Methods, devices, and systems for determining the driving force of a hydraulic cylinder

Abstract

This disclosure provides a method, apparatus, and system for determining the driving force of a hydraulic cylinder, relating to the field of engineering machinery. The method includes: obtaining the current measured length of a first hydraulic cylinder in a system, the system including the first hydraulic cylinder and a boom connected to the first hydraulic cylinder; determining the current driving force of the first hydraulic cylinder based on the current measured length of the first hydraulic cylinder and a driving force model, the driving force model being determined as follows: establishing a virtual work equation for a second hydraulic cylinder in the system; establishing a dynamic equation for the system; establishing a geometric constraint equation for the second hydraulic cylinder, the geometric constraint equation being that the measured length of the second hydraulic cylinder is equal to the calculated length of the second hydraulic cylinder obtained from the position vectors of the two endpoints of the second hydraulic cylinder in the global coordinate system; and determining the driving force model based on the virtual work equation, the dynamic equation, and the geometric constraint equation, the driving force model reflecting the relationship between the measured length of the second hydraulic cylinder and the driving force.

Description

Technical Field

[0001] This disclosure relates to the field of engineering machinery, and in particular to a method, apparatus and system for determining the driving force of a hydraulic cylinder. Background Technology

[0002] The booms of construction machinery such as concrete pump trucks, aerial work platforms, truck-mounted cranes, and excavators are typically driven by hydraulic cylinders. The driving force of these hydraulic cylinders plays a crucial role in boom trajectory control and vibration suppression. Therefore, determining the driving force of the hydraulic cylinders is of paramount importance.

[0003] In one related technology, a pressure sensor is used to measure the pressure in the rod-side and rodless-side chambers of a hydraulic cylinder, respectively. The measured pressure is multiplied by the area of ​​the pressure-acting surface to calculate the thrust difference between the rod-side and rodless-side chambers, thereby determining the driving force of the hydraulic cylinder. In another related technology, a force sensor is used to directly measure the driving force of the hydraulic cylinder. Summary of the Invention

[0004] The inventors noted that determining the driving force of a hydraulic cylinder in related technologies is costly. Through analysis, they discovered that using pressure sensors requires a large number of sensors, increasing the cost of determining the driving force. Using force sensors, due to the varying models of hydraulic cylinders, custom-made force sensors are needed, further increasing the cost. Furthermore, pressure or force sensors are highly susceptible to vibration loads from the machinery itself, wind loads from the environment, and impact loads during operation. This makes them prone to damage when measuring forces exceeding their range, and the repair and replacement process for pressure or force sensors is cumbersome, thus reducing the efficiency of determining the driving force of the hydraulic cylinder.

[0005] To address the aforementioned problems, the present disclosure proposes the following solutions.

[0006] According to one aspect of the present disclosure, a method for determining the driving force of a hydraulic cylinder is provided, comprising: acquiring the current measured length of a first hydraulic cylinder in a system, the system including the first hydraulic cylinder and a boom connected to the first hydraulic cylinder; determining the current driving force of the first hydraulic cylinder based on the current measured length of the first hydraulic cylinder and a driving force model, the driving force model being determined as follows: establishing a virtual work equation for a second hydraulic cylinder in the system, the virtual work equation reflecting the relationship between the generalized driving force of the system and the first virtual work done by the driving force of the second hydraulic cylinder, the second virtual work done by the reaction force of the driving force, and the motion description variables of the second hydraulic cylinder, the motion description variables including the global coordinate system of the system. The system is defined by: determining the translational displacement and rotational vectors; establishing the system's dynamic equations, which reflect the relationship between the system's generalized driving force, generalized inertial force, and generalized external force, wherein the generalized inertial force is related to the second-order rate of change of the motion description variable; establishing the geometric constraint equations for the second hydraulic cylinder, wherein the measured length of the second hydraulic cylinder is equal to the calculated length of the second hydraulic cylinder obtained from the position vectors of its two endpoints in the global coordinate system; and determining the driving force model based on the virtual work equation, the dynamic equations, and the geometric constraint equations, wherein the driving force model reflects the relationship between the measured length of the second hydraulic cylinder and the driving force.

[0007] In some embodiments, the method for determining the driving force of the hydraulic cylinder further includes determining at least one of the current configuration, current velocity, and current acceleration of the boom connected to the first hydraulic cylinder based on the current driving force of the first hydraulic cylinder.

[0008] According to another aspect of the present disclosure, a method for establishing a driving force model is provided, comprising: establishing a virtual work equation for a second hydraulic cylinder in a system, the virtual work equation reflecting the relationship between the generalized driving force of the system and the first virtual work done by the driving force of the second hydraulic cylinder, the second virtual work done by the reaction force of the driving force, and the motion description variables of the second hydraulic cylinder, the motion description variables including translational displacement and rotational vector in the global coordinate system of the system; establishing a dynamic equation for the system, the dynamic equation reflecting the relationship between the generalized driving force of the system and the generalized inertial force and the generalized external force of the system, the generalized inertial force being related to the second-order rate of change of the motion description variables; establishing a geometric constraint equation for the second hydraulic cylinder, the geometric constraint equation being that the measured length of the second hydraulic cylinder is equal to the calculated length of the second hydraulic cylinder obtained from the position vectors of the two endpoints of the second hydraulic cylinder in the global coordinate system; and determining the driving force model based on the virtual work equation, the dynamic equation, and the geometric constraint equation, the driving force model reflecting the relationship between the measured length of the second hydraulic cylinder and the driving force.

[0009] In some embodiments, establishing the driving force model further includes obtaining a first position vector of the point of action of the driving force on the push rod in the second hydraulic cylinder in the global coordinate system, and a second position vector of the point of action of the reaction force on the cylinder body in the second hydraulic cylinder in the global coordinate system; determining the first virtual work based on the first position vector; and determining the second virtual work based on the second position vector.

