A dual-friction parameter identification and adaptive synchronization control method for a multi-axis electro-hydraulic system

Abstract

This invention discloses a dual friction parameter identification and adaptive synchronous control method for a multi-axis electro-hydraulic system, comprising: constructing a dynamic model of a hydraulic leveling system including a LuGre friction model; using a genetic algorithm to perform offline optimization identification of the friction parameters of the LuGre friction model to obtain initial estimated parameters; based on the initial estimated parameters, designing an adaptive parameter adjustment law based on control error to fine-tune the friction parameters in the LuGre friction model online in real time, forming a dual friction parameter identification framework consisting of offline identification and online adaptation; using the dual identification framework, designing an integrated adaptive feedforward integral sliding mode controller, introducing the online fine-tuned friction parameters into the sliding mode control law for feedforward compensation, and ensuring that synchronous control and online estimation of friction parameters are performed synchronously; based on the dynamic model, distributing the virtual torque in the overdrive coupling system, and designing an inner-loop voltage controller to achieve pressure control under constant back pressure.

Description

Technical Field

[0001] This invention belongs to the field of electro-hydraulic servo control technology, specifically relating to a method for dual friction parameter identification and adaptive synchronous control of a multi-axis electro-hydraulic system. Background Technology

[0002] In heavy forging and pressing equipment, the multi-axis leveling system of a hydraulic press plays a crucial role in ensuring the smooth and synchronous downward pressing of the moving crossbeam (slider). It typically consists of a slider, leveling cylinder, pressure reducing valve, and servo proportional valve, achieving passive leveling. With the increasing demands for forming precision in industrial production, the synchronous control accuracy of the leveling system has become a key indicator.

[0003] However, hydraulic leveling cylinders exhibit extremely complex nonlinear friction characteristics during actual operation, especially in the low-speed pressing stage. This nonlinear friction leads to low-speed "creeping" and oscillations in the system, severely affecting the smooth operation and high-precision synchronous control of the hydraulic press. To implement effective friction compensation, an accurate friction dynamics model must be established. Currently, simplified friction models are often used in engineering, but they are insufficient to describe the true dynamic friction behavior. Although advanced nonlinear friction models such as LuGre can better reflect these dynamic characteristics, they include several parameters that are difficult to measure directly, such as stiffness coefficients and damping coefficients.

[0004] Existing parameter acquisition methods mostly employ either offline identification or online adaptation: simple offline identification cannot cope with the time-varying friction parameters caused by oil temperature changes, mechanical wear, etc., during long-term operation of hydraulic systems; while simple online adaptive control, if it fails to provide accurate initial parameter values ​​in the initial stage, often leads to slow algorithm convergence speed, or even system instability when encountering external disturbances.

[0005] For example, Chinese patent application number CN202210222556.X proposes a friction compensation control method for an electro-hydraulic servo system. It establishes a nonlinear friction model, identifies parameters offline using a genetic algorithm, and feeds forward to compensate for friction. However, this scheme is mainly for single-axis systems and does not consider the case of multi-axis coupling. Furthermore, the parameters obtained offline are fixed and cannot adapt to the time-varying friction during the motion process in real time.

[0006] Chinese patent application number CN109986828A proposes a four-corner leveling system for composite material presses that achieves total tonnage control. It uses pressure / position control to achieve leveling, but ignores the nonlinear friction characteristics at low speeds and lacks explicit compensation and robust control methods for the dynamic friction characteristics at low speeds. It is difficult to effectively suppress crawling oscillations and synchronization deviations under multi-axis coupling.

[0007] Therefore, there is an urgent need in this field for a multi-axis electro-hydraulic system control method that can effectively overcome the initial uncertainty and time-varying characteristics of friction parameters while achieving high-precision synchronous control. Summary of the Invention

[0008] The purpose of this invention is to provide a method for identifying dual friction parameters and adaptive synchronization control of a multi-axis electro-hydraulic system, so as to solve the technical problems of low-speed crawling, oscillation and insufficient synchronization accuracy caused by nonlinear friction in the existing multi-axis leveling system.

