Parameter identification device and method based on lugre friction model

Abstract

The application discloses a parameter identification device and method based on a Lugre friction model. The method comprises the following steps: creating a PID closed-loop control system configured with the Lugre friction model, drawing a first characteristic curve of output rotating speed w and friction torque F fric ; identifying Coulomb friction and stribeck speed of the friction torque F fric according to the first characteristic curve; obtaining a peak voltage Umax input by a servo motor; inputting a speed extremely slowly changing identification voltage to the servo motor, the identification voltage rising from an initial voltage to the peak voltage Umax at first and then falling from the peak voltage Umax to a negative peak voltage Umax; obtaining a displacement S between the servo motor and a controlled object, and drawing a second characteristic curve of the displacement S and the identification voltage; identifying bristle stiffness coefficient σ0 according to the second characteristic curve; creating a current loop of the servo motor in the PID closed-loop control system; drawing a third characteristic curve of displacement response of the servo motor; and identifying bristle damping coefficient σ1 according to the third characteristic curve.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of servo control, in particular to a parameter identification method based on Lugre friction model. BACKGROUND

[0002] At present, there are many friction models applied in servo control system. According to the control objects and requirements, the models are inconsistent, and the corresponding friction compensation methods also have many ways. According to the literature reference, the classical Coulomb friction and viscous friction model cannot truly simulate the dynamic process of actual friction, so the friction compensation cannot achieve good results. SUMMARY

[0003] Based on this, the embodiment of the present application discloses at least one parameter identification method based on Lugre friction model. Through the method disclosed by the present application, based on the comprehensive analysis of the dynamic characteristics and static characteristics of the Lugre friction model, the parameters are effectively and accurately identified based on the characteristic curve, the identified parameter identification deviates from the initial set value, and the precision error caused by friction disturbance is suppressed.

[0004] In order to realize the above content, the method comprises:

[0005] S10, at least two input voltages are provided for a servo motor, and a viscous friction coefficient σ2 is obtained according to the output of the servo motor at different input voltages;

[0006] S21, a PID closed-loop control system configured with Lugre friction model is created, and motor parameters and rotational inertia of the controlled object of the PID closed-loop control system are obtained;

[0007] S22, a transfer function (G) of the input voltage and the output speed of the servo motor is obtained, and the friction torque F fric at the stable speed is calculated according to the transfer function (G), the motor parameters and the rotational inertia;

[0008] S23, a first characteristic curve of the output speed w and the friction torque F fric is drawn;

[0009] S24, the Coulomb friction and stribeck speed of the friction torque F fric are analyzed according to the first characteristic curve;

[0010] S31, the peak voltage Umax input by the servo motor is obtained;

[0011] S32, input a speed very slowly changing identification voltage to the servo motor, the identification voltage is raised from an initial voltage to the peak voltage Umax at first, and is descended from the peak voltage Umax to the negative peak voltage Umax at last;

[0012] S33, obtain the displacement S between the servo motor and the controlled object, and draw the second characteristic curve of the displacement S and the identification voltage;

[0013] S34, analyze the formula of the displacement S when the speed is very slowly changing according to the static friction characteristic;

[0014] S35, the rotating speed w=0 when the speed of the identification voltage is slowly changing, and calculate the bristle stiffness coefficient σ0 according to the formula of the known viscous friction coefficient σ2, the maximum static friction force Fs, the coulomb friction force Fc, the stribeck speed and the displacement S;

[0015] S41, create the current loop of the servo motor in the PID closed loop control system;

[0016] S42, provide a given desired current loop, and draw the third characteristic curve of the displacement response in the servo motor;

[0017] S43, obtain the peak time tm according to the third characteristic curve;

[0018] S44, calculate the bristle damping coefficient σ1 according to the peak time tm, the bristle stiffness coefficient σ0 and the viscous friction coefficient σ2.

[0019] The embodiment of the application discloses at least one parameter identification device based on Lugre friction model.

