In accordance with the principles and parameters of the D − H connecting rod coordinate system of the manipulator, the homogeneous transformation relationship between the joints of the manipulator can also be expressed by the rotation matrix and the translation vector, so the homogeneous transformation moments of the front and rear joints of the manipulator are shown in Figure 3.

The homogeneous transformation matrix is expressed as T , the rotation matrix as R and translation matrix as P , then the homogeneous transformation matrix from joint n − 1 to joint n can be expressed as T n n − 1 , as shown in Eq. (1). Establishment of a joint coordinate system of the manipulator by using the D − H method, as shown in Figure 4. T   n − 1 = n   [ cos ⁡ θ n − sin ⁡ θ n ⁡ cos ⁡ θ n sin ⁡ θ n ⁡ sin ⁡ θ n α n ⁡ cos ⁡ θ n sin ⁡ θ n cos ⁡ θ n ⁡ cos ⁡ θ n − cos ⁡ θ n ⁡ cos ⁡ θ n α n ⁡ sin ⁡ θ n 0 sin ⁡ θ n cos ⁡ θ n d n 0 0 0 1 ] (1)

Based on Table 1, the transformation relation matrix T 1 from coordinate system X 0 − Y 0 to coordinate system X 1 − Y 1 is firstly established according to the D - H principle, as shown in Eq. (2). Using the same method, the subsequent transformation relation matrices between the two adjacent coordinate systems are T 2 , T 3 , T 4 , and T 5 , respectively. The expressions of the five coordinate-change matrices are shown in Eqs 3-6: T 1 = [ cos ⁡ θ 1 0 sin ⁡ θ 1 α 1 ⁡ cos ⁡ θ 1 sin ⁡ θ 1 0 0 α 1 ⁡ sin ⁡ θ 1 0 1 0 d 1 0 0 0 1 ] (2) T 2 = [ cos ⁡ θ 2 - sin ⁡ θ 1 0 α 2 ⁡ cos ⁡ θ 2 sin ⁡ θ 2 cos ⁡ θ 2 - cos ⁡ θ 2 α 2 ⁡ sin ⁡ θ 2 0 0 1 d 2 0 0 0 1 ] (3) T 3 = [ cos ⁡ θ 3 0 sin ⁡ θ 3 α 3 ⁡ cos ⁡ θ 3 sin ⁡ θ 3 0 0 α 3 ⁡ sin ⁡ θ 3 0 1 0 d 3 0 0 0 1 ] (4) T 4 = [ cos ⁡ θ 4 0 sin ⁡ θ 4 α 4 ⁡ cos ⁡ θ 4 sin ⁡ θ 4 0 0 α 4 ⁡ sin ⁡ θ 4 0 1 0 d 4 0 0 0 1 ] (5) T 5 = [ cos ⁡ θ 5 0 sin ⁡ θ 5 α 5 ⁡ cos ⁡ θ 5 sin ⁡ θ 5 0 0 α 5 ⁡ sin ⁡ θ 5 0 1 0 d 5 0 0 0 1 ] (6)

All revolute joints of the manipulator in this article are represented by the D - H parameters related to position and pose. The motion of the manipulator in this article is chain motion. By multiplying the homogeneous transformation matrix T i of each joint according to the subscript number, the total transformation matrix of the manipulator from the cloud platform to the end effector can be obtained, as shown in Eq. (7). T 5 1 = T 1 T 2 T 3 T 4 T 5 (7)

The simplified model of the manipulator of the mining roof bolter is shown in Figure 5. When the angle θ of each joint is known, the end position X , Y , Z can be obtained; on the contrary, when the end position X , Y , Z is known, the angle of each joint can be obtained, so the inverse solution of the manipulator of the mining roof bolter can be obtained.

