A friction compensation control method for excavators based on stroke characteristics

Abstract

The present invention discloses a friction compensation control method for an excavator based on stroke characteristics, including introducing stroke and direction information to establish a friction model of an electro-hydraulic servo system; performing a constant speed segmented trajectory tracking test to obtain friction data of the electro-hydraulic servo system; establishing an identification objective function and fitness value; introducing nonlinear adaptive inertia weights, asynchronous learning coefficient change methods and elite mutation strategies to improve the particle swarm optimization algorithm; and using the improved particle swarm algorithm to accurately identify unknown parameters of the friction model. The friction model of the electro-hydraulic servo system of the present invention can comprehensively describe the friction characteristics between the stroke position, speed and direction of the electro-hydraulic servo system. The improved particle swarm identification algorithm can solve the problems of slow convergence speed and falling into a local optimal solution, effectively improve the modeling accuracy of the electro-hydraulic servo system, and further improve the trajectory tracking accuracy and operating efficiency of the system.

Description

Technical Field

[0001] The invention relates to a friction compensation control method for an excavator based on stroke characteristics, and belongs to the technical field of hydraulic control. Background Art

[0002] Many complex working conditions have put forward strict requirements on the construction accuracy of excavators. For example, the leveling accuracy of the Shiyezhou River in the Yangtze River needs to be ±50mm (the deepest water depth is 17m and the leveling width is 8m). The inherent friction in the electro-hydraulic servo system will cause the excavator working device to creep at low speed, trajectory distortion and steady-state error, which will reduce the working performance and control accuracy of the whole machine.

[0003] The compensation control method based on the friction model is an effective means to improve the trajectory accuracy of the excavator, but the premise is to establish a friction model that is accurately applicable to the characteristics of the excavator. When the excavator is performing operations such as digging and loading, leveling and repairing slopes, the hydraulic cylinder of the working device needs to switch directions repeatedly. The friction characteristics of the excavator must change with the stroke position of the hydraulic cylinder. The existing friction model can explain the friction mechanism of the excavator electro-hydraulic servo system to a certain extent. However, the existing friction model only uses a single speed signal as input. On the other hand, the lack of hydraulic cylinder position and direction information behind the existing friction model limits its compensation control accuracy.

[0004] With a friction model suitable for the characteristics of excavators, accurate and intelligent identification of unknown parameters of the friction model is also a technical focus. Traditional identification methods such as least squares, maximum likelihood method, and step method have long calculation cycles and cannot find the optimal parameters. The particle swarm algorithm is used to identify the unknown parameters of the friction model, and the global optimal solution can be obtained without complex rules. However, the algorithm has the limitations of premature convergence and falling into the local optimal solution.

[0005] Therefore, how to establish an excavator friction model that takes into account the stroke characteristics, accurately and intelligently identify the unknown parameters of the friction model, and then use a compensation control method based on the friction model to control the excavator to solve the low-speed creeping, trajectory distortion and steady-state error caused by friction is a technical problem that technical personnel in this field urgently need to solve. Summary of the invention

[0006] Objective: To overcome the deficiencies in the prior art, the present invention provides an excavator friction compensation control method based on stroke characteristics.

[0007] Technical solution: To solve the above technical problems, the technical solution adopted by the present invention is:

[0008] A friction compensation control method for an excavator based on stroke characteristics comprises the following steps:

[0009] Step 1: Considering the hydraulic cylinder stroke characteristics of the excavator electro-hydraulic servo system, a friction model of the excavator electro-hydraulic servo system is constructed.

[0010] Step 2: Perform a constant speed segmented trajectory tracking test to obtain the friction data of the excavator's electro-hydraulic servo system.

[0011] Step 3: According to the friction data of the excavator electro-hydraulic servo system, the improved particle swarm algorithm is used to identify the unknown parameters of the friction model of the excavator electro-hydraulic servo system, and the identified unknown parameters of the friction model of the excavator electro-hydraulic servo system are substituted into the friction model of the excavator electro-hydraulic servo system to obtain a complete friction model of the excavator electro-hydraulic servo system.

[0012] Step 4: According to the excavator load pressure, the actual friction calculated by the complete excavator electro-hydraulic servo system friction model is calculated, the excavator electro-hydraulic servo system feedback is calculated, the friction compensation amount is calculated according to the excavator electro-hydraulic servo system feedback, and the friction compensation amount is superimposed on the excavator electro-hydraulic servo system PID control signal.