[0020] The device is applied to the PID closed loop control system configured with Lugre friction model;

[0021] The device comprises:

[0022] The viscous friction coefficient calculation module is used for providing at least two input voltages to the servo motor, and obtaining the viscous friction coefficient σ2 according to the output of the servo motor at different input voltages;

[0023] The friction torque calculation module is used for obtaining the motor parameters of the PID closed loop control system and the rotational inertia of the controlled object, obtaining the transfer function (G) of the input voltage and the output rotating speed of the servo motor, and calculating the friction torque F when the speed is stable according to the transfer function (G), the motor parameters and the rotational inertia fric ;

[0024] a first characteristic curve plotting module for plotting a first characteristic curve of the output rotating speed w and the friction torque F fric ;

[0025] a first characteristic curve analyzing module for analyzing the Coulomb friction and the stribeck speed of the friction torque F fric according to the first characteristic curve;

[0026] a second characteristic curve plotting module for obtaining a peak voltage Umax inputted by the servo motor; obtaining an identification voltage inputted by the servo motor at a very slow change of speed, the identification voltage being raised from an initial voltage to the peak voltage Umax at first, and then being lowered from the peak voltage Umax to the negative peak voltage Umax; obtaining a displacement S between the servo motor and the controlled object, and plotting a second characteristic curve of the displacement S and the identification voltage;

[0027] a second characteristic curve analyzing module for analyzing an equation of the displacement S at a very slow change of speed according to the static friction characteristic; the rotating speed w=0 at a slow change of the identification voltage, and the equation of the displacement S according to the known viscous friction coefficient σ2, the maximum static friction force Fs, the Coulomb friction Fc and the stribeck speed, and calculating the bristle stiffness coefficient σ0;

[0028] a third characteristic curve plotting module for creating a current loop of the servo motor in the PID closed loop control system; providing a given desired current loop, and plotting a third characteristic curve of the displacement response in the servo motor;

[0029] a third characteristic curve analyzing module for obtaining a peak time tm according to the third characteristic curve; and for calculating a bristle damping coefficient σ1 according to the peak time tm, the bristle stiffness coefficient σ0 and the viscous friction coefficient σ2.

[0030] In the above solutions, the exemplary embodiments of the present application are described in detail below with reference to the accompanying drawings, and other features and advantages of the embodiments of the present application are also made clear. BRIEF DESCRIPTION OF DRAWINGS

[0031] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly introduced below, and it should be understood that the following drawings only show some of the embodiments of the present application, and therefore should not be regarded as a limitation on the scope, and for those skilled in the art, other related drawings can also be obtained without creative labor.

[0032] Figure 1 The Simulink simulation model of Lugre friction in the embodiments is shown in the figure.

[0033] Figure 2 A graph of the relationship between displacement S and friction force for the example analysis of static friction hysteresis characteristics;

[0034] Figure 3 A graph of the transfer function response for the example analysis of static friction damping characteristics;

[0035] Figure 4 A graph of the input and output for the example analysis of Stribeck effect;

[0036] Figure 5 A graph of the input and output for the example analysis of friction hysteresis characteristics;

[0037] Figure 6 A physical simulation model for the example analysis of separation friction;

[0038] Figure 7 A graph of the input and output of separation friction for the example analysis of separation friction;

[0039] Figure 8 A graph of the relationship between the calculated friction torque and the actual friction torque under open loop for the method in the example;

[0040] Figure 9 A simulink simulation model of the PID speed closed loop for the method in the example;

[0041] Figure 10 A graph of the relationship between the calculated friction torque and the actual friction torque under closed loop for the method in the example;

[0042] Figure 11 A graph of the output rotational speed and friction torque for the method in the example;

[0043] Figure 12 A graph of the relationship between the input identification voltage and displacement for the method in the example;

[0044] Figure 13 A simulation model of the method in the example with the addition of a current loop in the PID closed loop control system;

[0045] Figure 14 A graph of the current step response for the method in the example;

[0046] Figure 15 A graph of the displacement step response for the method in the example. DETAILED DESCRIPTION

[0047] In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the application. Those skilled in the art will understand that the application can be practiced without such details. In other instances, well-known elements have been shown in block diagram form in order not to obscure the application in unnecessary detail. Additionally, for the most part, details concerning network communications, electromagnetic signaling techniques, user interfaces, and the like, have been omitted inasmuch as such details are not considered necessary to obtain a complete understanding of the application, and are considered within the scope of

[0048] Those skilled in the art will appreciate that the application can be embodied in a system, a method, or a computer program product. Accordingly, the application can take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, microcode, etc.) or an embodiment combining software and hardware aspects that can all generally be referred to herein as a "circuit," "module" or "system." Furthermore, the application can take the form of a computer program product on any tangible medium of expression having computer-usable program code embodied in the medium.

