Research on positioning control strategy of hydraulic support pushing system based on multistage speed control valve | Scientific Reports

Scientific Reports volume 14, Article number: 19046 (2024) Cite this article

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The precise position control of the hydraulic support pushing system in the coal mining face is a key technical support for intelligent coal mining. At present, the hydraulic support pushing system uses the electro-hydraulic directional valve as the control element. However, the electro-hydraulic directional valve has problems such as discrete input values, low switching frequency, delay, inability to adjust flow, and large flow fluctuations during the switching process, which results in relatively low positioning control accuracy of the hydraulic support pushing system. Therefore, this study introduces a multi-stage speed control valve that is suitable for underground coal mine conditions and can achieve flow regulation. At the same time, a segmented control strategy combining Bang-Bang control and online predictive control is proposed. Bang-bang control is used for fast propulsion with large flow rate, large range, and short time. Online predictive control method is used to achieve precise positioning control with small flow rate and small range, thereby solving the problem of low positioning control accuracy caused by the imperfect characteristics of electro-hydraulic directional valves. Finally, this study verified the effectiveness of the proposed scheme through simulation and experiments. The results showed that compared with existing logic positioning control methods based on electro-hydraulic directional valves, the proposed scheme can improve the accuracy of single cylinder positioning control from 62 mm to within 10 mm.

Coal is the “ballast stone” of China’s energy security, and the safety and efficiency of coal mine production are crucial. As the first production site of coal mining, the intelligent level of the fully mechanized mining face is directly related to the safety production and mining efficiency of coal mine1,2. The straightness control of the fully mechanized mining face is the most crucial technology to achieve intelligent working face, and the straightness of the hydraulic support and scraper conveyor in the working face is ensured by pulling the hydraulic support and pushing the scraper conveyor, respectively. Therefore, the precise position control of the hydraulic support pushing system will become the focus of this study3.

For large mining height hydraulic supports, the pulling hydraulic support and pushing scraper conveyor correspond to the extension and retraction actions of the pushing cylinder, so the above process can be equivalent to the position control of the valve-controlled cylinder. At present, the application of valve-controlled cylinder systems is very extensive, and some fields have already achieved high-precision position control. Therefore, it is necessary to learn from mature valve-controlled cylinder technologies in other fields to carry out positioning control research on hydraulic support pushing systems. Commonly used control valves include high-speed on/off valves, electrohydraulic proportional valves, and electromagnetic directional valves.

The electrohydraulic proportional valve takes continuous signals as input and controls the oil proportionally4,5. The existing control methods for proportional valves include PID control6,7,8,9 adaptive robust control, sliding film control10,11,12,13, etc. These methods essentially adjust the current vector field in the form of high gain and high frequency feedback, thereby gradually converging the state to the target position.

The high-speed on–off valve completes the on–off time of the electromagnet by changing the duty cycle, thereby changing the size of the valve port and achieving flow control14. At present, hydraulic systems with high-speed switching valves as control components usually use pulse frequency modulation (PFM)/pulse width modulation (PWM) control methods15,16,17,18,19. However, these control methods require the switching speed of the valves to be relatively fast, usually requiring a response time of more than 10ms for a single opening and closing20.

The electromagnetic directional valve and electrohydraulic directional control valve approaches the target position through positive and negative switching, and achieves final positioning control through zero value switching. At present, the positioning control for electro-hydraulic directional valves is usually achieved by setting the advance amount21,22,23 and slowly approaching the target position24,25,26. Although the above methods have improved the positioning control accuracy within a certain range, they have certain limitations. The method of setting advance requires that the switching of the electro-hydraulic directional valve can only be carried out after the speed reaches steady state.

Regarding the research on the control valve components mentioned above, scholars often use hydraulic oil as the transmission medium. However, currently, hydraulic supports in coal mines often use high water-based emulsions (mixed with 5% emulsified oil and 95% water) as the transmission medium to meet the requirements of explosion-proof, flameproof, and clean and green underground coal mines. Due to the significant differences in physical and chemical properties between high water-based emulsions and hydraulic oils, there are significant differences in the design of corresponding control valve components. Control valves in high water-based emulsions require more consideration of a series of issues such as the sealing performance of the control valve and the smoothness of the flow channel.

Regarding the research on high water-based control valves, Liao et al.27 developed a new type of two position three-way proportional valve. The pilot valve and main valve adopt a seat structure, and servo motors are used to drive screw nuts and L-shaped drive rods. Zhao et al.28 designed an electro-hydraulic proportional directional valve with high-speed on/off valve pilot control, which achieves proportional control by changing the PWM signal duty cycle. Although the above research focuses on high-pressure, high flow, and high water based hydraulic systems in coal mines, there are currently no mature industrial application examples.

Due to its simple structure, low machining accuracy and cost, low oil requirements, high reliability, and long service life, the electro-hydraulic directional valve is still the main control component in the hydraulic support control system at present. However, the electro-hydraulic directional valve has undesirable characteristics such as discrete input values, limited switching frequency, and delay, and cannot perform flow regulation, resulting in low position control accuracy.

Through underground testing, it has been shown that the positioning control accuracy based on electro-hydraulic directional valves is basically within 70 mm at present. This is still a certain gap from the Chinese “General Technical Specification for Smart Mine Information System”, which stipulates that the deviation between supports during continuous propulsion of the entire working face is less than 50 mm. Therefore, at present, after the hydraulic support is moved, manual adjustment is still required.

The team has been committed to the research of positioning control of electro-hydraulic directional valves in coal mines. Hou et al.29 predicts the advance in the positioning control process through iterative learning method, and then realizes positioning control. Although this method improves the positioning accuracy, it uses offline statistical method, which makes the electro-hydraulic directional valve only switch at a stable speed, reducing the range of use. In order to solve the above problems, Hou et al.30 proposes a positioning control strategy based on online predictive feedback control, reconstructs the advance model through online learning algorithms, and completes the switching conditions and switching control methods. However, during the experiment, it was found that due to the low switching frequency and inability to adjust the flow rate of the electro-hydraulic directional valve, there were significant fluctuations in the flow rate during the switching process under high flow conditions, resulting in difficulties in data acquisition for the above method in the machine learning process.

