Online identification method and device for friction model parameters of servo feeding system

Abstract

The invention belongs to the related technical field of servo feeding system analysis, and discloses an online identification method and device for parameters of a friction model of a servo feeding system, and the method comprises the steps: (1) adding a position related item h (x) on a conventional friction model to obtain the friction model of the servo feeding system; (2) acquiring an experimental Stribeck curve of the friction torque of the servo driving system at different speed positions based on the experimental data; (3) inputting different positions x and different speeds v corresponding to the experimental data into a friction model, fitting the friction model to obtain friction model parameters and a fitting Stribeck curve, and meanwhile, adjusting the friction model parameters by adopting a particle swarm algorithm until the friction model parameters which enable the error between the experimental Stribeck curve and the fitting Stribeck curve to be minimum are found; and (4) correcting the parameters of the friction model in real time by adopting a recursive least square method to realize real-time identification of the parameters of the friction model. The precision is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field related to servo feed system analysis, and more specifically, relates to an online identification method and device for friction model parameters of a servo feed system. Background Art

[0002] High-precision and high-performance servo feed systems have always been one of the main development directions of CNC machine tools. With the continuous progress of economic and technological levels, the demand for high-end products has gradually increased. In various fields such as aerospace, military and industry, servo feed systems are playing an increasingly important role, especially in special equipment such as robots, metallurgy, and medical treatment, which have higher requirements for servo feed systems in terms of precision. With this comes the demand for processing equipment with higher precision and higher performance. At the same time, high-performance processing equipment is also inseparable from high-performance and high-precision servo feed systems. Therefore, the research on high-precision servo feed systems is in line with the trend of the times.

[0003] CNC machine tools generally use traditional PID control, which has limited control capabilities for nonlinear errors in machine tools, and their servo feed systems are easily disturbed by mechanical clearance, pitch error, friction characteristics, machine tool vibration and other factors in the mechanical transmission link, which has a great impact on the machining accuracy of the machine tools. Among them, friction characteristic interference, especially nonlinear friction interference, will have a great impact on the control accuracy of the feed system, and may cause creeping and large following errors during the commutation and startup stages.

[0004] In view of the influence of friction on the control accuracy of CNC machine tools, researchers have adopted a variety of methods to reduce the influence of friction, such as using more effective lubricants to improve the lubrication level of the two contact surfaces and reduce the difference between dynamic friction and static friction; improving the structure of the machine tool and reducing its transmission links; replacing structures such as air-floating guides and air-floating bearings with less friction to reduce the influence of friction, as well as various technologies that can improve the surface condition of the contact surface. However, these methods are too expensive and complicated to operate, and do not consider the different friction forces corresponding to different strokes. The existing friction models do not consider the influence of motion stroke on friction, which leads to a low degree of fit between the friction model and the actual situation, and the corresponding accuracy is not ideal, and the friction problem cannot be fundamentally solved. Therefore, it is very necessary to study and establish a simulation friction model for the servo feed system and the corresponding feedforward compensation. Summary of the invention

[0005] In view of the above defects or improvement needs of the prior art, the present invention provides an online identification method and device for friction model parameters of a servo feed system, which aims to solve the problem of not considering the influence of motion stroke on friction force.

[0006] To achieve the above object, according to one aspect of the present invention, an online identification method for friction model parameters of a servo feed system is provided, the identification method comprising the following steps:

[0007] (1) The position-related term h(x) is added to the traditional friction model to obtain the friction model of the servo feed system;

[0008] (2) Based on experimental data, obtain the experimental Stribeck curve of the friction torque of the servo drive system at different speeds and positions;

[0009] (3) inputting different positions x and different speeds v corresponding to the experimental data into the friction model, fitting the friction model to obtain friction model parameters and a fitted Stribeck curve, and adjusting the friction model parameters by using a particle swarm algorithm until finding the friction model parameters that minimize the error between the experimental Stribeck curve and the fitted Stribeck curve;

[0010] (4) The recursive least squares method is used to perform real-time correction on the friction model parameters to achieve real-time identification of the friction model parameters.

