Online Estimation Measurement Method and Device for Valve Orifice Pressure Drop of Direct-Acting Electro-Hydraulic Control Valve

By establishing a dynamic model and integral hydraulic model of the direct-moving electro-hydraulic control valve, combined with the immersion and invariance principle, online pressure drop estimation without pressure sensor is achieved, the accuracy and cost of hydraulic valve pressure drop measurement is solved, and digital and lightweight design is realized.

CN119878656BActive Publication Date: 2025-08-01ZHEJIANG UNIV
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Patent Information

Application Number
CN202510379906.7
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-03-28
Publication Date
2025-08-01
Estimated Expiration
2045-03-28

AI Technical Summary

Technical Problem

In the prior art, pressure drop measurement of hydraulic valves requires additional pressure sensors, resulting in increased costs and potential fault points, and errors are introduced from the valve port, making it difficult to achieve accurate measurements.

Method used

By dividing the direct-moving electro-hydraulic control valve into electric drive assembly and slide valve assembly, a dynamic model is established, a disturbance observer and integral hydraulic model are designed, and the online estimation of pressure drop is combined with immersion and invariant principles to avoid the use of pressure sensors.

Benefits of technology

It realizes efficient, fast and accurate pressure drop measurement, ensures real-time measurement, and integrates the pressure drop measurement function into the direct-acting electro-hydraulic control valve to realize the digital and lightweight design of hydraulic basic components.

✦ Generated by Eureka AI based on patent content.

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Abstract

The present invention discloses an online estimation and measurement method and device for the valve port pressure drop of a direct-acting electro-hydraulic control valve. The method includes the following steps: dividing the direct-acting electro-hydraulic control valve into an electric drive component and a spool valve component, and respectively establishing dynamic models of the electric drive component and the spool valve component with respect to the coil thrust; constructing a state space equation based on the unmodeled terms in the dynamic model in combination with the spring force and the hydrodynamic force; then designing a disturbance observer, and fitting an integral hydrodynamic force model based on the spool displacement and the pressure drop; and finally, performing online estimation of the pressure drop based on the immersion and invariance principle. The present invention avoids the use of a pressure sensor. On the one hand, it can achieve efficient and rapid pressure drop measurement, ensuring the real-time performance of the measurement; on the other hand, it integrates the pressure drop measurement function into the direct-acting electro-hydraulic control valve, providing a design idea with fast response, high precision, low cost, light weight, and digitalization for the pressure drop measurement and control of the core control valve in the construction machinery hydraulic system.
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Description

Technical Field

[0001] The present invention relates to the field of construction machinery, and particularly to an online estimation and measurement method and device for the valve port pressure drop of a direct-acting electro-hydraulic control valve. Background Art

[0002] Under the background of Industry 4.0, hydraulic components are increasingly integrated with intelligent functions such as condition monitoring and fault diagnosis. For hydraulic valves, these intelligent functions require additional pressure sensors to measure the valve port pressure drop. However, to prevent affecting the internal flow field of the valve, the actual installation position of the sensor is usually far from the valve port, which leads to errors caused by frictional losses and local losses being introduced into the calculation. To accurately measure the pressure drop, the pressure sensor must be installed as close as possible to the valve port inside the valve body. Moreover, the size of the pressure sensor must be small and compact, which significantly increases the cost and additionally introduces potential failure points. With the continuous development and application of electro-hydraulic proportional technology, the trend of intelligentization is becoming more and more obvious, putting forward higher requirements for the valve port pressure drop test technology of electro-hydraulic control valves. Summary of the Invention

[0003] The purpose of the present invention is to propose an online estimation and measurement method and device for the valve port pressure drop of a direct-acting electro-hydraulic control valve in view of the deficiencies of the prior art.

[0004] The purpose of the present invention is achieved through the following technical solutions: An online estimation and measurement method for the valve port pressure drop of a direct-acting electro-hydraulic control valve, the method comprising the following steps:

[0005] (1) Divide the direct-acting electro-hydraulic control valve into an electric drive assembly and a spool valve assembly, and respectively establish dynamic models of the electric drive assembly and the spool valve assembly with respect to the coil thrust; construct a state space equation based on the unmodeled terms in the dynamic model combined with the spring force and the hydrodynamic force;

[0006] (2) Design a disturbance observer, and fit an integral hydrodynamic force model based on the spool displacement and the pressure drop;

[0007] (3) Perform online estimation of the pressure drop based on the immersion and invariance principle.

