Research on a Pressure Control Method for a Liquid Supply System Based on Online Updating of a Radial Basis Function Neural Network

Abstract

In order to solve the problem of frequent pressure fluctuations caused by fluid quantity variation in hydraulic support liquid supply systems and the pressure response lag caused by long-distance pipelines, an online updated radial basis function neural network (RBF neural network) control method was proposed for the long-distance liquid supply system. Based on the analysis of the measured pressure fluctuations of the mining face and the process of the stable pressure liquid supply system, the influencing factors of the stable pressure liquid supply flow demand were obtained. The flow set of the stable pressure liquid supply system was established and fitted in the SimulationX–Simulink co-simulation model and the online correction was carried out by using the characteristics of the repeated action of the hydraulic support. Finally, the online updating RBF neural network regulator was established to realize the pressure regulator control of the pumping station, and the experimental platform was set up for verification. The results show that this method can effectively reduce the pressure fluctuations caused by the change in the flow demand of the mining face, and can adjust the flow rate of the mining face, reduce the pressure impact, and improve the efficiency of the machine.

1. Introduction

After years of development and innovation, the coal industry has gradually developed from traditional mining to mechanized and automated mining [1]. However, due to the complex and diverse coal seam conditions and the lack of coordinated and orderly control methods for all the equipment utilized in fully mechanized mining faces [2,3], intelligent and automated coal mines still present important issues that need to be urgently solved. The liquid supply system of the emulsion pump station, as the power source of the hydraulic support of the mining face support equipment, directly affects the stability of the mining face support and the safe advance of the mining face [4]. However, the pump station is difficult to adapt to the strong time-varying conditions because of the large difference in liquid flow required by different hydraulic support operation types. Moreover, the gradual application of centralized liquid supply further increases the difficulty of control. Therefore, it is of great significance to study the pressure regulation control method of long-distance liquid supply systems [5,6,7].

At present, the flow regulation method of pumping stations mainly adopts two ways: multi-pump linkage and frequency conversion regulation. The control technology mainly includes the traditional signal feedback control form such as pressure and the form of neural network fitting and predictive control. Among them, Hashim [8] used PLC control and remote monitoring to improve the performance of the pump station of the pipeline transmission system. Studzonski [9] introduced the algorithm for controlling the water supply pump by pipeline load and node pressure, which can ensure the required pressure while reducing energy consumption. Briceno-Leon [10] discussed how pump characteristics and set point curves affect the optimal number of variable frequency pumps (VSPs) and fixed point pumps (FSPs) and proposed an optimal pumping configuration for any pump and set point curve with minimal energy consumption. Lyu [11] comprehensively utilized the coordinated control of the valve and pump station to generate control commands of the pump station and valve based on model compensation and tracking error, which ensured good tracking accuracy while achieving a high level of energy efficiency. The above control methods all adopt the form of real-time signal feedback but lack pressure prediction compensation, and the response time is affected by the frequency converter. Tan [12] trained the collected system pressure based on the Elman neural network and predicted the frequency conversion adjustment to stabilize the system pressure near the target value. Balla [13] established a simplified model of pump station control to linearize the daily demand peak point considering pipeline loss and water resistance and applied the model in the predictive control scheme to achieve good results. Tian [14,15] determined the flow demand of hydraulic support by establishing a shearer speed prediction model and introduced power matching technology to optimize the output of the emulsion pump station. Li [16] proposed a hydraulic support liquid supply prediction model based on shearer position and other parameters, which solved the problem of time prediction of a long sequence of liquid supply and realized intelligent liquid supply combined with multi-pump linkage. Ma [17] proposed the concept of overlapping time for micro-pump systems and realized the reduction in pressure pulse from the perspective of control theory. Vodovozov [18] provided a head and pressure prediction method by modeling and analyzing centrifugal multi-pump pumping stations to keep system performance in the optimal efficiency range. In the above studies, the demand is predicted and regulated by the relevant signals of the system. However, the designed liquid supply control methods are easy to aim at constant pressure, which may cause frequent pressure fluctuation in the unloading valve interval when applied to the emulsion pump station.