To describe the working space of the manipulator of the mining roof bolter, the root of the manipulator is set as ( 0,0,0 ) , and according to the forward kinematics solution of the manipulator, ( x , y , z ) can be obtained. The random number is obtained by using the R a n d function in M A T L A B in accordance with the limit of each joint, and the random value is put into the forward kinematics equation to obtain the vector of the corresponding position. The working cloud diagram of the manipulator of the mining roof bolter is obtained, as shown in Figures 6–9.

From Figures 7–9, it can be seen that the working range of the manipulator of mining roof bolter is X ∈ [ 500,3200 ] , Y ∈ [ − 900 , + 900 ] , Z ∈ [ − 1100,2500 ] ; the working space of the manipulator of the mining roof bolter is approximately a part of the ellipse, and the simulated working space is compacted in the structure. Each joint of the simulated moving space is in line with the actual moving space, which can truly describe the working space of the manipulator.

In this article, genetic algorithm ( G A ) , particle swarm optimization algorithm ( P S O ) , whale algorithm ( W O A ) , and search algorithm ( G P S ) are combined with P I D and F O P I D , respectively, Through different combined control strategies, the control effect of the valve-controlled hydraulic cylinder is further analyzed and compared.

For the optimization algorithms used in different control strategies, an objective function is usually set to select the optimal value. The common error performance indicators include ISE (square deviation integral), ITSE (time square deviation integral), IAE (absolute deviation integral), ITAE (time absolute deviation integral), etc. In servo control, the ITAE (time absolute deviation integral) performance index weights the error, so that the error signal converges to zero as soon as possible. Therefore, this article takes the ITAE performance index as the objective function for parameter tuning (Semmari et al., 2017) as shown in Figure 11.

Here, the specific parameters of each algorithm are set as follows: P S O parameter settings: M a x _ i t e r = 200 , N = 20 , C 1 = C 2 = 1.49 ; the G A parameters are set as: N = 50 , M a x _ i t e r = 200 and the variation parameter is 0.8, and the variation probability is 0.75; The W O A − F O P I D parameter is set to: dim = 5 , M a x _ i t e r = 50 , S e a r c h A g e n t s _ n o = 100 ; W O A − P I D is set to: dim = 3 , M a x _ i t e r = 50 , S e a r c h A g e n t s _ n o = 100 _, the simulation time is second (s). The comparison of different combination strategies and control indexes is shown in Tables 2, 3. Figure 11 shows the comparison of the dynamic response curves of each combination strategy of the regulating system, a is the step-response diagram of each algorithm and P I D combination strategy, and b is the step-response diagram of each algorithm and F O P I D combination strategy. The comparison of the W O A algorithm-based P I D and F O P I D combined control strategies is shown in Figure 11. The numerical iteration curve of the W O A − F O P I D fitness function is shown in Figure 11.

(1) W E 9 - 62 T - H R W R 160 - U - R E V . D mathematical modeling and simulation test of the hydraulic motor

W E 9 - 62 T - H R W R 160 - U - R E V . D integer order mathematical model (Dasgupta et al., 1996; Maiti et al., 2008; Long et al., 2018; Caponetto et al., 2019; Wachholz et al., 2019; Do et al., 2020): G ( s ) = ϖ m ( s ) U ( s ) = K α K i m s 2 + c s + K s + K y K q D m ( s 2 ϖ h 2 + 2 ξ h ω h + 1 ) = 1 2.1393 × 10 − 7 s 4 + 4.66 × 10 − 5 s 3 + 2.79 × 10 − 3 s 2 + 1.42 × 10 − 2 s + 0.61 (9) W E 9 - 62 T - H R W R 160 - U - R E V . D fractional mathematical model of the hydraulic motor (Dimeas et al., 2017; Do et al., 2020; Ma; Higazy, 2020): G ( s ) = ϖ m ( s ) U ( s ) = K α K i m s 2 + c s + K s + K y K q D m ( s 2 ϖ h 2 + 2 ξ h ω h s + 1 ) = 1 2.14 × 10 − 7 s 3.99 + 4.66 × 10 − 5 s 3.0042 + 0.0028 s 1.998 + 0.0143 s + 1 0.61 (10)