[0049] The embodiment discloses a parameter identification method based on Lugre friction model. The steps of the method are implemented at least in a combination of a server and a display device.

[0050] The server generally includes a memory and a processor. The memory mainly includes a program storage area and a data storage area. The program storage area can store an operating system (such as an Android operating system, referred to as "Android system", or an iOS operating system, or other operating systems, which can also be referred to as "system"), at least one application required by a function (such as a sound playing function, an image playing function, etc.), and programs related to the embodiment. The data storage area can store data created according to the use of the terminal 300, including related setting information or use condition information of the application displayed on the display screen, etc. In addition, the memory can include a high-speed random access memory, and can also include a non-volatile memory, such as at least one magnetic disk storage device, a flash memory device, and other volatile solid-state memory devices. The processor provides a high-speed computing capability, and can call and execute the programs stored in the memory.

[0051] The display screen can be used to display information input by a user or information provided to the user and various applications installed on the electronic terminal. The display screen can include a display panel, which can be configured in the form of a liquid crystal display (LCD), an organic light-emitting diode (OLED), or the like. Further, a touch panel can cover the display panel, and when the touch panel detects a touch operation thereon or in the vicinity thereof, the touch panel transmits the same to the processor to determine the type of the touch event, and then the processor provides a corresponding visual output on the display panel according to the type of the touch event.

[0052] It should be noted that in the Lugre friction model, Z represents the average deformation of the bristles, and is expressed as where w is the angular velocity of the servo motor.

[0053] At this time, the deformation of the bristles is expressed as

[0054] At this time, the deformation of the bristles is expressed as

[0055] where sgn(w) is a sign function, and g(w) is a function that always outputs a positive value and is not a symmetric function with respect to the speed. The factors affecting the g(w) function include, but are not limited to, the material of the contact surface, whether a lubricant is added, the temperature, etc., and as the speed increases, the g(w) function has a monotonically decreasing output trend.

[0056] It is known that the Lugre friction model is expressed as

[0057] where σ0 is the stiffness coefficient of the bristles, Fc is the Coulomb friction force, Fs is the maximum static friction force, and ws is the Stribeck speed.

[0058] At the same time, the friction force F fric in the Lugre friction model is related to the bending degree of the bristles, and is expressed as where σ1 is the damping coefficient of the bristles.

[0059] In addition, the friction force F fric in the Lugre friction model is proportional to the relative speed of the contact surface of the servo motor and the controlled object, i.e., there is a viscous characteristic of dynamic friction, and the sum of the static friction force and the dynamic friction force is expressed as

[0060] where σ2 is the viscous friction coefficient.

[0061] Based on this, at the time of speed stabilization, the friction force F fricmay be equivalently represented as,

[0062]

[0063] Further, according to Figure 1 Simulink simulation model of Lugre friction force. The Lugre friction model in the table is parameterized in this embodiment.

[0064]

[0065] Based on this, the static friction hysteresis characteristics are analyzed in this embodiment.

[0066] When the force applied between the two contact surfaces of the servo motor and the controlled object is less than the maximum static friction force, the static friction force is equivalent to a spring, and the two contact surfaces will not slide relative to each other, but there is a relative displacement.

[0067] Then according to the average deformation of the bristles, that is,

[0068] When w>0,

[0069] When w<0,

[0070] Based on this,

[0071] That is,

[0072] When the applied force is stable, no sliding occurs between the two contact surfaces under the action of static friction. Therefore, the angular velocity w of the motor tends to 0; At this time, g(w) can be regarded as a constant a, and the bristle deformation dz / dt is equal to 0.

[0073] Then there is,

[0074] Therefore,

[0075] When s=0, the friction force F fric is 0 and b1=0.