Therefore, based on the electro-hydraulic directional valve, this study introduces a multi-stage speed control valve suitable for high-pressure, high flow, and high water-based environments. Through the combination of the multi-stage speed control valve and the electro-hydraulic directional valve, the rapid propulsion of large flow and the slow positioning process of small flow are achieved. In order to further improve the positioning control accuracy and control efficiency of the system, a segmented positioning control strategy based on multi-stage speed control valves and electro-hydraulic directional valves is proposed. By combining online predictive feedback positioning control strategy with bang-bang control, the problem of low positioning control accuracy caused by the undesirable characteristics of electro-hydraulic directional valves is solved. In the online predictive feedback control scheme, the process from the zero-switching signal of the electrohydraulic reversing valve to the final stop of the hydraulic cylinder in the process of low flow positioning is divided into two stages. The optimal identification of the prediction model in the first stage is achieved through recursive least square (RLS) method with forgetting factor. The machine learning algorithm based on Online Sequential Extreme Learning Machine (OS-ELM)31,32 is used to fit the target trajectory in the second stage online. Finally, the switching control method is used to make the system switch under the condition of zero switching, so that the system can obtain the optimal switching lead, and then improve the positioning control precision of the shifting system.

Finally, in order to verify the effectiveness of the proposed scheme, simulation and experiments were conducted, and the results showed that the position control scheme based on multi-stage speed control valves can effectively improve the positioning control accuracy of the hydraulic support pushing system in the working face.

This study focuses on positioning control as the goal, and pushing cylinder only needs to reach the target position from the current position, without accurate requirements for the trajectory of the current process. Therefore, this article proposes an electrohydraulic position control system suitable for stepwise adjustment of output displacement, with mining electrohydraulic directional valves and multi-stage speed control valves as the core control components. The forward, reverse, and stop actions of the pushing cylinder are achieved through the electrohydraulic directional valve, and the system control accuracy is increased through stepwise speed adjustment of the multi-stage speed control valve.

As shown in Fig. 1, it is a hydraulic schematic diagram of a positioning control system based on multi-stage speed control valve. The left side is the pushing system, and the right side is the loading system. The pushing system achieves positioning control through multi-level speed control valve and electrohydraulic directional valve, regulates the flow of the system through throttle valves, and regulates the oil source pressure through bypass overflow valves. In the loading system, pressure regulation is carried out through a proportional relief valve, which changes the back pressure of the return oil in the loading cylinder. Finally, different load forces are adjusted through a dual cylinder loading method.

Hydraulic schematic diagram of position control based on multi-stage speed control valve.

The electrohydraulic directional valve mainly realizes the control of the start-stop action and movement direction of the pushing oil cylinder. As shown in Fig. 2, there is a basic circuit of the electrohydraulic directional valve. The solenoid pilot valve 1 and 2 are used to control the on–off of the main valve 1 and 2 respectively. The two groups form a circuit.

Basic control circuit of the electrohydraulic directional valve.

The schematic diagram of the single group structure of the electrohydraulic directional valve is shown in Fig. 3. When the electromagnetic iron is energized, the small ball in the pilot valve is pushed to move to the right, and the working port of the pilot valve opens. High pressure liquid enters the control port K of the main valve through the pilot valve from the pump station outlet. At this time, the return valve core and the inlet valve core of the main valve open sequentially, and finally the P and A ports of the electrohydraulic directional valve are connected, thereby achieving liquid supply. On the contrary, when the electromagnet loses power, the pilot valve resets, the working port closes, and the pressure in the control chamber of the main valve is unloaded to 0. The return valve core and inlet valve core of the main valve are sequentially closed. At this time, the P port of the electrohydraulic directional valve is closed, stopping the liquid supply.

Schematic diagram of single group electrohydraulic directional valve structure.

Due to the low switching frequency of the electrohydraulic directional valve and the inability to adjust the flow rate, we have introduced a multi-stage speed control valve suitable for underground coal mines that can adjust the flow rate in stages. The multi-stage speed control valve completes the switching of different flow channels of the main valve through different switching combinations of electromagnetic pilot valves, thereby achieving different flow regulation. As shown in Fig. 4, it is a basic circuit of a multi-stage speed control valve, which controls the opening and closing of different flow channels in the main valve through electromagnetic pilot valves 1 and 2, thereby achieving multi-stage adjustment of oil flow.

Hydraulic schematic diagram of multi-stage speed control valve.

The schematic diagram of the main valve structure of the multi-stage speed control valve is shown in Fig. 5. When the electromagnetic iron is energized, high-pressure liquid enters the control port of the main valve through the pilot valve. At this time, the corresponding main valve flow channel opens, and the port P and port A together achieve liquid supply. The entire valve through different combinations of electromagnetic pilot valve switch, control of the main valve in the different flow on and off. Finally, achieve adjustment of different flow rates. To meet the actual on-site needs, if more levels of flow regulation are needed, hydraulic control fine flow channels with different apertures can be set up in the main valve. Each hydraulic control fine flow channel is equipped with a corresponding small flow pilot operated check valve string, each controlled by an electromagnetic pilot valve. Therefore, multi-level flow regulation can be achieved by opening different apertures and different numbers of flow channels in the main valve.

Structural diagram of the main valve of the multi-stage speed control valve.

As the executing component of the system, the pushing cylinder has nonideal control characteristics due to the nonlinearity of sealing friction and dynamic oil pressure, which in turn affects the positioning control accuracy of the system. In this study, based on practical operating conditions, in order to simplify the subsequent controller design process, the valve controlled single cylinder system only considers the inertia and friction loads of the actuator. Considering the requirements of subsequent control strategies, the friction characteristics and chamber pressure characteristics of the pushing oil cylinder are analyzed separately.

According to Newton’s second law, the piston dynamics equation can be obtained as follows:

In the equation, \(\nu ({\text{m/s}})\) represents the speed of the piston, \(x({\text{m}})\) represents the position of the piston, \(F_{hyd} (N)\) represents the hydraulic driving force, \(A_{1} ({\text{m}}^{2} )\) and \(A_{2} ({\text{m}}^{2} )\) are the areas of the piston and rod chambers, respectively. \(P_{1} (P{\text{a}})\) and \(P_{2} (P{\text{a}})\) represent the pressure of the piston and rod chambers, respectively.

For the hydraulic support pushing cylinder, its friction force mainly comes from external load friction and internal sealing friction of the hydraulic cylinder. All frictional load forces on the pushing cylinder can be regarded as a nonlinear function that is only related to piston speed, expressed as \(f(v)\)33,34. The following is an analysis of the pressure characteristics of the hydraulic support pushing oil cylinder chamber. For a chamber with a relatively uniform pressure distribution, we can represent the dynamic pressure model of the chamber as:

In the formula, \(\beta (P{\text{a}})\) represents the elastic modulus of the liquid, \(V_{0} (L)\) represents the volume of the chamber, \(Q_{{{\text{in}}}} ({\text{L/min}})\) and \(Q_{{{\text{out}}}} ({\text{L/min}})\) are the flow rates entering and exiting the chamber, respectively.

