# Intelligent Control Strategy of Electrohydraulic Drive System for Raising Boring Power Head

Authors: Jun Zhang; Qinghua Liu; Yun Chen; Jiguo Wang; Jinpu Feng; Qingliang Meng; Wei Cao; Wei Tu; Xiaohui Gao
Journal: Scientific Programming
 (2022)

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## Abstract

The power head is the key part of the rock breaking work of the raise boring machine. Because the power head cannot adjust speed in time with the change in complex rock stratum, it leads to high failure rate, low work efficiency, and even accidents, so it is urgent to improve the controllability of the power head. In this paper, the electrohydraulic coupling mathematical model of the power head is established using the characteristic equations of dynamics and hydraulic components, and the control strategy of the fractional electrohydraulic drive system of the power head is proposed; genetic algorithm (GA), particle swarm optimization (PSO), and whale optimization algorithm (WOA) are used to adjust the parameters of FOPID, so as to improve the control effect of electrohydraulic system. The results show that the step response of WOA-FOPID control strategy is also better than that of genetic algorithm (GA) and particle swarm optimization (PSO). It can reach a stable state in 0.02 seconds, and the overshoot is only 0.12137%. The test verifies the correctness of the adaptive control and simulation results of the power head, which can effectively improve the adaptability of the power head to complex coal seams.


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## Body

## 1. Introduction

Due to the advantages of the high safety, relatively low cost, and ensuring the safety of operators to the greatest extent, the reverse well drilling rig is widely used in underground roadway space, mine development, subway tunnel, and other projects, and the drilling technology is also a fundamental change technology for well hole drilling. In recent years, with the improvement of intelligent control technology of the drive system of the reverse well drilling rig, it has not only accelerated the speed of excavation but also greatly alleviated the labor intensity.The power head is the key component of the reverse well drilling rig, and its control method and effect directly affect the safety and stability of the reverse well drilling rig in construction. At the same time, the intelligent control of the power head also has a positive role in promoting the intelligent construction of coal mines nationwide. Therefore, the intelligent control strategy of the electrohydraulic drive system of the power head has attracted the attention of the majority of scientific researchers at home and abroad. For example, Wang and Yang [1], and others studied the relationship between the four parameters of drill pipe tension, torque, rotational speed, and drilling speed in the power head control system. Shen and Liu [2] formulated the mathematical modeling and robust integral adaptive controller of the power head valve-controlled hydraulic motor based on Padde’s theorem and the reverse step derivation method, which improved the accuracy and tracking speed of the system control. Yang [3] proposed a fuzzy PID control algorithm based on the problem of synchronization of four hydraulic motors in the power head device, which improved the synchronization accuracy of the motor. Cheng [4] used Amesim and MATLAB-Simulink to construct a joint simulation model of the test bench drilling simulation system, and Cheng Lilin designed a fuzzy adaptive PID controller to analyze the control performance of the power head system. Zhang [5] used the method of co-simulation between Amesim and MATLAB-Simulink, the adaptability of different control algorithms of traditional PID fuzzy and feedback linear synovial membrane structure to the position tracking control of valve-controlled asymmetrical hydraulic cylinders is analyzed, and the problems of nonlinearity and low control accuracy of the electrohydraulic control system