[0008] Further, the state space equation is as follows:

[0009] ;

[0010] Wherein, represents three state variables, is the spool displacement, is the current flowing through the coil, is the combined hydrodynamic force, representing the unmodeled term, represents the spring preload of the spool valve, is the total mass of the spring mass system, is the viscosity coefficient, is the equivalent resistance of the coil, is the equivalent inductance of the coil, is the force - current coefficient.

[0011] Furthermore, a sliding - mode controller is designed, where the spool acceleration only acts on the control law, and a disturbance observer for estimating error convergence is designed as follows:

[0012] ;

[0013] where is the convergence speed parameter of the disturbance observer, and z is the auxiliary vector.

[0014] Furthermore, the integral hydrodynamic force model is as follows:

[0015] ;

[0016] where is the stable hydrodynamic force, is the pressure drop across the two metering edges, is the vector of steady - state hydrodynamic force coefficients related to pressure to be determined; is the vector of steady - state hydrodynamic force coefficients independent of pressure to be determined, and is the undetermined coefficient of the exponent; all values are obtained through experimental calibration and subsequent processing.

[0017] Furthermore, the specific process of step (3) is as follows:

[0018] (3.1) Establish an estimation error manifold based on the dynamic model of the direct - acting electro - hydraulic control valve; describe the estimated pressure drop based on the estimation error manifold;

[0019] (3.2) Define the valve orifice pressure drop estimation error based on the estimated pressure drop;

[0020] (3.3) Combine the integral hydrodynamic force model and update the control law and the sliding - mode controller based on the immersion and invariance principle;

[0021] (3.4) Design a correction term to make the estimation error converge and obtain the estimation law of the original pressure drop estimation term;

[0022] (3.5) Consider the stability of the controller based on the Lyapunov function to obtain the final control law and realize the online estimation of the pressure drop.

[0023] Furthermore, the estimation error manifold is defined as:

[0024] ;

[0025] where is the introduced estimated error correction term, is the original pressure drop estimation term; the total estimated pressure drop is described as:

[0026] .

[0027] Furthermore, the final control law is:

[0028] ;

[0029] wherein, and are the sliding surface convergence parameters, is the spool acceleration, is the reference speed signal for the control law, and are the third and fourth order derivatives of displacement respectively, , .

[0030] In a second aspect, the present invention also provides an on-line estimation and measurement device for the orifice pressure drop of a direct-acting electro-hydraulic control valve. Executable code is stored in the memory. When the processor executes the executable code, the on-line estimation and measurement method for the orifice pressure drop of a direct-acting electro-hydraulic control valve as described above is implemented.

[0031] In a third aspect, the present invention also provides a computer-readable storage medium, on which a program is stored. When the program is executed by a processor, the on-line estimation and measurement method for the orifice pressure drop of a direct-acting electro-hydraulic control valve as described above is implemented.

[0032] In a fourth aspect, the present invention also provides a computer program product, including a computer program. When the computer program is executed by a processor, the on-line estimation and measurement method for the orifice pressure drop of a direct-acting electro-hydraulic control valve as described above is implemented.

[0033] Advantages of the present invention: Compared with the prior art, the present invention establishes an integral hydrodynamic force model to characterize the mathematical relationship between the integral hydrodynamic force and the pressure drop, adopts a time-varying system parameter estimation algorithm, regards the variables in the system model as unknown parameters, utilizes the immersion and invariance (I&I) principle, calculates the error derivative through the system equilibrium equation, and then integrates to reduce the error, so as to achieve accurate estimation of the pressure drop; the present invention avoids the use of a pressure sensor. On the one hand, it can achieve efficient and rapid pressure drop measurement and ensure the real-time performance of the measurement; on the other hand, it integrates the pressure drop measurement function into the direct-acting electro-hydraulic control valve, realizes the digital and lightweight design and development of hydraulic basic components, and provides a fast-response, high-precision, low-cost, lightweight, and digital design idea for the pressure drop measurement and control of the core control valve in the construction machinery hydraulic system. Description of the Drawings

[0034] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0035] Figure 1 It is a cross-sectional view of a direct-acting electro-hydraulic control valve.