Therefore, on the basis of the analysis of the steady pressure liquid supply process, the RBF neural network is applied to predict the demand of the pumping station, and the online updating method is used to dynamically compensate the uncertain conditions, such as fluid leakage and load change. Due to its strong fitting performance, the RBF neural network has been widely used in fluid control and time series prediction [19,20]. Xu [21] used the RBF neural network to fit the numerical model of convection dynamics, and adopted the NSGA-II optimization algorithm to optimize the hydraulic performance of the ring jet pump with multiple objectives, thus improving the head ratio and efficiency of the ring jet pump. Lei [22] and You [23], respectively, used RBF neural networks to provide prediction models with good anti-interference performance for thermal systems with large delays and time delays, which met the control requirements. Uddin [24] used the Levenberg–Marquardt algorithm to study the transient thin film flow of Maxwell nanofluids on a horizontal disk under the action of radiation, magnetic field, and Joule heat. After completing the construction of the online updated RBF neural network controller, the SimulationX–Simulink co-simulation model and experiment were used to verify the effectiveness of the control method, which provides a guarantee for the realization of safe hydraulic support.

2. Measurement and Analysis of Liquid Supply Pressure

2.1. Rated Liquid Supply System Pressure

The pressure stability of the liquid supply system is an important indicator to measure whether the flow of the emulsion pump station meets the demand of the hydraulic support. Figure 1 shows the measured pressure curve at the outlet of a pump station on a mining face. The rated liquid supply flow is 400 L/min.

It can be seen from Figure 1 that when the amount of fluid used in the hydraulic support system of the mining face is different, the rated liquid supply leads to three kinds of pressure fluctuations detailed below.

(a) The support performs a large amount of liquid action: due to insufficient liquid supply, the system pressure is continuously reduced to below the unloading valve load pressure, and the pressure is increased when the action is completed. (b) The support performs a small amount of fluid action: the system pressure fluctuates rapidly and frequently between the loading and unloading pressure of the unloading valve. (c) The support does not perform an action: the system pressure fluctuates regularly between the loading and unloading pressure of the unloading valve due to the leakage.

2.2. Stable Pressure Liquid Supply Process

In order to improve the characteristics of frequent fluctuation of rated liquid supply pressure, a matching stable pressure liquid supply was proposed according to the flow requirements of different movements of the hydraulic support [16]. The pressure curve of the stabilized liquid supply process is shown in Figure 2. This process is divided into four stages detailed below.

(a)

System slow leakage stage

No action is performed at this stage; the pump station is unloaded and the system slowly decreases from unloading pressure p_h to loading pressure p_l due to leakage. The duration of stage a is calculated using the following formula:

$$T_0=\frac{V_h-V_l}{Q_{out}}$$

(1)

where Q_out is the leakage flow, and V_h and V_l are the volume of the accumulator pressure at p_h and p_l.

(b)

System rapid supply fluid stage

In this stage, no action is performed; the pump station is in the loading state to fill the accumulator with liquid, and the system pressure rises rapidly from p_l to p_h. In this stage, the leakage of the system can be ignored due to the short time. The duration of stage b is calculated using the following formula:

$$T_1=\frac{V_h-V_l}{Q_{\mathfrak{p}}}$$

(2)

where Q_p is the liquid supply flow of the pumping station.

(c)

Accumulator supply fluid stage

At the beginning of this stage, because the unloading valve is in the unloading state, the accumulator supplies liquid to the hydraulic support.

(d)

Pumping station supply fluid stage

As the support action reduces the system pressure to the unloading valve loading pressure, the pumping station enters the loading state. At this stage, the pumping station simultaneously supplies liquid to the accumulator and the hydraulic support and ensures that the system pressure rises. Under ideal conditions, the pressure rises at a uniform speed, and the hydraulic support completes the stroke ∆L while the system pressure rises to the unloading pressure of the unloading valve. The hydraulic support cylinder pressure is determined using the following formula:

$$p{A}_{in}=F_q+\theta \nu A_{out}+ma$$

(3)

where p is the real-time pressure, A_in and A_out are the areas of the inlet and outlet cavities of the hydraulic cylinder, F_q is the load of the hydraulic cylinder, θ is the resistance coefficient of the hydraulic cylinder related to the action speed, m is the load mass of the hydraulic cylinder, and a is the action acceleration of the hydraulic cylinder. The hydraulic cylinder stroke is satisfied using the following formula:

$$\mathsf{\Delta }L=v_1{T}_3+\frac{1}{2}a{T}_3^2$$

(4)