[0011] Furthermore, the expression of the friction model is:

[0012]

[0013] In the formula, F fric represents the total friction force calculated by the model, f C represents Coulomb friction, sgn(v) represents the sign function of velocity, which takes values ​​of +1, -1 or 0, and f s represents the adhesive friction, v represents the relative speed, and v s represents the Stribeck speed, which defines the transition speed between Coulomb friction and adhesive friction; σ2 represents the viscous friction coefficient, which is used to express the linear relationship between speed and friction; h(x) represents the position-related term, and x represents the position of the drive shaft.

[0014] Furthermore, experimental data collection is carried out on the servo feed workbench, and the friction torque of the workbench corresponding to a series of speed positions is collected at the speed position. The stable friction torque of the corresponding uniform speed section is extracted from the obtained experimental data, and the experimental Stribeck curve of the friction torque of the servo drive system at different speed positions is obtained.

[0015] Furthermore, the steps of using the particle swarm algorithm to correct the friction model parameters are as follows:

[0016] 5.1 Initializing friction model parameters f C , f s , v s,σ2,h(x), determine the search space and initialize the parameters position and velocity;

[0017] 5.2 Set the fitness function and use it to determine whether the parameter position is optimal at this time;

[0018] 5.3 If the current position of the parameter is better than the best position of the individual, the best position of the individual is replaced by the current position;

[0019] 5.4 Continuously update the parameters of speed and position;

[0020] 5.5 Repeat steps 5.3 and 5.4, and continue to iterate until the maximum number of iterations or the fitness function reaches the optimal value and no longer decreases. At this time, the friction model parameter f is obtained. C , f s , v s ,σ2,h(x).

[0021] Furthermore, one of the recursive least squares calculation processes is to obtain the error:

[0022] e(t)=y(t)-φ(t) T θ(t-1),

[0023] Where y(t) is the actual observation value; φ(t) is the input data; θ(t-1) is the estimated value of the model parameter at the previous moment.

[0024] Furthermore, the gain vector used by the recursive least squares method is updated as

[0025]

[0026] Parameter vector update: θ(t)=θ(t-1)+K(t)e(t);

[0027] Where λ is the forgetting factor, which is used to weigh the impact of historical data and new data and ranges from 0 to 1. P(t-1) is the initial value of the covariance matrix P(t-1) at the previous moment.

[0028] Furthermore, the correction steps of the friction model parameters are:

[0029] 6.1. The servo drive system will identify the friction parameter f at a certain working speed v and running distance x C , f s , v s ,σ2,h(x) as the original parameters of the friction equation;

[0030] 6.2. Use displacement sensors and speed sensors to collect the speed v and running distance x of the servo transmission system in real time, substitute v and x into the friction model, and obtain the model friction torque prediction value F1;

[0031] 6.3 Use the torque sensor to directly obtain the friction torque F2 of the current servo transmission system, calculate the error e(t) through RLS, calculate the gain vector, and then C , f s , v s ,σ2,h(x) is updated;

[0032] 6.4 Repeat steps 6.2 and 6.3 repeatedly to continuously update the parameter f C , f s , v s ,σ2,h(x).

[0033] Furthermore, the real-time correction of the friction model parameters by the recursive least squares method also includes a step of reducing the length of the friction torque data used by the recursive least squares method, specifically: establishing a servo control system model in Simulink; then, by setting friction torque signals of different time lengths, recording the residual sum of squares (Fmodel-Fmeasure) of the servo control system model output Fmodel and the experimental measurement value Fmeasure under different signal lengths. ^2 , when the residual tends to be stable, select the friction torque data length at this time.

[0034] The present invention also provides an online identification system for friction model parameters of a servo feed system. The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it executes the online identification method for friction model parameters of a servo feed system as described above.

[0035] The present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the online identification method of the friction model parameters of the servo feed system as described above.

[0036] In general, compared with the prior art, the above technical solution conceived by the present invention has the following advantages in the online identification method and device of the friction model parameters of the servo feed system provided by the present invention:

[0037] Beneficial effects:

[0038] 1. The present invention adds position-related terms to the traditional model. The position-related terms take into account the feed position and positive and negative directions of the drive shaft, describe the nonlinear friction behavior of the mechanical axis at a long stroke, realize the long-term correction of the friction model, and improve the accuracy, which is conducive to better reducing the impact of friction on the control accuracy of CNC machine tools, and avoids the traditional friction model ignoring the impact of position-related friction caused by manufacturing errors, misalignment and environment.