[0036] Figure 2 This is the principle block diagram of the voltage drop online estimation method.

[0037] Figure 3 It is a system principle diagram of the test device for testing the hydraulic system of the present invention.

[0038] Figure 4 This is a diagram of an experimental device for testing a hydraulic system according to the present invention.

[0039] Figure 5 It is a schematic diagram of the pressure estimation results under steady-state displacement and steady-state pressure drop conditions.

[0040] Figure 6 This is a diagram showing the estimated result and actual pressure drop when the valve core moves from -1mm to 1mm within 0 to 10MPa.

[0041] Figure 7 It is a schematic diagram of the pressure estimation results under dynamic displacement and pressure drop conditions.

[0042] Figure 8 is the pressure estimation result under step signal condition.

[0043] Figure 9 It is a structural diagram of an online estimation and measurement device for valve port pressure drop of a direct-acting electro-hydraulic control valve according to the present invention. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described below with reference to the accompanying drawings and examples. It should be understood that the specific examples described herein are only used to explain the present invention and are not intended to limit the present invention.

[0045] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. The specific implementation method includes the following steps:

[0046] Step 1, establish the mathematical model of the direct-acting electro-hydraulic control valve system. The direct-acting electro-hydraulic control valve (DECV), which is widely used in current industrial systems, is a highly digital component among current hydraulic valves. They are usually powered by solenoids, and the armature of the solenoid overcomes the hydraulic force to control the spool displacement to regulate the flow rate.

[0047] Step 1-1, according to Newton's second law, the force balance equation of the spool in the direct-acting electro-hydraulic control valve system is:

[0048] (1)

[0049] In equation (1), represents the coil thrust, represents the counteracting spring force, represents the viscous force, represents the inertial force, represents the hydraulic force, represents the unmodeled terms.

[0050] The direct-acting electro-hydraulic control valve system can be regarded as consisting of two parts: the electric drive component and the spool valve component. Among them, the electric drive component can be regarded as an electrical system composed of a resistor and an inductor in series. The dynamic model of the electric drive component is formulated as follows:

[0051] (2)

[0052] In equation (2), is the equivalent voltage across the coil, used as the controller input; is the equivalent inductance of the coil; is the current flowing through the coil; is the equivalent resistance of the coil; is the coil thrust as described in equation (1), and is the force-current coefficient.

[0053] As for the spool valve component, it can be regarded as a second-order inertial system. The modeled dynamic system is as follows:

[0054] (3)

[0055] Where is the total mass of the spring-mass system; is the viscous coefficient; is the spring stiffness, is the spool displacement, is the unmodeled dynamics. When , the spool works in the middle position and the flow rate is 0. Represents the pre-tightening compression of the shift spring. It should be noted that the flutter signal is superimposed on the final output signal of the controller to keep the spool in a quasi-static state, so the friction force is regarded as a viscous force.

[0056] Step 1-2: Model the hydrodynamic force. The hydrodynamic force generally includes the steady hydrodynamic force and the transient hydrodynamic force. The magnitude of the time-transient hydrodynamic force is affected by the total damping length and is expressed as Equation (4):

[0057] (4)

[0058] where C d is the flow coefficient, w is the area gradient. Due to the symmetric structure design of the spool assembly being 0, the transient hydrodynamic force is regarded as 0.

[0059] The total steady hydrodynamic force of the piston valve with two metering edges is given by the following equation:

[0060] (5)

[0061] where is the steady hydrodynamic force; is the velocity coefficient; is the jet angle, is the pressure drop between the two metering edges.

[0062] Select three state variables and combine the spring force , the unmodeled terms of the spring force and the hydrodynamic force, and then establish the comprehensive hydrodynamic force to represent them. Finally, the dynamic system can be written as a state-space equation:

[0063] (6)

[0064] where , representing the spring pre-tightening force of the spool valve.