Assuming that the flow rate of the stabilized liquid supply is Q_s, the balanced formula of the amount of liquid used in the hydraulic cylinder, the amount of liquid filled in the accumulator, the amount of leakage in the system, and the amount of liquid supplied at the stabilized pressure in the pumping station are satisfied using the following formula:

$$Q_s{T}_3=\mathsf{\Delta }L{A}_m+Q_{out}{T}_3+V_h-V_l$$

(5)

According to Formulas (1)~(5), when the rated capacity of the accumulator, the amount of leakage in the system, and the resistance coefficient of the hydraulic cylinder are constant, the flow rate of the ideal stabilized liquid supply changes with the action area of the hydraulic cylinder, the action stroke, and the load size of the hydraulic cylinder during the action of the hydraulic support.

3. Simulation Model

3.1. Hydraulic Support System

Based on the data of a certain mining face, a Simulation-X model of the stable pressure liquid supply system was designed. The hydraulic support model was named the ZY6800/24/50D hydraulic support. A total of 120 sets were divided into five groups, and each action of the hydraulic support was connected to the displacement sensor for feedback. (See

Table 1. The main parameters of the hydraulic model.

Name	Parameter		Value	Units
Emulsion	Density		998	kg/m3
	Dynamic viscosity		6	cP
Energy accumulator	Capacity		20	L
Long-distance steel pipe	Diameter		65	mm
	Wall thickness		12	mm
Hydraulic support	type		ZY6800/24/50D	/
	Column cylinder	Amount	2	/
		Cylinder diameter	320/230	mm
		Rod diameter	290/210	mm
		Setting load	2533	kN
	Pushing cylinder	Amount	1	/
		Cylinder diameter	180	mm
		Rod diameter	120	mm

and Figure 3).

3.2. RBF Neural Network Control

As a local approximation network, the RBF neural network can map the relationship between each sensing factor of the liquid supply system and the flow rate of the pumping station. The RBF neural network consists of n input layer neurons, h hidden layer neurons, and m output layer neurons [17]. (See Figure 4)

(1)

Input layer

The number of input layer neurons is consistent with the dimensions of the input vector in the sample. The selected input parameters are pipeline length, hydraulic support group number, hydraulic support action type, hydraulic support action stroke, pressure limit of unloading valve, and whether the hydraulic support action is about to be put in place. In order to adapt to different distance liquid supply lines and working conditions during mining, Simulation-X data sets were collected. Among them, the input parameters were consistent with the actual downhole long-distance liquid supply status, and the pipeline lengths were selected as 600 m, 1200 m, 1800 mm, 2400 m, and 3000 m, respectively. The serial numbers of each hydraulic support group are marked as group 0, group 1, group 2, group 3, or group 4. The four movements of hydraulic support are marked as serial numbers 0, 1, 2, and 3. The hydraulic support column displacement used was 0.2 m and 0.3 m; there are two kinds. There are four kinds of displacement: 0.6 m, 0.7 m, 0.8 m, and 0.9 m. The commonly used unloading pressures of the unloading valve are marked as serial numbers 0 and 1. Whether or not the hydraulic support action feedback from the displacement sensor is complete is marked as 0 or 1, and the combination mode of each parameter is shown in Figure 5. When each group of data is collected, the stable pressure liquid supply curve as shown in Figure 2 is the standard, and the corresponding stable pressure liquid supply flow rate is recorded as the output.

Input $X={[x_1,x_2,x_3,\cdots ,x_n]}^{\mathrm{T}}$; input variables are passed to the hidden layer.

(2)

Hidden layer

The transfer function of a single neuron is as follows:

$$r_{{}^i}=\exp [-\frac{{\left(x-x_i\right)}^{\mathrm{T}}\left(x-x_i\right)}{2{\sigma }^2}],i=1,2,\cdots ,h$$

(6)

where σ is the smooth factor.