[0039] 2. The recursive least squares method is used to adaptively update the friction model parameters. The real-time collected data is used to enhance the adaptability of the friction model under different operating and environmental conditions, and the online identification and updating of the friction model parameters are realized.

[0040] 3. The data length used by RLS is limited to update the friction model parameters with less real-time friction torque data. By reducing the input data points and the scale of matrix calculation, the operating efficiency of the RLS algorithm is improved, the time overhead of data processing is reduced, and it is suitable for implementation in real-time systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a flow chart of an online identification method of friction model parameters of a servo feed system provided by the present invention;

[0042] Figure 2 It is a schematic diagram of the Simulink simulation model of the feeding system;

[0043] Figure 3 It is a schematic diagram of the three-loop control structure of the feed system;

[0044] Figure 4 It is the particle swarm algorithm identification flow chart. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0046] Friction has a great influence on the control accuracy of the servo feed system. Considering the influence of different working conditions and environmental conditions on the physical system during actual operation, this may lead to changes in system performance and failure of compensation based on the friction model. Especially in machines with long strokes and ball screws, the position dependence caused by spindle pitch error and assembly tolerance cannot be ignored. In order to make the friction model accurately reflect the physical entity, the present invention adds position-related terms to the traditional model. The position-related terms take into account the feed position and positive and negative directions of the drive shaft. RLS (recursive least squares) can update the friction parameters according to the current small amount of friction torque.

[0047] See also Figure 1 , Figure 2 , Figure 3 and Figure 4The online identification method of the friction model parameters of a servo feed system provided by the present invention mainly comprises the following steps:

[0048] Step 1: Add the position-related term h(x) to the traditional friction model to obtain the friction model of the servo feed system.

[0050] A position-dependent term h(x) is added, which takes into account the feed position and positive and negative directions of the drive axis.

[0051] The expression of the friction model is:

[0052]

[0053] In the formula, F fric represents the total friction force calculated by the model, f C represents Coulomb friction, sgn(v) represents the sign function of velocity, which takes values ​​of +1 (positive motion), -1 (negative motion) or 0 (stationary), f s represents the adhesive friction, v represents the relative speed, and v s represents the Stribeck velocity, which defines the transition speed between Coulomb friction and adhesive friction. σ2 represents the viscous friction coefficient, which is used to represent the linear relationship between speed and friction. h(x) represents the position-related term, x represents the position of the drive shaft, which is the input variable of the position-related term. The function h(x) has no fixed expression and is used to describe the nonlinear behavior of friction force related to the position and direction of the drive shaft.

[0054] Step 2: Based on the experimental data, the experimental Stribeck curve of the friction torque of the servo drive system at different speeds and positions is obtained.

[0055] Experimental data collection is carried out on the servo feed workbench. The friction torque of the workbench corresponding to a series of speed positions from low speed to high speed is collected. The stable friction torque of the corresponding uniform speed section is extracted from the obtained experimental data, and the Stribeck curve of the friction torque of the servo drive system at different speed positions is obtained.

[0056] Step three, input different positions x and different speeds v corresponding to the experimental data into the friction model, and the friction model is fitted to obtain friction model parameters and a fitted Stribeck curve. At the same time, a particle swarm algorithm is used to adjust the friction model parameters until the friction model parameters that minimize the error between the experimental Stribeck curve and the fitted Stribeck curve are found.

[0057] After obtaining the Stribeck curve of the friction torque of the servo drive system at different speeds and positions, the friction model Due to different input positions x and different speeds v, different friction torques F will be obtained. fric，ss Data, using heuristic algorithm - particle swarm algorithm, constantly C , f s , v s , σ2, h(x) and other parameters are adjusted so that the formula e stat =(F sr(v) -F fric，ss ) 2 Minimum error, F sr(v) is the Stribeck curve obtained by experiment, F fric，ss is the fitted Stribeck curve. When the error e stat When it is minimum, get f C , f s , v s ,σ2,h(x) and other parameters.

[0058] The steps of using particle swarm algorithm to correct the friction model parameters are as follows:

[0059] 5.1 Initializing friction model parameters f C , f s , v s ,σ2,h(x), determine the appropriate search space, and initialize the parameters position and velocity.