[0010] In some embodiments, when the dimension of the motion description variables of the system is equal to the dimension of the system's degrees of freedom, and there are no flexible components in the system, the dynamic equation is:

[0011]

[0012] Where M is the mass matrix of the system, and q is the motion description variable of the system. For the generalized acceleration of the system, Q is the generalized inertial force of the system. e Let T be the generalized external force of the system, where T = [T1, T2, ..., T]. n ] T T i Let f be the generalized driving force coefficient vector of the i-th second hydraulic cylinder, f = [f1, f2, ..., f n ] T f i Let T be the magnitude of the driving force of the i-th second hydraulic cylinder, 1≤i≤n, where n is the number of all second hydraulic cylinders in the system. Tf represents the generalized driving force of the system.

[0013] In some embodiments, when the dimension of the motion description variables of the system is equal to the dimension of the system's degrees of freedom, and when there are flexible components in the system, the dynamic equation is:

[0014]

[0015] Where M is the mass matrix of the system, and q is the motion description variable of the system. For the generalized acceleration of the system, Q is the generalized inertial force of the system. d Q is the generalized elastic force of the system. e Let T be the generalized external force of the system, where T = [T1, T2, ..., T]. n ] T T i Let f be the generalized driving force coefficient vector of the i-th second hydraulic cylinder, f = [f1, f2, ..., f n ] T f i Let T be the magnitude of the driving force of the i-th second hydraulic cylinder, 1≤i≤n, where n is the number of all second hydraulic cylinders in the system. T f represents the generalized driving force of the system.

[0016] In some embodiments, when the dimension of the motion description variable of the system is less than the dimension of the system's degrees of freedom, and there are no flexible components in the system, the dynamic equation is:

[0017]

[0018] Where M is the mass matrix of the system, and q is the motion description variable of the system. For the generalized acceleration of the system, Q is the generalized inertial force of the system. e Let T be the generalized external force of the system, where T = [T1, T2, ..., T]. n ] T T i Let f be the generalized driving force coefficient vector of the i-th second hydraulic cylinder, f = [f1, f2, ..., f n ] T f i Let T be the magnitude of the driving force of the i-th second hydraulic cylinder, 1≤i≤n, where n is the number of all second hydraulic cylinders in the system. T f is the generalized driving force of the system, Φ C The structural constraint equations are as follows: Let λ be the Jacobian matrix of the structural constraint equations, λ be the Lagrange multiplier, and the dimension of λ be the same as that of the structural constraint equations Φ. CThey have the same dimension.

[0019] In some embodiments, when the dimension of the motion description variable of the system is less than the dimension of the system's degrees of freedom, and when there are flexible components in the system, the dynamic equation is:

[0020]

[0021] Where M is the mass matrix of the system, and q is the motion description variable of the system. For the generalized acceleration of the system, Q is the generalized inertial force of the system. d Q is the generalized elastic force of the system. e Let T be the generalized external force of the system, where T = [T1, T2, ..., T]. n ] T T i Let f be the generalized driving force coefficient vector of the i-th second hydraulic cylinder, f = [f1, f2, ..., f n ] T f i Let T be the magnitude of the driving force of the i-th second hydraulic cylinder, 1≤i≤n, where n is the number of all second hydraulic cylinders in the system. T f is the generalized driving force of the system, Φ C The structural constraint equations are as follows: Let λ be the Jacobian matrix of the structural constraint equations, λ be the Lagrange multiplier, and the dimension of λ be the same as that of the structural constraint equations Φ. C They have the same dimension.

[0022] According to another aspect of the present disclosure, an apparatus for determining the driving force of a hydraulic cylinder is provided, comprising: an acquisition module configured to acquire the current measured length of a first hydraulic cylinder in a system, the system including the first hydraulic cylinder and a boom connected to the first hydraulic cylinder; and a first determination module configured to determine the current driving force of the first hydraulic cylinder based on the current measured length of the first hydraulic cylinder and a driving force model, the driving force model being determined by: establishing a virtual work equation for a second hydraulic cylinder in the system, the virtual work equation reflecting the relationship between the generalized driving force of the system and the first virtual work done by the driving force of the second hydraulic cylinder, the second virtual work done by the reaction force of the driving force, and motion description variables of the second hydraulic cylinder, the motion description variables including... The system's translational displacement and rotational vectors in the global coordinate system are defined; the system's dynamic equations are established, reflecting the relationship between the system's generalized driving force, generalized inertial force, and generalized external force, wherein the generalized inertial force is related to the second-order rate of change of the motion description variable; the geometric constraint equations for the second hydraulic cylinder are established, wherein the measured length of the second hydraulic cylinder is equal to the calculated length of the second hydraulic cylinder obtained from the position vectors of its two endpoints in the global coordinate system; the driving force model is determined based on the virtual work equation, the dynamic equations, and the geometric constraint equations, reflecting the relationship between the measured length of the second hydraulic cylinder and the driving force.

[0023] According to another aspect of the present disclosure, an apparatus for establishing a driving force model is provided, comprising: a first establishing module configured to establish a virtual work equation for a second hydraulic cylinder in a system, the virtual work equation reflecting the relationship between the generalized driving force of the system and the first virtual work done by the driving force of the second hydraulic cylinder, the second virtual work done by the reaction force of the driving force, and the motion description variables of the second hydraulic cylinder, the motion description variables including translational displacement and rotational vector in the global coordinate system of the system; and a second establishing module configured to establish a dynamic equation for the system, the dynamic equation reflecting the relationship between the generalized driving force of the system and the generalized driving force of the system. The relationship between inertial force and the generalized external force of the system, wherein the generalized inertial force is related to the second-order rate of change of the motion description variable; a third establishing module is configured to establish the geometric constraint equation of the second hydraulic cylinder, wherein the geometric constraint equation is that the measured length of the second hydraulic cylinder is equal to the calculated length of the second hydraulic cylinder obtained from the position vectors of the two endpoints of the second hydraulic cylinder in the global coordinate system; a second determining module is configured to determine the driving force model based on the virtual work equation, the dynamic equation and the geometric constraint equation, wherein the driving force model reflects the relationship between the measured length of the second hydraulic cylinder and the driving force.

[0024] According to another aspect of the present disclosure, an electronic device is provided, including: a memory; and a processor coupled to the memory, configured to execute the method described in any of the above embodiments based on instructions stored in the memory.