(3)

Output layer

The output layer performs direct summation of neurons and summation with different connection weights, respectively:

$$S_D=\sum _{i=1}^n{r}_i$$

(7)

$$S_{Nj}=\sum _{i=1}^n{y}_{ij}{r}^i,j=1,2,\cdots ,\mathrm{h}$$

(8)

where y_ij is the connection weight of the hidden layer j neuron and the i neuron when summing. The number of neurons in the output layer is consistent with the output vector dimension k, where the output is the flow value Q and the calculation method is as follows:

$$y=\frac{S_{Nj}}{S_D}$$

(9)

Because of the complex and variable operating conditions of hydraulic support, it is necessary to identify the model fit in real time to ensure that the model fit mismatch can be updated online. For RBF neural networks, performance improvement depends on the addition of hidden layer neurons or reasonable adjustment of network weights [25,26]. When evaluating whether the current fitting meets the accuracy requirements, MSE, the mean square error of the pressure collected by the system and the stable pressure supply pressure within 1 s between the end of the action and the start of the next action, is selected as the judgment index, and the calculation formula of MSE is as follows:

$$\begin{array}{c}MSE=\frac{1}{N}{\displaystyle \sum _{i=1}^N}{\left[y_{pv}(t)-y_{sp}(t)\right]}^2\end{array}$$

(10)

where N is the data length, y_pv is the current pressure value, and y_sp is the target pressure value of the stabilized liquid supply. The basis of judgment is:

$$\{\begin{array}{l}\sqrt{MSE}<\beta y_{sp}, notupdate\\ \sqrt{MSE}\ge \beta y_{sp}, update\end{array}$$

(11)

where β is the proportional coefficient determined according to the operating fluctuation. When the group i data are input into the network, the prior output fitted by the label network using the previous group i − 1 data is f⁽ⁱ⁻¹⁾(x). If the prior output f⁽ⁱ⁻¹⁾(x) of the network for this group meets the requirement that Formula (11) does not update, the network does not add neurons. If the prior output f⁽ⁱ⁻¹⁾(x) meets the update requirements, new hidden layer neurons are added to improve the network performance.

When the decision needs to be updated online, the posterior estimate output formula of the RBF neural network is as follows:

$$f^{(i)}(x)=f^{(i-1)}(x)+e_i{R}_i(x)$$

(12)

where e_i = y_i − f⁽ⁱ⁻¹⁾(x) is the prior error of the RBF neural network, and R_i(x) is the Gaussian radial basis function. Then, remember that the number of hidden layer neurons before this update is n − 1; therefore, the network output after the update is determined as follows:

$$f^{(i)}(x)={\displaystyle \sum _{k=1}^{n-1}{\omega }_k{R}_k(x)}+e_i{R}_i(x)={\displaystyle \sum _{k=1}^n{\omega }_k{R}_k(x)}$$

(13)

where ω_k is the network weight of the k neuron. The new hidden layer neuron parameters are as follows:

$$\{\begin{array}{c}{\omega }_n=e_i\\ w_n=x_i\\ {\sigma }_n=k\parallel x_i-w_{ir}\parallel \end{array}$$

(14)

where ω_n is the weight of the new neuron, w_n is the center of the radial basis function of the new neuron, x_i is the input vector of the i training, σ_n is the width of the radial basis function of the n neuron, k is the overlap factor of the neuron relative to the input space, and w_ir is the neuron parameter closest to the norm of the i neuron.

The generated Simulink control model is shown in Figure 6.

4. Analysis of Simulation Result

The flow data of the stabilized liquid supply system under different operating conditions of the support were calculated by batch processing for training, and the parameters were adjusted to make the results optimal. The simulation of pressure wave propagation speed, single stabilized liquid supply control, and multiple online updating stabilized liquid supply control were carried out in the model, and the pressure fluctuation of the system was obtained.

4.1. Velocity of Pressure Wave Propagation

In order to obtain the propagation speed of pressure wave in the pipeline for the advance adjustment of the flow rate of the pumping station, two points A and B, which are 600 m apart on the pipeline during normal operation, are selected to generate a pressure shock immediately when the unloading valve is loaded. The signals of two points A and B are recorded as shown in Figure 7.

