# Development of Automatic Electric Drive Drilling System for Core Drilling
## 4 Drilling System Mode
### Constant-Pressure Drilling Mode  
The constant-pressure drilling mode was consistent with that of a conventional core drilling rig. In this mode, WOB is constant. The hoisting system controlled the feed rate for this rig to control the WOB and drill the formation sample. Although the feed rate is objectively the same as the ROP, it cannot be assumed that the hoisting system can directly control the ROP because it is also related to RPM. Owing to the mechanical friction and clearance of the system, when the hosting system motor is fed with constant torque, the WOB changes with engineering parameters. For this nonlinear and time-varying system, it is essential to ensure that the feed rate and WOB setpoint are constant during drilling to maintain a stable system state. A proportional integration differentiation (PID) controller minimizes the error between the setpoint and outside measurement. The PID controller is commonly used in closed-loop systems as follows:  
\[u(t)=K_{p}(e(t)+\frac{1}{T_{i}}\int_{0}^{t}e(t)dt+T_{d}\frac{de(t)}{dt})+u_{0} \tag{22}\]  
where \(e(t)\) is the deviation signal between the accurate measurement and setpoint, \(K_{p}\) is the coefficient of the proportional controller, \(T_{i}\) is a constant for the integral controller, \(T_{d}\) is a constant for the derivative controller, and \(u_{0}\) is the bias. Because the state of the drilling system is different for different rocks, before drilling, the operator can reduce the axial vibrations via the \(K_{p}\), \(T_{i}\), and \(T_{d}\) gains, which can change depending on the rock sample with engineering experience. The Ziegler-Nichols method is a recommended method for the PID parameter setting of the particular rock. Drilling system operators can choose different torques and speeds to increase or decrease the ROP and the maximum WOB. The parameter tuning process of the PID control in this mode is as follows. In the drilling process, the empirical parameter of the proportional coefficient of the pressure system is approximately two based on the input PID, and the change in the WOB curve is observed by inputting a different WOB. When the WOB curve reaches a stable value within a short time, the steady-state error of the system can be eliminated by changing the critical parameter, and the system stability can be increased by changing the differential parameter as required. The experimental results show that the curve of the bit weight control is better when the proportion coefficient is five and the integral coefficient is 0.1. Given a 500-3000 N bit weight, the whole device can reach the target bit weight in a relatively short time; therefore, the WOB PID control of the experimental device in this study does not use a differential adjustment, and the final proportional coefficient is determined as 5, and the integral coefficient is determined to be 0.1, as shown in Figure 8.  
In this mode, the hoisting motor is in torque control mode, and the rotation motor is in speed control mode. Owing to the servo motor's characteristics, the motor's speed varies with the load during drilling, and the motor accelerates when the load does not reach its output torque. However, before the drill bit touches the rock sample, the motor's load is minimal; thus, the speed of the motor is exceptionally high, and the feed speed is high, which can easily cause immediate impact and damage to the drill bit. Therefore, it is necessary to limit the servo motor speed to prevent the bit from feeding too quickly in the no-load state. Simultaneously, the set speed is converted into the ROP, which must be higher than the ROP when drilling the rock sample; otherwise, the servo motor will not reach the given output torque. According to the mechanical structure, the relationship between the ROP and motor speed can be expressed as Equation (23). \[\text{ROP}=\frac{60\pi\textit{n}d}{1000i} \tag{23}\]  
where \(n\) is the speed of the hoisting motor, \(d\) is the diameter of the transmission gear reference circle, and \(i\) is the reduction ratio.