[0025] According to another aspect of the present disclosure, a system for determining the driving force of a hydraulic cylinder is provided, comprising: at least one of the means for determining the driving force of a hydraulic cylinder according to any of the above embodiments and the means for establishing a driving force model; and a displacement sensor configured to measure at least one of the current measurement length of the first hydraulic cylinder and the measurement length of the second hydraulic cylinder.

[0026] According to another aspect of the present disclosure, an engineering machine is provided, including the system described above for determining the driving force of a hydraulic cylinder.

[0027] According to another aspect of the present disclosure, a computer-readable storage medium is provided, including computer program instructions, wherein the computer program instructions, when executed by a processor, implement the method described in any of the above embodiments.

[0028] According to another aspect of the present disclosure, a computer program product is provided, including a computer program, wherein the computer program, when executed by a processor, implements the method described in any of the above embodiments.

[0029] In this embodiment of the disclosure, by obtaining the current measured length of the hydraulic cylinder and determining the current driving force of the hydraulic cylinder based on the current measured length and driving force model, the use of multiple pressure sensors or specially customized force sensors is eliminated, thereby reducing the cost of determining the driving force of the hydraulic cylinder. Furthermore, it avoids the situation where pressure or force sensors are easily damaged by the vibration load of the construction machinery itself, the wind load of the environment, and the impact load during operation, requiring cumbersome maintenance and replacement, thus improving the efficiency of determining the driving force of the hydraulic cylinder.

[0030] The technical solutions of this disclosure will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of this disclosure or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this disclosure. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1This is a schematic flowchart of a method for determining the driving force of a hydraulic cylinder according to some embodiments of the present disclosure;

[0033] Figure 2 This is a flowchart illustrating a method for establishing a driving force model according to some embodiments of the present disclosure;

[0034] Figure 3 This is a schematic diagram of a hydraulic cylinder and boom according to some embodiments of the present disclosure;

[0035] Figure 4 This is a schematic diagram of a device for determining the driving force of a hydraulic cylinder according to some embodiments of the present disclosure;

[0036] Figure 5 This is a schematic diagram of the structure of an apparatus for establishing a driving force model according to some embodiments of the present disclosure;

[0037] Figure 6 This is a schematic diagram of the structure of an electronic device according to some embodiments of the present disclosure. Detailed Implementation

[0038] The technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this disclosure, and not all embodiments. Based on the embodiments of this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0039] Unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of this disclosure.

[0040] At the same time, it should be understood that, for ease of description, the dimensions of the various parts shown in the accompanying drawings are not drawn according to actual scale.

[0041] Techniques, methods, and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and equipment should be considered part of the specification.

[0042] In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values.

[0043] It should be noted that similar labels and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be discussed further in subsequent figures.

[0044] Figure 1This is a schematic flowchart illustrating a method for determining the driving force of a hydraulic cylinder according to some embodiments of the present disclosure.

[0045] In step 102, the current measured length of the first hydraulic cylinder in the system is obtained. The system includes the first hydraulic cylinder and a boom connected to the first hydraulic cylinder.

[0046] In some embodiments, the first hydraulic cylinder includes a cylinder body and a push rod, and the currently measured length is the length from the bottom of the cylinder body to the end of the push rod, obtained by measurement at the current moment.

[0047] In step 104, the current driving force of the first hydraulic cylinder is determined based on the current measured length of the first hydraulic cylinder and the driving force model. The process of establishing the driving force model will be discussed later. Figure 2 Please provide an explanation.

[0048] In the above embodiments, by obtaining the current measured length of the hydraulic cylinder and determining the current driving force of the hydraulic cylinder based on the current measured length and driving force model, it is not necessary to use multiple pressure sensors or specially customized force sensors, thereby reducing the cost of determining the driving force of the hydraulic cylinder. Furthermore, it avoids the situation where pressure or force sensors are easily damaged by the vibration load of the construction machinery itself, the wind load of the environment, and the impact load during operation, which would lead to cumbersome maintenance and replacement. This improves the efficiency of determining the driving force of the hydraulic cylinder.

[0049] In some embodiments, the method for determining the driving force of the hydraulic cylinder further includes determining at least one of the current configuration, current velocity, and current acceleration of the boom connected to the first hydraulic cylinder based on the current driving force of the first hydraulic cylinder, thereby achieving the purpose of determining the motion state of the boom. For example, the boom is a folding boom that achieves extension, folding, and other motion states via the driving of the hydraulic cylinder.

[0050] Figure 2 This is a flowchart illustrating a method for establishing a driving force model according to some embodiments of the present disclosure.

[0051] In step 202, the virtual work equation of the second hydraulic cylinder in the system is established. The virtual work equation reflects the relationship between the first virtual work done by the generalized driving force of the system and the driving force of the second hydraulic cylinder, the second virtual work done by the reaction force of the driving force, and the motion description variables of the second hydraulic cylinder. The motion description variables include the translational displacement and rotational vector in the global coordinate system of the system.

[0052] The second hydraulic cylinder can be the same as or different from the first hydraulic cylinder.

[0053] In some embodiments, a first position vector of the point of application of the driving force on the push rod in the second hydraulic cylinder in the global coordinate system and a second position vector of the point of application of the reaction force on the cylinder body in the second hydraulic cylinder in the global coordinate system are obtained. A first virtual work is determined based on the first position vector; and a second virtual work is determined based on the second position vector. The origin of the global coordinate system can be a point of a component in the system, such as a point on the hydraulic cylinder that is stationary relative to the ground.

[0054] In step 204, the dynamic equation of the system is established. This dynamic equation reflects the relationship between the generalized driving force of the system, the generalized inertial force of the second hydraulic cylinder, and the generalized external force of the system. The generalized inertial force is related to the second-order rate of change of the motion description variable.

[0055] In step 206, the geometric constraint equation of the second hydraulic cylinder in the system is established. The geometric constraint equation is that the measured length of the second hydraulic cylinder is equal to the calculated length of the second hydraulic cylinder obtained from the position vectors of the two endpoints of the second hydraulic cylinder in the global coordinate system.

[0056] In step 208, the driving force model is determined based on the above-mentioned virtual work equation, dynamic equation and geometric constraint equation. This driving force model reflects the relationship between the measured length of the second hydraulic cylinder and the driving force.