Fractional order F O P I D controller is expressed as: (Elkhazali, 2013; Maâmar and Rachid, 2014; Tolba et al., 2018): G c = 0.487 + 5.4042 s − 0.023 + 5.4837 s 1.2908 (11)

Integer order P I D controller expression is: (Zamani et al., 2009; Ding et al., 2017; Ren et al., 2019)_: G c = 30 + 1.6952 s − 2 + 24.5197 s (12)

Respectively, four types of the intelligent control algorithm are used for parameter tuning of the F O P I D controller—integer order parameter, the F O P I D controller—fractional order controlled object, the P I D controller—fractional integer order controlled object, and the F O P I D controller—fractional integer order controlled object. From Table 3 and Figure 13, according to the results of the simulation experiments, the P I D control is not dominant in a complex system compared to FOPID, overshoot amount at about 30%, and settling time floating around 0.7 s; According to the results of the data based on W O A algorithm parameters tuning of the system has a certain advantage, settling time reduced to 0.3 s.

On the whole, the F O P I D controller has shown a better control effect on the fractional order-controlled object, and the overshoot has been reduced. According to the data results, the optimization ability of the W O A algorithm is obvious, which makes the controlled system have better stability. For the fractional controlled object, the stability can be achieved in 0.19s, and the overshoot is 3.49%. This fully reflects the superiority of the fractional order F O P I D controller, as shown in Figure 13.

In response speed, adjustment time, and steady-state accuracy, the fractional order W O A − F O P I D controller has a better control effect than the fractional order G P S − F O P I D controller, integer order G P S − P I D controller, fractional order G A − F O P I D controller, integer order G A − P I D controller, fractional order P S O − F O P I D controller, integer order P S O − P I D controller, and integer order W O A − F D controller. In this study, the intelligent optimized whale algorithm W O A is directly applied to the systematic controllers of the oil cylinder D O A 090470 - 1 ( 1 ) and D O A 090260 - 1 in the manipulator for parameter tuning, and the control strategies of different combinations are compared and analyzed (Table 4).

(2) Mathematical modeling and simulation test of the hydraulic cylinder D O A 090470 - 1 ( 1 )

The integer order mathematical model of the hydraulic cylinder D O A 090470 - 1 ( 1 ) (Zhan et al., 2015; Dingyu, 2020): G ( s ) = X P U = K q A p K i k x s ( s 2 ϖ h 2 + 2 ξ h ϖ h s + 1 ) = 48.625 s ( 3.6 × 10 − 3 s 2 + 0.727 s + 1 ) (13) G ( s ) = X P U = K q A p K i k x s ( s 2 ϖ h 2 + 2 ξ h ϖ h s + 1 ) = 48.625 s ( 7.38 × 10 - 4 s 2.0214 + 1.48 × 10 − 3 s 0.9731 + 1.99 × 10 − 2 ) (14)

Integer order P I D controller expression (Elkhazali, 2013; Maâmar and Rachid, 2014; Tolba et al., 2018): G c = 18.4022 + 30 s − 1 (15)

Fractional order F O P I D controller expression (Zamani et al., 2009; Ding et al., 2017; Ren et al., 2019): G c = 29 . 9442 + 29 . 9660 s − 0 . 0308 + 13 . 1634 s 1 . 104 (16)

Figure 14 and Table 5 show that the P I D controller is not fit in complex systems, and the results show that it fails to fulfill fine-tuning, especially as the controlled object gradually stabilizes after 6.06s when the P I D fractional order acts. In the complex system, the F O P I D controller has a better control effect on the fractional order controlled object, and the overshoot is 8.672%, which can be settled in 0.02s. The D O A 090470 - 1 ( 1 ) hydraulic cylinder parameter is shown in Table 6.

