and \(U_{c}\) is the cutting speed of the cutter (m/s).  
Figure 8: The structure diagram of the autonomic adaptive control system.  
Figure 7: Amplitude changing device display.  
According to the successful experience of some dredgers in recent years, the \(U_{c}\) value of a five-knife cutter can reach 1.3 m/s, and the \(U_{c}\) value of six-knife cutter can reach 1.6 m/s.  
The value of \(U_{c}\) is related to the characteristic parameters of soil. The more difficult the soil is to be dug, the greater the value of \(U_{c}\).  
A common cutter cutting speed is 1.0-3.5 m/s; for general soil, the cutter cutting speed is mostly set at about 1.5 m/s. Transverse velocity refers to the moving speed of the reamer, that is, the stepper motor is used as the power source to control the speed of horizontal movement along the radial direction of the reamer axis.  
Calculation formula of transverse velocity:  
\[U_{sw}=\tan[\alpha-(3^{\circ}\sim 6^{\circ})]\cdot\pi\cdot D\cdot n \tag{2}\]  
In Equation (2): \(\alpha\) is the back angle of the cutting angle and is recommended to be within 9\({}^{\circ}\)-12\({}^{\circ}\), with a high speed cutter, the value would be smaller; \(n\) is the rotation of cutter; and \(D\) is the diameter of the cutter.  
Calculation formula of feed:  
\[\rho=\frac{Q\cdot\eta\cdot\cos\theta}{L\cdot D\cdot\rho_{1}\cdot U_{sw}} \tag{3}\]  
In Equation (3): \(L\) is the length of the cutter; \(\rho\) is the cutter feed rate; \(\rho_{1}\) is 0.4-1, depending on the soil quality; \(\eta\) is the efficiency of 0.8-1, depending on the cutter form and soil quality; and \(Q\) is the angle between the swing track of the cutter and the transverse shifting cable of 30\({}^{\circ}\)-40\({}^{\circ}\).  
(2)  
Cutter state parameters--depth, center distance, angle  
When the cutter is working, different digging depths will lead to different cutter power.  
In the research process, the sum of the two cutters is guaranteed to be constant at the same speed, and the sum of the power of the two cutters is calculated in different combined forms to match the minimum power of the two cutters at the same total depth.  
Here, we selected 30 groups of data with different digging angles, which were 90\({}^{\circ}\) + 30\({}^{\circ}\), 89\({}^{\circ}\) + 31\({}^{\circ}\), 88\({}^{\circ}\) + 32\({}^{\circ}\), and \(\dots\) 60\({}^{\circ}\) + 60\({}^{\circ}\) and replaced by 1 to 30 groups, respectively. According to the two-dimensional cutting theoretical formula, the power relationship of 30 groups with different combinations with a certain total depth was obtained (as shown in Figure 9).  
The research curve shows that when the sum of the depth of the cutter is a certain value, the total power of the two cutters is the same as that of the cutter. Therefore, when  
Figure 9: Power diagram showing 30 different combinations.  
setting the working parameters of the cutter in the normal working environment, the depth of the two cutters should be consistent.  
The concrete calculation formula of digging depth is as follows:  
\[h=\frac{Q_{s}}{2 Ul_{sw}\cdot\rho} \tag{4}\]  
In Equation (4): \(Q_{S}\) is the dredger yield (m\({}^{3}\)/h).