[0057] In the above embodiments, the driving force model is determined by establishing the virtual work equation, dynamic equation, and geometric constraint equation of the second hydraulic cylinder, thereby obtaining the relationship between the measured length of the second hydraulic cylinder and the driving force. This eliminates the need for parameters such as pressure or force in the driving force model, thus reducing the cost of establishing the driving force model. Furthermore, it avoids the situation where pressure or force sensors are easily damaged by the vibration load of the engineering machinery itself, the wind load of the environment, and the impact load during operation, which would require cumbersome maintenance and replacement. This improves the efficiency of establishing the driving force model.

[0058] Figure 3 This is a schematic diagram of a hydraulic cylinder and boom according to some embodiments of the present disclosure.

[0059] like Figure 3 As shown, the boom 11 is connected to the hydraulic cylinder 12. The hydraulic cylinder 12 includes a cylinder body 301 and a push rod 302.

[0060] In some embodiments, the current length of the second hydraulic cylinder is measured by a displacement sensor 303. For example, the displacement sensor 303 is a laser displacement sensor, disposed on a horizontal line at the bottom of the outer surface of the cylinder body of the second hydraulic cylinder. The laser displacement sensor measures the current length of the second hydraulic cylinder by directing a laser 305 toward a baffle 304 disposed at the end of the push rod.

[0061] In some embodiments, the method for establishing a driving force model includes the following steps:

[0062] like Figure 3 As shown, a coordinate system is established, including establishing a local coordinate system and a global coordinate system at the center of mass of the cylinder body and the push rod of the i-th second hydraulic cylinder, respectively.

[0063] As one implementation method, the cylinder body and push rod of the hydraulic cylinder are modeled as rigid bodies respectively, and the center of mass O of the cylinder body of the i-th second hydraulic cylinder is set. i The local coordinate system established at this location is The center of mass O of the push rod of the i-th second hydraulic cylinder i+1 Establish a local coordinate system The global coordinate system is (g1, g2, g3). The motion description variables for rigid body i are: Where u i For example, the center of mass O of a rigid body i The translational displacement θ in the global coordinate system i Let θ be the rotation vector of a rigid body (e.g., its local coordinate system) in the global coordinate system. i The corresponding rotation matrix R i for:

[0064]

[0065] Where, α i For the rotation vector θ i The scalar value of the corresponding rotation angle, i.e. I is the antisymmetric matrix of the vector ·, and I3 is the third-order identity matrix.

[0066] At point O i Local coordinate system established at the location The mathematical expression can be represented as:

[0067]

[0068] in, In the initial state, with point O i Local coordinate system with origin Rotation matrix in global coordinate system It is a constant matrix.

[0069] Local coordinate system Any point above refers to any point on the cylinder body of the second hydraulic cylinder. Position vector in global coordinate system It can be represented as:

[0070]

[0071] in, Let O be the center of mass. i The position vector in the global coordinate system at the initial state; For point In the local coordinate system The position vector below, It is a constant vector.

[0072] Taking the derivative with respect to time t, we can obtain the point. The translational velocity vector in the global coordinate system is:

[0073]

[0074] in, I3 is a third-order identity matrix. For the generalized velocity of the system, For the generalized acceleration of the system, Γ i Let q be the motion description variable for rigid body i. i A Boolean matrix representing the transformations between the system's motion description variable q and the variable q.

[0075] Taking the derivative with respect to time t, we can obtain the point. The translational acceleration vector in the global coordinate system is:

[0076]

[0077] The following is combined Figure 3 This section introduces the establishment of the virtual work equation δW for the i-th second hydraulic cylinder in the system. i Some implementation methods.

[0078] like Figure 3 As shown, as one implementation method, let the driving force of the i-th second hydraulic cylinder be F. i F i The point of action on the i-th second hydraulic cylinder push rod is F i It can be represented as:

[0079]

[0080] Wherein, the driving force of the i-th second hydraulic cylinder is f. i The unit direction vector of the axis of the push rod of the i-th second hydraulic cylinder F i It can be represented as:

[0081]

[0082] The reaction force of the driving force of the i-th second hydraulic cylinder is Its point of action on the cylinder body of the i-th second hydraulic cylinder is It can be represented as:

[0083]

[0084] The magnitude of the reaction force of the driving force of the i-th second hydraulic cylinder is f. i The unit direction vector of the axis of the push rod of the i-th second hydraulic cylinder is

[0085] The virtual work δW done by the driving force of the i-th second hydraulic cylinder i for:

[0086]

[0087] in, It is a point Position vector in global coordinate system The imaginary variable, It is a point Position vector in global coordinate system The imaginary variable.

[0088] According to formula (1), the following formula can be obtained:

[0089]

[0090] According to formulas (3), (4) and (5), we can obtain:

[0091]

[0092] in, For the generalized driving force of the i-th second hydraulic cylinder, Let be the generalized driving force coefficient vector of the i-th second hydraulic cylinder.

[0093] The following is combined Figure 3 This paper introduces some methods for establishing the dynamic equations of a system.

[0094] As one implementation, when the dimension of the system's motion description variables is equal to the dimension of the system's degrees of freedom, and there are no flexible components in the system, the dynamic equation is:

[0095]

[0096] Where M is the mass matrix of the system, which includes the mass matrices of the hydraulic cylinders and the boom, and q is the motion description variable of the system. For the generalized inertial force of the system, Q is the generalized acceleration of the system.e Let T be the generalized external force of the system, where T = [T1, T2, ..., T]. n ] T T i Let f be the generalized driving force coefficient vector of the i-th second hydraulic cylinder, f = [f1, f2, ..., f n ] T f i Let be the magnitude of the driving force of the i-th second hydraulic cylinder, 1≤i≤n, where n is the number of all second hydraulic cylinders in the system. T is the generalized driving force of the i-th second hydraulic cylinder. T f represents the generalized driving force of the system.