[0009] To achieve the above objectives, the present invention adopts the following technical solution: a method for dual friction parameter identification and adaptive synchronous control of a multi-axis electro-hydraulic system, comprising the following steps:

[0010] Step S1: Construct a dynamic model of the hydraulic leveling system that includes the LuGre friction model;

[0011] Step S2: Use a genetic algorithm to perform offline optimization and identification of the friction parameters of the LuGre friction model to obtain the initial estimated parameters;

[0012] Step S3: Based on the initial estimated parameters, design an adaptive parameter adjustment law based on control error to fine-tune the friction parameters in the LuGre friction model online in real time, forming a dual friction parameter identification framework consisting of offline identification and online adaptation.

[0013] Step S4: Using the dual friction parameter identification framework, design an integrated adaptive feedforward integral sliding mode controller, introduce the online fine-tuned friction parameters into the sliding mode control law for feedforward compensation, and ensure that synchronous control and online estimation of friction parameters are performed synchronously.

[0014] Step S5: Based on the dynamic model of the hydraulic leveling system, the virtual torque in the overdrive coupling system is distributed, and an inner loop voltage controller is designed to control the pressure under constant back pressure.

[0015] Further, in step S1, a dynamic model of the hydraulic leveling system incorporating the LuGre friction model is constructed, and the implementation method is as follows:

[0016] The hydraulic leveling system includes a slider, a leveling cylinder, a pressure reducing valve, and a servo proportional valve. During the slider's descent, the leveling cylinder acts on the slider to achieve passive leveling. The leveling cylinder is independently controlled by the load port. The rod chamber of the leveling cylinder is controlled by the pressure reducing valve, and the rodless chamber is controlled by the servo proportional valve.

[0017] For a single leveling cylinder, its mathematical model simplifies to:

[0018]

[0019] In the formula, Indicates the mass of the piston rod; The second derivative of the piston rod displacement is expressed as the acceleration of the piston rod. This indicates the pressure inside the rodless cavity. This indicates the pressure inside the rod cavity. This represents the force-bearing area on the rodless side of the piston. This indicates the area of ​​the piston rod chamber that experiences force. This indicates the frictional force experienced by the leveling cylinder; Indicates the driving force of the leveling cylinder;

[0020] Among them, the friction force adopts the LuGre nonlinear friction model;

[0021] Treating the slider as a rigid body, its dynamic model is established, and the geometric relationship between the displacement of the four leveling cylinders and the slider deflection angle is combined to obtain a slider dynamic model that includes multi-cylinder coupling and friction terms.

[0022] By combining the mathematical model of the leveling cylinder and the dynamic model of the slider that includes multi-cylinder coupling and friction terms, the dynamic model of the hydraulic leveling system is obtained.

[0023] Furthermore, the mathematical model of the LuGre nonlinear friction model is as follows:

[0024]

[0025] In the formula, Indicates the bristle stiffness coefficient; , Let represent the average deformation of the bristles and its derivative, respectively; Indicates the bristle damping coefficient; Indicates the viscous damping coefficient; The derivative of the piston rod displacement, i.e., the piston velocity; Represents the Stribeck curve function; Represents Coulomb friction; This represents static friction. This indicates Stribeck's speed.

[0026] Furthermore, in step S2, when using a genetic algorithm to perform offline optimization and identification of the friction parameters of the LuGre friction model, static parameter identification is performed first, followed by dynamic parameter identification; wherein, the static parameters include the viscous friction coefficient. Coulomb friction Static friction and Stribeck speed Dynamic parameters include the bristle stiffness coefficient. and bristle damping coefficient .

[0027] Furthermore, in step S3, an adaptive parameter adjustment law based on control error is designed to fine-tune the friction parameters in the LuGre friction model online in real time. The implementation method is as follows:

[0028] Define the adaptive parameters in the LuGre friction model as follows: , , ;

[0029] An adaptive update law is constructed by multiplying the control error by the system operating state variables, and then calculating the adaptive derivatives of the estimated values ​​of each friction parameter. The specific formulas are as follows:

[0030]

[0031] in, This represents the approach law for each friction parameter; The learning law represents the various friction parameters; Indicates system operating status variables; Indicates control error; , representing the One leveling cylinder; , When the values ​​are 1, 2, and 3, they respectively refer to the three defined adaptive parameters. , , ;

[0032] Subsequently, the adaptive derivatives of the estimated friction parameters are discretized and integrated to obtain the updated estimated values ​​of each friction parameter at the current time. The calculation formula is as follows:

[0033]

[0034] in, Indicates the current sampling time. Indicates the previous sampling time. The system sampling period is used to obtain the updated first friction parameter estimates at the current time. Second friction parameter estimate and the estimated value of the third friction parameter .