[0060] 5.2 Set a suitable fitness function and use it to determine whether the parameter position is optimal at this time.

[0061] 5.3 If the current position of the parameter is better than the best position of the individual, the best position of the individual is replaced by the current position.

[0062] 5.4 Continuously update the parameters of speed and position.

[0063] 5.5 Repeat steps 5.3 and 5.4, and continue to iterate until the maximum number of iterations or the fitness function reaches the optimal value and no longer decreases. At this time, f C , f s , v s , σ2, h(x) and other friction parameters.

[0064] Step 4: Use recursive least squares method to correct the friction model parameters in real time to achieve real-time identification of the friction model parameters.

[0065] RLS (recursive least squares method) is used to continuously correct the friction parameters to achieve real-time identification of the friction parameters. RLS is an online real-time update algorithm that is used to recursively estimate the friction model parameters through the gradual input of new data to minimize the sum of square errors between the model output and the actual observed values. It can efficiently process real-time data and is suitable for parameter identification and adaptive control of dynamic systems.

[0066] The core calculation process of RLS is to obtain the error:

[0067] e(t)=y(t)-φ(t) T θ(t-1),

[0068] Where y(t) is the actual observation value; φ(t) is the input data (regression vector); θ(t-1) is the estimated value of the model parameters at the previous moment.

[0069]

[0070] Parameter vector update: θ(t) = θ(t-1) + K(t)e(t)

[0071] Where λ is the forgetting factor, which is used to weigh the impact of historical data and new data and ranges from 0 to 1. P(t-1) is the initial value of the covariance matrix P(t-1) at the previous moment, which is generally set to a diagonal matrix with all diagonal elements taking a large positive number.

[0072] The correction steps of friction model parameters are:

[0073] 6.1. The servo drive system will identify the friction parameter f at a certain working speed v and running distance x C , f s , v s ,σ2,h(x) are used as the original parameters of the friction equation.

[0074] 6.2. Use displacement sensors and speed sensors to collect the speed v and running distance x of the servo transmission system in real time, substitute v and x into the friction model, and obtain the model friction torque prediction value F1.

[0075] 6.3 Use the torque sensor to directly obtain the friction torque F2 of the current servo transmission system, calculate the error e(t) through RLS, calculate the gain vector, and then C , f s , v s , σ2, h(x) and other parameters are updated.

[0076] 6.4 Repeat steps 6.2 and 6.3 repeatedly to continuously update the parameter f C , f s , v s,σ2,h(x).

[0077] In this step, the length of the friction torque data used by RLS is also reduced to improve the efficiency and speed of online identification. The specific operations are as follows:

[0078] 7.1 By analyzing the system composition of the experimental workbench, simplifying its control system and mechanical transmission system, and establishing a servo control system model in Simulink. Because Simulink simulation can run a variety of experiments in a virtual environment, it reduces the cost of the experiment.

[0079] 7.2 By setting the friction torque signal of different time lengths, record the residual sum of squares (Fmodel-Fmeasure) of the servo control system model output Fmodel and the experimental measurement value Fmeasure under different signal lengths. ^2 , when the residual tends to be stable, select the input signal time length at this time.

[0080] The present invention also provides an online identification system for friction model parameters of a servo feed system. The system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it executes the online identification method for friction model parameters of a servo feed system as described above.

[0081] The present invention also provides a computer-readable storage medium, which stores machine-executable instructions. When the machine-executable instructions are called and executed by a processor, the machine-executable instructions prompt the processor to implement the online identification method of the friction model parameters of the servo feed system as described above.

[0082] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. An online identification method for friction model parameters of a servo feed system, characterized in that: The identification method comprises the following steps: (1) The position-related term h(x) is added to the traditional friction model to obtain the friction model of the servo feed system; (2) Based on experimental data, obtain the experimental Stribeck curve of the friction torque of the servo drive system at different speeds and positions; (3) inputting different positions x and different speeds v corresponding to the experimental data into the friction model, fitting the friction model to obtain friction model parameters and a fitted Stribeck curve, and adjusting the friction model parameters by using a particle swarm algorithm until finding the friction model parameters that minimize the error between the experimental Stribeck curve and the fitted Stribeck curve; (4) The recursive least squares method is used to perform real-time correction on the friction model parameters to achieve real-time identification of the friction model parameters.