of the power head are solved. Foreign hydraulically driven reverse well drilling rig, power head drive using electrohydraulic proportional PID control technology, control unit using PLC or engineering controller [6–9], due to the introduction of computer control technology, and a variety of more complex control logic and PID control algorithms can be realized. The above literature research has made certain contributions to the intelligent control of the electrohydraulic drive system of the power head of the reverse well drilling rig and laid a certain foundation for the intelligent control algorithm of the power head. However, the research in the above articles is based on the traditional PID control algorithm. Especially in downhole operation, complex uncertainties such as surrounding rock parameters and downhole force of the drill will make the driving head of the drill unable to adjust the control parameters in time, resulting in low drilling efficiency, short service life of rock breaking hob, and even damage to the drill bit, sticking, etc. Under special working conditions, the traditional PID control effect is not ideal, even if the PID is re-parameter tuned, it still cannot achieve a good control effect, and it is essentially impossible to overcome the shortcomings of traditional PID control technology. Therefore, the complex system has a low control accuracy, reflecting the poor sensitivity and other issues, and it is difficult to explore the intelligent control principle of the electrohydraulic drive system of the power head from a deep level, and the parameter selection of the PID controller has a great impact on the control effect, the traditional parameter tuning method is still based on experience, and it is difficult to find a set of parameters with good control effect in a short period of time.The fractional order FOPID controller has 5-bit adjustable parameters. Compared with other control laws, it has better dynamic performance, parameter adjustment flexibility, and control accuracy [10–12], and there is a great vacancy in the research and application of fractional order FOPID in the research of electrohydraulic system control method of raising boring. Based on the internal control principle of the reaming operation of the power head of the reverse well drilling rig, if the control effect is required to have good timeliness and reliability, the parameter adjustment research of the intelligent control algorithm is also indispensable, such as the particle swarm algorithm [13–15], the genetic algorithm [16], the gravity search algorithm [17], the neural network algorithm [18], the ILMI algorithm [19], and the whale optimization algorithm [20], which are all applied in the PID controller, improving the control effect of the traditional PID controller. The method of parameter tuning that relies on experience is got ridden.Based on this, this paper establishes the electrohydraulic coupling model of the power head of raise boring machine from the dynamic principle, electrohydraulic coupling properties, and the characteristic equation of hydraulic components and puts forward the control method of the power head electrohydraulic drive system based on fractional FOPID. To further improve the control effect of the system, the genetic algorithm (GA), particle swarm algorithm (PSO), whale optimization algorithm (WOA), three groups of intelligent optimization algorithms are used to adjust the FOPID and PID controller parameters, and the influence of the above different combination algorithms on the control system is evaluated, to provide theoretical guidance for the reliability of the reaming operation of the reverse well drilling rig [21–24]. Finally, field experiments were conducted in Liuqiao Town, Suixi County, Anhui Province, to prove the effectiveness of WOA-FOPID control strategy in electrohydraulic drive control system. It further provides new theoretical guidance for the intelligent control strategy of the electrohydraulic drive system of the power head.


