Drive system feedforward control method based on improved LuGre friction model

Abstract

The application provides a drive system feedforward control method based on an improved LuGre friction model, improves a traditional LuGre friction model, combines a smooth transition function with the traditional LuGre friction model, combines the model with a zero speed cross window, and provides an improved LuGre friction model, which realizes the characterization of the asymmetry of the friction force, suppresses the friction force oscillation near zero speed, and further improves the tracking accuracy of the ball screw drive system. The application solves the problem that the traditional LuGre friction model is discontinuous once the asymmetry of the friction is described, reduces the "reverse response" of the feed system at the reversing position, and effectively weakens the friction force oscillation phenomenon near zero speed through the zero speed cross window, and improves the robustness of the friction model.

Description

Technical Field

[0001] This invention relates to the field of mechanical design and manufacturing, specifically to a feedforward control method for a drive system based on an improved LuGre friction model, which is used to improve the drive system's ability to suppress frictional disturbances. Background Technology

[0002] In recent years, with the increasing national investment in the research and development of domestically produced high-end CNC machining equipment, domestic CNC technology has greatly improved. The demand for high-precision machining and high-speed movement is growing. How to achieve a balance between high precision, high speed, and cost control is a crucial issue for the sustainable development of domestically produced high-end CNC machining equipment. Simply focusing on mechanical structure will lead to a significant increase in costs and will quickly encounter precision bottlenecks. Therefore, improving the control algorithm of the CNC system is a better solution.

[0003] Currently, most high-end CNC machine tools still primarily use ball screw drives. During operation, these drive systems are affected by frictional disturbances. If these disturbances cannot be effectively suppressed, the motion accuracy of the drive system will decrease, consequently affecting the machining quality of the products. To address this, researchers have proposed various control strategies. Friction model-based control strategies, due to their comprehensive description of frictional characteristics and ease of integration with other control structures, have been widely applied to drive systems. However, while these strategies reduce commutation errors, they also introduce new errors ("inverse response"). The proposed solutions to this "inverse response" primarily involve using unit pulses for driving, but the amplitude of these pulse signals places extremely stringent requirements on the identification of the mechanical system model. Therefore, these methods remain theoretical and are difficult to apply in practical engineering. Summary of the Invention

[0004] To address the problems existing in the prior art, reduce the impact of frictional interference on the performance of the drive system, reduce the "inverse response" caused by frictional compensation, and facilitate practical engineering applications, this invention proposes a feedforward control method for the drive system based on an improved LuGre friction model. This method can improve the tracking performance of the drive system and has significant engineering application value for improving the machining accuracy and efficiency of machine tools.

[0005] The technical solution of this invention is as follows:

[0006] A feedforward control method for a drive system based on an improved LuGre friction model includes the following steps:

[0007] Step 1: Establish an improved LuGre friction model for the machining drive system:

[0008]

[0009] The improved LuGre friction model adopts a bristle model; where Ff Friction force; v refers to the relative velocity between the contact surfaces; z refers to the average deformation of the bristles. σ0 refers to the rate at which the average deformation of the bristles changes over time; σ0 refers to the bristle stiffness; σ1 refers to the bristle damping; f v The damping of the lubricant between the contact surfaces; η1 is the conditional expression for solving the zero-velocity oscillation problem; v w λ and ε are intermediate variables, g(v) is a continuous Stribeck curve that is asymmetric about the origin;

[0010] Step 2: Perform actual sampling on the drive system. Based on the sampling data, identify the parameters of the improved LuGre friction model established in Step 1 to obtain the identified improved LuGre friction model.

[0011] Step 3: Use the improved LuGre friction model obtained in Step 2 to perform feedforward control of the drive system.

[0012] Furthermore, the expression for the continuous Stribeck curve g(v) that is asymmetric about the origin is as follows:

[0013] g(v)=g + (v)η Av (v)-g - (v)η Bv (v)

[0014] Where η Av (v) represents a positive smooth transition function; η Bv (v) represents a negative smooth transition function; g + (v) represents a positive, continuous Stribeck curve; g - (v) represents a negative continuous Stribeck curve.

[0015] Furthermore, the smooth transition function is constructed using the hyperbolic tangent function, where:

[0016] η Av (v) = 0.5tanh(ξv) + 0.5

[0017] η Bv (v)=η Av (v)-1

[0018] ξ represents the magnitude of the slope of the transition curve.