In order to calculate the transmission speed of pressure waves in the pipeline, correlation analysis is required for signals at point A and point B [27]. Suppose that the pressure fluctuation signals of sensors A and B are A(t) and B(t), respectively, which can be expressed as:

$$\begin{array}{c}A(t)=f(t)+N_A(t)\\ B(t)=f(t+{\tau }_0)+N_B(t)\end{array}$$

(15)

where f(t) is the pressure fluctuation during the loading of the unloading valve, and N_A(t) and N_B(t) are the background noise of the two sensors, respectively. Then, conduct the correlation analysis for A(t) and B(t) as follows:

$$\begin{array}{ll}{R}_{AB}(\tau )& =\underset{T\to \infty }{\lim }\frac{1}{T}{{\displaystyle \int }}_0^{T}A(t)B(t+\tau )\mathrm{d}t\\ & ={{\displaystyle \underset{T\to \infty }{\lim }\int }}_0^T\left[f(t)+N_A(t)\right]\cdot \left[f(t+{\tau }_0+\tau )+N_B(t+\tau )\right]\mathrm{d}t\end{array}$$

(16)

Since the pressure fluctuation signal is independent of the background noise, and the pressure fluctuation signal is not correlated with the background noise signal, the above formula can be written as:

$$R_{AB}(\tau )=\underset{T\to \infty }{\lim }{{\displaystyle \int }}_0^T\left[f(t)f(t+{\tau }_0+\tau )+N_A(t)N_B(t+\tau )\right]\mathrm{d}t$$

(17)

Therefore, the signal at points A and B is filtered to eliminate the interference of N_A(t) and N_B(t), while the signal at points A and B needs to be centralized and its mean value subtracted. When the correlation function R_AB(τ) reaches its peak, the corresponding τ is the time corresponding to the pressure wave from sensor A to sensor B, thus the transmission speed of the pressure wave at this time can be calculated as shown in Figure 8. Based on the results of correlation analysis, it is calculated that the velocity of the pressure wave in the pipeline is 1456 m/s.

Meanwhile, wave velocity is calculated by the formula:

$$u_m=\sqrt{\frac{1/p_m}{\frac{D}{E_{p}e}+\frac{1}{E_1}+(\frac{1}{E_p}+\frac{1}{E_1}){\alpha }_g}}{C}_1$$

(18)

where a small amount of gas is mixed in the emulsion, p_m is the density of the liquid and the gas-mixed fluid, D is the pipe diameter, E_p is the elastic modulus of the pipe, E₁ is the elastic modulus of the emulsion, α_g is the volume concentration of the gas, and C₁ is the correction factor related to the pipe constraints. The result is 1524 m/s, which is 4.4% different from the simulation, and the correctness of the model is verified within the error range.

According to the obtained pressure wave propagation velocity, the flow rate of the pumping station can be adjusted in advance in the stabilized pressure liquid supply control, which can reduce the lag caused by the pipeline pressure propagation.

4.2. Single Stabilized Pressure Liquid Supply Control

As a comparison, system pressure data were collected in the simulation model when the rated liquid supply support was descending, pulling, rising, and pushing. The flow rate was 400 L/min, and the results are shown in Figure 9.

The RBF neural network was used to carry out a single non-online update of the stable pressure liquid supply control system.

A total of 300 data sets were randomly divided into training sets, test sets, and verification sets, and normalized processing was carried out. In this paper, the Gaussian function is chosen as the radial basis function of hidden layer neurons. In order to ensure the good generalization ability of the neural network, the parameters of the RBF neural network were optimized using cross-validation. The initial hidden layer neuron number was 30, the learning rate was 0.03, and the radial basis function width was 16.

After training and fitting, the average absolute error MAE of the training collection volume value was finally obtained as 3.21 L/min, the average absolute error of the test set flow was 3.38 L/min, the fitting root mean square error RMSE of the training set reached 3.76 L/min, and the test set reached 3.62 L/min after iteration. Its flow value meets the requirement of a stable pressure liquid supply system in a pumping station. The regression analysis diagram of the training effect is shown in Figure 10. As can be seen from the figure, the overall correlation coefficient R reaches 0.99965, the slope of the fitting line is 1, and the intercept is −0.00033. It can be seen that the neural network achieved a good fitting of the data.