[0065] Step 2: Based on the disturbance observer, measure the hydrodynamic force to establish an integral hydrodynamic force model for embedding in the online pressure estimation model to achieve the pressure drop estimation measurement while normally controlling the spool displacement.

[0066] Step 2-1: The use of the disturbance observer requires a model-based control algorithm. Use the tracking differentiator algorithm of Equation (7) below to ensure the continuity of the reference signal:

[0067] (7)

[0068] where is the reference position signal for the control law; is the reference speed signal for the control law; is the tracking signal and is the control conversion speed. The high-order reference state higher than the reference speed order is obtained by the difference method to reduce the signal delay.

[0069] Step 2-2, in view of the significant change of the hydrodynamic force within the working range, in order to achieve the real-time robustness against valve uncertainties and disturbances, a sliding mode controller with the following form is designed:

[0070] (8)

[0071] where and are the sliding surface convergence parameters; , and are the position, speed, and acceleration tracking errors respectively. The derivation results are as follows:

[0072] (9)

[0073] Spool acceleration is also obtained through a differential circuit. As known from the previous text, its order is relatively high and there is a certain amount of noise ripple in the value, making it difficult to directly estimate the pressure drop. Therefore, it is only used in the control law. And and are the third and fourth derivatives of the displacement respectively.

[0074] Step 2-3, according to the equivalent principle, the control law is designed as follows:

[0075] (10)

[0076] where, is the boundary layer chattering parameter, q represents the sliding mode surface convergence parameter, and s represents the sliding mode surface;

[0077] Substituting into (9), then equation (9) is updated as follows:

[0078] (11)

[0079] Step 2-4, design a disturbance observer to converge and define the estimation error . According to (6), it can be expressed as:

[0080] (12)

[0081] In order to achieve the fast convergence of the disturbance estimation to 0, the designed disturbance observer is shown as the following equation to ensure that the estimation error approaches 0 exponentially:

[0082] (13)

[0083] where is the convergence speed parameter of the disturbance observer. Define the auxiliary vector as:

[0084] (14)

[0085] Combining (12) and (13), and then differentiating (14) gives:

[0086] (15)

[0087] Therefore, the exponential convergence of the estimation error is guaranteed, and the disturbance observer can be designed as:

[0088] (16)

[0089] Step 2 - 5, define the Lyapunov function as follows:

[0090] (17)

[0091] Differentiating gives:

[0092] (18)

[0093] Step 2 - 6, the main factors affecting the integral hydrodynamic force are the pressure drop and the spool displacement. The pressure drop condition is selected in the range of 0 - 12 MPa with a step size of 3 MPa. The spool displacement condition is selected at a step of 10% within the range of - 100% to 100% stroke. The product of the cubic function of the spool displacement and the low - order function of the pressure drop is used to fit the force model. The final model is established as follows:

[0094] (19)

[0095] where is the pressure - related steady - state hydrodynamic force coefficient vector to be determined; is the pressure - independent steady - state hydrodynamic force coefficient vector to be determined, and are the undetermined coefficients of the exponents. All these values are obtained through experimental calibration and subsequent processing. When mm, the first value of is set to 0 to keep the force constant. According to the measurement results, the fitting results are as follows:

[0096] (20)

[0097] So far, the models of the integral hydrodynamic force and the DEVC have been established.

[0098] Step 3: Based on the immersion and invariance (I&I) principle, perform online estimation of the pressure drop. The I&I principle requires the establishment of an error manifold , which is designed to become an invariant attractor manifold through an adaptive control law. This involves ensuring that the pressure drop estimation error trajectory converges within the manifold.

[0099] Step 3-1: The estimation error manifold of the dynamic model based on DECV is defined as:

[0100] (21)

[0101] where is the introduced estimation error correction term, and is the original pressure drop estimation term. The total estimated pressure drop is described as:

[0102] (22)

[0103] Step 3-2: Define the valve orifice pressure drop estimation error as follows:

[0104] (23)

[0105] According to (19) and (20), note that , and . The control law estimated based on the I&I principle is updated as:

[0106] (24)

[0107] Meanwhile, according to (11), the sliding surface derivative is updated as follows:

[0108] (25)

[0109] Step 3-3: Next, only need to design in the control law, that is, and , so that acts as an invariant attractor manifold.