If the electrohydraulic directional valve switches from a non-zero state to a zero state, considering the compressibility of the liquid, the dynamic equation for the pressure and flow rate of the liquid flowing out of the two chambers of the pushing cylinder is:

In the formula, \(Q_{1} { = }C_{{\text{d}}} A_{{{\text{x}}1}} \sqrt {\frac{2}{\rho }\left( {P_{1} - P_{{\text{r}}} } \right)} ,\;\;Q_{2} { = }C_{{\text{d}}} A_{{{\text{x2}}}} \sqrt {\frac{2}{\rho }\left( {P_{2} - P_{{\text{r}}} } \right)}\). The flow coefficient of the throttle hole of the electrohydraulic directional valve is represented by \(C_{{\text{d}}}\), the pressure of the tank is represented by \(P_{{\text{r}}} (P{\text{a}})\), the flow rate entering the piston and rod chambers of the pushing cylinder is represented by \(Q_{1} (L/{\text{min}})\) and \(Q_{2} (L/min)\), respectively. The orifice area of the electrohydraulic directional valve connected to the piston and rod chambers of the pushing cylinder is represented by \(A_{{{\text{x}}1}} ({\text{m}}^{2} )\) and \(A_{{{\text{x2}}}} ({\text{m}}^{2} )\), respectively. The density of the emulsion is represented by \(\rho ({\text{kg/m}}^{3} )\), the speed of the piston is represented by \(\nu ({\text{m/s}})\). The corresponding elastic modulus when the pressure is \(P_{1} ({\text{Pa}})\) and \(P_{2} ({\text{Pa}})\) is represented by \(\beta_{{1}} ({\text{Pa}})\) and \(\beta_{{2}} ({\text{Pa}})\), respectively. According to the above formula, the dynamic pressure depends on \(P_{{\text{i}}}\) and \(\nu\).

If the electrohydraulic directional valve switches from zero state to non-zero state, the dynamic equation of pressure and flow entering the two chambers of the pushing cylinder through the electrohydraulic directional valve is:

In the formula, \(Q_{1} = C_{{\text{d}}} A_{0} \sqrt {\frac{2}{\rho }(P_{{\text{s}}} - P_{1} )} ,\;\;Q_{2} = C_{{\text{d}}} A_{0} \sqrt {\frac{2}{\rho }(P_{{\text{s}}} - P_{2} )}\), \(A_{0} ({\text{m}}^{2} )\) is the orifice area of the throttle valve, and \(P_{{\text{s}}} (P{\text{a}})\) is the pressure of the oil source.

Based on the above analysis, we can also conclude that the dynamic characteristics of pressure at this time are still determined by and \(P_{{\text{i}}}\) and \(\nu\). In this study, the controller design was simplified as follows: if the electrohydraulic directional valve is in state \(U_{{{\text{cmd}}}}^{0}\), \(F_{hyd}\) is 0; if it is in state \(U_{{{\text{cmd}}}}^{ + }\), \(F_{hyd}\) is a positive number; if it is in state \(U_{{{\text{cmd}}}}^{ - }\), \(F_{hyd}\) is a negative constant.

This study uses an electrohydraulic directional valve and a multi-stage speed control valve as control elements, and uses the multi-stage speed control valve to regulate the flow rate. The electrohydraulic directional valve is used to control the direction of the pushing cylinder and its stop action. In order to ensure good static and dynamic performance of the system, combined with the input and output characteristics of the system, a segmented control strategy is adopted. The difference between the target position \(r\) and the actual position \(x\) is defined as the position error \({\text{s}}\), \({\text{s}} = x - r\). When the position error \({\text{s}}\) is greater than or equal to the threshold D, bang-bang control is used to control the large flow rate of the multi-stage speed control valve, eliminating significant errors in a short period of time and achieving optimal control of time. When the position error \({\text{s}}\) is less than the threshold D, the small flow rate of the multi-stage speed control valve is used for precise control in small range and for a long time within this range. Considering the input constraints, system nonlinearity, and delay issues during the positioning control process of the multi-stage speed control valve and the electrohydraulic directional valve, the final small flow positioning control adopts an online learning based predictive feedback control strategy to improve control accuracy and achieve optimal control accuracy.

When the system is in the quick positioning area, i.e. \(\left| {\text{s}} \right| \ge D\), the bang-bang control strategy is adopted, which has the greatest advantage of fast response speed. At this time, the large flow rate of the multi-stage speed control valve can quickly approach the target value in the shortest time, achieving optimal control of the system time and improving the efficiency of hydraulic support pushing control. At this point, the expression for the control algorithm is:

In the formula, D is the displacement threshold obtained through experiments; \(G_{{\text{m}}}\) represents the high flow control of the multi-stage speed control valve, while \(U_{{{\text{cmd}}}}^{ + }\) and \(U_{{{\text{cmd}}}}^{ - }\) represent the positive and negative switching of the electrohydraulic directional valve. Due to the segmented control strategy adopted in the positioning control of the moving system based on multi-level speed control valves, the determination of threshold D adopts the “backtracking” approach, which starts from the final positioning target state and pushes back to the current state to obtain the displacement threshold of the multi-level speed control valve under different switching states. Here, we use multiple experimental methods to statistically determine the threshold D.

When the system is in the precise positioning area, i.e. \(\left| {\text{s}} \right| < D\). To solve the problem of low accuracy in the positioning control process of electrohydraulic directional valve, an online predictive control positioning control method is adopted. This method is based on actual data and identifies the required model through learning algorithms. Specifically, a prediction model is established through optimization algorithms, and the target trajectory is fitted online through machine learning algorithms. Finally, the switching control method is used to switch the system while meeting the zero switching condition, allowing the system to obtain the optimal switching advance and accurate positioning value. The control block diagram is shown in Fig. 6.

Control block diagram of online predictive feedback positioning control method.

By constructing an advance model through learning algorithms and issuing commands at the optimal advance through switching control methods, precise positioning values can be obtained. The key to positioning control lies in how to determine the zero value switching conditions. Therefore, we will analyze the dynamic process from the zero-value switching control signal to the final stop of the pushing cylinder.

The control command describes the process after switching from positive input to zero value input. When the zero-value switching signal occurs, it includes two stages. The first stage is the process of switching the electrohydraulic directional valve from the connected state between port A and port P to the connected state between port A and port T, including the delay stage and pressure drop process; The second stage is the process from the connection between port A and port T to the final stop of the hydraulic cylinder.