[0013] As a preferred solution, the friction model of the excavator electro-hydraulic servo system is calculated by the following formula:

[0014]

[0015] Among them, F f is the actual friction of the electro-hydraulic servo system of the excavator, y is the displacement of the hydraulic cylinder, z is the average deformation of the bristles, v is the movement speed of the hydraulic cylinder of the electro-hydraulic servo system, and f m (y) is the static friction coefficient, f c (y) is the Coulomb friction coefficient, v s (y) is the Stribeck curve speed, σ0(y) is the bristle stiffness coefficient, σ1(y) is the bristle damping coefficient, σ2(y) is the viscous damping coefficient, g(v) is the Stribeck curve phenomenon, representing the phenomenon that friction decreases with increasing speed, v2 and v1 are switching speeds, v2>v1.

[0016] As a preferred solution, the specific steps of step 2 are as follows:

[0017] S2.1. Set the hydraulic cylinder friction test stroke of the excavator electro-hydraulic servo system as a, the entire effective stroke of the hydraulic cylinder as b, and divide the entire effective stroke into [b / a] segments.

[0018] S2.2. Set the expected trajectory of the hydraulic cylinder in the [b / a] stroke as a triangular wave. Under the triangular wave trajectory, the hydraulic cylinder moves at a uniform speed with an acceleration of 0. The friction model of the excavator electro-hydraulic servo system in formula (1) can be written as the static theoretical friction F fj , which is expressed as follows:

[0019]

[0020] Static theoretical friction F fj In the model expression, the unknown parameter f needs to be identified m (y), f c (y), v s (y) and σ2(y).

[0021] S2.3. Collect the working pressure in the rod chamber and rodless chamber of the hydraulic cylinder in the [b / a] stroke section in turn to obtain the actual static friction experimental value F for each stroke section. fcj , and its calculation formula is as follows:

[0022] F cj =A1p1-A2p2-F l (3)

[0023] Among them, A1 and A2 are the effective working areas of the rodless cavity and the rod cavity respectively, p1 is the rodless cavity pressure, p2 is the rod cavity pressure, F l For external load force.

[0024] The static friction experimental value can be obtained by formula (3).

[0025] The goal of static parameter identification is to find a set of optimal parameters f m (y), f c (y), v s (y), σ2(y) makes the static friction test value F fcj The static friction F fj Try to be equal, as follows:

[0026]

[0027] In the actual identification process, the minimum sum of squares of the two is used as the objective function J1 of static parameter identification, as shown in the following formula:

[0028]

[0029] Where k is the measured value at the kth speed and n is the total number of measurements.

[0030] S2.4, set the control signal of the excavator electro-hydraulic servo system of the [b / a] segment stroke to y step The small-amplitude step signal puts the excavator electro-hydraulic servo system in a pre-slip state. In the pre-slip state, the friction model of the excavator electro-hydraulic servo system in formula (1) can be written as the dynamic theoretical friction F fd , which is expressed as follows:

[0031]

[0032] Dynamic theory friction F fd In the model expression, the unknown parameters σ0(y) and σ1(y) need to be identified.

[0033] Collect the working pressure in the rod cavity and the rodless cavity to obtain the dynamic friction test data F for each stroke fcd , and its calculation formula is as follows:

[0034]

[0035] Where m is the equivalent mass of the moving parts of the hydraulic cylinder, is the acceleration, p L is the load pressure, F l For external load force.

[0036] The dynamic friction test value can be obtained by formula (7).

[0037] In the actual identification process, the minimum sum of squares of the two is used as the objective function J2 of dynamic parameter identification, as shown in the following formula:

[0038]

[0039] Among them, r is the measurement value at the rth speed, and u is the total number of measurements.

[0040] As a preferred solution, in step 3, the static friction parameter f under a certain stroke is first identified. m (y), f c (y), v s (y), σ2(y), and then identify the dynamic friction parameters σ0(y) and σ1(y) under the stroke, until all strokes are traversed, and then establish the friction model of the excavator electro-hydraulic servo system considering the stroke characteristics. The specific steps are as follows:

[0041] S3.1: Establish the identification objective function and fitness value, and find a set of optimal parameters to make the experimentally measured electro-hydraulic servo system friction data as equal as possible to the established friction model.

[0042] The fitness value of the identification algorithm is designed based on the objective function J. The larger the fitness value, the more accurate the identified parameters. The relationship between the fitness f and the identification objective function J is f=1 / J. When J is static, J=J1, and when J is dynamic, J=J2.

[0043] S3.2: Initialization. Initialize particle settings, set population size M, maximum number of iterations T max 、f m (y), f c (y), v s The initial values ​​of (y) and σ2(y).