## 2. Mathematical Modeling

This article takes a deep well lane full-section test drilling rig (raising boring) as an example to study, which is the most widely used [25] and belongs to the lower lead upward expansion type. In order to apply intelligent drilling technology to raise boring machine, taking the power head as the research object, PLC and HMI are used to design the rock breaking control system. Four variable displacement piston pumps a11vlo130lrd are connected in series into two groups, which are driven by 132 kw motors to drive four mcr15a1500w80z32a0m2l4 2S 506u two-speed radial piston motors, and the hydraulic motor also controls the rotation of the power head [26, 27]. The overall idea of the structure composition, construction process, and control scheme of the reverse well drilling rig and the power head is shown in Figure 1.Figure 1
Overall train of thought block diagram.To facilitate the theoretical modeling and analysis, the basic assumptions of hydraulic motor modeling are made. On this basis, the proportional amplifier, electrohydraulic proportional control valve, power head electrohydraulic coupling model, and the transfer function of power head hydraulic motor speed are established, respectively. The signal output by the controller is a voltage signal or a current signal, which is a component that amplifies its input signal and simplifies this model to a proportional link because of its input and output characteristics. Its transfer function is as follows:(1)Gi=IsUis=Kb,where Kb is the gain of the proportional amplifier.The current signal output by the proportional link is based on dynamics and electromagnetic induction to drive the proportional solenoid movement, and then, the valve spool generates motion, thereby controlling the size of the valve opening and the direction of the liquid in and out. The working principle of the electrohydraulic proportional control valve is established, and the following expressions are established for the relationship between the coil current in the electromagnet, the driving force of the electromagnet, and the displacement of the valve core:(2)u=Ldidt+Rc+rρi,Fdt=KIUt,FMt=md2xdt2+cdxdt+ksx..The transfer function obtained by pulling the change of (2) is as follows:(3)G2=XsIs=Kxis2+2ωnξs+ωn2.In the formula,ωn is the natural frequency of the spool, ξ is the damping ratio of the spool, and Kxi is the gain of the electrohydraulic proportional valve.The electrohydraulic coupling model of the power head is composed of the hydraulic motor connected to the power head through the deceleration device, so the following relationship is established according to the flow continuity of the hydraulic motor valve, the static characteristic equation, the dynamic balance equation of the shaft, andCd:(4)qL=CdAx1ρps−pL,qL=Dmdθmdt+CtmpL+Vt4βedpLdt,T=DmPL=Jd2θmdt+Bmdθmdt+Gθm+Tf,Tf=Jesωds+Beωds+Tdsi..As can be seen from Figure1, the hydraulic motor and the power head are connected through the deceleration device, and the angular velocity exists: r⟶. A pull transform on equation (4) is performed to get the following equation:(5)T=DmPLs,=iJ1+Jesωds+iBm+Beωd+Tdsi.From (5), it can be known that the equivalent inertia of the power head Jd=iJ1+Je is equivalent to viscous damping coefficient Bd=iBm+Be. The transfer function of the electrohydraulic coupling power head model under no-load state is sorted out:(6)Gd1s=ωdsUis=Kds2+2ωnξs+ωn2s2/ωd2+2ξd/ωds+1,where Kd=KαKxiKqDm/iDm2+BdCtm+Kc, ωd=βeiDm2+BdCtm+Kc/VtJd, and ξd=JdβeCtm+Kc+BdV/2βeVtJdiDm2+BdCtm+Kc.Proportional amplifier, electrohydraulic proportional valve, and hydraulic motor-related parts of the parameters are as follows: the inertia of the motor shaftJ is 67 kg·m2, r⟶ is 0.4755 kg·m2, the total volume Vt of the connecting pipe is 3 × 10−4 m3, the elastic modulus of the system is 6.9 × 108 N/m2, the flow gain Kq is 2.42 m2/s, the motor displacement is 2.39 × 10−4m3/rad, the gear ratio of the reducer is i of 6.817, and the open-loop transmission function of the power displacement signal by calculating the angular velocity of the power head is as follows:(7)Gd1s=ωdsUis=Kds2+2ωnξs+ωn2s2/ωd2+2ξd/ωds+1,=8.476×1045.487×10−5s4+0.0252s3+2.85s2+432.59s+10000.By (7), we obtain the system without interference and control Bode diagram as shown in Figure 2.Figure 2
Open-loop Bode diagram of the system without interference and control.From Figure2, it can be seen that when the amplitude-frequency characteristics reach zero decibels, the phase-frequency characteristics are below −180° line, and the phase lag point has a negative stability margin at the 180° point, so there is a stability problem in the system, but due to the stability of the system itself and the dynamic characteristics, to make the system have a stable margin, it is necessary to add a controller to adjust to meet the stability requirements.


## 3. Fractional Order FOPID Controller Design

As a branch of the control field, fractional order (FOPID) control has many advantages such as flexible and precise parameter adjustment, large system stability margin, and strong system robustness and has been widely used in different types of controller design [28–30]. Fractional order PIλDμ control was first proposed by Igor Podlubny, and its superiority over traditional PID control was demonstrated through response analysis [28–30], [31-36]. Fractional order PIλDμ controller of the order of parameters λ and μ can take any real number, in the P−I−D plane, according to the different controller parameters to take the value; FOPID control system structure is shown in Figure 3. Compared with traditional PID control, fractional PIλDμ control can more subtly reflect the transition process from proportional control to integral control and differential control, to achieve a control effect with higher accuracy, better stability, and stronger anti-interference ability.Figure 3
Structure of the FOPID control system.The mathematical expression for the FOPID controller is as follows:(8)Cs=UsRs=Kp+Kisλ+Kdsμ,where Kp is the proportional gain, Ki is the integral gain, Kd is the differential gain, and λ and μ are the fractional and integral orders, respectively.