If the target position is defined as \(r\) and the current displacement value of the oil cylinder is \(x\), then the position error \(s = x - r\). Assuming that the system's state values are \(s\left( {\text{t}} \right)\) and \(\nu \left( {\text{t}} \right)\) when zero value switching occurs, and the future state values after the end of the first stage are \(s_{{{\text{pred}}}} \left( {\text{t}} \right)\) and \(\nu_{{{\text{pred}}}} \left( {\text{t}} \right)\), then both satisfy:

For the second stage, due to meeting:

Therefore, the dynamic speed is only determined by the speed itself, and the changes in the system trajectory during this stage can be expressed as:

where \({\text{s}}_{{\text{s}}}\) is the final stable value of the position error, and \(H\left( \nu \right)\) is the trajectory function of the second stage. If, after the end of the first phase, the system status meets:

when switching to zero at states \(s\left( {\text{t}} \right)\) and \(\nu \left( {\text{t}} \right)\), the system can ultimately stop near the target position.

For the sake of analysis, \(e_{s}\) is defined as the distance from a certain state point \(s\) to the target trajectory \(H\left( \nu \right)\):

Taking the derivative of (12):

According to the above equation, when the hydraulic cylinder moves forward and the pressure in the piston chamber is greater than zero, \(\dot{e}_{s} > 0\); when the hydraulic cylinder moves in reverse and the pressure in the rod chamber is greater than zero, \(\dot{e}_{s} < 0\). From this, it can be concluded that under any condition, the switching control method of the electrohydraulic directional valve is:

For the two models in the above equation, the RLS with forgetting factor is used for optimal identification of prediction model \({\text{s}}_{{{\text{pred}}}} \left( {\text{t}} \right)\), and the OS-ELM algorithm is used for online fitting of target trajectory model \(H\left( {\nu_{{{\text{pred}}}} \left( {\text{t}} \right)} \right)\).

The prediction model mainly predicts the future state value after the end of the first stage, which can be expressed as formula (8). During the pressure drop process, the pressure \(\hat{P}_{{\text{i}}} \left( {{\text{Pa}}} \right)\) in the chamber connected to the port P of the electrohydraulic directional valve can be expressed as a function related to the steady-state pressure \(P_{{{\text{iss}}}}\) in the chamber connected to the port P and the pressure drop duration \(T_{{\text{m}}}\):

At this stage, due to \(\nu_{{{\text{ss}}}} > \nu_{{{\text{stribeck}}}}\), \(f(v)\) can be expressed as35:

At this point, the pushing system satisfies:

Due to the fact that when \(t = 0\), the speed \(\nu = \nu_{ss}\), and when \(t = T_{m}\), the speed \(\nu = \nu_{m}\), and since \(\Delta \nu_{m} = \nu_{m} - \nu_{ss}\), it can be obtained:

By integrating formulas (20), we can obtain:

Based on the above analysis, it can be concluded that the state increment after the end of the first stage is:

Based on the above analysis, \(\Delta \nu\) and \(\Delta s\) are functions related to \(\nu_{{{\text{ss}}}}\) and \(P_{iss}\) can be approximated as:

In the above equation, \(\gamma\) and \(\lambda\) are parameter vectors, \(\varphi\) is the feature vector, where \(\varphi = \left( {\begin{array}{*{20}c} {\nu_{{{\text{ss}}}} } & {P_{iss} } & 1 \\ \end{array} } \right)^{T}\). Due to the different parameters of the prediction model during the forward and reverse movement of the hydraulic cylinder, they are respectively represented as \(\gamma_{p} ,\gamma_{n}\) and \(\lambda_{p} ,\lambda_{n}\). As \(\Delta {\text{s}}\) and \(\Delta \nu\) can be represented as:

Therefore, by combining (22) and (23), by collecting the values of data \(s_{pred}\), \(s_{0}\), \(\nu_{ss}\) and \(\nu_{pred}\) through experiments, the parameter vector for a single switch can be obtained. By continuously collecting data during the zero-value switching process, and finally using recursive least squares with forgetting factors for online identification, the optimal parameter vectors \(\gamma\) and \(\lambda\) can be obtained. By incorporating the above results into formulas (24) and (8), the future state values after the end of the first stage can be obtained.

In the second stage, the driving force of the pushing cylinder is unloaded to 0, and the oil cylinder relies on all frictional forces \(f(v)\) to slide and finally stop. The target trajectory model mainly fits the trajectory of the pushing oil cylinder during this process. Due to the model uncertainty of all frictional forces \(f(v)\) on the pushing cylinder, it is not possible to directly represent the parameterized structural form of \(H\left( \nu \right)\) through a mathematical model. Moreover, due to the continuous changes in the target trajectory function \(H\left( \nu \right)\) in actual working conditions, in order to dynamically adapt to changes caused by the environment, it is necessary to use online learning methods to update the system model through the continuous changes in actual data.

Here, the OS-ELM algorithm is used to achieve online fitting of the objective function. This method can fully utilize the universal approximation ability and extreme learning speed of machine learning, increase the dynamic adaptability of the system model, and thereby reduce the positioning error of the moving system. The data required for the fitting algorithm is:

In the above data, \(s^{\prime}_{{\text{i}}} {\text{ = x}}_{{\text{i}}} - {\text{x}}_{{\text{s}}}\); In the function \(H\left( \nu \right)\), \(\nu_{{\text{i}}}\) is the input value and \(s^{\prime}_{{\text{i}}}\) is the output value. Due to the different dimensions of the parameters collected in the experiment, normalization was used to preprocess the original data.

The OS-ELM algorithm does not require the setting of hidden layer functions. It uses input data to randomly generate hidden layer input weights and biases. By setting the number of hidden layer neurons, the output weights of the network are calculated, and the model is sequentially updated using the RLS method. For an OS-ELM model with L hidden layer nodes, its output can be expressed as:

In the above equation, \(\omega_{i}\), \(b_{i}\) and \(\beta_{i}\) respectively represent the input weight, bias, and output weight of the ith hidden layer node; As the activation function of the hidden layer, \(G\left( {\omega_{i} ,b_{i} ,x_{m} } \right)\) uses the radial basis function (such as Gaussion function), that is, \(G\left( {\omega_{i} ,b_{i} ,x_{m} } \right) = \exp ( - b_{i} \left\| {x_{m} - \omega_{i} } \right\|)\). Write the above formula in matrix form:

The algorithm process of OS-ELM is as follows:

Initialization.