[0044] S3.3: Update the particle's position and velocity.

[0045] The inertia weight and learning coefficient are calculated according to formulas (10) and (11), and then the position x of particle i is updated according to the following formula: id and speed v id .

[0046]

[0047] Among them, p id is the optimal position of particle i, p gd is the global optimal position experienced by all particles, d = 1, 2, ..., D, D is the search space dimension, ω is the inertia weight, c1 and c2 are learning coefficients.

[0048] S3.4: Calculate the fitness value. Calculate the fitness value of each particle, compare the individual and global fitness values ​​of a single particle with the best individual and global fitness values, and retain the best value.

[0049] S3.5: Based on the elite mutation strategy P g * The best global position is compared with the original fitness value and the optimal value is retained.

[0050] S3.6: Determine the termination condition. If the predetermined minimum error is met or the maximum number of iterations is reached, the optimal solution of the static parameters is output; if the condition is not met, return to step 3.3.

[0051] S3.7: Set the static parameter f in step 3.2 m (y), f c (y), v s Replace the initial values ​​of σ(y) and σ2(y) with the initial values ​​of dynamic parameters σ0(y) and σ1(y). Set the position range and speed range of the dynamic parameters to be identified. Based on the identified static parameters, identify the dynamic parameters, continue to execute steps 3.3 to 3.6, and output the optimal solution of the dynamic parameters.

[0052] S3.8: Identify each stroke friction parameter in turn until the entire stroke divided by the hydraulic cylinder of the electro-hydraulic servo system is identified, and establish a complete friction model of the excavator electro-hydraulic servo system.

[0053] As a preferred solution, the inertia weight ω is calculated as follows:

[0054]

[0055] Among them, f i is the fitness value of particle i, corresponding to a set of friction parameters, ω maxand ω min is the maximum and minimum value of ω, f avg and f max They are the average fitness value and the minimum fitness value of all particles at present.

[0056] As a preferred solution, the learning coefficients c1 and c2 are calculated as follows:

[0057]

[0058] Among them, c 11 、c 12 is the initial and final value of c1, c 21 、c 22 is the initial and final value of c2, t is the current iteration number, T max is the maximum number of iterations.

[0059] As a preferred solution, the elite mutation strategy P g * , the calculation formula is as follows:

[0060]

[0061] Where M is the population size, v id is the velocity of the ith particle, P g is the global best position experienced by all particles, P i is the global best position experienced by the ith particle, r is the distance between the particle’s history and the current global best position, r max is the maximum distance between the particle’s history and the current global best position.

[0062] As a preferred solution, the calculation formula of the feedback E of the excavator electro-hydraulic servo system is as follows:

[0063]

[0064] Among them, V is the equivalent volume of the hydraulic cylinder, n is the flow ratio of the two chambers of the hydraulic cylinder, β e is the effective bulk elastic modulus, K t is the total flow pressure coefficient, s is the Laplace operator, T is the time constant, K a is the amplifier gain, K b is the current gain, K q is the flow gain coefficient, A1 is the effective working area of ​​the rodless cavity, p L is the load pressure, F f Actual friction of electro-hydraulic servo system for excavator.

[0065] Beneficial effects: The present invention provides an excavator friction compensation control method based on stroke characteristics, proposes an improved LuGre model to comprehensively describe the friction characteristics between the stroke position, speed and direction of the excavator electro-hydraulic servo system, and improves the particle swarm optimization algorithm to accurately identify the unknown friction parameters, thereby improving the identification accuracy and efficiency. Then, the compensation control method based on the friction model is used to control the excavator, solve the problems of low-speed creeping, trajectory distortion and steady-state error caused by friction, and lay the foundation for intelligent control, theoretical analysis, smart construction and other functions. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 This is the schematic diagram of a typical excavator single-link electro-hydraulic servo system.

[0067] Figure 2 It is a flow chart for identification of friction model of excavator based on stroke characteristics.

[0068] Figure 3 It is a schematic diagram of the friction measurement curve and the initial values ​​of the friction parameters.

[0069] Figure 4 Yes m and f c Schematic diagram of the coefficient's changing trend in different intervals of the hydraulic cylinder.

[0070] Figure 5 is σ2 and v s Schematic diagram of the coefficient's changing trend in different intervals of the hydraulic cylinder.

[0071] Figure 6 It is a schematic diagram of the changing trend of σ0 and σ1 coefficients in different ranges of the hydraulic cylinder. DETAILED DESCRIPTION

[0072] The present invention will be further described below in conjunction with specific embodiments.