[0035] Furthermore, in step S4, an integrated adaptive feedforward integral sliding mode controller is designed, and its implementation method is as follows:

[0036] Taking the zero deflection angle of the slider around the x-axis and y-axis as the control objective, the deflection angle error and its derivative are defined, and the integral sliding surface is designed as follows:

[0037]

[0038] in, This indicates the error in the deflection angle of the slider around the x-axis; This indicates the error in the slider's deflection angle around the y-axis; This represents the slope of the sliding surface used for integration about the x-axis; This represents the slope of the sliding surface used for integration about the y-axis; This represents the integral gain of the i-th leveling cylinder controlled around the x-axis; This represents the integral gain of the i-th leveling cylinder controlled around the y-axis;

[0039] The virtual control input torque consists of an equivalent control term and a robust switching control term, with frictional feedforward compensation introduced to obtain the virtual control torque. and .

[0040] Furthermore, in step S5, the virtual torque in the overdrive coupling system is distributed based on the dynamic model of the hydraulic leveling system. The implementation method is as follows:

[0041] When the slider moves at a constant velocity in a straight line, the total force is controlled in the z-axis direction according to the slider dynamics model to obtain the average target pressure. ;

[0042] Based on the constraint that the slider is a rigid body and has no torsional internal force, the target pressure of each leveling cylinder is obtained. Must meet ;in This represents the target pressure of the i-th leveling cylinder. =1,2,3,4;

[0043] Combining the above relationships and virtual control torque and The target pressure of each of the four leveling cylinders was calculated. .

[0044] Furthermore, in step S5, an inner-loop voltage controller is designed to perform pressure control under constant back pressure. The implementation method is as follows:

[0045] A PID controller is used to control the pressure in the rodless chamber of each leveling cylinder;

[0046] Define pressure error The discretized PID control output is:

[0047]

[0048] in, Represents a time variable. express Pressure error at any time express Constant pressure to achieve goals express The actual pressure at all times Indicates the first The PID control output voltage at each sampling time. Indicates the current sampling time. Indicates the first Discrete pressure error at each sampling time; Indicates the first Discrete pressure error at each sampling time; Indicates the first Discrete pressure error at each sampling time, Indicates incrementing from 0 to The summation variable; This represents the proportional gain controlled by voltage. This represents the integral gain of the voltage control. Represents the differential gain of voltage control; Indicates the sampling period.

[0049] The present invention also provides a dual friction parameter identification and adaptive synchronization control system for a multi-axis electro-hydraulic system, including a memory, a processor, and computer program instructions stored in the memory and executable by the processor. When the processor executes the computer program instructions, it can implement the above-mentioned method.

[0050] The present invention also provides a computer device, comprising: at least one processor, at least one memory, and computer program instructions stored in the memory, which implement the above-described method when executed by the processor.

[0051] Compared with existing technologies, this invention has the following advantages: In a multi-axis leveling system, this invention employs a genetic algorithm to offline identify the parameters of the LuGre friction model, optimizing with the goal of minimizing the mean square error between the actual given value and the estimated value, resulting in fast identification speed. Even without knowing the specific parameter values, optimization search within a given parameter range can identify a good initial parameter value while avoiding local optima. Addressing the overdrive coupling characteristics of multi-axis leveling systems, this invention utilizes a dual parameter identification framework comprised of offline identification using a genetic algorithm and online adaptive fine-tuning. It designs an adaptive feedforward integral sliding mode controller and virtual torque allocation to ensure that online estimation of friction parameters and high-precision synchronous control are performed simultaneously. This dual strategy of offline initial value and online fine-tuning overcomes the shortcomings of simple offline identification in adapting to time-varying parameters and avoids the risk of slow convergence or instability caused by improper initial values ​​in simple online adaptive control. Furthermore, this invention introduces the online fine-tuned friction parameters into the sliding mode control law for feedforward compensation, effectively suppressing low-speed crawling and oscillation, significantly improving the system's operational smoothness and synchronous control accuracy. Attached Figure Description

[0052] Figure 1 This is a flowchart illustrating the implementation of the method for dual friction parameter identification and adaptive synchronous control of a multi-axis electro-hydraulic system provided in this embodiment of the invention.