(3) Mathematical modeling and simulation test of the hydraulic cylinder D O A 090260 - 1

Integer order mathematical model of the hydraulic cylinder D O A 090260 - 1 (Zhan et al., 2015; Dingyu, 2020): G ( s ) = X P U = K q A p K i k x s ( s 2 ϖ h 2 + 2 ξ h ϖ h s + 1 ) = 48.625 s ( 2 × 10 − 3 s 2 + 0.0726 s + 1 ) (17) G ( s ) = X P U = K q A p K i k x s ( s 2 ϖ h 2 + 2 ξ h ϖ h s + 1 ) = 48.625 s ( 4.11 × 10 − 5 s 1.9946 + 0.0015 s 0.9989 + 0.02 ) (18)

Expression of the integer order PID controller [41–43]: G c = 11.2292 + 30 s − 2 + 1.35 × 10 − 8 s (19)

Expression of the fractional order F O P I D controller (Zamani et al., 2009; Ding et al., 2017; Ren et al., 2019): G c = 0.4758 + 27.2283 s − 2.5323 + 29.9673 s 1.0212 (20)

Figure 15 and Table 7 show that the F O P I D controller has a better control effect for fractional controlled objects, and the overshoot can reach 6.84% in 0.5s. On the whole, the F O P I D controller is more stable than the P I D controller, and the P I D control strategy shows almost the same control effect, which is about 20%. In the actual support work of the manipulator, if there is an overshoot in the oil cylinder displacement control system, it will lead to the inaccurate positioning in the drilling hole, which will take more time, and even influence the effectiveness of electronic components in the manipulator. If 16 bolts need to be installed in a roadway section, the mechanical arm takes one more minute for installation of each bolt due to the overshoot, and takes another 16 min in total to complete the support work of a section. Cost function vs. iterations is plotted for the mathematical modeling and simulation tests of the hydraulic cylinder, as shown in Figure 16.

The plan of an electric–control system is shown in Figure 19. The control system adopts a modular design, and each functional module runs independently without interference, so as to avoid whole equipment paralysis due to a single failure. The electric control system can be divided into five modules: main circuit unit, power unit, protection unit, signal conditioning isolation unit, and logic control unit. The block diagram of the control system module is shown in Figure 20.

The main circuit module defines the main structure of the system, and the isolation switch is applied as the switch of the main circuit power supply of the electrical control box to control the oil pump circuit. In terms of control, a vacuum contactor is used in the oil pump circuit, and installed the resistance and capacitance absorption device, to absorb the high voltage generated by the motor in the vacuum contactor disconnection. There are three current transmitters on the cables of each circuit to complete the acquisition of analog quantity.

The power module is mainly composed of a main transformer and four air circuit breakers. The main transformer has three voltage ranges of the input tap: 1,250, 1,140, and 1,025 V. When the voltage is unstable in the coal mine, the transformer tap can be adjusted with the voltage change to ensure the stability of the output voltage, and then ensure the reliability of the control loop. A 24 V tap provides power for the lamp, 220 V for the contactor coil and power modules, and 127 V for the intrinsic safe power supply.

The short-circuit protection of the main circuit and the transformer circuit is realized by a circuit breaker. The motor over-current, overload, and phase break of each driving mechanism are prevented by the P L C controller. Leakage locking, leakage monitoring, and overheating are prevented by using an integrated protector. Signal acquisition of the main circuit and the control circuit by a current transmitter and protection unit on each branch cable is processed and judged by an electronic circuit and controller program.

The signal isolation module and the signal conversion module together constitute the signal conditioning isolation module. The isolation module realizes the conversion of (non) intrinsic safety signal, the input and output of various controllers and peripheral devices in the control system. The logic control unit is the core part of the entire electrical system, which can complete various protection functions and communication functions of the motor, and also realize the corresponding control functions: the actual running state of each motor is judged through the calculation and processing of the collection parameters of the system; if a fault occurs, appropriate trip instructions are issued according to the type of fault.