## 4. Whale Optimization Algorithm

Based on the advantages of fractional order PID control algorithm, this paper proposes a control strategy based on WOA-FOPID algorithm. There are many kinds of parameter tuning methods for FOPID. According to the regulation characteristics of the algorithm itself, it is mainly divided into traditional method tuning and intelligent optimization algorithm tuning, and the intelligent optimization algorithm is widely used because of its self-adaptability. In this paper, genetic algorithm (GA), particle swarm optimization (PSO), and whale optimization algorithm (WOA) are combined with FOPID control theory, respectively, and the above three intelligent optimization algorithms are used to set FOPID control parameters. The structure of intelligent control algorithm FOPID control system is shown in Figure4.Figure 4
Structure diagram of the intelligent control algorithm FOPID control system.To fully explore the advantages of genetic algorithm (GA), particle swarm optimization (PSO), and whale optimization algorithm (WOA), three intelligent optimization algorithms are combined with PID and FOPID, respectively, and the speed control effect of power motor is further analyzed through different control strategies. The flow chart of setting FOPID parameters by the developed intelligent optimization algorithm is shown in Figure5.Figure 5
Flow chart of intelligent optimization algorithm for tuning FOPID parameters.


## 5. Parameter Setting and Optimization Process of Real Analysis and Optimization Flow Simulation Analysis

There are many kinds of parameter tuning methods for FOPID. With the development of intelligent and control technology, according to the regulation characteristics of the algorithm itself, it is mainly divided into traditional method and intelligent optimization algorithm. The intelligent optimization algorithm is widely used because of its self-adaptability. The whale optimization algorithm (WOA) has been widely used because of its simple optimization mechanism and fast solution speed. The algorithm searches for the optimal solution by simulating the predation behavior of humpback whales [37–39] and solves the D-dimensional optimization problem in which f(x) is the optimization objective function:(9)Minfx,s.t.1≤x≤u.In servo control, the ITAE performance index weights the error so that the error signal converges to zero as soon as possible. The optimization objective function generates the objective function of control parameter optimization under the ITAE index, which is defined as follows:(10)fy=∑t=0NLtet.Here,N is the number of search targets; L (t) is the time series; and e (t) is the error signal between the response frequency and the reference frequency. The smaller the Fy, the better the effect of dynamic response. As shown in Figure 6, the contents and steps of WOA are summarized.Figure 6
WOA steps and contents.In this paper, genetic algorithm (GA), particle swarm optimization (PSO), and whale optimization algorithm (WOA) are combined with PID and FOPID, respectively. Through different combined control strategies, the control effect of raising boring power head is further analyzed and compared. The specific parameter settings of each algorithm are shown in Table1.Table 1
Specific parameter setting table of each algorithm.
PSOGAWOA-FOPIDWOA-PIDMax_er2002005050N2050——C11.49———C21.49———Variation parameters—0.8——Variation probability—0.75——Dim——53Search agent no.——100100It can be seen in Table2 for comparison of different combination strategies and control indicators, the dynamic response curve comparison diagram of each combination strategy of the regulation system is shown in Figure 7. Figure 7(a) is the step response diagram of each intelligent optimization algorithm and PID combination strategy, and Figure 7(b) is the step response diagram of each intelligent optimization algorithm and FOPID combination strategy; the comparison of PID and FOPID combined control strategies based on WOA is shown in Figure 8.Table 2
Comparison of different combination strategies and control indicators.
CombinationDynamic indexStandard varianceOvershoot (%)Stabilization time (S)PSO-PID0.0630930.17210.84GA-PID0.0630930.12170.84WOA-PID0.036248.350.1PSO-FOPID0.063492.81970.51GA-FOPID0.037786.93090.16WOA-FOPID0.035350.121370.02Figure 7
Comparison of dynamic response curves of each combination strategy of regulation system. (a) PID combination strategy. (b) FOPID combination strategy.
(a)(b)Figure 8
Comparison of control strategies based on WOA.As can be seen in Figure7, after adding PID and FOPID controllers, the system can quickly tend to a stable state. Comparing Figure 7(a) with Figure 7(b), in the control based on the same algorithm, the FOPID control is significantly better than the PID control in terms of response time and dynamic response; in Figure 7(a), the step response of WOA-FOPID control strategy is obviously better than the control strategy based on GA and PSO algorithm, and the overshoot is 8 35%, only 0.5%. Stable state is reached in 1 s; in Figure 7(b), the step response of WOA-FOPID control strategy is also better than the control strategy based on GA and PSO algorithm, at 0.5%. It reaches a stable state within 02 s, and the overshoot is only 0.5% 12137%. The simulation results in Figures 7(a) and 7(b) show that in the PID/FOPID combination strategy, the whale optimization algorithm (WOA) has more advantages than the genetic algorithm (GA) and particle swarm optimization algorithm (PSO) in the process of intelligent parameter adjustment.Figure8 compares the two controllers based on WOA. The results show that WOA-FOPID is more dominant, which further verifies the superiority of FOPID controller. In these combination strategies, it is concluded that the optimal controller is the FOPID controller based on WOA, and the parameters of the controller are as follows:(11)Gc=15.2654+20s−1.0039+9.5963s1.1118.