[0110] For the convergence of the control law, the derivative of can be obtained as follows:

[0111] (26)

[0112] If is considered to be slowly varying, that is, , there is:

[0113] (27)

[0114] Take the estimation law as (28):

[0115] (28)

[0116] Then the derivative of the estimation error can be updated as follows:

[0117] (29)

[0118] Therefore, the estimation error will exponentially converge to 0 by simply designing an appropriate correction term

[0119] Take the estimation correction term The partial derivative is (30):

[0120] (30)

[0121] where is the convergence rate of the estimation. In other words, the estimation correction term is:

[0122] (31)

[0123] Then the estimation error exponentially converges:

[0124] (32)

[0125] The final estimation law is designed as follows:

[0126] (33)

[0127] Step 3 - 4. Prove the stability of the overall controller by defining a Lyapunov function As shown in (34):

[0128] (34)

[0129] Then its derivative is:

[0130] (35)

[0131] Therefore, ensuring is sufficient to make . The final control law is:

[0132] ​(36)

[0133] Corresponding to the embodiment of the online estimation measurement method for the valve port pressure drop of the aforementioned direct-acting electro-hydraulic control valve, the present invention also provides an embodiment of an online estimation measurement device for the valve port pressure drop of a direct-acting electro-hydraulic control valve.

[0134] See Figure 9 , an online estimation measurement device for the valve port pressure drop of a direct-acting electro-hydraulic control valve provided by an embodiment of the present invention includes a memory and one or more processors. Executable code is stored in the memory. When the processor executes the executable code, it is used to implement the online estimation measurement method for the valve port pressure drop of a direct-acting electro-hydraulic control valve in the above embodiment.

[0135] The embodiment of the online estimation measurement device for the valve port pressure drop of a direct-acting electro-hydraulic control valve provided by the present invention can be applied to any device with data processing capabilities. The any device with data processing capabilities can be a device or apparatus such as a computer. The device embodiment can be implemented by software, or by hardware or a combination of software and hardware. Taking software implementation as an example, as a logically meaningful device, it is formed by the processor of any device with data processing capabilities where it is located reading the corresponding computer program instructions in the non-volatile memory into the memory for operation. From the hardware level, as Figure 9 shown, it is a hardware structure diagram of any device with data processing capabilities where the online estimation measurement device for the valve port pressure drop of a direct-acting electro-hydraulic control valve provided by the present invention is located. In addition to Figure 9 the shown processor, memory, network interface, and non-volatile memory, the any device with data processing capabilities where the device in the embodiment is located usually also includes other hardware according to the actual functions of the any device with data processing capabilities, which will not be elaborated here.

[0136] The specific implementation processes of the functions and roles of each unit in the above device are specifically described in detail in the implementation processes of the corresponding steps in the above method, which will not be elaborated here.

[0137] For the device embodiment, since it basically corresponds to the method embodiment, the relevant parts can be referred to the partial description of the method embodiment. The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place, or may be distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the present invention solution. Those of ordinary skill in the art can understand and implement it without creative labor.

[0138] An embodiment of the present invention further provides a computer-readable storage medium, on which a program is stored. When the program is executed by a processor, an online estimation and measurement method for the valve port pressure drop of a direct-acting electro-hydraulic control valve in the above embodiment is implemented.

[0139] The computer-readable storage medium may be an internal storage unit of any device with data processing capabilities described in any of the foregoing embodiments, such as a hard disk or memory. The computer-readable storage medium may also be an external storage device of any device with data processing capabilities, such as a plug-in hard disk, a Smart Media Card (SMC), an SD card, a Flash Card, etc. equipped on the device. Further, the computer-readable storage medium may also include both an internal storage unit and an external storage device of any device with data processing capabilities. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capabilities, and may also be used to temporarily store data that has been output or will be output.

[0140] The present invention also provides a computer program product, including a computer program. When the computer program is executed by a processor, an online estimation and measurement method for the valve port pressure drop of a direct-acting electro-hydraulic control valve is implemented.