Figure 11 shows the comparison between the predicted value of the test set and the flow value of the ideal stabilized liquid supply, and its goodness of fit R² reaches 0.99906, meeting the requirement of the stabilized liquid supply.

In the model, the hydraulic support descending, pulling, raising, and pushing actions are carried out successively, and the pressure fluctuation curve is finally obtained as shown in Figure 12. It can be seen that the pressure-stabilized control method can effectively reduce the pressure fluctuation in the process of descending and pushing, increase the pressure in the process of pulling and rising, and reduce the overall operation time from 21.5 s to 16 s, saving 25.6% of the operation time, thus effectively improving the efficiency.

4.3. Online Updating of Stabilized Liquid Supply Control

Although the RBF neural network can fit the training set data well, if the data collection deviation or the working condition changes during production, it causes a large error in the stable pressure supply flow, which makes it difficult to meet the real-time requirements of the mining surface. Therefore, it is necessary to update the stabilized pressure supply flow control online. The online update takes advantage of the continuous repetitive action of the hydraulic support and compares the system pressure with the target pressure of the stabilized liquid supply at each action. If the control indicator threshold is exceeded, the liquid supply flow parameter is adjusted accordingly so that the next flow rate is more accurate.

In the simulation, assume there is a sudden leakage of the liquid supply system at the mining face, that is, add a leakage port of 30 L/min, and then the online updating control process is carried out on this basis. After several operation cycles of the support, the liquid supply flow rate was recorded and the error between the flow rate and that of the corresponding stable pressure was determined, as shown in Figure 13. It can be seen that after the change in working conditions, the maximum error of liquid supply flow is 13.6%, and the error of liquid supply flow is continuously reduced in each operation cycle. After five iterations, the error is all less than 4%, which meets the demand for the stable pressure liquid supply.

The pressure curve of a single hydraulic support during multiple online updating cycles is shown in Figure 14. As can be seen from the figure, due to the increase in leakage, in the first operation cycle, the liquid supply flow is insufficient, and the system pressure is low at the end of the operation, especially when the descending action is more obvious, and a large pressure impact is generated at the end of the operation. After five iterations of the action cycle, there is no great pressure impact during and at the end of the action. The results show that the online updating RBF neural network has good adaptability to the change in operating conditions.

5. Experiment

In order to further verify the effectiveness of the control method, a stable pressure liquid supply control experimental platform was built. The experimental equipment and principles used are shown in Figure 15, including three parts: the stable pressure control system, the pumping station system, and the hydraulic support system.

In order to ensure liquid supply, two variable frequency drives were used in the experiment to drive the 200 L/min and 80 L/min emulsion pumps in parallel, and pressure sensors were installed behind the unloading valve. Three oil cylinders were used to simulate the hydraulic support, among which two cylinders were used to simulate the column cylinder and one was used to simulate the pushing cylinder. The parameters of the platform are shown in

Table 2. Parameters of the experimental platform.

Name	Parameter	Value	Units
Emulsion	Density	998	kg/m3
Emulsion pump	Flow	200/80	L/min
Energy accumulator	Capacity	20	L
Loading cylinder	Amount	3	/
	Cylinder/rod diameter	110/80	mm
Column cylinder	Amount	2	/
	Cylinder/rod diameter	160/105	mm
Pushing cylinder	Amount	1	/
	Cylinder/rod diameter	160/105	mm

, and the platform is shown in Figure 16.

The control program of the stable liquid supply is written in LabVIEW, the data acquisition and transmission are realized using a PCI data acquisition card, and the MATLAB script can be integrated into LabVIEW for control [28].

First, as a comparison, a rated liquid supply experiment and a PID control experiment were carried out in the platform [29]. The pressure curve of the acquisition system is shown in Figure 17 and Figure 18. Then, an online updating RBF neural network control experiment was conducted. After several online updates, the output flow stabilized, and the system pressure is shown in Figure 19.

In the test of the stable pressure liquid supply control system, the three operation pressures of the support dropping column, shifting frame, and pushing and sliding meet the demand of stable pressure liquid supply, only the lifting column action does not reach the unloading pressure when the operation is completed because the maximum liquid supply flow of the pump station is only 280 L/min.