Randomly generate hidden layer weights \(\omega_{i}\) and deviations \(b_{i}\), and calculate the hidden layer output matrix \(K_{0}\).

Calculate the initial output weight \(\beta_{0} { = }\mathop {\min }\limits_{\beta } \left\| {K_{0} \beta - T_{0} } \right\| = K_{0}^{\dag } T_{0}\).

The generalized inverse matrix \(K_{0}^{\dag }\) of \(K_{0}\) is:

where \(P_{0} = \left( {K_{0}^{T} K_{0} } \right)^{ - 1}\).

When k = 0, it indicates that the upcoming data will enter OS-ELM.

Continuous learning.

Calculate the hidden layer output matrix \(K_{{{\text{k + }}1}}\).

Calculate output weights \(\beta_{m + 1}\).

Let \(m = m + 1\), return to the continuous learning stage.

Continuously updating parameters \(K\) and \(\beta\), until the data learning is completed.

By combining the above two control methods, the pushing system can ultimately meet the requirements of fast and accurate positioning control. The expression for the switching control method is:

In the above formula, \(G_{{\text{s}}}\) represents low flow control and \({\text{G}}_{{\text{m}}}\) represents high flow control.

In order to verify the effectiveness of the proposed multi-level speed control valve and its corresponding segmented control strategy in positioning the hydraulic support pushing system, a controller model was designed and simulated based on the analysis of the hydraulic system.

This article establishes a SimulationX physical simulation model as shown in Fig. 7, using the electrohydraulic directional valve and multi-stage speed control valve as control components and the pushing oil cylinder of the ZY3200/08/18D shield hydraulic support as execution components.

Simulation model based on SimulationX.

In the simulation, the emulsion pump station provides power source for the pushing system, and the system flow is regulated through a throttle valve. During the positioning control process, the flow rate is switched between large and small through a multi-level speed control valve. The propulsion cylinder is controlled to start and stop and move in the direction through an electrohydraulic directional valve. In the loading system, the output of different loading forces is achieved through a proportional relief valve. Table 1 shows the key parameters involved in the simulation process.

Subsequently, the proposed segmented control strategy was compiled in Matlab. Finally, a joint simulation platform based on SimulationX and Matlab was built as shown in Fig. 8. In the figure, the left box shows the segmented control strategy involved, and the right box shows the import module of the SimulationX physical simulation model. In the simulation, the controller receives real-time position, pressure, and speed signals generated by the physical model and controls the control voltage in the physical model through a control program.

Co-simulation diagram of positioning control system based on multi-stage speed control valve.

In the simulation, square wave signals with switching frequency of 0.05 Hz and steady-state values of 700 mm and 200 mm were used as target positions. Through a segmented control strategy based on multi-stage speed control valves, positioning control simulation experiments were conducted at different steady-state speeds. The position threshold D in the segmented control strategy is set to 150 mm. The Simulation curve of positioning control state based on multi-level speed control valve is shown in Fig. 9.

Simulation curve of positioning control state based on multi-level speed control valve.

The “a–h” in Fig. 10 are locally enlarged images of “a–h” in Fig. 8. Based on these two figures, we can see that after experiencing rapid positioning, starting from 550 mm, the multi-stage speed control valve switches to a small flow rate of 15 L/min for precise positioning control. During the initial positioning, due to insufficient data required for positioning control, the required model has not been identified, resulting in a process of peaks and valleys; subsequently, with the continuous increase of observation data, the required model gradually gained recognition, but there will still be a process of rising waves. This is due to the continuous fluctuations in speed and pressure during the switching process of the electrohydraulic directional valve, which results in insufficient accuracy of model required for positioning control. Through continuous training of observation data, prediction models and target trajectories are continuously modified, and good identification results are finally obtained at t1(15 s). As a result, stable fluctuations can be achieved near the target position. Although the target position is adjusted to 300 mm, stable positioning control can still be achieved due to the good fitting of the model within this range.

Partially enlarged image in Fig. 9.

Figure 11 shows the fitting results of the target trajectory at time t1(15 s), indicating that the OS-ELM algorithm can fit the observed data well.

Target trajectory observation data and target trajectory fitting results at time t1.

At t2 (40 s), switch the system flow to a larger flow value, and first quickly locate it through the large flow of the multi-stage speed control valve. Subsequently, at time t3(42.5 s), adjust the small flow rate of the multi-stage speed control valve during the precise positioning control process to 40 L/min. At this time, due to the unobservable prediction model and target trajectory within the speed range, significant fluctuations still occurred. However, as the observation data increased, the prediction model and target trajectory were continuously corrected, and finally good identification results were obtained at t4(51.5 s), achieving stable fluctuation positioning control. Later, when the target position is adjusted to 300 mm, stable and fluctuating positioning control can be quickly achieved due to the good identification of the model within this range.

Figure 12 shows the fitting results of the target trajectory at time t4(51.5 s), indicating that the OS-ELM algorithm also fits the observed target trajectory data well.

Target trajectory observation data and target trajectory fitting results at time t4.

At t5(80 s), adjust the system flow again. After undergoing the rapid positioning process, adjust the flow during the precise positioning process to a smaller value through a multi-stage speed control valve. At this moment, due to the good identification results of the prediction model and target trajectory within this range, stable fluctuation positioning control will be quickly achieved. Although the target position has been adjusted afterwards, stable fluctuation positioning control can still be achieved.

In summary, the OS-ELM algorithm has strong dynamic adaptability and can quickly fit target trajectory observation data, while the proposed segmented control strategy meets the required positioning control accuracy.

This study combines actual working conditions and builds an experimental platform based on the principle of similarity, according to the hydraulic schematic shown in Fig. 1.

Figure 13 shows the experimental platform of the positioning control system based on multi-stage speed control valves in this study. In this experimental platform, the proportional relief valve installed on the return oil side of the loading end oil circuit achieves different loading forces by adjusting different return oil back pressures. Set the relief valve on the side of the loading pump source to a smaller pressure value, and at this time, the loading pump source only serves to replenish oil.

Experimental platform for positioning control system based on directional valve and multi-stage speed control valve in real-time using Matlab/Simulink/Real time. Figure has been taken by Author, Tengyan Hou.