[0097] When the dimension of the system's motion description variables is equal to the dimension of the system's degrees of freedom, and when the system contains flexible components, the dynamic equation is:

[0098]

[0099] Where M is the mass matrix of the system, and q is the motion description variable of the system. For the generalized acceleration of the system, Q is the generalized inertial force of the system. e For the generalized external force of the system, Q d Let T be the generalized elastic force of the system, where T = [T1, T2, ..., T]. n ] T T i Let f be the generalized driving force coefficient vector of the i-th second hydraulic cylinder, where f = [f1, f2, ..., f n ] T f i Let be the magnitude of the driving force of the i-th second hydraulic cylinder, 1≤i≤n, where n is the number of all second hydraulic cylinders in the system. T is the generalized driving force of the i-th second hydraulic cylinder. T f represents the generalized driving force of the system.

[0100] When the dimension of the system's motion description variables is less than the dimension of the system's degrees of freedom, and there are no flexible components in the system, the dynamic equation is:

[0101]

[0102] Where M is the mass matrix of the system, and q is the motion description variable of the system. For the generalized acceleration of the system, Q is the generalized inertial force of the system. e Let T be the generalized external force of the system, where T = [T1, T2, ..., T]. n ] T Ti Let f be the generalized driving force coefficient vector of the i-th second hydraulic cylinder, where f = [f1, f2, ..., f n ] T f i Let be the magnitude of the driving force of the i-th second hydraulic cylinder, 1≤i≤n, where n is the number of all second hydraulic cylinders in the system. T is the generalized driving force of the i-th second hydraulic cylinder. T f is the generalized driving force of the system, Φ C The structural constraint equations of the system are... Let λ be the Jacobian matrix of the structural constraint equations, λ be the Lagrange multiplier, and the dimension of λ be the same as that of the structural constraint equations Φ. C They have the same dimension.

[0103] When the dimension of the system's motion description variables is less than the dimension of the system's degrees of freedom, and the system contains flexible components, the dynamic equation is:

[0104]

[0105] Where M is the mass matrix of the system, and q is the motion description variable of the system. For the generalized acceleration of the system, Q is the generalized inertial force of the system. d Q is the generalized elastic force of the system. e Let T be the generalized external force of the system, where T = [T1, T2, ..., T]. n ] T T i Let f be the generalized driving force coefficient vector of the i-th second hydraulic cylinder, where f = [f1, f2, ..., f n ] T f i Let be the magnitude of the driving force of the i-th second hydraulic cylinder, 1≤i≤n, where n is the number of all second hydraulic cylinders in the system. T is the generalized driving force of the i-th second hydraulic cylinder. T f is the generalized driving force of the system, Φ C The structural constraint equations of the system are... Let λ be the Jacobian matrix of the structural constraint equations, λ be the Lagrange multiplier, and the dimension of λ be the same as that of the structural constraint equations Φ. C They have the same dimension.

[0106] The generalized elastic force, generalized external force, and generalized driving force mentioned above are all column vectors.

[0107] The following is combined Figure 3 This section introduces the establishment of the geometric constraint equations for the i-th second hydraulic cylinder in the system. Some implementation methods.

[0108]

[0109] Among them, L i Let be the measured length of the i-th second hydraulic cylinder. It is the end point of the push rod of the i-th second hydraulic cylinder. Position vector in the global coordinate system It is the end point of the cylinder block. The position vector in the global coordinate system.

[0110] Taking the derivative with respect to time t, we get for:

[0111]

[0112] The measured length L of the i-th second hydraulic cylinder i The derivative with respect to time t.

[0113] Taking the second derivative with respect to time t, we can obtain for:

[0114]

[0115] in, yes The derivative with respect to time t.

[0116] The following section introduces some implementation methods for determining the driving force model based on the virtual work equation, dynamic equation, and geometric constraint equation.

[0117] The geometric constraint equations of all second hydraulic cylinders in the system By performing a set, we obtain the constraint equations for the system from all the second hydraulic cylinders.

[0118] Establish the average constraint equations for all second hydraulic cylinders in the system. The average constraint equation reflects the relationship between the system's motion description parameters, generalized velocity, generalized acceleration and the current measured length, first-order and second-order rates of change of the current measured length of all second hydraulic cylinders in the system.

[0119] For example, the constraint equation at time τ within the time segment [t, t+ξ] starting from the current time t. It can be approximated by a second-order Taylor expansion:

[0120]

[0121] in, Therefore To derive the velocity constraint equations, To derive the acceleration constraint equations, and They can be represented as:

[0122]

[0123] in,

[0124] Within the time interval [t, t+ξ], the average constraint equations for all second hydraulic cylinders in the system are... for:

[0125]

[0126] According to formula (11), the average constraint equation can be determined. for:

[0127]

[0128] in,

[0129] In some embodiments, when the dimension of the system's motion description variables is equal to the dimension of the system's degrees of freedom and there are no flexible components in the system, according to formulas (6) and (13), the vector f = [f1, f2, ..., f] composed of the driving forces of all the second hydraulic cylinders in the system can be obtained. n ] T for:

[0130] f = -(ΛM) -1 T T ) -1 (B+ΛM -1 Q e )

[0131] In some embodiments, when the dimension of the system's motion description variables is equal to the dimension of the system's degrees of freedom, and flexible components exist in the system, according to formulas (7) and (13), the vector f = [f1, f2, ..., f] composed of the driving forces of all the second hydraulic cylinders in the system can be obtained. n ] T for:

[0132] f = -(ΛM) -1 T T ) -1 (B+AM -1 (Q e -Q d ))

[0133] In some embodiments, when the dimension of the system's motion description variables is less than the dimension of the system's degrees of freedom and there are no flexible components in the system, equation (8) is expressed using the Baumgarte stabilization method as follows:

[0134]

[0135] in, ξ1 and ξ2 are the positive damping coefficient and positive stiffness coefficient, respectively, and their values ​​can be determined based on the operator's experience, for example, the range of values ​​is 5-50.

[0136] According to formulas (13) and (14), the vector f = [f1, f2, ..., f] composed of the driving forces of all the second hydraulic cylinders in the system can be obtained. n ] T The column vector formed by the Lagrange multiplier λ for:

[0137]

[0138] in,

[0139] In some embodiments, when the dimension of the system's motion description variables is less than the dimension of the system's degrees of freedom, and when there are flexible components in the system, equation (9) is expressed using the Baumgarte stabilization method as follows:

[0140]

[0141] in, ξ1 and ξ2 are the positive damping coefficient and positive stiffness coefficient, respectively, and their values ​​can be determined based on the operator's experience, for example, the range of values ​​is 5-50.