[0019] Furthermore, the positive continuous Stribeck curve g + (v) is:

[0020] g + (v)=γ 1+[tanh(γ 2+ v)-tanh(γ 3+ v)]+γ 4+ tanh(γ 5+ v)+γ 6+ v

[0021] The negative continuous Stribeck curve is

[0022] g - (v)=γ 1- [tanh(γ 2- v)-tanh(γ 3- v)]+γ 4- tanh(γ 5- v)+γ 6- v

[0023] Where γ 1+ ~γ 6+ Represents the parameters of the positive continuous Stribeck model; γ 1- ~γ 6- This represents the parameters of the negative continuous Stribeck model.

[0024] Furthermore, in step 2, the identification process is divided into first identifying static parameters and then identifying dynamic parameters; where the static parameters are the Stribeck model parameters in the continuous Stribeck curve; and the dynamic parameters are λ, ε, ξ, σ0 and σ1.

[0025] Furthermore, the static parameters are identified as follows:

[0026] First, gradually increase the voltage of the machining drive system until the system's worktable shows visible movement. Based on the voltage at this point, the driving force is converted into the maximum static friction force.

[0027] Secondly, given multiple different speed values, voltage is applied to the machining drive system so that the feedback speed of the system's worktable reaches the set speed value. The voltage values ​​corresponding to different speed values ​​are obtained, and the voltage values ​​are converted into frictional force to obtain speed-frictional force data.

[0028] The parameters of the Stribeck model were identified by fitting velocity-friction data.

[0029] Furthermore, an optimization algorithm is used for dynamic parameter identification:

[0030] First, the improved LuGre friction model is discretized:

[0031]

[0032] Secondly, set the sampling time ΔT and the initial conditions z(0) and Input the corresponding velocity v(k) to obtain the corresponding LuGre friction force F. f (k); The friction force estimation error is set to be...

[0033] e(k)=F rf (k)-F if (k)

[0034] by

[0035]

[0036] Let F be the objective function. if (k) represents the frictional force obtained by converting the voltage value at the corresponding speed, and N represents the number of speed values ​​set.

[0037] Furthermore, based on the above method, the present invention also proposes a computer-readable storage medium and system.

[0038] One of the computer-readable storage media stores computer-executable instructions, which, when executed, are used to implement the above-described method.

[0039] A computer system includes: one or more processors, and a computer-readable storage medium for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the above-described method.

[0040] Beneficial effects

[0041] This invention improves the traditional LuGre friction model by combining a smooth transition function with the traditional LuGre friction model and by combining the model with a zero-velocity cross window, thus proposing an improved LuGre friction model. This model not only represents the asymmetry of friction force but also suppresses friction force oscillations near zero velocity, further improving the tracking accuracy of the ball screw drive system.

[0042] This invention has the following two advantages:

[0043] 1. It solves the problem that the traditional LuGre friction model becomes discontinuous once it describes frictional asymmetry, and reduces the "inverse response" of the feed system at the reversal point.

[0044] 2. The zero-velocity cross window effectively reduces the frictional oscillation phenomenon near zero velocity and improves the robustness of the friction model.

[0045] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0046] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0047] Figure 1 The figures show a comparison of the Stribeck curves of the improved LuGre friction model and the traditional LuGre friction model; (a) Stribeck curve of the continuous LuGre model; (b) Stribeck curve of the improved LuGre model.

[0048] Figure 2 This is a comparison of different smooth transition functions when the smooth transition rate is 1.

[0049] Figure 3 The effects of zero-velocity window parameter changes on the curve are compared: (a) the effect of parameter ε; (b) the effect of parameter λ.

[0050] Figure 4 This is a comparison chart of the predicted friction force between classic LuGre and improved LuGre;

[0051] Figure 5 This is a diagram of the experimental scheme for the drive system control strategy;

[0052] Figure 6 Comparison of experimental results; (a) Actual trajectory diagram; (b) Error curve diagram; (c) Enlarged view of a part. Detailed Implementation

[0053] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0054] For high-end CNC equipment driven by ball screws, including turret lathes, tool lathes, slitting lathes, machining centers, grinding machines, and various other equipment requiring precision transmission, in order to reduce the impact of frictional interference on the performance of the drive system and reduce the "inverse response" caused by frictional compensation, while also facilitating practical engineering applications, this embodiment proposes a feedforward control method for the drive system based on an improved LuGre friction model. This method can improve the tracking performance of the drive system and has significant engineering application value for improving the machining accuracy and efficiency of machine tools.

[0055] Specifically, the following steps are included:

[0056] Step 1: Establish an improved LuGre friction model for the machining drive system.

[0057] The research process for establishing the improved LuGre friction model is presented here:

[0058] The basic inventive concept of improving the LuGre friction model is: in order to effectively suppress the interference caused by nonlinear friction and the inverse response generated by friction compensation, the traditional LuGre model is combined with a smooth transition function and a zero velocity window, thereby realizing the continuous switching of the forward and reverse friction forces and better robustness.