[0073] In this embodiment, the friction modeling of the single-link electro-hydraulic servo system of the excavator is carried out. Figure 1 As shown in the figure, the single-link electro-hydraulic servo system mainly includes a controller, a main valve and a hydraulic cylinder. The input voltage signal of the controller is converted into a current signal, which is used to control the flow of the main valve and then control the movement of the piston rod of the hydraulic cylinder. A wire displacement sensor is used to obtain the displacement of the hydraulic cylinder. Two pressure sensors are also installed on the hydraulic cylinder to measure the internal pressure.

[0074] A friction compensation control method for excavators based on stroke characteristics, the process is as follows Figure 2 As shown, the specific steps include:

[0075] S1. Considering the stroke characteristics, a friction model of the excavator electro-hydraulic servo system is established.

[0076] Considering the influence of the structure, installation error and uneven surface finish of the single-link electro-hydraulic servo of the excavator, the stroke and direction information are introduced to improve the LuGre model, and the friction model F of the excavator electro-hydraulic servo system with friction characteristics changing with stroke position is established. f , as shown below:

[0077]

[0078] Where y is the displacement of the hydraulic cylinder, bristles are the description of the friction contact surface of the hydraulic cylinder at the microscopic level, z is the average deformation of the bristles, v is the movement speed of the hydraulic cylinder of the electro-hydraulic servo system, and f m (y) is the static friction coefficient, f c (y) is the Coulomb friction coefficient, v s (y) is the Stribeck speed, σ0(y) is the bristle stiffness coefficient, σ1(y) is the bristle damping coefficient, σ2(y) is the viscous damping coefficient, and g(v) is the Stribeck phenomenon, which represents the phenomenon that friction decreases as speed increases. v2 and v1 are switching speeds, v2>v1.

[0079] Specifically, it is necessary to identify six unknown parameters in the friction model [f m (y), f c (y), v s (y), σ2(y), σ0(y), σ1(y)], introducing the hydraulic cylinder stroke and direction information, which is reflected in the six unknown parameters that are different from the fixed values ​​of other models and are a set of parameters corresponding to different strokes. Among them, [f m (y), f c (y), v s (y), σ2(y)] are the static parameters of the friction model, and [σ0(y), σ1(y)] are the dynamic parameters of the friction model.

[0080] S2, perform a constant speed segmented trajectory tracking test to obtain friction data of the electro-hydraulic servo system. This includes the following steps:

[0081] S2.1. Set the hydraulic cylinder friction test stroke of the excavator electro-hydraulic servo system as a, and the total effective stroke of the hydraulic cylinder as b. Divide the total effective stroke into [b / a] (round down) parts, perform the same test on each section, and obtain the friction data under different strokes.

[0082] In the embodiment, the hydraulic cylinder has a stroke a of 400 mm, the effective stroke b of the excavator boom hydraulic cylinder is 1675 mm, the entire stroke of the boom is divided into 4 parts, each section is subjected to the same test, and friction data under different strokes are obtained.

[0083] S2.2. Set the expected trajectory of the hydraulic cylinder in the [b / a] stroke as a triangular wave. Under the triangular wave trajectory, the hydraulic cylinder moves at a uniform speed with an acceleration of 0. The friction model of the excavator electro-hydraulic servo system in formula (1) can be written as the static theoretical friction F fj , which is expressed as follows:

[0084]

[0085] Static theoretical friction F fj In the model expression, the unknown parameter f needs to be identified m (y), f c (y), v s (y) and σ2(y). From the lowest v min To the highest v max , a total of [v max / v min ] (round down) group speed. According to the high speed v max To low speed v min The friction test was carried out in the order of [v min ,4v min ] range, the control system is set to v max / 2 speed reciprocating motion n time times, restore the lubrication of the entire system to normal conditions.

[0086] In the embodiment, the desired trajectory of the hydraulic cylinder of the electro-hydraulic servo system of each section is set to a triangular wave in turn. At this time, the hydraulic cylinder of the electro-hydraulic servo system of the excavator will be in a constant speed motion state, from the lowest 5mm / s to the highest 200mm / s, with a total of 40 sets of speeds set. The friction test is carried out in the order from high speed to low speed, and the bucket is empty at the same time. When the arm joint moves without load, the bucket does not contact the soil, so there will be no interference force on the arm joint that contacts the soil. At this time, the load force of the arm joint is mainly the weight of the arm and the bucket. Before conducting a low-speed test in the range of [5mm / s, 20mm / s], the control system reciprocates 3 times at a speed of 100mm / s to restore the lubrication of the entire system to normal.