[0053] Figure 2 This is a schematic diagram illustrating the implementation principle of the method for dual friction parameter identification and adaptive synchronous control of a multi-axis electro-hydraulic system provided in this embodiment of the invention.

[0054] Figure 3 This is a schematic diagram of the hydraulic leveling system in an embodiment of the present invention;

[0055] Figure 4 This is a diagram showing the identification results of the genetic algorithm in an embodiment of the present invention;

[0056] Figure 5 This is a diagram showing the parameter adaptation results of an embodiment of the present invention;

[0057] Figure 6 This is a simulation result diagram of an embodiment of the present invention. Detailed Implementation

[0058] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0059] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0060] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0061] like Figure 1 As shown, this embodiment provides a method for dual friction parameter identification and adaptive synchronous control of a multi-axis electro-hydraulic system, including the following steps:

[0062] Step S1: Construct a dynamic model of the hydraulic leveling system that includes the LuGre friction model;

[0063] Step S2: Use a genetic algorithm to perform offline optimization and identification of the friction parameters of the LuGre friction model to obtain the initial estimated parameters;

[0064] Step S3: Based on the initial estimated parameters, design an adaptive parameter adjustment law based on control error to fine-tune the friction parameters in the LuGre friction model online in real time, forming a dual friction parameter identification framework consisting of offline identification and online adaptation.

[0065] Step S4: Using the dual friction parameter identification framework, design an integrated adaptive feedforward integral sliding mode controller, introduce the online fine-tuned friction parameters into the sliding mode control law for feedforward compensation, and ensure that synchronous control and online estimation of friction parameters are performed synchronously.

[0066] Step S5: Based on the dynamic model of the hydraulic leveling system, the virtual torque in the overdrive coupling system is distributed, and an inner loop voltage controller is designed to control the pressure under constant back pressure.

[0067] In this embodiment, taking a press leveling system with a slider weight of 1 ton as an example, the system parameters are: the area A of the rodless chamber of the leveling cylinder is... m2; the area of ​​the rod cavity is a. m2; bulk modulus of elasticity βe is 700e6 pa; piston rod mass mp is 20 kg; at 1 second, the eccentric torque Mx in the X direction is 750 N / m, and the eccentric torque My in the Y direction is 675 N / m.

[0068] The following section will elaborate on the relevant aspects of this method.

[0069] S1. Construct a dynamic model of the hydraulic leveling system that includes dynamic friction characteristics.

[0070] The hydraulic leveling system consists of a slider, a leveling cylinder, a pressure reducing valve, and a servo proportional valve. During the slider's descent, the leveling cylinder acts on the slider to achieve passive leveling. The hydraulic leveling system is as follows: Figure 3 As shown; where 1 represents the drive cylinder, 2 represents the slider, and 3 represents the leveling cylinder. The leveling cylinder is independently controlled by the load port. The rod-side chamber of the leveling cylinder is controlled by a pressure reducing valve, and the rodless chamber is controlled by a servo proportional valve.

[0071] For a single leveling cylinder, its mathematical model simplifies to:

[0072]

[0073] In the formula, Indicates the mass of the piston rod; The second derivative of the piston rod displacement is expressed as the acceleration of the piston rod. This indicates the pressure inside the rodless cavity. This indicates the pressure inside the rod cavity. This represents the force-bearing area on the rodless side of the piston. This indicates the area of ​​the piston rod chamber that experiences force. This indicates the frictional force experienced by the leveling cylinder; This indicates the driving force of the leveling cylinder.

[0074] The friction force adopts the LuGre nonlinear friction model, and its mathematical model is as follows:

[0075]

[0076] In the formula, Indicates the bristle stiffness coefficient; , Let represent the average deformation of the bristles and its derivative, respectively; Indicates the bristle damping coefficient; Indicates the viscous damping coefficient; The derivative of the piston rod displacement, i.e., the piston velocity; Represents the Stribeck curve function; Represents Coulomb friction; This represents static friction. This indicates Stribeck's speed.

[0077] The relationship between the displacement of the four leveling cylinders and the deflection angle of the movable beam is as follows:

[0078]

[0079] The displacement of the four leveling cylinders is , Indicates the initial displacement. This represents the sine vector of the deflection angle. ,in and These represent the deflection angles of the slider around the x-axis and y-axis, respectively. Here is the coefficient matrix:

[0080]

[0081] in, and These represent half the length of the slider in the x and y directions, respectively (i.e., the distance from the geometric center to the axis of the leveling cylinder).