In the experiment, a single rod cylinder with piston and rod diameters of 110 mm and 80 mm was used for the pushing part, and the pushing stroke was 1000 mm. The extension and retraction process of the pushing cylinder was used to simulate pushing the scraper conveyor and pulling the hydraulic support. The magnetostrictive sensor (MTS) is used to measure the speed and displacement values of the piston of the pushing cylinder in real time. The flow rate of the system is measured through a high-pressure flow meter (CT 300), and the pressure is measured through three pressure sensors (MIK-P 300). The sensors and real-time control system used in the experiment are shown in Fig. 14. The real-time control system used in this experiment mainly consists of an upper computer (PC), a lower computer, an Altay PCI 5654 data acquisition card, and a PLC controller. The control algorithms involved in the experiment are compiled using Matlab. When the controller receives signals such as position, pressure, and speed collected by sensors, it controls the electrohydraulic directional valve and multi-stage speed control valve in real-time using Matlab/Simulink/Real time.

The sensors and real-time control system used in the experiment. Figure has been taken by Author, Tengyan Hou.

Considering the delay characteristics of control components and the limitations of switching frequency in the positioning control process based on multi-stage speed control valves, combined with the actual working conditions of coal mines underground, the switching control method has been modified and simplified.

Firstly, in order to avoid the phenomenon of readjustment or repeated switching near the target position caused by the inability of switching instructions to switch at \({\text{e}}_{{\text{s, pred}}} (t) = 0\), it is necessary to ensure that the time required for \({\text{e}}_{{\text{s, pred}}} (t) = 0\) is greater than \(T_{\min }\). Therefore, based on actual working conditions, in order to meet the switching condition, the solution process for the increment \({\text{e}}_{{\text{s, pred}}}\) is simplified. Therefore, the increment of \({\text{e}}_{{\text{s, pred}}}\) can be expressed as:

In the above equation, \(K_{\max }\) represents the maximum value of \(\left| {K\left( \nu \right)} \right|\) in the feasible speed range, \(P_{ip\max }\) is the maximum pressure of the oil inlet chamber, and \(T_{\min }\) is the minimum switching interval.

Secondly, in the actual switching process, it is not realistic to perform zero value switching at \({\text{e}}_{{\text{s, pred}}} (t) = 0\). Considering the requirements for positioning control accuracy in actual working conditions, it is allowed to have certain errors in the final positioning. Therefore, considering the above two aspects comprehensively, the switching control method has been revised:

The above equation \(\varepsilon_{c}\) is a non-zero constant; E is also a non-zero constant, determined by the feasible range of velocity, the maximum pressure in the oil inlet chamber, and the minimum switching interval.

In this experiment, the key parameters involved are shown in Tables 1 and 2. The experiment adopts the same positioning testing method as the simulation. The target position is a square wave signal with a switching frequency of 0.025 Hz and stable values of 700 mm and 300 mm, respectively. The segmented control position threshold D is 150 mm.

The experimental curve of positioning control state based on multi-stage speed control valve is shown in Fig. 15. The “A–F” in Fig. 16 and the “a–f” in Fig. 17 are locally enlarged images of the “A–F” in the displacement curve in Fig. 15 and the "a-f" in the displacement error curve in Fig. 15, respectively. Based on the above figures, we can see that during the pushing process, it first experienced a rapid positioning stage, and entered a precise positioning stage near 550 mm. At this time, a peak and valley process that is consistent with the simulation phase trend appears, which is due to insufficient observation data, making it difficult to fully identify the model required by the control algorithm. Subsequently, with the increase of training data, the prediction model and target trajectory were continuously modified, and finally a good identification result was obtained at time t1(19 s), so it stabilized within the threshold range of the target position. At this stage, there is no process of rising wave by wave, and there is no process of fluctuation near the target position, because the switching control method is modified and simplified in the actual positioning control process, and the positioning control error threshold is increased to avoid frequent switching of the electrohydraulic reversing valve caused by small pressure and speed fluctuations. Afterwards, although the target position was adjusted to 300 mm, the model required by the control method was well recognized within this steady-state speed range, so it can still quickly stop within the target position error threshold range.

Experimental curve diagram of positioning control state based on multi-level speed control valve.

Partial enlarged view of “A–F” in the displacement curve in Fig. 15.

Partial enlarged view of “a–f” in the displacement error curve in Fig. 15.

Figure 18 shows the fitting results of the target trajectory experimental data at time t1. It can be concluded that the overall trend of the fitting curve of the experimental data is consistent with that of the simulation data, which verifies the correctness of the simulation and also demonstrates that the OS-ELM algorithm can well fit the observed data obtained in the experiment.

Experimental data and fitting results of target trajectory at time t1.

Starting from t2(80 s), adjust the system flow rate to a larger input value. After experiencing rapid positioning, the multi-level speed control valve is switched to a small flow value, and the system enters the precise positioning stage. At this time, it will still experience a significant fluctuation process. This is because the prediction model within the speed range was not well identified and the target trajectory was not observed. However, with the continuous increase of observation data, the model required for the control method was well recognized, and eventually stopped steadily within the error threshold range near the target position from t3(88 s). Although the target position is adjusted again afterwards, it can still quickly stop within the target position error threshold range. Figure 19 shows the experimental data and fitting results of the target trajectory at t3. The results show that the overall trend of the experimental data and simulation data fitting results is basically consistent, indicating that the proposed OS-ELM algorithm has strong dynamic adaptability and can fit the target trajectory observation data well, meeting the needs of positioning control.

Experimental data and fitting results of target trajectory at time t3.

Starting from time t4(160 s), the steady-state speeds of different segmented regions were adjusted again. However, due to the good identification of the prediction model and the good fitting of the target trajectory at this time, the controller can still achieve the target control effect after experiencing the rapid positioning zone. Similarly, although the target position is adjusted again, stable positioning control results can still be achieved. At certain moments during the experimental process, complex dynamic processes that did not appear in the simulation occurred. On the one hand, this was because the actual process of pushing the oil cylinder was more complex than the simulation process. On the other hand, it was due to the presence of noise in the signal acquisition process, different measurement equipment and methods in the actual measurement process. In summary, although there are certain differences in dynamic details between actual measurement results and simulation results, the overall trend during the positioning process remains consistent.

In order to better demonstrate the positioning control method proposed in this study, this paper will conduct a single positioning control experiment on a system with well identified prediction models and target trajectories, and analyze the changes in displacement, flow rate, and pressure in the two chambers of the oil cylinder during the positioning control process. As shown in Fig. 20, the displacement change curve during the positioning control process based on a multi-stage speed control valve is obtained under a liquid supply flow rate of 64 L/min. We can conclude that when the position error is set to 10 mm, after rapid advancement and precise positioning, the hydraulic cylinder finally stabilizes and stops at 707 mm, within the set error threshold range.