[0087] S2.3. Collect the working pressure in the rod chamber and rodless chamber of the hydraulic cylinder in the [b / a] stroke section in turn to obtain the actual static friction experimental value F for each stroke section. fcj , and its calculation formula is as follows:

[0088] F cj =A1p1-A2p2-F l (3)

[0089] Among them, A1 and A2 are the effective working areas of the rodless cavity and the rod cavity respectively, p1 is the rodless cavity pressure, p2 is the rod cavity pressure, F l For external load force.

[0090] The static friction experimental value can be obtained by formula (3).

[0091] The goal of static parameter identification is to find a set of optimal parameters f m (y), f c (y), v s (y), σ2(y) makes the static friction test value F fcj The static friction F fj Try to be equal, as follows:

[0092]

[0093] In the actual identification process, the minimum sum of squares of the two is used as the objective function J1 of static parameter identification, as shown in the following formula:

[0094]

[0095] Where k is the measurement value at the kth speed, k∈[1,n], and n is the total number of measurements.

[0096] S2.4. Conduct data testing of dynamic friction parameters.

[0097] Set the electro-hydraulic servo system of [b / a] section to y in sequence step A small-amplitude step signal puts the electro-hydraulic servo system in a pre-slip state.

[0098] In the pre-slip state, the friction model of the excavator electro-hydraulic servo system in formula (1) can be written as the dynamic theoretical friction F fd , which is expressed as follows:

[0099]

[0100] Dynamic theory friction F fd In the model expression, the unknown parameters σ0(y) and σ1(y) need to be identified.

[0101] In the embodiment, the electro-hydraulic servo system of each stroke a is sequentially set to a 0.1 mm small amplitude step signal, so that the electro-hydraulic servo system is in a pre-slip state.

[0102] S2.5. Collect the working pressure in the rod cavity and the rodless cavity, calculate the pressure difference, and calculate the dynamic friction test data F according to the following force balance expression fcd :

[0103]

[0104] Where m is the equivalent mass of the moving parts of the hydraulic cylinder, is the acceleration, p L is the load pressure.

[0105] The dynamic friction test value can be obtained by formula (7).

[0106] In the actual identification process, the minimum sum of squares of the two is used as the objective function J2 of dynamic parameter identification, as shown in the following formula:

[0107]

[0108] Among them, r is the measurement value at the rth speed, and u is the total number of measurements.

[0109] S3. Improve the particle swarm algorithm to identify the unknown parameters of the friction model. First, identify the static friction parameter f under a certain stroke. m (y), f c (y), v s (y), σ2(y), and then identify the dynamic friction parameters σ0(y) and σ1(y) under the stroke, until all strokes are traversed, and then establish the friction model of the excavator electro-hydraulic servo system considering the stroke characteristics. It includes the following steps:

[0110] S3.1. Establish the identification objective function and fitness value, and find a set of optimal parameters to make the friction data of the electro-hydraulic servo system measured experimentally as equal as possible to the established friction model.

[0111] The fitness value of the identification algorithm is designed based on the objective function. The larger the fitness value, the more accurate the identified parameters. The relationship between the fitness f and the identification objective function J is f = 1 / J. J = J2 for dynamic parameter identification and J = J1 for static parameter identification.

[0112] S3.2. Use the improved particle swarm algorithm to identify the unknown parameters of the friction model. The improved particle swarm algorithm is reflected in three aspects:

[0113] Improvement 1, nonlinear adaptive inertia weight ω. The inertia weight ω is directly related to the convergence speed of the algorithm. The algorithm has a strong global search capability at the beginning of the iteration and focuses on local search in the later stage of the iteration. The formula of nonlinear adaptive inertia weight ω is as follows:

[0114]

[0115] Among them, f i is the fitness value of particle i, corresponding to a set of friction parameters, ω max and ω min is the maximum and minimum value of ω, f avg and fmax are the average fitness value and the maximum fitness value of all particles at present. When the fitness of particles tends to be the same or the local optimum, ω will increase. When they tend to be dispersed, ω will decrease.

[0116] Improvement 2, asynchronous change method of learning coefficients c1 and c2. c1 and c2 are cognitive and social coefficients used to determine the impact of individual and group experience on particle trajectories. In the early stage of iteration, a large c1 and a small c2 are used, which is conducive to global search ability. In the later stage of iteration, a small c1 and a large c2 are used, which is conducive to global convergence. Therefore, the asynchronous change equation of the learning coefficient is as follows:

[0117]

[0118] Among them, c 11 、c 12 、c 21 、c 22 are the initial and final values ​​of c1 and c2, and T max is the maximum number of iterations, and t is the number of iterations.