[0076] At this time, a slowly changing force is applied, and the size of the applied force increases at a very slow speed in the form of a ramp until the size of the force is 95% of the maximum static friction force F s , then maintain the application of force for a period of time, and then make the applied force decrease at a very slow speed until the size of the force is -95% of the maximum static friction force F s , repeat the cycle several times. Since the speed of change is very slow, the applied force is basically equal to the friction force, so the relationship between the force and the displacement can be plotted Figure 2The displacement S and frictional force F shown fric The relationship curve, also known as the first characteristic curve, is given by the first characteristic curve. Based on the first characteristic curve, b2 = -F. s / σ0*ln(0.0975).

[0077] Furthermore, this embodiment analyzes the damping characteristics of static friction.

[0078] A force is applied, namely the output torque of the servo motor. If the output torque does not exceed the maximum static friction torque, then there will be no slippage between the two contact surfaces, but there will still be a small displacement between the two contact surfaces. The relationship between the small displacement and the magnitude of the applied force is analyzed as follows in this embodiment.

[0079] According to Newton's laws of motion

[0080] Since no slippage occurred, it can be approximated that:

[0081] x = z and

[0082] That is,

[0083] Therefore, F(t) = JS 2 x(t)+(σ1+σ2)Sx(t)+σ0x(t).

[0084] Therefore, the transfer function G(s) from the applied force to the output small displacement is:

[0085]

[0086] The transfer function G(s) can be approximated as a damped second-order system. Generally, the bristle stiffness coefficient σ0 is very large, while the viscous friction coefficient σ2 is very small, which cannot provide a good damping effect; however, the bristle damping coefficient σ1 can provide a better damping effect.

[0087] For example, when the applied torque is 1 Nm and the applied moment of inertia of the object is J = 1 kg / m², the simulated response curve is as follows: Figure 3 As shown.

[0088] Furthermore, this embodiment analyzes the Stribeck effect.

[0089] As the velocities of the two contact surfaces gradually increase, the frictional force F... fric It will first decrease, then gradually increase. A signal with a slowly increasing velocity is input into the Lugre friction model. Figure 4 Showing frictional force F fric The output.

[0090] Further, the embodiment analyzes the friction hysteresis characteristics.

[0091] When there is a unidirectional sinusoidal variable velocity between two contact surfaces, the friction force F fric There is a hysteresis characteristic. The friction force F fric is greater than the friction force F fric during the speed reduction process. The faster the speed changes, the wider the hysteresis loop curve. Based on the Lugre friction model, the input signal is a sinusoidal speed, the speed w is variable, and the output is the friction force. The friction force is plotted Figure 5 The input and output curves are shown, and the results verify that the Lugre friction model can realize dynamic friction hysteresis characteristics.

[0092] Further, the embodiment analyzes the variable separation friction.

[0093] Apply a slowly increasing force, and if the applied force can just cause the object to slide with a non-negligible displacement, then the applied force is the separation friction. It should be noted that the separation friction and the maximum static friction are not completely equivalent. The maximum static friction is a constant value, while the separation friction is a variable value.

[0094] Under normal circumstances, when the applied force exceeds the maximum static friction, the object will slide, that is, the maximum static friction is equal to the separation friction. Through literature research, it is shown that the greater the increase rate of the applied force, the more likely the object will slide when the applied force has not reached the maximum static friction, so the size of the separation friction is related to the increase rate of the applied force.

[0095] Based on the Lugre friction model, the embodiment can simulate the variable separation friction by applying applied forces with different increase rates.

[0096] Simscape in simulink can establish a physical simulation model.

[0097] A single mass (m = 1 Kg) rigid body is established using Simscape, which has a rotating shaft that can provide an applied torque to drive the rigid body to rotate, and the rotating shaft can output the rotating speed (w). Lugre friction is added to the model, and the simulink simulation is shown as Figure 6 .

[0098] The initial value of the applied torque is 0, and the torque increase rate is 1 Nm / s. The oscilloscope observes the friction force and the output speed. As shown in the figure, when the applied torque approaches 1.415 Nm, that is, the separation friction is 1.415 Nm, the output speed of the rigid body changes significantly. Record the separation friction under different change rates of the applied torque, as Figure 7The results show that the separation friction is variable at different applied torque increasing rates.