[0082] Treating the slider as a rigid body, we establish a Cartesian coordinate system with the geometric center as the origin, the vertical upward axis as the z-axis, the longer side as the x-axis, and the wider side as the y-axis. Based on the dynamic equations and geometric relationships, we obtain the dynamic model of the slider:

[0083]

[0084] In the formula, Indicates the mass of the slider; This represents the displacement of the movable beam in the z-direction; Represents gravitational acceleration; Indicates the first The output force of each leveling cylinder ( =1,2,3,4); , These represent the moments of inertia of the movable beam about the x and y directions, respectively. , These represent the deflection angles of the movable beam about the x and y axes, respectively. , These represent half the length of the movable beam in the x and y directions, respectively. , These represent the deflection moments of the movable beam about the x and y axes, respectively.

[0085] Combining, we can obtain

[0086]

[0087] In the formula, Indicates the first Friction during the movement of the leveling cylinder ( =1,2,3,4).

[0088] The rod chamber of the leveling cylinder is controlled at a constant pressure using a pressure reducing valve. The kinetic model is simplified as follows:

[0089]

[0090] Organized

[0091]

[0092] In the formula, , .

[0093] The hydraulic model is as follows:

[0094] Establish the dynamic equation for the system cavity pressure:

[0095]

[0096] in, ; The flow rate into the large chamber of the leveling cylinder; This represents the dynamics of an unmodeled system, including leaks, etc. This indicates the volume of the oil inlet chamber of the leveling cylinder. This indicates the initial volume of the oil inlet chamber.

[0097]

[0098] in, Indicates the valve orifice flow coefficient; Indicates the gradient of valve orifice area; Expressing oil density; This indicates the spool control gain of the servo proportional valve. This indicates the control voltage of the servo proportional valve. This indicates the pump source pressure.

[0099] Based on the above calculations, a slider dynamics model incorporating multi-cylinder coupling and friction terms is obtained. Combining the mathematical model of the leveling cylinder and the slider dynamics model incorporating multi-cylinder coupling and friction terms, the dynamics model of the hydraulic leveling system is obtained.

[0100] S2. Use a genetic algorithm to perform offline optimization and identification of friction parameters to obtain initial estimated parameters.

[0101] Friction parameters include static and dynamic parameters, so two operating conditions will be set for identification.

[0102] When the leveling cylinder moves at a constant speed v in uniform linear motion, the internal state variable z reaches a steady state. .

[0103] The steady-state friction model is as follows:

[0104]

[0105] Therefore, it can be seen that static parameters include the coefficient of viscous friction. Coulomb friction Maximum static friction and Stribeck speed .

[0106] To make the friction force output by the model approximate the friction force of the actual system, a fitness function based on the mean square error of a genetic algorithm is designed:

[0107]

[0108] Dynamic parameters include bristle stiffness coefficient and bristle damping coefficient The genetic algorithm program is almost identical to that used for static parameter identification. When using a genetic algorithm for offline optimization identification of friction parameters, static parameter identification is performed first, followed by dynamic parameter identification.

[0109] The implementation steps of the genetic algorithm are as follows:

[0110] Step 1: Set the parameter set to be identified and set the upper and lower bounds of each parameter; the population size is 100 and the maximum number of iterations is 300.

[0111] Step 2: Substitute each set of parameters in the population into the dynamic equation, calculate the mean square error between the simulation output and the actual sampling points, and use this to calculate the fitness value of each set of parameters in the population.

[0112] Step 3: Apply the selection operator to the population;

[0113] Step 4: Apply the crossover operator to the population;

[0114] Step 5: Apply the mutation operator to the population. After selection, crossover, and mutation operations, the next generation population is obtained.

[0115] Step 6: Determine whether the termination condition is met. If it is met, output the individual with the highest fitness obtained during the process as the optimal solution, obtain the offline identification result of the friction model parameters, and terminate the calculation; otherwise, go to step 2.

[0116] The identification results are as follows Figure 4 As shown in Table 1 below:

[0117] Table 1

[0118]

[0119] S3. Based on the initial estimated parameters, an adaptive parameter adjustment law based on control error is designed to realize online real-time fine-tuning of friction parameters.