[0119] In the embodiment, c 11 =0.5, c 12 =2, c 21 =0.5, c 22 =2.

[0120] Improvement 3, elite mutation strategy P g * .P g is the global best position experienced by all particles. The search potential of each particle in the iteration process is not exactly the same, and the dominant particles should be given more space exploration opportunities. When the mutated global best position has better performance, it will participate in the new iteration process. The formula is as follows:

[0121]

[0122] Among them, t is the number of iterations, M is the population size, and v id is the velocity of the ith particle, P g is the global best position experienced by all particles, P i is the global best position experienced by the ith particle, r is the distance between the particle’s history and the current global best position, r max is the maximum distance between the particle’s history and the current global best position.

[0123] In step S3.2, the improved particle swarm algorithm is used to identify the unknown parameters of the friction model. First, the static parameters of the friction model of a section of travel a are identified [f m (y), f c (y), vs (y), σ2(y)], and then identify the dynamic parameters [σ0(y), σ1(y)] based on the identified static parameters until all trips b are identified. The specific operation process is as follows:

[0124] (1) Initialization. Initialize particle settings, set the population size M, and the maximum number of iterations T max 、f m (y), f c (y), v s The initial values ​​of (y) and σ2(y).

[0125] In the embodiment, the population size M is set to 100, the maximum number of iterations T max =500. m (y), f c (y), v s The initial values ​​of (y) and σ2(y) can be roughly set by the actual measured static friction curve, such as Figure 3 As shown: The arm hydraulic cylinder is in V min The friction force measured during the motion is f m The initial value of (y), v max The intersection point of the extended line of the friction force measured during speed motion and the y-axis is f c The initial value of (y), the slope of the friction force in the high-speed section is the initial value of σ2(y), and the speed point at which the Stribeck effect ends is v s Therefore, the position interval x of the static parameter to be identified is set id f m (y)∈[20,60], x id f c (y)∈[3,13], x id v s (y)∈[10,30], x id σ2(y)∈[0.1,1] and velocity interval v id f m (y)∈[10,30], v id f c (y)∈[1,7], v id v s (y)∈[5,15], v id σ2(y)∈[0.1,0.5].

[0126] (2) Update the particle's position and velocity.

[0127] The inertia weight and learning coefficient are calculated according to formulas (9) and (10), and then the position x of particle i is updated according to the following formula: id and speed v id .

[0128]

[0129] Among them, p id is the optimal position of particle i, p gd is the global best position experienced by all particles, d = 1, 2, ..., D, where D is the dimension of the search space.

[0130] (3) Calculate the fitness value. Calculate the fitness value of each particle, compare the individual and global fitness values ​​of a single particle with the best individual and global fitness values, and retain the best value.

[0131] (4) Perform elite mutation. According to formula (11), mutate the best global position, compare it with the original fitness value, and retain the optimal value.

[0132] (5) Determine the termination condition. If the predetermined minimum error is met or the maximum number of iterations is reached, the optimal solution of the static parameters is output; if the condition is not met, return to step (2).

[0133] (6) Replace the static parameters in step (1) with dynamic parameters. Set the position range and speed range of the dynamic parameters to be identified. Based on the identified static parameters, identify the dynamic parameters, continue to execute steps (2) to (5), and output the optimal solution for the dynamic parameters.

[0134] In the embodiment, the position interval x of the dynamic parameter to be identified is set id σ0(y)∈[1000,3000], x id σ1(y)∈[100,300] and velocity interval v id σ0(y)∈[500,1500], v id σ1(y)∈[50,150]. Based on the identified static and dynamic parameter data, the dynamic parameters are identified, and steps (2) to (5) are continued to output the optimal solution of the dynamic parameters.

[0135] (7) Identify each stroke friction parameter in turn until the entire stroke of the hydraulic cylinder of the electro-hydraulic servo system is identified, and establish an electro-hydraulic servo system friction model that takes into account the stroke characteristics.

[0136] In the embodiment, the friction parameter variation diagram of the boom-linked electro-hydraulic servo system under different strokes is as follows: Figure 4-6 As shown in the figure, they respectively represent the variation trend of the friction coefficient of the hydraulic cylinder of the excavator arm in different intervals. Figure 4 f m (y) and f c (y) The variation trend of coefficient in different intervals of hydraulic cylinder, Figure 5 is σ2(y) and v s(y) The variation trend of coefficient in different intervals of hydraulic cylinder, Figure 6 is the changing trend of σ0(y) and σ1(y) coefficients in different intervals of the hydraulic cylinder.