Displacement variation curve of positioning control based on multi-stage speed control valve.

Figures 21 and 22 show the pressure change curves of the two chambers of the hydraulic cylinder during the positioning control process. It can be concluded that during the start-up process, the pressure of the two chambers of the hydraulic cylinder will suddenly increase. When switching to low flow, the pressure will quickly decrease, and when the hydraulic cylinder stops, the pressure will quickly drop to 0.

Pressure variation curve of piston chamber.

Pressure variation curve of rod chamber.

As shown in Fig. 23, the flow rate change curve during the positioning control process. It can be concluded that during the start-up stage, the flow rate will suddenly increase to a certain level, and then quickly drop back to the system supply flow rate. This is caused by the sudden increase in pressure during the start-up process. When switching to low flow rate, the system flow rate will rapidly decrease. When the hydraulic cylinder stops, the flow rate does not quickly decrease to 0. This is because the working principle of the turbine flow sensor relies on the fluid to drive the turbine to rotate, thereby generating a signal to measure the flow rate. When the cylinder suddenly stops, the fluid in the pipeline will maintain a certain amount of inertia for a certain period of time.

Flow variation curve during positioning control process.

In order to better demonstrate the effectiveness of the proposed control strategy, we conducted comparative experiments on positioning control using simple logic control methods under different liquid supply flow rates. The experimental results are shown in Fig. 24. It can be seen that the positioning control error increases with the different supply flow rates. When the supply flow rates are 48 L/min, 56 L/min, and 64 L/min, the hydraulic cylinder finally stops at 736 mm, 749 mm, and 762 mm, with position errors of 36 mm, 49 mm, and 62 mm, respectively.

Positioning control curve diagram under simple logic control method.

By comparing Figs. 20 and 24, we can conclude that when the error threshold is set to 10mm, the positioning control method based on multi-stage speed control valves can improve the positioning control error from within 62mm to within 10mm compared to existing simple logic positioning control.

Based on the above analysis, it can be concluded that the segmented control strategy using multi-stage speed control valves for positioning control can reduce positioning errors and switching frequency on the one hand; On the other hand, precise positioning control with low traffic can narrow the prediction learning range and increase the accuracy of machine learning data collection. The effectiveness and superiority of the proposed scheme have been demonstrated.

This article proposes a positioning control strategy based on multi-stage speed control valves to address the problem of low positioning control accuracy in the hydraulic support pushing system in coal mines. Firstly, an analysis was conducted on the hydraulic support pushing system, and a multi-stage speed control valve suitable for underground coal mines was proposed. Subsequently, a positioning control strategy was proposed for the propulsion system, and the effectiveness of the proposed scheme was verified through simulation and experiments. Based on the analysis and results, the following conclusion can be drawn:

In response to the problems of low switching frequency, inability to adjust flow rate, and large flow fluctuation during the positioning process of existing electrohydraulic directional valves in coal mines, a multi-stage speed control valve has been introduced to achieve staged flow regulation and reduce pressure impact during the hydraulic cylinder stopping process.

A segmented control strategy combining Bang-Bang control and online predictive control is proposed for positioning control using multi-stage speed control valves and electrohydraulic directional valves as control components. Using learning algorithms to continuously revise the prediction model; By utilizing the universal approximation ability and maximum learning speed of the OS-ELM algorithm to fit the target trajectory, the optimal switching advance is determined through switching control methods. This solves the problem of low positioning control accuracy caused by the nonideal characteristics of control components.

Simulation and experiments have shown that the positioning control method based on multi-stage speed control valves can meet the required positioning control needs with fewer switching times. Compared with traditional simple logic control based on electro-hydraulic directional valves, the positioning control error has increased by within 10mm from the original 62mm. This not only improves the positioning control accuracy, but also improves the moving efficiency and reduces energy consumption.

This study focuses on the position control of a single hydraulic support bracket. The ultimate requirement for underground coal mines is to ensure the straightness of the hydraulic support bracket throughout the entire working face. Therefore, the next step will be to conduct multi cylinder synchronous control research for different movement modes of the hydraulic support bracket.

All data generated or analysed during this study are included in this published article.

Wang, G. F. et al. Digital model and giant system coupling technology system of smart coal mine. J. China Coal Soc. 47(1), 61–74 (2022).

Google Scholar

Wei, W. Y. Development status and prospects of intelligent mining technology in fully mechanized mining faces. J. Coal Sci. Technol. 50(S2), 244–253 (2022).

Google Scholar

Ren, H. W. et al. Dynamic impact experiment and response characteristics analysis for 1:2 reduced-scale model of hydraulic support. J. Int. J. Min. Sci. Technol. 31(3), 347–356 (2021).

Article Google Scholar

Lei, C., Ce, Z., Bo, J. & Tangbo, Y. Simulation and experimental research on steady flow force compensation for a servo proportional valve. Flow Meas. Instrum. 94, 104257 (2023).

Google Scholar

Yuan, X. J. et al. Dynamic modeling method for an electro-hydraulic proportional valve coupled mechanical–electrical-electromagnetic-fluid subsystems. J. Magn. Magn. Mater. 587, 171312 (2023).

Article CAS Google Scholar

Qin, Z. B. et al. PID Auto tuning method for spool position control of electrohydraulic proportional valve. J. Zhejiang Univ. Eng. Sci. 49(8), 1503–1508 (2015).

Google Scholar

Aniruddha, S. et al. Actuation of an electrohydraulic manipulator with a novel feedforward compensation scheme and PID feedback in servo-proportional valves. Control Eng. Pract. 135, 105490 (2023).

Article Google Scholar

Gyan, W. et al. Energy saving and Fuzzy-PID position control of electro-hydraulic system by leakage compensation through proportional flow control valve. ISA Trans. 101, 269–280 (2020).

Article Google Scholar

Sun, J. M. Control method of proportional solenoid valve-based on feedforward compensation. J. Chin. J. Electron Dev. 42(1), 106–110 (2019).

Google Scholar

Tran, V. T., Korikov, A. M. & Nguyen, T. T. Synthesizing of a sliding control law for a hydraulic automatic stabilization system. J. Phys. Conf. Ser. 2291(1), 012016 (2022).

Article Google Scholar

Wan, Z. S. & Fu, Y. Integral nonsingular terminal sliding mode control of hydraulic servo actuator based on extended state observer. J. Shock Vibr. 2021, 1–12 (2021).