[0059] (1) Design a smooth transition function

[0060] The asymmetry of friction models is typically represented using piecewise functions, leading to a contradiction between model continuity and frictional asymmetry. Therefore, to address the inability of continuous LuGre models to describe frictional asymmetry, a smooth transition function is combined with the continuous LuGre friction model to achieve a smooth transition between forward and reverse friction forces. A new model based on the bristle model is constructed as follows:

[0061]

[0062] In equation (1), F f Friction force; v refers to the relative velocity between the contact surfaces; z refers to the average deformation of the bristles; z also refers to the rate of change of the average deformation of the bristles over time; σ0 refers to the bristle stiffness; σ1 refers to the bristle damping; f v The resistance of the lubricant between the contact surfaces is referred to as the damping; g(v) is the newly constructed continuous Stribeck curve that is asymmetric about the origin.

[0063] The traditional continuous Stribeck function is

[0064] γ1[tanh(γ2v)-tanh(γ3v)]+γ4tanh(γ5v)+γ6v

[0065] Where γ1[tanh(γ2v)-tanh(γ3v)] represents the Stribeck effect; γ4tanh(γ5v) represents Coulomb friction; and γ6v represents viscous friction. To achieve a smooth transition between forward and reverse friction forces, we splice the continuous Stribeck curves of both directions to obtain a continuous Stribeck curve that is asymmetric about the origin, as expressed below:

[0066] g(v)=g + (v)η Av (v)-g - (v)η Bv (v) (2)

[0067] g + (v)=γ 1+ [tanh(γ 2+ v)-tanh(γ 3+ v)]+γ 4+ tanh(γ 5+v)+γ 6+ v (3)

[0068] g - (v)=γ 1- [tanh(γ 2- v)-tanh(γ 3- v)]+γ 4- tanh(γ 5- v)+γ 6- v (4)

[0069] In equations (2) to (4), g + (v) represents a positive, continuous Stribeck curve; g - (v) represents a negative continuous Stribeck curve; η Av (v) represents a positive smooth transition function; η Bv (v) represents a negative smooth transition function; γ 1+ ~γ 6+ Represents the parameters of the positive continuous Stribeck model; γ 1- ~γ 6- The parameters represent the negative continuous Stribeck model; Table 1 shows several common smooth transition functions, where ξ represents the slope of the transition curve.

[0070] Table 1 Three common transition functions

[0071]

[0072] As the velocity approaches positive infinity, the continuous Stribeck curve g(v), which is asymmetric about the origin, degenerates into gi. + (v).

[0073] η Av =0.5 + 0.5 = 1, η Bv =η Av -1 = 0 (5)

[0074] g(v)=g + (v)η Av (v)-g - (v)η Bv (v)=g + (v) (6)

[0075] As the velocity approaches negative infinity, the continuous Stribeck curve g(v), which is asymmetric about the origin, degenerates into gi. - (v).

[0076] η Av =-0.5+0.5=0, η Bv =η Av-1 = -1 (7)

[0077] g(v)=g + (v)η Av (v)-g - (v)η Bv (v)=g - (v) (8)

[0078] from Figure 1 It can be seen that, due to the origin symmetry of the hyperbolic tangent function, the continuous friction model cannot express the asymmetry of friction, while the improved LuGre friction model achieves the characterization of friction asymmetry while ensuring the continuous differentiability of the friction curve.

[0079] Figure 2 Three common smoothing transition functions are used to smooth the transition rate ξ = 1. The hyperbolic tangent function has the largest transition sharpness, while the exponential function has the smallest. The magnitude of the transition sharpness determines the speed at which the friction force switches between forward and reverse directions. Ideally, a larger transition sharpness will make the friction model more accurate, but in reality, the time delay and control step size of the drive system limit its value from being too large.

[0080] (2) Zero-speed cross window modeling

[0081] Velocity signal noise near zero velocity can cause oscillations in the classic LuGre friction model during velocity reversal. Therefore, this embodiment establishes a zero-velocity cross-window to improve the robustness of the LuGre friction model. The improved LuGre model combining the zero-velocity cross-window with a smooth transition function is as follows:

[0082]

[0083] In equation (9), both the improved LuGre model and the traditional LuGre model adopt the bristle model, where η1 is the conditional expression for solving the zero-velocity oscillation problem; v w λ is the window velocity, ε is the window slope parameter, and ε is the window width parameter; for example Figure 3 As shown in (a), the larger ε is, the wider the zero-velocity cross-window, while the smaller ε is, the narrower the zero-velocity cross-window. Figure 3 As shown in (b), the parameter λ sets the slope angle of the curve. The larger λ is, the gentler the curve is, and the smaller λ is, the steeper the curve is.