[0142] According to formulas (13) and (15), the vector f = [f1, f2, ..., f] composed of the driving forces of all the second hydraulic cylinders in the system can be obtained. n The column vector consisting of T and the Lagrange multiplier λ for:

[0143]

[0144] in,

[0145] In the above embodiments, by establishing local coordinate systems at the center of mass of the cylinder body and the push rod of the second hydraulic cylinder, any point on the second hydraulic cylinder can be represented using the local coordinate system. At the same time, by using a rotation matrix, any point on the local coordinate system can be expressed using the global coordinate system, thereby reducing the difficulty of establishing the driving force model and improving the efficiency of establishing the driving force model.

[0146] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus embodiments, since they largely correspond to the method embodiments, the descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0147] Figure 4 This is a schematic diagram of a device for determining the driving force of a hydraulic cylinder according to some embodiments of the present disclosure.

[0148] like Figure 4 As shown, the device for determining the driving force of the hydraulic cylinder includes an acquisition module 401 and a first determination module 402.

[0149] The acquisition module 401 is configured to acquire the current measured length of the first hydraulic cylinder in the system, which includes the first hydraulic cylinder and a boom connected to the first hydraulic cylinder.

[0150] The first determining module 402 is configured to determine the current driving force of the first hydraulic cylinder based on the current measured length of the first hydraulic cylinder and the driving force model, wherein the driving force model is determined as follows:

[0151] Establish the virtual work equation for the second hydraulic cylinder in the system. This virtual work equation reflects the relationship between the first virtual work done by the generalized driving force of the system and the driving force of the second hydraulic cylinder, the second virtual work done by the reaction force of the driving force, and the motion description variables of the second hydraulic cylinder. The motion description variables include the translational displacement and rotational vector in the global coordinate system of the system.

[0152] Establish the dynamic equation of the system, which reflects the relationship between the driving force of the generalized system, the generalized inertial force of the system, and the generalized external force of the system. The generalized inertial force is related to the second rate of change of the motion description variable.

[0153] Establish the geometric constraint equation for the second hydraulic cylinder, which states that the measured length of the second hydraulic cylinder is equal to the calculated length of the second hydraulic cylinder obtained from the position vectors of the two endpoints of the second hydraulic cylinder in the global coordinate system.

[0154] The driving force model is determined based on the virtual work equation, dynamic equation, and geometric constraint equation. The driving force model reflects the relationship between the measured length of the second hydraulic cylinder and the driving force.

[0155] In some embodiments, the apparatus for determining the driving force of the hydraulic cylinder further includes other modules to perform the method for determining the driving force of the hydraulic cylinder in any of the above embodiments.

[0156] Figure 5This is a schematic diagram of the structure of an apparatus for establishing a driving force model according to some embodiments of the present disclosure.

[0157] like Figure 5 As shown, the device for determining the driving force of the hydraulic cylinder includes a first establishing module 501, a second establishing module 502, a third establishing module 503, and a second determining module 504.

[0158] The first establishment module 501 is configured to establish the virtual work equation of the second hydraulic cylinder in the system. The virtual work equation reflects the relationship between the generalized driving force of the second hydraulic cylinder and the first virtual work done by the driving force of the second hydraulic cylinder, the second virtual work done by the reaction force of the driving force, and the motion description variables of the second hydraulic cylinder. The motion description variables include translational displacement and rotational vector in the global coordinate system of the system.

[0159] The second establishment module 502 is configured to establish the dynamic equations of the system, which reflect the relationship between the generalized driving force of the system, the generalized inertial force of the system, and the generalized external force of the system. The generalized inertial force is related to the second-order rate of change of the motion description variable.

[0160] The third establishment module 503 is configured to establish the geometric constraint equation of the second hydraulic cylinder, which states that the measured length of the second hydraulic cylinder is equal to the calculated length of the second hydraulic cylinder obtained from the position vectors of the two endpoints of the second hydraulic cylinder in the global coordinate system.

[0161] The second determining module 504 is configured to determine a driving force model based on the virtual work equation, the dynamic equation and the geometric constraint equation. The driving force model reflects the relationship between the measured length of the second hydraulic cylinder and the driving force.

[0162] In some embodiments, the apparatus for determining the driving force model further includes other modules to perform the method for establishing the driving force model of any of the above embodiments.

[0163] Figure 6 This is a schematic diagram of the structure of an electronic device according to some embodiments of the present disclosure.

[0164] like Figure 6 As shown, the electronic device 600 includes a memory 601 and a processor 602 coupled to the memory 601. The processor 602 is configured to execute the method of any of the foregoing embodiments based on instructions stored in the memory 601.

[0165] The memory 601 may include, for example, system memory, fixed non-volatile storage media, etc. The system memory may store, for example, an operating system, application programs, a boot loader, and other programs.

[0166] Electronic device 600 may also include input / output interface 603, network interface 604, storage interface 605, etc. These interfaces 603, 604, and 605, as well as the memory 601 and processor 602, can be connected via, for example, a bus 606. Input / output interface 603 provides a connection interface for input / output devices such as monitors, mice, keyboards, and touchscreens. Network interface 604 provides a connection interface for various networked devices. Storage interface 605 provides a connection interface for external storage devices such as SD cards and USB flash drives.

[0167] This disclosure also provides a system for determining the driving force of a hydraulic cylinder, including at least one of the means for determining the driving force of a hydraulic cylinder and the means for establishing a driving force model according to any of the above embodiments; and a displacement sensor configured to measure at least one of the current measurement length of a first hydraulic cylinder and the measurement length of a second hydraulic cylinder.

[0168] This disclosure also provides an engineering machinery system, including the aforementioned system for determining the driving force of a hydraulic cylinder. Examples of engineering machinery include concrete pump trucks, aerial work platforms, truck-mounted cranes, and excavators.

[0169] This disclosure also provides a computer-readable storage medium including computer program instructions that, when executed by a processor, implement the method of any of the above embodiments.

[0170] This disclosure also provides a computer program product, including a computer program that, when executed by a processor, implements the method of any of the above embodiments.