[0120] like Figure 2As shown, the adaptive parameters in the LuGre friction model are first defined as follows: , , .

[0121] An adaptive update law is constructed by multiplying the control error by the system operating state variables, and then calculating the adaptive derivatives of the estimated values ​​of each friction parameter. The specific formulas are as follows:

[0122]

[0123] in, This represents the approach law for each friction parameter; The learning law represents the various friction parameters; Indicates system operating status variables; Indicates control error; , representing the One leveling cylinder; , When the values ​​are 1, 2, and 3, they respectively refer to the three defined adaptive parameters. , , .

[0124] Subsequently, the adaptive derivatives of the estimated friction parameters are discretized and integrated to obtain the updated estimated values ​​of each friction parameter at the current time. The calculation formula is as follows:

[0125]

[0126] in, Indicates the current sampling time. Indicates the previous sampling time. The system sampling period is used to obtain the updated first friction parameter estimates at the current time. Second friction parameter estimate and the estimated value of the third friction parameter .

[0127] The adaptive parameter results of the four leveling cylinders are as follows: Figure 5 As shown, (a) represents the parameters in the four leveling cylinders. The adaptive results, (b) represent the parameters in the four leveling cylinders. The adaptive result, (c) represents the parameters in the four leveling cylinders. The adaptive results.

[0128] S4. Using a dual friction parameter identification framework, an integrated adaptive feedforward integral sliding diaphragm controller is designed to ensure that synchronous control and online estimation of friction parameters are carried out simultaneously.

[0129] Specifically, an integrated adaptive feedforward integral sliding diaphragm controller is designed. Based on the calculated mechanical mathematical model, the controller aims to achieve a zero rotation angle while simultaneously performing feedforward compensation for friction. The specific calculations are as follows:

[0130] Define the deflection angle error: , , , The sliding surface is designed as follows:

[0131]

[0132] in, This indicates the error in the deflection angle of the slider around the x-axis; This indicates the error in the slider's deflection angle around the y-axis; This represents the slope of the sliding surface used for integration about the x-axis; This represents the slope of the sliding surface used for integration about the y-axis; This represents the integral gain of the i-th leveling cylinder controlled around the x-axis; This represents the integral gain of the i-th leveling cylinder controlled around the y-axis.

[0133] Differentiating the sliding surface function and substituting it into the dynamic model, we get:

[0134]

[0135] The control input T consists of two parts: the equivalent control term. Robust switching control items .

[0136] The virtual control torque can be obtained as follows:

[0137]

[0138] in, ; , Indicates switching gain; , For symbolic functions:

[0139] .

[0140] S5. Based on the dynamic model of the hydraulic leveling system, the virtual torque in the overdrive coupling system is distributed, and an inner loop voltage controller is designed to achieve pressure control under constant back pressure.

[0141] The slider moves at a constant linear velocity during pressing, and the total force is controlled along the z-axis using the slider formula:

[0142]

[0143] As a rigid body, the slider does not exhibit any internal forces that cause distortion during the audit process; therefore, it exists... .

[0144] Therefore, combining the above formulas, we get:

[0145]

[0146] In the formula, Indicates the target pressure of the four leveling cylinders ( =1,2,3,4).

[0147] Four target pressures are obtained through torque distribution. PID control is used for the pressure, and the specific calculation is as follows:

[0148] The error is defined as:

[0149] For the servo proportional valve control input voltage or control command of the hydraulic cylinder Meanwhile, in actual control, the continuous model needs to be discretized, so the PID control output of the kth sampling period is:

[0150]

[0151] in, Represents a time variable. express Pressure error at any time express Constant pressure to achieve goals express The actual pressure at all times Indicates the first The PID control output voltage at each sampling time. Indicates the current sampling time. Indicates the first Discrete pressure error at each sampling time; Indicates the first Discrete pressure error at each sampling time; Indicates the first Discrete pressure error at each sampling time, Indicates incrementing from 0 to The summation variable; This represents the proportional gain controlled by voltage. This represents the integral gain of the voltage control. Represents the differential gain of voltage control; Indicates the sampling period.

[0152] The control effect in this embodiment is as follows: Figure 6 As shown, the maximum displacement value among the four leveling cylinders is selected as the system synchronization target value, and the displacement error is obtained by subtracting the displacement of the other leveling cylinders from it.