[0084] Depend on Figure 3It can be seen that the zero-velocity cross-window consists of three stages: the zero-velocity stage, the transition stage, and the steady-state stage. The window value η1 is 0 in the zero-velocity stage and stabilizes at 1 after the transition stage. Therefore, the zero-velocity cross-window can also be understood as the opening and closing of the bristle deformation rate; that is, the bristle deformation rate is zero in the zero-velocity stage, while it gradually increases to a normal value in the transition stage. Subsequently, the zero-velocity cross-window has no effect on the friction force prediction. It is precisely because of this characteristic of the zero-velocity cross-window that the improved LuGre friction model's resistance to interference near zero velocity is significantly enhanced.

[0085] Depend on Figure 4 It is evident that the improved LuGre friction model integrating a zero-velocity cross-window performs better in resisting oscillations than the classic LuGre friction model, but this comes at the cost of sacrificing some accuracy in friction force calculation. Therefore, a balance must be struck between the accuracy of friction force estimation and model oscillations when selecting the cross-window parameters. In this embodiment, the cross-window parameters ε are set to 0.4 and λ to 9.

[0086] In summary, the improved LuGre friction model proposed in this embodiment can represent the Stribeck effect using a continuously differentiable function, and has the following three advantages: ① The improved LuGre model can describe friction curves with different forward and reverse friction forces; ② The zero-velocity cross-window is combined with the improved LuGre model to reduce model oscillations; ③ The improved LuGre model can avoid force spikes during directional motion.

[0087] Step 2: After establishing the improved LuGre friction model, the parameters of the model need to be identified based on the actual sampling data of the drive system to obtain the identified improved LuGre friction model.

[0088] To obtain accurate friction model parameters, the identification process is divided into two stages: first, static parameter identification, and then dynamic parameter identification. The static parameters are the Stribeck model parameters in the continuous Stribeck curve; the dynamic parameters are λ, ε, ξ, σ0, and σ1.

[0089] The static parameter identification process is as follows:

[0090] First, gradually increase the voltage of the machining drive system until the system's worktable shows visible movement. Based on the voltage at this point, multiply it by the force-to-electricity conversion coefficient to obtain the driving force, which is the maximum static friction force.

[0091] Next, given multiple sets of different speed values ​​(v = [±0.5, ±1, ±3, ±5, ±8, ±10, ±12, ±15, ±20, ±25], unit: mm / s), voltage is applied to the machining drive system to make the feedback speed of the system's worktable reach the set speed value, and the voltage values ​​corresponding to different speed values ​​are obtained. The voltage values ​​are converted into frictional force using the relationship F = U × B × 2π / 0.006 (where U is the control voltage, unit: V; F is the frictional force, unit: N; B is the motor torque constant, unit: Nm / A; 0.006 is the lead screw, unit: m), and the speed-frictional force data are obtained. The speed-frictional force data are plotted in the XY coordinate system, and the experimental results are fitted using the least squares method to identify the Stribeck model parameters.

[0092] Dynamic parameter identification is performed using a genetic optimization algorithm:

[0093] First, the improved LuGre friction model is discretized:

[0094]

[0095] Secondly, the sampling time ΔT = 0.0001s and the initial conditions z(0) = 0 and Input the corresponding velocity v(k) to obtain the corresponding LuGre friction force F. f (k); The friction force estimation error is set to be...

[0096] e(k)=F rf (k)-F if (k)

[0097] by

[0098]

[0099] Let F be the objective function. if (k) represents the frictional force obtained by converting the voltage value at the corresponding speed, and N represents the number of speed values ​​set.

[0100] The genetic optimization algorithm is used to optimize and obtain the minimum value of the objective function, thereby obtaining the optimal predicted parameters.

[0101] Next, we will conduct an improved LuGre friction feedforward experiment to verify the results.

[0102] In the experiment, the drive table used in this invention mainly includes an INOVANCE servo drive (drive model: IS620-S5R5, matching motor model: MS1H3-13C15CB), a ball screw table, and a Heidenhain linear encoder (encoder model: LS177, encoder resolution: 0.1μm, signal: TTL differential). The servo drive motor is equipped with an absolute rotary encoder, and the servo drive I / O port can convert the absolute encoder signal of the motor into an incremental differential signal. The number of TTL pulses output per minute can be customized. This invention adopts a model-based feedforward control strategy, such as... Figure 5 As shown. To verify the feasibility and effectiveness of the proposed improved LuGre friction model, both the classic LuGre friction model and the improved LuGre friction model were used. The actual compensation effect of the model was verified while ensuring that the feedforward P / PI parameters were the same.