2. The method for online identification of friction model parameters of a servo feed system according to claim 1, characterized in that: The expression of the friction model is: In the formula, F fric represents the total friction force calculated by the model, f C represents Coulomb friction, sgn(v) represents the sign function of velocity, which takes values ​​of +1, -1 or 0, and f s represents the adhesive friction, v represents the relative speed, and v s represents the Stribeck speed, which defines the transition speed between Coulomb friction and adhesive friction; σ2 represents the viscous friction coefficient, which is used to express the linear relationship between speed and friction; h(x) represents the position-related term, and x represents the position of the drive shaft.

3. The method for online identification of friction model parameters of a servo feed system according to claim 1, characterized in that: Experimental data collection is carried out on the servo feed workbench, and the friction torque of the workbench corresponding to a series of speed positions is collected at the speed position. The stable friction torque of the corresponding uniform speed section is extracted from the obtained experimental data, and the experimental Stribeck curve of the friction torque of the servo drive system at different speed positions is obtained.

4. The method for online identification of friction model parameters of a servo feed system according to claim 2, characterized in that: The steps of using particle swarm algorithm to correct the friction model parameters are as follows: 5.1 Initializing friction model parameters f C , f s , v s ,σ2,h(x), determine the search space and initialize the parameters position and velocity; 5.2 Set the fitness function and use it to determine whether the parameter position is optimal at this time; 5.3 If the current position of the parameter is better than the best position of the individual, the best position of the individual is replaced by the current position; 5.4 Continuously update the parameters of speed and position; 5.5 Repeat steps 5.3 and 5.4, and continue to iterate until the maximum number of iterations or the fitness function reaches the optimal value and no longer decreases. At this time, the friction model parameter f is obtained. C , f s , v s ,σ2,h(x).

5. The method for online identification of friction model parameters of a servo feed system according to claim 1, characterized in that: One of the calculation processes of the recursive least squares method is to obtain the error: e(t)=y(t)-φ(t) T θ(t-1), Where y(t) is the actual observation value; φ(t) is the input data; θ(t-1) is the estimated value of the model parameter at the previous moment.

6. The method for online identification of friction model parameters of a servo feed system according to claim 5, characterized in that: Gain vector update used by recursive least squares Parameter vector update: θ(t)=θ(t-1)+K(t)e(t); Where λ is the forgetting factor, which is used to weigh the impact of historical data and new data and ranges from 0 to 1. P(t-1) is the initial value of the covariance matrix P(t-1) at the previous moment.

7. The method for online identification of friction model parameters of a servo feed system according to claim 6, characterized in that: The correction steps of friction model parameters are: 6.

1. The servo drive system will identify the friction parameter f at a certain working speed v and running distance x C , f s , v s ,σ2,h(x) as the original parameters of the friction equation; 6.

2. Use displacement sensors and speed sensors to collect the speed v and running distance x of the servo transmission system in real time, substitute v and x into the friction model, and obtain the model friction torque prediction value F1; 6.3 Use the torque sensor to directly obtain the friction torque F2 of the current servo transmission system, calculate the error e(t) through RLS, calculate the gain vector, and then C , f s , v s ,σ2,h(x) is updated; 6.4 Repeat steps 6.2 and 6.3 repeatedly to continuously update the parameter f C , f s , v s ,σ2,h(x).

8. The method for online identification of friction model parameters of a servo feed system according to claim 1, characterized in that: The real-time correction of friction model parameters by recursive least square method also includes the step of reducing the length of friction torque data used by recursive least square method, specifically: establishing a servo control system model in Simulink; then, by setting friction torque signals of different time lengths, recording the residual sum of squares (Fmodel-Fmeasure) of the servo control system model output Fmodel and the experimental measurement value Fmeasure under different signal lengths. ^2 , when the residual tends to be stable, select the friction torque data length at this time.

9. An online identification system for friction model parameters of a servo feed system, characterized in that: The system includes a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, the online identification method of the friction model parameters of the servo feed system according to any one of claims 1 to 8 is executed.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions. When the machine-executable instructions are called and executed by the processor, the machine-executable instructions prompt the processor to implement the online identification method of the friction model parameters of the servo feed system according to any one of claims 1-8.

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