## 6. Experiment

To verify the correctness and effectiveness of WOA-FOPID control strategy in the electrohydraulic drive control system of the power head of raise boring machine, the performance test of the power head of raise boring machine was carried out in Liuqiao Town, Suixi County, Anhui Province. The on-site commissioning layout is shown in Figure9.Figure 9
Site layout.To meet the normal operation of the rock breaking test rig, the rock breaking control system mainly adopts Siemens S7-1200 series PLC and its expansion module, combined with the control system designed by HMI to realize the start/stop action of the pump station motor, the forward/reverse action of the power head motor, the stepless speed regulation of the power head output shaft, the lifting/lowering action of the thrust cylinder, the pressure, displacement, stroke, constant pressure/constant torque drilling mode switching precise control of temperature control, and automatic operation of pump station. At the same time, the rock breaking control system is equipped with a remote control function to facilitate remote operation. S7-1200 series PLC and large screen display form the control core in the control cabinet, and each working condition monitoring and input/output drive unit cooperates with each other to ensure the stable operation of various control functions of the system. The general scheme of electric control system of raise boring machine is shown in Figure10.Figure 10
General scheme of the electric control system for raise boring rig.


### 6.1. Power Head Speed Control Scheme

Power head speed regulation control model in the process of power head speed adjustment potentiometer from minimum to maximum adjusts the displacement of variable pump from 0 to 145 ml/R and variable motor from 215 to 65 ml/R in turn. That is, in the first half of the speed regulation process, the displacement of the motor remains unchanged, and only the displacement of the variable pump is adjusted to meet the requirements of speed adjustment. In the second half, the maximum displacement output of the variable pump is maintained, and only the displacement of the variable motor is adjusted to meet the requirements of speed adjustment. In this way, no matter at any speed, the output torque is the maximum torque corresponding to the speed:(1)
Remote Control and Valve Group Control of Hydraulic Pump Station. Before the remote control of hydraulic pump station operates the control system, the pump station motor must be started first to make the pump station in working state. To avoid starting the pump station in another place, the system adds the start and stop button of the pump station motor on the control cabinet, and the start signal sent by the button acts on the soft starter remotely to realize the start and stop function of remote control motor.Control Scheme. The main pump motor is started by soft starter, and the start/stop signal of soft starter is controlled through the console button to realize the start/stop control function of corresponding motor. Control process is in Figures 11 and 12.The valve group control system sends the control command to PLC through the knob on the operation panel or the virtual button on HMI, and the output signal drives the corresponding solenoid valve action through the relay to realize the corresponding functions.(2)
The power head is driven by 160 ml/R variable pump and variable motor. To realize the adjustable steering and speed, the system designs a three-position knob to control the action of the electromagnetic directional valve, so as to realize the steering control of the power head. At the same time, the potentiometer is designed to input 0∼5 V analog signal, and then, through the calculation of PLC speed regulation model, the first conductive signal of 0∼10 V driving proportional amplifier is output, the proportional amplifier to output 200∼600 mA current is controlled, and then the speed of power head is controlled.Forward/Reverse Control Scheme of Power Head. Forward/reverse switching control is realized through three-position four-way solenoid directional valve. That is, the control of the electromagnetic directional valve is realized through the console knob or the remote controller knob, to realize the control of the forward/reverse switching function. Control flow is shown in Figure 13.Stepless Speed Regulation Control Scheme of Power Head Output Shaft. The flow is adjusted by controlling the swing angle of variable pump, to realize the function of stepless speed regulation of power head output shaft. That is, the proportional electromagnet is controlled by the knob potentiometer, and then, the swing angle of the variable pump is controlled to realize the function of stepless speed regulation of the output shaft of the power head. Control flow is shown in Figure 14.Figure 11
Control flow diagram of the main pump motor.Figure 12
Control flow diagram of the auxiliary pump motor.Figure 13
Flow chart of forward/reverse control of the power head.Figure 14
Flow chart of stepless speed regulation control of power head output shaft.