The control cabinet consists of a PLC controller module, HMI module, and a receiver module. Each working condition monitoring unit and input/output driving unit cooperate with each other to ensure the stable operation of each control function of the system. The hardware structure block diagram of the control system is shown in Figure 19. Digital input drive unit, analog input drive unit, and the antenna are the control center of the main input module, in which the knob and switch sensor units input information to the digital input drive unit; the handle potentiometer and analog sensor input information to the analog input drive unit; the remote transmitter inputs information to the receiver module through the antenna. The digital output drive unit comprises of a light, an indicator light, and a switching electro-magnetic valve; the analog output drive unit includes a variable pump and a proportional electro-magnetic valve. The hardware structural block diagram is shown in Figure 21. In addition, this study carried out the design of the power circuit and selection of the main components.

The software system is composed of an operation signal processor, video signal processor, fault information alarm software, equipment parameter setting software, data display and analysis software, data storage and analysis software, and signal output control software. Its structural block diagram is shown in Figure 22.

The electronic control system adopts the Siemens 200 series P L C host and its corresponding expansion module (analog output/input), and communicates with the remote control receiving unit through the P L C host’s own R S 485 communication interface ( M o d b u s ⋅ R T U ) , so as to precisely conduct motions, such as pump motor start and stop, large manipulator movements, expansion of the front and rear top tightening cylinders, forward and reverse rotations of the rotary motor, cylinder’s forward and backward, horizontal rotary positively and negatively, vertical rotary positively and negatively, adjustment of the oil cylinder, cylinder of gripper opening and closing, upper rod of manipulator sending, opening and closing of manipulator, drilling rod storeroom forward and reversing rotary, pin hydraulic cylinder opening and closing, water valve opening and closing, detection and protection of the hydraulic system through the acquisition of oil tank temperature and hydraulic system pressure sensor signals, and the display on the remote transmitter screen through R S 485 communication. A position sensor is installed to detect the position of the mainframe and the drilling rod store to ensure the precision control of automatic drilling/un-drilling. Motor intelligent integrated protector can display the real-time voltage and current of the system, with protection functions avoiding over voltage, under voltage, overload, short circuit, circuit break, phase break, leakage, display, and store alarm fault in real time. A proportional electro-hydraulic valve can adjust the hydraulic valve opening and pressure value through the P W M output signal of the P L C analog expansion module and proportional amplifier. Manual/automatic control of a locomotive can be realized by an internal ladder diagram program operation. Automatic control adopts the one-button operation, where the equipment can automatically complete the drilling/un-drilling process and have the suspension function and the one-button emergency stop function for the operator to deal with the emergency situation in the process of an automatic operation.

A hydraulic anchor rod drill truck was carried out to the ground training drill from August 22 to August 23,2019, arrived to the coal mine on August 24, on August 25, in 11,505W, the transport lane carried out an industrial test, on August 26 implemented fire debugging, operation, and on August 28 began an advanced supporting anchor cable test behind the excavator. The periodic summary is as follows:

As of September 9, 38 holes were drilled, among which 35 were anchored, 3 holes were drilled during the test, respectively 3.0, 5.0, and 5.5 m, without anchoring.

With a 6.3 m grouting anchor, it takes about 4 min on average to move forward to adjust the position of the drill truck, 14 min on average to drill, 8 min on average to withdraw the drill, 4 min on average to install the anchor cable, and 30 min on average in total. Fourteen representative boreholes in the early experimental period were selected for analysis, as follows in Table 8.

According to the experimental conclusions:

(1) After the control system design is completed, it is debugged and applied on the roof bolter. The control system realizes the remote pump station start–stop control, hydraulic cylinder position control, and meets the requirements of the process operation. The experiment proves that the W O A − F O P I D control strategy in an electro-hydraulic drive control system of effectiveness. The control strategy can make the electric hydraulic drive control in good real-time performance, accuracy, and rapidity. The manipulator can achieve high precision control in the underground roadway and can be used as a new control method for roof bolter.