By comparing the collected pressure curves, it can be seen that the pressure stability control method improved in different degrees in terms of pressure stability and support action time efficiency.

In terms of pressure stability, the amplitude of the rated liquid supply pressure wave is large, especially the movement of pulling and rising with a large amount of liquid, where the minimum pressure is reduced to 18.9 MPa, the maximum pressure fluctuation amplitude is 12.6 MPa, and the rated liquid supply pressure fluctuation number is nine times during the whole process. The traditional PID control method effectively reduces the amplitude of pressure fluctuation, and the system pressure is controlled between the opening and closing pressure of the unloading valve, but the number of pressure fluctuations in the whole process is eight times and does not decrease significantly. The online updated RBF neural network control ensures that the pressure is controlled between the opening and closing pressure of the unloading valve, and the pressure fluctuation amplitude is only 3.5 MPa, which reduces the fluctuation amplitude by 72%. The whole process pressure fluctuation frequency is only four times, which reduces the fluctuation frequency by 55%.

In terms of the action time efficiency of the hydraulic support, under the rated liquid supply, the time required for one action cycle of the hydraulic support is 20.6 s, and the time required for PID control and online updated RBF neural network control is the same, both of which are 18.5 s, and the time efficiency is increased by 10.2%.

System flow curves under different liquid supply modes are drawn, as shown in Figure 20. As can be seen from the figure, in terms of the response speed of the pumping station, the online updated RBF neural network control can predict the flow rate of the pumping station in advance, and adjust the flow rate of the pumping station in the action gap of the hydraulic support. Compared with the traditional PID control method, the response time is 1.5–2 s earlier. In terms of energy consumption, considering the motor energy consumption curve [30] comprehensively, the energy consumption required by the PID control method is reduced by about 24.5%, and the energy consumption required by the online updating of the RBF neural network control method is reduced by about 29%, effectively reducing energy waste.

However, this control method still has some limitations. This control method simplifies the action of the hydraulic support model. For the action of the hydraulic support with a small amount of liquid, such as the action of the protection plate and the lifting of the bottom cylinder, the response flow value cannot be accurately predicted due to the irregularity of the movement. It is still an important research problem to increase the adaptability of the pump station control method to provide hydraulic support for small actions.

6. Conclusions

Due to the large difference in the required flow rate of hydraulic support in different operations required for mining faces, and the lag of pressure response of long-distance liquid supply systems, it is difficult to achieve pressure regulation control. Therefore, based on the analysis of the process of stabilized pressure supply in a long-distance pipeline, a new online updating RBF neural network control method for a long-distance liquid supply system was proposed and verified by simulation and experiment. The results show that:

(1) The stabilized pressure liquid supply flow of the long-distance liquid supply system is affected by the parameters of the hydraulic cylinder area, stroke, load, etc. By collecting multiple groups of pressure-stabilized liquid supply data for fitting, the average absolute error MAE of liquid supply flow can reach 3.38 L/min, and the root mean square error, RMSE, can reach 3.76 L/min, which can accurately judge liquid supply flow to achieve the aim of pressure-stabilized control.

(2) Through the processing and correlation analysis of the pressure fluctuation signal of the long-distance liquid supply pipeline, the transmission speed of the pressure wave in the liquid supply pipeline is 1456 m/s. The response speed of the system can be improved by adjusting the inverter in the controller system.

(3) The updated RBF neural network control method can adapt to the changes in working conditions, and the model can be identified in real time by the repetitive characteristics of the hydraulic support, which can reduce the pressure fluctuation of the system and improve the efficiency of the machine. The experimental results show that compared with the rated liquid supply, the amplitude of pressure fluctuation is reduced by 72%, the frequency of fluctuation is reduced by 55%, the time efficiency is increased by 10.2%, and the required energy consumption is reduced by about 29%. Compared with the PID control method, the response time of the pumping station is 1.5–2 s earlier, the frequency of fluctuation is reduced by 50%, and the energy consumption is reduced by 5.6%, which effectively reduces the pressure fluctuation of the system and improves operation efficiency.