[0099] The embodiment analyzes the above static and dynamic characteristics by mathematical modeling of the Lugre friction model, and proposes a method of implementing parameter identification based on characteristic curve data.

[0100] S10, providing a plurality of input voltages to the servo motor in an open-loop control state, and obtaining a viscous friction coefficient σ2 according to the output of the servo motor at different input voltages.

[0101] The specific steps of obtaining the viscous friction coefficient σ2 in S10 are as follows.

[0102] S11, providing an input voltage to the servo motor in an open-loop control state, the input voltage rising from 0V to 10V, each time changing by 1V, and maintaining stability for 10s each time. Record the motor speed corresponding to the input voltage after each change.

[0103] S12, calculating the back electromotive force Ea according to the motor speed.

[0104] S13, calculating the friction torque according to the input voltage and the back electromotive force.

[0105] The comparison of the calculated friction torque and the actual friction torque is shown in Figure 8 .

[0106] S14, calculating the viscous friction coefficient σ2 according to Figure 1 It can be analyzed that when the input voltage increases by 1V, the angular velocity of the servo motor increases by about 0.1677 rad / s, and the friction torque increases by about 0.067 Nm.

[0107] S15, calculating the viscous friction coefficient σ2, i.e. σ2 = 0.067 / 0.1677 = 0.3995 Nms / rad.

[0108] S21, creating a PID closed-loop control system configured with the Lugre friction model, and obtaining the motor parameters of the PID closed-loop control system and the moment of inertia of the controlled object.

[0109] The motor parameters and the moment of inertia in this embodiment are shown in the table.

[0110] Motor armature inductance L Motor armature resistance R Motor back EMF coefficient Ce Motor torque coefficient Ck Inertia of the controlled object J 0.01(H) 3.75 (Ω) 5.7 (V / (rad / s)) 5.7 (Nm / A) 1 Kg / m ^ 2]]

[0111] The simulink simulation of the PID closed-loop control system of the Lugre friction is shown in Figure 9 .

[0112] In the figure, the transfer function G(s) of the input voltage and the output speed of the servo motor is as follows:

[0113]

[0114] S22, obtain the transfer function (G) of the input voltage and the output speed of the servo motor, and calculate the friction torque F at the stable speed according to the transfer function (G), the motor parameters and the moment of inertia fric .

[0115] In this embodiment, the desired angular velocity w of the servo motor is initially 0, and then increases by 0.002 degrees per second every 20 seconds. When the speed is stable, if there is no friction torque, the input voltage of the servo motor is equal to the back electromotive voltage, so in the PID closed-loop control system with friction torque, a part of the torque generated by the motor input voltage is used to offset the friction torque, so the control voltage U calculated by the PID is approximately

[0116] where w is the desired output speed, F fric represents the Lugre friction torque, and K represents the motor drive amplification coefficient, K=6 in the embodiment.

[0117] Then, the control amount U calculated by the PID at the stable speed is known, and the desired angular velocity w is also known, so the friction torque can be calculated according to the above formula.

[0118] Figure 10 It is shown that the friction torque calculated according to the formula is basically consistent with the friction torque output by the actual friction model.

[0119] S23, draw Figure 11 The first characteristic curve of the output speed w and the friction torque F fric , that is, the Stribeck curve, is shown.

[0120] S24, analyze the Coulomb friction and stribeck speed of the friction torque F fric according to the first characteristic curve.

[0121] where the maximum static friction Fs=1.499 Nm is determined according to the intersection of the first characteristic curve and the longitudinal coordinate in the coordinate system.

[0122] In S24, the Coulomb friction Fc=1.004 Nm and ws=0.001 rad / s are determined according to the stable part of the first characteristic curve.

[0123] S31, obtain the peak voltage Umax input to the servo motor.

[0124] Wherein, according to the static friction hysteresis characteristics, since Fs=1.499Nm, 95% of the motor input torque is selected, then the calculated peak voltage of the servo motor input should be U=Fs*0.95 / Ck*R=0.936875V≈0.937V.

[0125] S32, the servo motor input a speed very slowly changing recognition voltage, the recognition voltage is a ramp very slowly increasing speed, and from an initial voltage to 0.9V, and then from the peak voltage Umax to-0.9V, repeat several times.