[0137] S4. Design a friction compensation controller to improve trajectory tracking accuracy.

[0138] The friction feedforward compensator is designed based on the principle of structural invariance and the principle of electro-hydraulic proportional system of the excavator robot. L The actual friction is estimated based on the established friction model, and the friction compensation is calculated by feedback E. The corresponding friction compensation is superimposed on the original PID control signal to make the influence of friction zero, thereby improving the trajectory tracking accuracy. Feedback E is specifically:

[0139]

[0140] Among them, V is the equivalent volume of the hydraulic cylinder, n is the flow ratio of the two chambers of the hydraulic cylinder, β e is the effective bulk elastic modulus, K t is the total flow pressure coefficient, s is the Laplace operator, T is the time constant, K a is the amplifier gain, K b is the current gain, K q is the flow gain coefficient.

[0141] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A friction compensation control method for an excavator based on stroke characteristics, characterized in that: The steps include: Step 1: Considering the hydraulic cylinder stroke characteristics of the excavator electro-hydraulic servo system, a friction model of the excavator electro-hydraulic servo system is constructed; Step 2: Perform a constant speed segmented trajectory tracking test to obtain friction data of the excavator electro-hydraulic servo system; Step 3: According to the friction data of the excavator electro-hydraulic servo system, the improved particle swarm algorithm is used to identify the unknown parameters of the friction model of the excavator electro-hydraulic servo system, and the identified unknown parameters of the friction model of the excavator electro-hydraulic servo system are substituted into the friction model of the excavator electro-hydraulic servo system to obtain a complete friction model of the excavator electro-hydraulic servo system; Step 4: According to the load pressure of the excavator, the actual friction calculated by the complete friction model of the excavator electro-hydraulic servo system is calculated, the feedback of the excavator electro-hydraulic servo system is calculated, the friction compensation amount is calculated according to the feedback of the excavator electro-hydraulic servo system, and the friction compensation amount is superimposed on the PID control signal of the excavator electro-hydraulic servo system; The friction model of the excavator electro-hydraulic servo system is calculated as follows: Among them, F f is the actual friction of the electro-hydraulic servo system of the excavator, y is the displacement of the hydraulic cylinder, z is the average deformation of the bristles, v is the movement speed of the hydraulic cylinder of the electro-hydraulic servo system, and f m (y) is the static friction coefficient, f c (y) is the Coulomb friction coefficient, v s (y) is the Stribeck curve speed, σ0(y) is the bristle stiffness coefficient, σ1(y) is the bristle damping coefficient, σ2(y) is the viscous damping coefficient, g(v) is the Stribeck curve phenomenon, v2 and v1 are the switching speeds, v2>v1; The specific steps of step 2 are as follows: S2.

1. Set the hydraulic cylinder friction test stroke of the excavator electro-hydraulic servo system as a, the entire effective stroke of the hydraulic cylinder as b, and divide the entire effective stroke into [b / a] segments; S2.2, set the expected trajectory of the hydraulic cylinder in the [b / a] stroke as a triangular wave in sequence. Under the triangular wave trajectory, the hydraulic cylinder moves at a uniform speed with an acceleration of 0. According to the friction model of the excavator electro-hydraulic servo system in formula (1), the static theoretical friction F is obtained: fj , which is expressed as follows: Static theoretical friction F fj In the model expression, the unknown parameter to be identified is f m (y), f c (y), v s (y) and σ2(y); S2.

3. Collect the working pressure in the rod chamber and rodless chamber of the hydraulic cylinder in the [b / a] stroke section in turn to obtain the actual static friction experimental value F for each stroke section. fcj , and its calculation formula is as follows: F cj =A1p1-A2p2-F l (3) Among them, A1 and A2 are the effective working areas of the rodless cavity and the rod cavity respectively, p1 is the rodless cavity pressure, p2 is the rod cavity pressure, F l is the external load force; The goal of static parameter identification is to find a set of optimal parameters f m (y), f c (y), v s (y), σ2(y) makes the static friction test value F fcj The static friction F fj Try to be equal, as follows: In the actual identification process, the minimum sum of squares of the two is used as the objective function J1 of static parameter identification, as shown in the following formula: Where k is the measured value at the kth speed, and n is the total number of measurements; S2.4, set the control signal of the excavator electro-hydraulic servo system of the [b / a] segment stroke to y step The small-amplitude step signal puts the excavator electro-hydraulic servo system in a pre-slip state. In the pre-slip state, the dynamic theoretical friction F is obtained according to the friction model of the excavator electro-hydraulic servo system in formula (1): fd , which is expressed as follows: Dynamic theory friction F fd In the model expression, the unknown parameters to be identified are σ0(y) and σ1(y); Collect the working pressure in the rod cavity and the rodless cavity to obtain the dynamic friction test data F for each stroke fcd , and its calculation formula is as follows: Where m is the equivalent mass of the moving parts of the hydraulic cylinder, is the acceleration, p L is the load pressure, F l is the external load force; In the actual identification process, the minimum sum of squares of the two is used as the objective function J2 of dynamic parameter identification, as shown in the following formula: Among them, r is the measurement value at the rth speed, and u is the total number of measurements.