[0171] The embodiments of this disclosure have now been described in detail. To avoid obscuring the concept of this disclosure, some details known in the art have not been described. Those skilled in the art can fully understand how to implement the technical solutions disclosed herein based on the above description.

[0172] Those skilled in the art will understand that embodiments of this disclosure can be provided as methods, systems, or computer program products. Therefore, this disclosure can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this disclosure can take the form of a computer program product embodied on one or more computer-usable non-transitory storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0173] This disclosure is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It should be understood that the functions specified in one or more flowchart illustrations and / or one or more blocks in a block diagram 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 functions for implementing the functions in the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0174] 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.

[0175] 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.

[0176] While specific embodiments of this disclosure have been described in detail by way of examples, those skilled in the art should understand that the examples are for illustrative purposes only and not intended to limit the scope of this disclosure. Those skilled in the art should understand that modifications can be made to the above embodiments or equivalent substitutions can be made to some technical features without departing from the scope and spirit of this disclosure. The scope of this disclosure is defined by the appended claims.

Claims

1. A method for determining driving force of hydraulic cylinders, comprising: obtaining a current measured length of a first hydraulic cylinder in a system, the system comprising the first hydraulic cylinder and an arm connected to the first hydraulic cylinder; determining a current driving force of the first hydraulic cylinder according to the current measured length of the first hydraulic cylinder and a driving force model, the driving force model being determined according to the following manner: establishing a virtual work equation of a second hydraulic cylinder in the system, the virtual work equation reflecting a relationship between a generalized driving force of the system and a first virtual work done by a driving force of the second hydraulic cylinder, a second virtual work done by a reaction force of the driving force and a motion description variable of the second hydraulic cylinder, the motion description variable comprising a translational displacement and a rotational vector in a global coordinate system of the system; establishing a dynamic equation of the system, the dynamic equation reflecting a relationship between the generalized driving force of the system and a generalized inertia force of the system and a generalized external force of the system, the generalized inertia force being related to a second order change rate of the motion description variable; establishing a geometric constraint equation of the second hydraulic cylinder, the geometric constraint equation being that a measured length of the second hydraulic cylinder is equal to a calculated length of the second hydraulic cylinder according to position vectors of two end points of the second hydraulic cylinder in the global coordinate system; collecting the geometric constraint equations of all second hydraulic cylinders in the system to obtain a constraint equation of the all second hydraulic cylinders; establishing an average constraint equation of the all second hydraulic cylinders according to the constraint equation of the all second hydraulic cylinders, the average constraint equation reflecting a relationship between the motion description variable of the system, a generalized velocity of the system, a generalized acceleration of the system and a current measured length of the all second hydraulic cylinders, a first order change rate of the current measured length of the all second hydraulic cylinders, a second order change rate of the current measured length of the all second hydraulic cylinders; determining the driving force model according to the virtual work equation, the dynamic equation and the average constraint equation, the driving force model reflecting a relationship between the measured length of the second hydraulic cylinder and the driving force.

2. The method according to claim 1, further comprising: determining at least one of a current configuration, a current velocity and a current acceleration of a motion of the arm connected to the first hydraulic cylinder according to the current driving force of the first hydraulic cylinder.

3. A method for establishing a driving force model, comprising: establishing a virtual work equation of a second hydraulic cylinder in a system, the virtual work equation reflecting a relationship between a generalized driving force of the system and a first virtual work done by a driving force of the second hydraulic cylinder, a second virtual work done by a reaction force of the driving force and a motion description variable of the second hydraulic cylinder, the motion description variable comprising a translational displacement and a rotational vector in a global coordinate system of the system; establishing a dynamic equation of the system, the dynamic equation reflecting a relationship between the generalized driving force of the system and a generalized inertia force of the system and a generalized external force of the system, the generalized inertia force being related to a second order change rate of the motion description variable; establishing a geometric constraint equation of the second hydraulic cylinder, the geometric constraint equation being that a measured length of the second hydraulic cylinder is equal to a calculated length of the second hydraulic cylinder obtained according to position vectors of two end points of the second hydraulic cylinder in the global coordinate system; collecting geometric constraint equations of all second hydraulic cylinders in the system to obtain constraint equations of the all second hydraulic cylinders; according to the constraint equations of the all second hydraulic cylinders, establishing average constraint equations of the all second hydraulic cylinders, the average constraint equations reflecting relationships between the motion description variables of the system, generalized velocities of the system, generalized accelerations of the system, and current measured lengths of the all second hydraulic cylinders, first-order change rates of the current measured lengths of the all second hydraulic cylinders, and second-order change rates of the current measured lengths of the all second hydraulic cylinders; determining the driving force model according to the virtual work equation, the dynamic equation, and the average constraint equations, the driving force model reflecting a relationship between the measured length of the second hydraulic cylinder and the driving force.

4. The method according to any one of claims 1 to 3, wherein, establishing the driving force model further comprises: obtaining a first position vector of a point of action of the driving force on a push rod in the second hydraulic cylinder in the global coordinate system, and a second position vector of a point of action of the reaction force on a cylinder body in the second hydraulic cylinder in the global coordinate system; determining the first virtual work according to the first position vector; determining the second virtual work according to the second position vector.

5. The method of any one of claims 1-3, wherein, when the dimension of the motion description variables of the system is equal to the dimension of the degrees of freedom of the system, and there is no flexible component in the system, the dynamic equation is: wherein is the mass matrix of the system, is the motion description variable of the system, is the generalized acceleration of the system, is the generalized inertia force of the system, is the generalized external force of the system, wherein , is the generalized driving force coefficient vector of the th second hydraulic cylinder, , is the driving force of the th second hydraulic cylinder, , n is the number of all second hydraulic cylinders in the system, is the generalized driving force of the system.

6. The method of any one of claims 1-3, wherein, when the dimension of the motion description variables of the system is equal to the dimension of the degrees of freedom of the system, and there is a flexible component in the system, the dynamic equation is: wherein is the mass matrix of the system, is the motion description variable of the system, is the generalized acceleration of the system, is the generalized inertial force of the system, is the generalized elastic force of the system, is the generalized external force of the system, wherein , is the generalized driving force coefficient vector of the first second hydraulic cylinder, , is the driving force of the first second hydraulic cylinder, , n is the number of all second hydraulic cylinders in the system, is the generalized driving force of the system.