[0153]

[0154]

[0155] in, This indicates the maximum displacement value among the four leveling cylinders at the current moment. This represents the synchronous displacement error of the i-th leveling cylinder; This represents the actual displacement value of the i-th leveling cylinder. .

[0156] This embodiment also provides a dual friction parameter identification and adaptive synchronization control system for a multi-axis electro-hydraulic system, including a memory, a processor, and computer program instructions stored in the memory and executable by the processor. When the processor executes the computer program instructions, it can implement the above-mentioned method.

[0157] This embodiment also provides a computer device, including: at least one processor, at least one memory, and computer program instructions stored in the memory, which implement the above-described method when executed by the processor.

[0158] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0159] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0160] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0161] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0162] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for identifying dual friction parameters and adaptive synchronous control of a multi-axis electro-hydraulic system, characterized in that, Includes the following steps: Step S1: Construct a dynamic model of the hydraulic leveling system that includes the LuGre friction model; Step S2: Use a genetic algorithm to perform offline optimization and identification of the friction parameters of the LuGre friction model to obtain the initial estimated parameters; Step S3: Based on the initial estimated parameters, design an adaptive parameter adjustment law based on control error to fine-tune the friction parameters in the LuGre friction model online in real time, forming a dual friction parameter identification framework consisting of offline identification and online adaptation. Step S4: Using the dual friction parameter identification framework, design an integrated adaptive feedforward integral sliding mode controller, introduce the online fine-tuned friction parameters into the sliding mode control law for feedforward compensation, and ensure that synchronous control and online estimation of friction parameters are performed synchronously. Step S5: Based on the dynamic model of the hydraulic leveling system, the virtual torque in the overdrive coupling system is distributed, and an inner loop voltage controller is designed to control the pressure under constant back pressure.

2. The method for dual friction parameter identification and adaptive synchronous control of a multi-axis electro-hydraulic system according to claim 1, characterized in that, In step S1, a dynamic model of the hydraulic leveling system incorporating the LuGre friction model is constructed. The implementation method is as follows: The hydraulic leveling system includes a slider, a leveling cylinder, a pressure reducing valve, and a servo proportional valve. During the slider's descent, the leveling cylinder acts on the slider to achieve passive leveling. The leveling cylinder is independently controlled by the load port. The rod chamber of the leveling cylinder is controlled by the pressure reducing valve, and the rodless chamber is controlled by the servo proportional valve. For a single leveling cylinder, its mathematical model simplifies to: In the formula, Indicates the mass of the piston rod; The second derivative of the piston rod displacement is expressed as the acceleration of the piston rod. This indicates the pressure inside the rodless cavity. This indicates the pressure inside the rod cavity. This represents the force-bearing area on the rodless side of the piston. This indicates the area of ​​the piston rod chamber that experiences force. This indicates the frictional force experienced by the leveling cylinder; Indicates the driving force of the leveling cylinder; Among them, the friction force adopts the LuGre nonlinear friction model; Treating the slider as a rigid body, we establish its dynamic model and combine the geometric relationship between the displacement of the four leveling cylinders and the slider deflection angle to obtain a slider dynamic model that includes multi-cylinder coupling and friction terms. By combining the mathematical model of the leveling cylinder and the dynamic model of the slider that includes multi-cylinder coupling and friction terms, the dynamic model of the hydraulic leveling system is obtained.

3. The method for dual friction parameter identification and adaptive synchronous control of a multi-axis electro-hydraulic system according to claim 2, characterized in that, The mathematical model of the LuGre nonlinear friction model is as follows: In the formula, Indicates the bristle stiffness coefficient; , Let represent the average deformation of the bristles and its derivative, respectively; Indicates the bristle damping coefficient; Indicates the viscous damping coefficient; The derivative of the piston rod displacement, i.e., the piston velocity; Represents the Stribeck curve function; Represents Coulomb friction; This represents static friction. This indicates Stribeck's speed.

4. The method for dual friction parameter identification and adaptive synchronous control of a multi-axis electro-hydraulic system according to claim 1, characterized in that, In step S2, when using a genetic algorithm to perform offline optimization and identification of the friction parameters of the LuGre friction model, static parameter identification is performed first, followed by dynamic parameter identification; among which, the static parameters include the viscous friction coefficient. Coulomb friction Static friction and Stribeck speed Dynamic parameters include the bristle stiffness coefficient. and bristle damping coefficient .