2. The friction compensation control method for an excavator based on stroke characteristics according to claim 1, characterized in that: The specific steps of step 3 are as follows: S3.1: Establish the identification objective function J and fitness value f, and find a set of optimal parameters to make the friction data of the electro-hydraulic servo system measured experimentally equal to the friction model of the excavator electro-hydraulic servo system established as much as possible; when J is static, J=J1, when J is dynamic, J=J2; the fitness f is 1 / J; S3.2: Initialize particle settings, set population size M, maximum number of iterations T max 、f m (y), f c (y), v s The initial values ​​of (y) and σ2(y); S3.3: Update the position and velocity of the particle, update the velocity of particle i and location The calculation formula is as follows: Among them, p id is the optimal position of particle i, p gd is the global best position experienced by all particles, d = 1, 2, ..., D, D is the search space dimension, ω is the inertia weight, c1 and c2 are learning coefficients, is the speed and position of particle i at the current moment t, r1 and r2 are random numbers; S3.4: Calculate the fitness value of each particle, compare the individual and global fitness values ​​of a single particle with the best individual and global fitness values, and retain the best value; S3.5: Based on the elite mutation strategy P g * The best global position is compared with the original fitness value, and the optimal value is retained; S3.6: If the predetermined minimum error is met or the maximum number of iterations is reached, the optimal solution of the static parameters is output; if the conditions are not met, return to step 3.3; S3.7: Set the static parameter f in step 3.2 m (y), f c (y), v s Replace the initial values ​​of σ(y) and σ2(y) with the initial values ​​of dynamic parameters σ0(y) and σ1(y); set the position interval and speed interval of the dynamic parameters to be identified; identify the dynamic parameters based on the identified static parameters, continue to execute steps 3.3 to 3.6, and output the optimal solution of the dynamic parameters; S3.8: Identify each stroke friction parameter in turn until the entire stroke divided by the hydraulic cylinder of the electro-hydraulic servo system is identified, and establish a complete friction model of the excavator electro-hydraulic servo system.

3. The friction compensation control method for an excavator based on stroke characteristics according to claim 2, characterized in that: The inertia weight ω is calculated as follows: Among them, f i is the fitness value of particle i, corresponding to a set of friction parameters, ω max and ω min is the maximum and minimum value of ω, f avg and f max They are the average fitness value and the minimum fitness value of all particles at present.

4. The friction compensation control method for an excavator based on stroke characteristics according to claim 2, characterized in that: The learning coefficients c1 and c2 are calculated as follows: Among them, c 11 、c 12 is the initial and final value of c1, c 21 、c 22 is the initial and final value of c2, t is the current iteration number, T max is the maximum number of iterations.

5. The friction compensation control method for an excavator based on stroke characteristics according to claim 4, characterized in that: The elite mutation strategy P g * , the calculation formula is as follows: Where M is the population size, v id is the velocity of the ith particle, P g is the global best position experienced by all particles, P i is the global best position experienced by the ith particle, r is the distance between the particle’s history and the current global best position, r max is the maximum distance between the particle’s history and the current global best position.

6. The friction compensation control method for an excavator based on stroke characteristics according to claim 1, characterized in that: The calculation formula of the feedback E of the excavator electro-hydraulic servo system is as follows: Among them, V is the equivalent volume of the hydraulic cylinder, n is the flow ratio of the two chambers of the hydraulic cylinder, β e is the effective bulk elastic modulus, K t is the total flow pressure coefficient, s is the Laplace operator, T is the time constant, K a is the amplifier gain, K b is the current gain, K q is the flow gain coefficient, A1 is the effective working area of ​​the rodless cavity, p L is the load pressure, F f Actual friction of electro-hydraulic servo system for excavator.

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