### 6.2. Implementation Plan

Field commissioning stage: This stage involves speed regulation of power head under shunt state. The experimental parameters are shown in Tables3–5:(1)
Stage I: the displacement of the power head motor is kept unchanged, and the displacement of the hydraulic pump is adjusted from0∼145ml/r. At this time, the driving current of the power head motor is about 43mA (the corresponding digital quantity is 2000). According to the driving characteristic curve, the maximum displacement of the power head motor is 216.5ml/r.(2)
Stage II: the displacement of the power head motor is kept unchanged, the discharge of the hydraulic pump is adjusted to the maximum value of145ml/r (theoretical value), the actual control driving current is about 586mA (corresponding to the digital quantity of 27000), and the flow of the corresponding pump is 140ml/r. At this time, the displacement of the power head motor remains at the maximum value of 216.5ml/r.(3)
Stage III: the maximum displacement of the hydraulic pump is kept unchanged at145ml/r, and the displacement of the power head motor is adjusted from 216.5ml/r to Vgmin. When the software controls the minimum displacement of the power head motor, the corresponding driving current is about 526mA, Vgmin is 0.185 times, and Vgmax=216.5ml/r×0.185=40.0525ml/r.(4)
Stage IV: the rotating speed of the power head is the maximum, and the Baote remains unchanged.Table 3
Experimental parameters (relationship between displacement and current of the power head motor).
Serial number12Electric current200600CompanymAmADisplacement216.50Companyml/rml/rMaximum speed29005500Companyr/minr/minTable 4
Experimental parameters (relationship between pump displacement and current).
Serial number12Electric current200600CompanymAmADisplacement1450Companyml/rml/rMaximum speed14501450Companyr/minr/minTable 5
Experimental parameters (electromagnet at technical data EP1 and EP2).
Technical data electromagnets at EP1 and EP2VoltageEP112 V (±20%)EP212 V (±20%)Control current (mA)Initial control value at displacementVgmin400200Control termination value at displacementVgmax1200600


### 6.3. Empirical Conclusion

①
Compared with “the power head parameter table of enhanced TD2000 drilling rig under shunting state and turning into working condition,” there is an error in the maximum displacement control of hydraulic pump station, with an error of about5ml/r. There is still a little room for optimization, which can be optimized on-site.②
Compared with “the power head parameter table of enhanced TD2000 drilling rig under shunting condition and turning into working condition,” the minimum displacement control of power head motor has error, and the error is about2ml/r, so the optimization needs to be careful (during plant commissioning, when the speed regulation exceeds a certain position, the speed of power head decreases instead).③
In the whole speed regulation process, the trend is basically consistent with the table of power head parameters under shunting condition of enhanced TD2000 drilling rig, but there is a little error at the two end points. The error is as described in points ① and ② above. The position number described in the table is included in the whole speed regulation process and does not need to be corrected separately. Only the corresponding speed identification needs to be carried out on-site. The corresponding position is marked.