[0141] The above embodiments are used to explain the present invention, rather than limit the present invention. Any modifications and changes made within the spirit and scope of the claims of the present invention fall within the protection scope of the present invention.

Claims

1. An on-line estimation and measurement method for the pressure drop across the valve port of a direct-acting electro-hydraulic control valve, characterized in that, The method includes the following steps: (1) Divide the direct-acting electro-hydraulic control valve into an electric drive component and a spool valve component, and establish dynamic models of the electric drive component and the spool valve component with respect to the coil thrust respectively; construct a state-space equation based on the unmodeled terms in the dynamic models combined with the spring force and the hydrodynamic force; (2) Design a disturbance observer to obtain the hydrodynamic force and the unmodeled terms, and fit an integral hydrodynamic force model based on the spool displacement and the pressure drop. The integral hydrodynamic force model is as follows: ; Among them, is the steady-state hydrodynamic force, is the pressure drop across the two metering edges, is the vector of pressure-related steady-state hydrodynamic force coefficients to be determined; is the vector of pressure-independent steady-state hydrodynamic force coefficients to be determined, and is the undetermined coefficient of the exponent; all values are obtained through experimental calibration and subsequent processing; (3) Conduct online estimation of the pressure drop based on the immersion and invariance principle; the specific process is as follows: (3.1) Establish an estimation error manifold based on the dynamic model of the direct-acting electro-hydraulic control valve; describe the estimated pressure drop based on the estimation error manifold; (3.2) Define the valve port pressure drop estimation error based on the estimated pressure drop; (3.3) Combine the integral hydrodynamic force model, and update the control law and the sliding mode controller based on the immersion and invariance principle; (3.4) Design a correction term to make the estimation error converge, and obtain the estimation law of the original pressure drop estimation term; (3.5) Consider the stability of the controller based on the Lyapunov function to obtain the final control law and realize the online estimation of the pressure drop.

2. An on-line estimation and measurement method for the valve port pressure drop of a direct-acting electro-hydraulic control valve according to claim 1, characterized in that, The state-space equation is as follows: ; Among them, represents three state variables, is the spool displacement, is the current flowing through the coil, is the comprehensive hydrodynamic force, representing the unmodeled terms, represents the spring preload of the spool valve, is the total mass of the spring-mass system, is the viscous coefficient, is the equivalent resistance of the coil, is the equivalent inductance of the coil, is the force-current coefficient.

3. An online estimation and measurement method for the valve port pressure drop of a direct-acting electro-hydraulic control valve according to claim 1, characterized in that, Design a sliding mode controller, with the spool acceleration only acting on the control law, and design a disturbance observer for the convergence of the estimation error; specifically as follows: ; wherein, is the convergence speed parameter of the disturbance observer, and z is the auxiliary vector.

4. An on-line estimation and measurement method for the valve port pressure drop of a direct-acting electro-hydraulic control valve according to claim 1, characterized in that The estimation error manifold is defined as: ; wherein is the introduced estimated error correction term, is the original pressure drop estimation term; the total estimated pressure drop is described as: 。 5. An online estimation and measurement method for the valve port pressure drop of a direct-acting electro-hydraulic control valve according to claim 1, characterized in that The final control law is: ; Among them, and are sliding surface convergence parameters, is the spool acceleration, is the reference speed signal for the control law, and are the third and fourth order derivatives of displacement respectively, , .

6. An on-line estimation and measurement device for the valve port pressure drop of a direct-acting electro-hydraulic control valve, comprising a memory and one or more processors, wherein executable code is stored in the memory, characterized in that, When the processor executes the executable code, it realizes an online estimation and measurement method for the valve port pressure drop of a direct-acting electro-hydraulic control valve as described in any one of claims 1-5.

7. A computer-readable storage medium having a program stored thereon, characterized in that, When the program is executed by the processor, it realizes an online estimation and measurement method for the valve port pressure drop of a direct-acting electro-hydraulic control valve as described in any one of claims 1-5.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it realizes an online estimation and measurement method for the valve port pressure drop of a direct-acting electro-hydraulic control valve as described in any one of claims 1-5.

Citation Information

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