5. The method for dual friction parameter identification and adaptive synchronous control of a multi-axis electro-hydraulic system according to claim 1, characterized in that, In step S3, an adaptive parameter adjustment law based on control error is designed to fine-tune the friction parameters in the LuGre friction model online in real time. The implementation method is as follows: Define the adaptive parameters in the LuGre friction model as follows: , , ; An adaptive update law is constructed by multiplying the control error by the system operating state variables, and then calculating the adaptive derivatives of the estimated values ​​of each friction parameter. The specific formulas are as follows: in, This represents the approach law for each friction parameter; The learning law represents the various friction parameters; Indicates system operating status variables; Indicates control error; , representing the One leveling cylinder; , When the values ​​are 1, 2, and 3, they respectively refer to the three defined adaptive parameters. , , ; Subsequently, the adaptive derivatives of the estimated friction parameters are discretized and integrated to obtain the updated estimated values ​​of each friction parameter at the current time. The calculation formula is as follows: in, Indicates the current sampling time. Indicates the previous sampling time. The system sampling period is used to obtain the updated first friction parameter estimates at the current time. Second friction parameter estimate and the estimated value of the third friction parameter .

6. The method for dual friction parameter identification and adaptive synchronous control of a multi-axis electro-hydraulic system according to claim 1, characterized in that, In step S4, an integrated adaptive feedforward integral sliding mode controller is designed, and its implementation method is as follows: Taking the zero deflection angle of the slider around the x-axis and y-axis as the control objective, the deflection angle error and its derivative are defined, and the integral sliding surface is designed as follows: in, This represents the error in the slider's deflection angle around the x-axis; This indicates the error in the slider's deflection angle around the y-axis; This represents the slope of the sliding surface used for integration about the x-axis; This represents the slope of the sliding surface used for integration about the y-axis; This represents the integral gain of the i-th leveling cylinder controlled around the x-axis; This represents the integral gain of the i-th leveling cylinder controlled around the y-axis; The virtual control input torque consists of an equivalent control term and a robust switching control term, with frictional feedforward compensation introduced to obtain the virtual control torque. and .

7. The method for dual friction parameter identification and adaptive synchronous control of a multi-axis electro-hydraulic system according to claim 1, characterized in that, In step S5, the virtual torque in the overdrive coupling system is distributed based on the dynamic model of the hydraulic leveling system. The implementation method is as follows: While the slider is moving at a constant velocity in a straight line, the average target pressure is obtained by controlling the total force in the z-axis direction according to the slider dynamics model. ; Based on the constraint that the slider is a rigid body and has no torsional internal force, the target pressure of each leveling cylinder is obtained. Must meet ;in This represents the target pressure of the i-th leveling cylinder. =1,2,3,4; Combining the above relationships and virtual control torque and The target pressure of each of the four leveling cylinders was calculated. .

8. The method for dual friction parameter identification and adaptive synchronous control of a multi-axis electro-hydraulic system according to claim 1, characterized in that, In step S5, an inner-loop voltage controller is designed to perform pressure control under constant back pressure. The implementation method is as follows: A PID controller is used to control the pressure in the rodless chamber of each leveling cylinder; Define pressure error The discretized PID control output is: in, Represents a time variable. express Pressure error at any time express Constant pressure to achieve goals express The real pressure at all times Indicates the first The PID control output voltage at each sampling time. Indicates the current sampling time. Indicates the first Discrete pressure error at each sampling time; Indicates the first Discrete pressure error at each sampling time; Indicates the first Discrete pressure error at each sampling time, Indicates incrementing from 0 to The summation variable; This represents the proportional gain controlled by voltage. This represents the integral gain of the voltage control. Represents the differential gain of voltage control; Indicates the sampling period.

9. A dual friction parameter identification and adaptive synchronous control system for a multi-axis electro-hydraulic system, characterized in that, It includes a memory, a processor, and computer program instructions stored in the memory and executable by the processor, wherein when the processor executes the computer program instructions, it can implement the method as described in any one of claims 1-8.

10. A computer device, characterized in that, include: At least one processor, at least one memory, and computer program instructions stored in the memory, which, when executed by the processor, implement the method as described in any one of claims 1-8.

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