Google Scholar

Zhu, X., Wang, Q., He, X. H., Du, M. Q. & Sha, Y. G. Study on the stability of an electronically controlled hydraulic drive vehicle based on sliding-mode control and fuzzy control algorithm. J. Phys. Conf. Ser. 1654(1), 012036 (2020).

Article Google Scholar

Mahal, A. A. & Hadi, A. R. S. Robust control for automatic voltage regulator system based on learning sliding mode control. J. Int. J. Adv. Mechatron. Syst. 11, 26–39 (2024).

Article Google Scholar

Hu, J. X., Li, J. J. & Zhong, D. Q. High speed on-off valves and their development trends. J. Mech. Electr. Prod. Dev. Innov. 22(2), 60–62 (2009).

Google Scholar

Hodgson, S., Tavakoli, M., Pham, M. T. & Leleve, A. Nonlinear discontinuous dynamics averaging and PWM-based sliding control of solenoid-valve pneumatic actuators. IEEE/ASME Trans. Mechatron. 20, 876–888 (2015).

Article Google Scholar

Kogler, H. & Scheidl, R. Linear motion control with a low-power hydraulic switching converter—part II: Flatness-based control. Proc. Inst. Mech. Eng. Part I: J. Syst. Control Eng. 229, 818–828 (2015).

Google Scholar

Song, N. et al. Design of a PWM/PFM hybrid modulation switching circuit for a four-switch buck-boost converter. J. Phys.: Conf. Ser. 1, 2740 (2024).

Google Scholar

Wang, F., Gu, L. & Chen, Y. A hydraulic pressure-boost system based on high-speed on-off valves. J. IEEE/ASME Trans. Mechatron. 18(2), 733–7432013 (2013).

Article Google Scholar

Liu, S. J. & Zhu, M. S. Research on optimal control of hydraulic position system based on PWM high speed switching valve. J. Mach. Tool Hydraul. 2, 48–49 (2000).

Google Scholar

Peng, S. et al. The use of a hydraulic DC-DC converter in the actuation of a robotic leg. In 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), Tokyo, Japan 5859–5864 (2013).

Zhao, S. T., Song, T., Zhou, Y. F. & Zhang, X. L. Application of iterative learning method in position control of switching hydraulic valves. J. Xi’an Jiaotong Univ. 37(5), 523–526 (2003).

Google Scholar

Yang, Y., Wang, Y. K. & Song, Y. H. Research on positioning control of injection molding machine opening and closing mechanism based on generative learning. J. China Mech. Eng. 19(18), 2152–2155 (2008).

Google Scholar

Ren, H. W. et al. A digital oil cylinder and its control method. Proc. Eng. 7, 23 (2021).

Google Scholar

Yang, H. F. et al. Research on hydraulic cylinder position control system based on electromagnetic directional valve. J. Mech. Design Manuf. Eng. 49(2), 101–104 (2020).

Google Scholar

Zhou, C. H., Wen, G. H. & Qing, Q. X. Research on electro-hydraulic position control system using electromagnetic directional valve. J. Wuhan Univ. (Eng. Ed.) 50(5), 760–765 (2017).

Google Scholar

Jin, B. et al. Research on dual valve parallel electro-hydraulic position control system. J. J. Mech. Eng. 2000(09), 72–75 (2000).

Article Google Scholar

Liao, Y. Y. Research on dynamic characteristics of high flow and high water based directional valve. D. Taiyuan Univ. Technol. 2015, 89 (2015).

Google Scholar

Zhao, R. H. et al. Research on the performance of a novel electro-hydraulic proportional directional valve with position-feedback groove. J. Proc. Inst. Mech. Eng. Part E J. Process Mech. Eng. 235(06), 1930–1944 (2021).

Article Google Scholar

Hou, T. Y. et al. Research on positioning control strategy for a hydraulic support pushing system based on iterative learning. J. Actuat. 12(8), 306 (2023).

Article Google Scholar

Hou, T. Y. et al. Positioning control strategy of hydraulic support pushing system in fully mechanized coal face. J. Electron. 12(17), 3628 (2023).

Article Google Scholar

Huang, G. B., Chen, L. & Siew, C. K. Universal approximation using incremental constructive feedforward networks with random hidden nodes. J. IEEE Trans. Neural Netw. 17(4), 879–892 (2006).

Article Google Scholar

Zhang, G. Y. et al. Seismic reservoir prediction method based on wavelet transform and convolution neural network and its application. J. China Univ. Petrol. Nat. Sci. Ed. 44(4), 83–93 (2020).

Google Scholar

Marton, L., Fodor, S. & Sepehri, N. A practical method for friction identification in hydraulic actuators. Mecha-tronics 21, 350–356 (2011).

Article Google Scholar

Tran, X. et al. Effect of friction model on simulation of hydraulic actuator. J. Proc. IMechE Part I Syst. Control Eng. 228, 690–698 (2014).

Google Scholar

Owen, W. S. & Croft, E. A. The reduction of stick-slip friction in hydraulic actuators. J. IEEE/ASME Trans. Mechatron. 8(3), 362–371 (2003).

Article Google Scholar

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This research was funded by National Natural Science Foundation of China (U1910212)—Study on high pressure, large flow and high water-based digital valve and its control method in mining.

These authors contributed equally: Ziming Kou and Juan Wu.

College of Mechanical and Vehicle Engineering, Taiyuan University of Technology, Taiyuan, 030024, China

Tengyan Hou, Ziming Kou, Juan Wu, Buwen Zhang & Yanwei peng

Institute of Intelligent Manufacturing and Digital Intelligence Mining, Yuncheng Vocational and Technical University, Yuncheng, 044000, China

Chaohong Shi, Ziming Kou & Juan Wu

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T.H. contributed to Conceptualization; T.H. and C.S. primarily wrote the manuscript; C.S. and Y.P. analyzed and described the manuscript theory; T.H. and B.Z. contributed methodology; Z.K. and J.W. contributed to Resources; T.H. contributed to writing—review and editing; Z.K. and J.W. contributed to supervision. All authors have read and agreed to the published version of the manuscript. All authors have reviewed and agreed to the submission of the manuscript for publication.

Correspondence to Ziming Kou or Juan Wu.

The authors declare no competing interests.

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Hou, T., Shi, C., Kou, Z. et al. Research on positioning control strategy of hydraulic support pushing system based on multistage speed control valve. Sci Rep 14, 19046 (2024). https://doi.org/10.1038/s41598-024-70087-1

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Received: 04 February 2024

Accepted: 13 August 2024

Published: 16 August 2024

DOI: https://doi.org/10.1038/s41598-024-70087-1

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