[0126] S33, because the speed of change is very slow, so the torque generated by the applied recognition voltage is approximately equal to the friction, then the displacement S and the voltage relationship of the second characteristic curve can be drawn. Figure 12 The displacement S and the voltage relationship of the second characteristic curve are shown.

[0127] S34, according to the static friction characteristics analysis of the displacement S at a very slow speed change formula; wherein, according to the static friction characteristics can have

[0128]

[0129] Wherein, because the speed change is very slow, the output speed is almost 0.

[0130] Therefore, b1=0,

[0131] Therefore, b1=0,

[0132] Wherein, b1=0,

[0133] S35, according to the second characteristic curve can be obtained b2=3.478e-5. In the speed of the recognition voltage changes slowly, the rotation speed w=0, and according to the known viscous friction coefficient σ2, the maximum static friction force Fs, the coulomb friction force Fc, the stribeck speed and the displacement S formula, the bristle stiffness coefficient σ0 is calculated.

[0134] Wherein, the identified parameters σ2=0.3995Nms / rad, Fs=1.499Nm, Fc=1.004Nm, ws=0.001rad / s, then σ0=-Fs*ln(0.0975) / b2=10033.

[0135] According to the static friction damping characteristics of the embodiment, a torque is input, and if there is a friction torque, when the torque is not enough to make the motor rotate, a certain displacement will occur due to the deformation of the bristles. Therefore, a Figure 13 The current loop shown can give a step torque, and the small displacement output can be observed.

[0136] S41, creating the current loop of the servo motor in the PID closed loop control system;

[0137] S42, given the desired current loop is 0.1A, at this time the motor will not rotate. The step response of the current is as follows Figure 14 The third characteristic curve of the servo motor displacement step response is drawn. Figure 15 The third characteristic curve of the servo motor displacement step response is drawn.

[0138] S43, according to the third characteristic curve, the peak time tm=0.01465s is obtained.

[0139] S44, it is known that J=1, theta0=10033, theta2=0.4.

[0140] Then according to the following formula, sigma1 can be calculated, that is

[0141]

[0142] It can be obtained that:

[0143]

[0144] sigma1=2delta w n -sigma2;

[0145] Therefore,

[0146] delta=0.734923; sigma1=318.53;

[0147] t m is the peak time, sigma0 is the bristle stiffness coefficient, sigma1 is the bristle damping coefficient, sigma2 is the viscous friction coefficient, and J is the rotational inertia of the controlled object.

[0148] Based on this, the difference between the identified parameters and the actual parameters based on the above characteristic curves and characteristics is shown in the following table.

[0149]

[0150]

[0151] Then, the method of the embodiment first analyzes the static and dynamic characteristics of friction through mathematical modeling of the Lugre model, and proposes a corresponding parameter identification based on characteristic curve data through mathematical model analysis. The accuracy of the identified parameters deviates less from the set value, and after obtaining the accurate mathematical model, the optimization of the control can be carried out to suppress the precision error caused by friction disturbance.

[0152] Further, the embodiment is based on a parameter identification device of Lugre friction model. The device is applied to a PID closed-loop control system configured with Lugre friction model.

[0153] The device comprises a viscous friction coefficient calculation module, a friction torque calculation module, a first characteristic curve drawing module, a first characteristic curve analysis module, a second characteristic curve drawing module, a second characteristic curve analysis module, a third characteristic curve drawing module and a third characteristic curve analysis module.

[0154] The viscous friction coefficient calculation module is used to provide at least two input voltages to a servo motor, and obtain a viscous friction coefficient σ2 according to the output of the servo motor at different input voltages.

[0155] The friction torque calculation module is used to obtain motor parameters of the PID closed-loop control system and rotational inertia of the controlled object; obtain a transfer function (G) of input voltage and output speed of the servo motor, and calculate a friction torque F at a stable speed according to the transfer function (G), the motor parameters and the rotational inertia. fric .

[0156] The first characteristic curve drawing module is used to draw a first characteristic curve of the output speed w and the friction torque F fric .