## 6.1. Power Head Speed Control Scheme

Power head speed regulation control model in the process of power head speed adjustment potentiometer from minimum to maximum adjusts the displacement of variable pump from 0 to 145 ml/R and variable motor from 215 to 65 ml/R in turn. That is, in the first half of the speed regulation process, the displacement of the motor remains unchanged, and only the displacement of the variable pump is adjusted to meet the requirements of speed adjustment. In the second half, the maximum displacement output of the variable pump is maintained, and only the displacement of the variable motor is adjusted to meet the requirements of speed adjustment. In this way, no matter at any speed, the output torque is the maximum torque corresponding to the speed:(1)
Remote Control and Valve Group Control of Hydraulic Pump Station. Before the remote control of hydraulic pump station operates the control system, the pump station motor must be started first to make the pump station in working state. To avoid starting the pump station in another place, the system adds the start and stop button of the pump station motor on the control cabinet, and the start signal sent by the button acts on the soft starter remotely to realize the start and stop function of remote control motor.Control Scheme. The main pump motor is started by soft starter, and the start/stop signal of soft starter is controlled through the console button to realize the start/stop control function of corresponding motor. Control process is in Figures 11 and 12.The valve group control system sends the control command to PLC through the knob on the operation panel or the virtual button on HMI, and the output signal drives the corresponding solenoid valve action through the relay to realize the corresponding functions.(2)
The power head is driven by 160 ml/R variable pump and variable motor. To realize the adjustable steering and speed, the system designs a three-position knob to control the action of the electromagnetic directional valve, so as to realize the steering control of the power head. At the same time, the potentiometer is designed to input 0∼5 V analog signal, and then, through the calculation of PLC speed regulation model, the first conductive signal of 0∼10 V driving proportional amplifier is output, the proportional amplifier to output 200∼600 mA current is controlled, and then the speed of power head is controlled.Forward/Reverse Control Scheme of Power Head. Forward/reverse switching control is realized through three-position four-way solenoid directional valve. That is, the control of the electromagnetic directional valve is realized through the console knob or the remote controller knob, to realize the control of the forward/reverse switching function. Control flow is shown in Figure 13.Stepless Speed Regulation Control Scheme of Power Head Output Shaft. The flow is adjusted by controlling the swing angle of variable pump, to realize the function of stepless speed regulation of power head output shaft. That is, the proportional electromagnet is controlled by the knob potentiometer, and then, the swing angle of the variable pump is controlled to realize the function of stepless speed regulation of the output shaft of the power head. Control flow is shown in Figure 14.Figure 11
Control flow diagram of the main pump motor.Figure 12
Control flow diagram of the auxiliary pump motor.Figure 13
Flow chart of forward/reverse control of the power head.Figure 14
Flow chart of stepless speed regulation control of power head output shaft.


## 6.2. Implementation Plan

Field commissioning stage: This stage involves speed regulation of power head under shunt state. The experimental parameters are shown in Tables3–5:(1)
Stage I: the displacement of the power head motor is kept unchanged, and the displacement of the hydraulic pump is adjusted from0∼145ml/r. At this time, the driving current of the power head motor is about 43mA (the corresponding digital quantity is 2000). According to the driving characteristic curve, the maximum displacement of the power head motor is 216.5ml/r.(2)
Stage II: the displacement of the power head motor is kept unchanged, the discharge of the hydraulic pump is adjusted to the maximum value of145ml/r (theoretical value), the actual control driving current is about 586mA (corresponding to the digital quantity of 27000), and the flow of the corresponding pump is 140ml/r. At this time, the displacement of the power head motor remains at the maximum value of 216.5ml/r.(3)
Stage III: the maximum displacement of the hydraulic pump is kept unchanged at145ml/r, and the displacement of the power head motor is adjusted from 216.5ml/r to Vgmin. When the software controls the minimum displacement of the power head motor, the corresponding driving current is about 526mA, Vgmin is 0.185 times, and Vgmax=216.5ml/r×0.185=40.0525ml/r.(4)
Stage IV: the rotating speed of the power head is the maximum, and the Baote remains unchanged.Table 3
Experimental parameters (relationship between displacement and current of the power head motor).
Serial number12Electric current200600CompanymAmADisplacement216.50Companyml/rml/rMaximum speed29005500Companyr/minr/minTable 4
Experimental parameters (relationship between pump displacement and current).
Serial number12Electric current200600CompanymAmADisplacement1450Companyml/rml/rMaximum speed14501450Companyr/minr/minTable 5
Experimental parameters (electromagnet at technical data EP1 and EP2).
Technical data electromagnets at EP1 and EP2VoltageEP112 V (±20%)EP212 V (±20%)Control current (mA)Initial control value at displacementVgmin400200Control termination value at displacementVgmax1200600