[0103] Figure 6 Experimental results for feedforward P / PI cascade control and frictional feedforward control are presented. Figure 6 It can be seen that, compared with the traditional LuGre friction model, the improved LuGre friction model can effectively reduce the "inverse response" and improve the motion control performance of the drive system. For ease of observation and analysis, the experimental results are summarized in Table 2. Table 2 shows that, compared with the traditional LuGre friction model, the improved LuGre friction model reduces the maximum error by 5.2%, the mean error by 4.3%, and the root mean square error by 35.4%.

[0104] Table 2 Comparison of control performance between classic LuGre friction feedforward and improved LuGre friction feedforward

[0105]

[0106] It can be seen that the feedforward control strategy based on the improved LuGre friction model has the following two advantages: (1) the improved LuGre friction feedforward control has a smaller maximum error; (2) it solves the contradiction between friction asymmetry and friction continuous differentiability, and effectively reduces the "inverse response" caused by friction compensation.

[0107] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A feedforward control method for a drive system based on an improved LuGre friction model, characterized in that: Includes the following steps: Step 1: Establish an improved LuGre friction model for the machining drive system: The improved LuGre friction model adopts a bristle model; wherein Friction The relative velocity between the contact surfaces; The average amount of deformation of the bristles; This refers to how quickly the average deformation of the bristles changes over time. Refers to the stiffness of the bristles; Refers to bristle damping; The damping of the lubricant between contact surfaces; The conditional expression for solving the zero-velocity oscillation problem; As an intermediate variable, and For model parameters, The continuous Stribeck curve is asymmetric about the origin; the drive system is a ball screw drive system; the continuous Stribeck curve is asymmetric about the origin. The expression is as follows: in This represents a positive smooth transition function; Represents a negative smooth transition function; Indicates a positive, continuous Stribeck curve; A continuous Stribeck curve indicating a negative direction; Step 2: Perform actual sampling on the drive system. Based on the sampling data, identify the parameters of the improved LuGre friction model established in Step 1 to obtain the identified improved LuGre friction model. Step 3: Use the improved LuGre friction model obtained in Step 2 to perform feedforward control of the drive system.

2. The feedforward control method for a drive system based on an improved LuGre friction model according to claim 1, characterized in that: The smooth transition function is constructed using the hyperbolic tangent function, where: This indicates the magnitude of the slope of the transition curve.

3. The feedforward control method for a drive system based on an improved LuGre friction model according to claim 1, characterized in that: Positive continuous Stribeck curve for: The negative continuous Stribeck curve is in Indicates the parameters of the positive continuous Stribeck model; This represents the parameters of the negative continuous Stribeck model.

4. The feedforward control method for a drive system based on an improved LuGre friction model according to claim 2, characterized in that: In step 2, the identification process is divided into two parts: first, static parameter identification, and then dynamic parameter identification; where the static parameters are the Stribeck model parameters in the continuous Stribeck curve; and the dynamic parameters are... , , , and .

5. The feedforward control method for a drive system based on an improved LuGre friction model according to claim 4, characterized in that: The static parameters are identified as follows: First, gradually increase the voltage of the machining drive system until the system's worktable shows visible movement. Based on the voltage at this point, the driving force is converted into the maximum static friction force. Secondly, given multiple different speed values, voltage is applied to the machining drive system so that the feedback speed of the system's worktable reaches the set speed value. The voltage values ​​corresponding to different speed values ​​are obtained, and the voltage values ​​are converted into frictional force to obtain speed-frictional force data. The parameters of the Stribeck model were identified by fitting velocity-friction data.

6. The feedforward control method for a drive system based on an improved LuGre friction model according to claim 4, characterized in that: Dynamic parameter identification is performed using an optimization algorithm: First, the improved LuGre friction model is discretized: Secondly, set the sampling time. and initial conditions and Enter the corresponding speed. The corresponding LuGre friction force is obtained. The friction force estimation error is set to be... by Let be the objective function. The frictional force is obtained by converting voltage values ​​at the corresponding speed, where N is the number of set speed values.

7. A computer-readable storage medium storing computer-executable instructions, characterized in that: When executed, the instructions are used to implement the method of any one of claims 1 to 6.

8. A computer system, characterized in that: include: One or more processors, a computer-readable storage medium, for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors cause the one or more processors to implement the method of any one of claims 1 to 6.

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