[0157] The first characteristic curve analysis module is used to analyze Coulomb friction and stribeck speed of the friction torque F fric according to the first characteristic curve.

[0158] The second characteristic curve drawing module is used to obtain a peak voltage Umax input to the servo motor; input a speed extremely slowly changing identification voltage to the servo motor, the identification voltage is first increased from an initial voltage to the peak voltage Umax, and then decreased from the peak voltage Umax to a negative peak voltage Umax; obtain a displacement S between the servo motor and the controlled object, and draw a second characteristic curve of the displacement S and the identification voltage.

[0159] The second characteristic curve analysis module is used to analyze an algorithm of the displacement S when the speed is extremely slowly changing according to static friction characteristics, and calculate a bristle stiffness coefficient σ0 according to an algorithm of the displacement S, the known viscous friction coefficient σ2, the maximum static friction force Fs, the Coulomb friction force Fc and the stribeck speed.

[0160] The third characteristic curve drawing module is used to create a current loop of the servo motor in the PID closed-loop control system; provide a given desired current loop, and draw a third characteristic curve of displacement response in the servo motor.

[0161] The third characteristic curve analysis module is configured to obtain a peak time tm according to the third characteristic curve, and to calculate σ1 as the bristle damping coefficient σ1 according to the peak time tm, the bristle stiffness coefficient σ0, and the viscous friction coefficient σ2.

[0162] The above only describes the preferred embodiments of the present application and is not used to limit the present application. Various modifications and changes can be made by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A parameter identification method based on the Lugre friction model, characterized in that, The method includes: S10, with at least two input voltages provided by the servo motor, the viscous friction coefficient σ2 is obtained based on the output of the servo motor at different input voltages; S21, Create a PID closed-loop control system configured with a Lugre friction model, and obtain the motor parameters and the moment of inertia of the controlled object in the PID closed-loop control system. The frictional torque F of the Lugre friction model fric Configured as follows: Fc is the Coulomb friction force, Fs is the maximum static friction force, sgn(w) is the step function, w is the angular velocity of the motor, and ws is the Stribeck velocity. S22, obtain the transfer function (G) of the input voltage and output speed of the servo motor, and calculate the frictional torque F at the stable speed based on the transfer function (G), the motor parameters, and the moment of inertia. fric ; S23, plot the output rotational speed w and frictional torque F. fric The first characteristic curve; S24, Analyze the frictional torque F based on the first characteristic curve. fric Coulomb friction and Stribeck velocity; S31, obtain the peak voltage Umax input to the servo motor; S32, the servo motor is input with a recognition voltage that changes very slowly. The recognition voltage first rises from an initial voltage to the peak voltage Umax, and then drops from the peak voltage Umax to a negative peak voltage Umax. S33, obtain the displacement S between the servo motor and the controlled object, and plot the displacement S and the second characteristic curve of the identification voltage; S34, Based on the static friction characteristics, the formula for calculating the displacement S when the velocity changes extremely slowly; U is the control voltage of the motor, Ck is the torque coefficient of the motor, R is the armature resistance of the motor, and b1 and b2 are calculation coefficients. S35, when the speed of the voltage change is slow, the rotation speed w = 0, and the bristle stiffness coefficient σ0 is calculated based on the known viscous friction coefficient σ2, the maximum static friction force Fs, the Coulomb friction force Fc, the stribeck speed and the displacement S. S41, Create a current loop for the servo motor in the PID closed-loop control system; S42, provide a given desired current loop, and plot the third characteristic curve of the displacement response in the servo motor; S43, Obtain the peak time tm based on the third characteristic curve; S44. Calculate the bristle damping coefficient σ1 based on the peak time tm, bristle stiffness coefficient σ0, and viscous friction coefficient σ2.

2. The parameter identification method based on the Lugre friction model according to claim 1, characterized in that, The viscous friction coefficient σ2 is obtained and configured as follows: S11, the servo motor is provided with at least two input voltages, and the motor speed corresponding to the input voltages is recorded; S12, Calculate the back electromotive force based on the motor speed; S13, calculate the frictional torque based on the input voltage and the back electromotive force; S14, obtain the friction torque and the motor speed increment corresponding to the increment of the input voltage; S15, Calculate the viscous friction coefficient σ2 based on the frictional torque and the increment of the motor speed.