## 6.3. Empirical Conclusion

①
Compared with “the power head parameter table of enhanced TD2000 drilling rig under shunting state and turning into working condition,” there is an error in the maximum displacement control of hydraulic pump station, with an error of about5ml/r. There is still a little room for optimization, which can be optimized on-site.②
Compared with “the power head parameter table of enhanced TD2000 drilling rig under shunting condition and turning into working condition,” the minimum displacement control of power head motor has error, and the error is about2ml/r, so the optimization needs to be careful (during plant commissioning, when the speed regulation exceeds a certain position, the speed of power head decreases instead).③
In the whole speed regulation process, the trend is basically consistent with the table of power head parameters under shunting condition of enhanced TD2000 drilling rig, but there is a little error at the two end points. The error is as described in points ① and ② above. The position number described in the table is included in the whole speed regulation process and does not need to be corrected separately. Only the corresponding speed identification needs to be carried out on-site. The corresponding position is marked.


## 7. Conclusion

Aiming at the problem of whether the power head of raise boring machine can be driven in complex environment during reaming operation, using the fine-tuning characteristics of FOPID control to apply to the nonlinear control object, a method of adjusting FOPID control parameters based on whale optimization algorithm (WOA) is proposed. Through the establishment of the electrohydraulic coupling model of the power head of the raise boring machine and the simulation analysis in MATLAB software, the following conclusions are obtained (Table6):(1)
From the simulation results of six different combined control strategies, it can be seen that the overall control effect of FOPID is much better than PID control in the overshoot and response time in the frequency response curve. In PID control, the overshoot is at least 8.35%, while the overshoot of FOPID control is at most 6.9309%. The results show that FOPID is more suitable for the electrohydraulic control of raising boring than PID, and the overall response time is shorter. It can adjust the angular speed of the power head in time and then control the fast and slow switching of the power head, which shows that FOPID control has a better application prospect in the electrohydraulic drive control of raising boring.(2)
Among the six combined control strategies, the combined strategy based on WOA has obvious advantages in each control method. The overshoot of WOA-PID control strategy in PID control is at least 8.35% and takes 0.1 s; the overshoot of WOA-FOPID control strategy in FOPID control is at least 0.12137%, with a time of 0.02 s. From the numerical iteration process of WOA objective function, it can be found that WOA has good optimization ability and convergence performance, which verifies the excellent performance of WOA in control parameter tuning. The experimental data show that the WOA-FOPID combined control strategy studied in this paper can respond to the input in time, and the FOPID parameters are adjusted through WOA, which has a good effect on the optimization of control parameters and can effectively improve the control accuracy of FOPID.(3)
After the design of the control system is completed, it is debugged and applied on the raise boring rig. The control system realizes various functions including remote pump station start and stop control and single/double drive motor switching control and meets the requirements of process operation. Experiments show that the WOA-FOPID control strategy is effective in the electrohydraulic drive control system. The control strategy can make the electrohydraulic drive control have good real time, accuracy, and rapidity and can realize fast power head. Slow switching and high-precision control can be used as the exclusive control system of raise boring rig.Table 6
Meaning of each character in the text.
SymbolParameter meaningParameter value or unitCdFlow coefficient of solenoid proportional directional valve—ρHydraulic oil densitykg/m3AArea of solenoid proportional directional valve portm2psOutlet oil supply pressureMPaxSpool displacement of solenoid proportional directional valvempLOutlet flow or load flow of solenoid proportional directional valvem3/sCtmTotal leakage coefficient of hydraulic motorCtm=Cim+Cem/2VtTotal volume of oil inlet chamber, oil return chamber, and connecting pipe of hydraulic motor—βeEffective bulk modulus of elasticity—DmVolume displacement per radian of hydraulic motor—θmAngular displacement of output shaft of hydraulic motor—JeEquivalent inertia of reducer—BeEquivalent damping coefficient of reducer—UInput voltage—FdWire coil—iCurrent in coil—RcCoil internal resistance—cDamping coefficient of valve core armature assembly—rpInternal resistance of amplifier—KIVoltage force gain of proportional electromagnet—mQuality of valve core armature assembly—LDisplacement of valve core—ksSpring stiffness of armature assembly—FMCurrent magnet driving force—



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*Source: 9336561-2022-07-15.xml*