7. The method of any one of claims 1-3, wherein, when the dimension of the motion description variables of the system is less than the dimension of the degrees of freedom of the system, and there is no flexible component in the system, the dynamic equation is: in, For the mass matrix of the system, For the motion description variables of the system, For the generalized acceleration of the system, For the generalized inertial force of the system, For the generalized external forces of the system, among which , For the first The generalized driving force coefficient vector of the second hydraulic cylinder The magnitude of the driving force of the second hydraulic cylinder, , where n is the number of all second hydraulic cylinders in the system. , The structural constraint equations are as follows: Let Jacobi be the structural constraint equation. For Lagrange multipliers, Dimension and structural constraint equations They have the same dimension.

8. The method of any one of claims 1-3, wherein, when the dimension of the motion description variables of the system is less than the dimension of the degrees of freedom of the system, and there is a flexible component in the system, the dynamic equation is: in, For the mass matrix of the system, For the motion description variables of the system, For the generalized acceleration of the system, For the generalized inertial force of the system, For the generalized elastic force of the system, For the generalized external forces of the system, among which , For the first The generalized driving force coefficient vector of the second hydraulic cylinder The magnitude of the driving force of the second hydraulic cylinder, , where n is the number of all second hydraulic cylinders in the system. As the generalized driving force of the system, The structural constraint equations are as follows: Let Jacobi be the structural constraint equation. For Lagrange multipliers, Dimension and structural constraint equations They have the same dimension.

9. An apparatus for determining a driving force of a hydraulic cylinder, comprising: an obtaining module configured to obtain a current measured length of a first hydraulic cylinder in a system, the system comprising the first hydraulic cylinder and an arm support connected to the first hydraulic cylinder; a first determining module configured to determine a current driving force of the first hydraulic cylinder according to the current measured length of the first hydraulic cylinder and a driving force model, the driving force model being determined according to the following manner: establishing a virtual work equation of a second hydraulic cylinder in the system, the virtual work equation reflecting a relationship between generalized driving forces of the system and a first virtual work made by a driving force of the second hydraulic cylinder, a second virtual work made by a reaction force of the driving force, and motion description variables of the second hydraulic cylinder, the motion description variables comprising translational displacement and rotational vectors in a global coordinate system of the system; establishing a dynamics equation of the system, the dynamics equation reflecting a relationship between a generalized driving force of the system and a generalized inertial force of the system and a generalized external force of the system, the generalized inertial force being related to a second-order change rate of the motion description variables; establishing a geometric constraint equation of the second hydraulic cylinder, the geometric constraint equation being that a measured length of the second hydraulic cylinder is equal to a calculated length of the second hydraulic cylinder obtained according to position vectors of two end points of the second hydraulic cylinder in the global coordinate system; grouping the geometric constraint equations of all the second hydraulic cylinders in the system to obtain constraint equations of the all the second hydraulic cylinders; establishing an average constraint equation of the all the second hydraulic cylinders according to the constraint equations of the all the second hydraulic cylinders, the average constraint equation reflecting a relationship between the motion description variables of the system, a generalized velocity of the system, a generalized acceleration of the system and a current measured length of the all the second hydraulic cylinders, a first-order change rate of the current measured length of the all the second hydraulic cylinders, and a second-order change rate of the current measured length of the all the second hydraulic cylinders; determining the driving force model according to the virtual work equation, the dynamics equation and the average constraint equation, the driving force model reflecting a relationship between the measured length of the second hydraulic cylinder and the driving force.

10. An apparatus for establishing a driving force model, comprising: a first establishing module configured to establish a virtual work equation of a second hydraulic cylinder in a system, the virtual work equation reflecting a relationship between a generalized driving force of the system and first virtual work done by a driving force of the second hydraulic cylinder, second virtual work done by a reaction force of the driving force, and motion description variables of the second hydraulic cylinder, the motion description variables including translational displacement and rotational vector in a global coordinate system of the system; a second establishing module configured to establish a dynamics equation of the system, the dynamics equation reflecting a relationship between a generalized driving force of the system and a generalized inertial force of the system and a generalized external force of the system, the generalized inertial force being related to a second-order change rate of the motion description variables; a third establishing module configured to establish a geometric constraint equation of the second hydraulic cylinder, the geometric constraint equation being that a measured length of the second hydraulic cylinder is equal to a calculated length of the second hydraulic cylinder obtained according to position vectors of two end points of the second hydraulic cylinder in the global coordinate system, wherein the apparatus for establishing a driving force model is further configured to group the geometric constraint equations of all the second hydraulic cylinders in the system to obtain constraint equations of the all the second hydraulic cylinders, and establish an average constraint equation of the all the second hydraulic cylinders according to the constraint equations of the all the second hydraulic cylinders, the average constraint equation reflecting a relationship between the motion description variables of the system, a generalized velocity of the system, a generalized acceleration of the system and a current measured length of the all the second hydraulic cylinders, a first-order change rate of the current measured length of the all the second hydraulic cylinders, and a second-order change rate of the current measured length of the all the second hydraulic cylinders; and determine the driving force model according to the virtual work equation, the dynamics equation and the average constraint equation, the driving force model reflecting a relationship between the measured length of the second hydraulic cylinder and the driving force. a second determining module configured to determine the driving force model according to the virtual work equation, the dynamic equation and the average constraint equation, the driving force model reflecting a relationship between a measured length of the second hydraulic cylinder and the driving force. 11.An electronic device, comprising: a memory; and a processor coupled to the memory and configured to execute a method according to any one of claims 1-8 based on instructions stored in the memory. 12.A system for determining a driving force of a hydraulic cylinder, comprising: at least one of the apparatus for determining a driving force of a hydraulic cylinder according to claim 9 and the apparatus for establishing a driving force model according to claim 10; and a displacement sensor configured to measure at least one of a current measured length of the first hydraulic cylinder and a measured length of the second hydraulic cylinder. 13.A working machine comprising the system for determining a driving force of a hydraulic cylinder according to claim 12.

14. A computer readable storage medium comprising computer program instructions, wherein, the computer program instructions, when executed by a processor, implement a method according to any one of claims 1-8.

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