3. The parameter identification method based on the Lugre friction model according to claim 1, characterized in that, The transfer function (G) is configured as follows: L is the armature inductance of the motor, R is the armature resistance of the motor, Ce is the back electromotive force coefficient of the motor, Ck is the torque coefficient of the motor, and J is the moment of inertia of the controlled object. When the speed is stable, the control voltage U is configured as follows: F fric Where is the Lugre friction torque, and K is the drive amplification factor of the servo motor; In S22, the frictional torque F is calculated based on the control voltage U when the speed is stable, the desired output speed of the servo motor, the transfer function (G), the motor parameters, and the moment of inertia. fric .

4. The parameter identification method based on the Lugre friction model according to claim 1, characterized in that, In S24, the maximum static friction force Fs is determined based on the intersection of the first characteristic curve and the vertical coordinate in the coordinate system.

5. The parameter identification method based on the Lugre friction model according to claim 1, characterized in that, In S24, the Coulomb friction force Fc and the stribeck velocity are determined based on the stable portion of the first characteristic curve.

6. The parameter identification method based on the Lugre friction model according to claim 1, characterized in that, The peak voltage Umax is configured as follows: Umax = Fs * 0.95 / Ck * R; Ck is the torque coefficient of the motor, and R is the armature resistance of the motor.

7. The parameter identification method based on the Lugre friction model according to claim 1, characterized in that, The formula for calculating the displacement S when the velocity changes extremely slowly is configured as follows: U is the control voltage of the motor, Ck is the torque coefficient of the motor, R is the armature resistance of the motor, and b1 and b2 are calculation coefficients. In S35, b1 and b2 are obtained based on the second characteristic curve; When the speed of the identification voltage changes slowly, the rotational speed w = 0, and based on the known viscous friction coefficient σ2, the maximum static friction force Fs, the Coulomb friction force Fc, the stribeck speed, and the calculated coefficients b1 and b2, the bristle stiffness coefficient σ0 is obtained.

8. The parameter identification method based on the Lugre friction model according to claim 1, characterized in that, In S44, the hair damping coefficient σ1 is calculated and configured as follows: t m σ0 is the peak time, σ1 is the bristle stiffness coefficient, σ2 is the viscous friction coefficient, and J is the moment of inertia of the controlled object.

9. A parameter identification device based on the Lugre friction model, characterized in that, The device is applied in a PID closed-loop control system equipped with a Lugre friction model; Wherein, the frictional torque F of the Lugre friction model fric Configured as follows: Fc is the Coulomb friction force, Fs is the maximum static friction force, sgn(w) is the step function, w is the angular velocity of the motor, and ws is the Stribeck velocity. The device includes: A viscous friction coefficient calculation module is used to obtain the viscous friction coefficient σ2 based on the output of the servo motor at different input voltages when at least two input voltages are provided to the servo motor. The friction torque calculation module is used to obtain the motor parameters and the moment of inertia of the controlled object in the PID closed-loop control system; obtain the transfer function (G) of the input voltage and output speed of the servo motor; and calculate the friction torque F at the steady speed based on the transfer function (G), the motor parameters, and the moment of inertia. fric ; The first characteristic curve plotting module is used to plot the output rotational speed w and frictional torque F. fric The first characteristic curve; The first characteristic curve analysis module is used to analyze the frictional torque F based on the first characteristic curve. fric Coulomb friction and Stribeck velocity; The second characteristic curve plotting module is used to obtain the peak voltage Umax input by the servo motor; to obtain the displacement S between the servo motor and the controlled object, and to plot the second characteristic curve of the displacement S and the identification voltage; The second characteristic curve analysis module is used to analyze the formula of the displacement S when the velocity changes very slowly based on the static friction characteristics. U is the control voltage of the motor, Ck is the torque coefficient of the motor, R is the armature resistance of the motor, and b1 and b2 are calculation coefficients. When the speed of voltage change is slow, the rotational speed w = 0, and the bristle stiffness coefficient σ0 is calculated based on the known viscous friction coefficient σ2, maximum static friction force Fs, Coulomb friction force Fc, stribeck velocity, and the displacement S.

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