CN114785233A - Parameter identification device and method based on Lugre friction model - Google Patents

Parameter identification device and method based on Lugre friction model Download PDF

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CN114785233A
CN114785233A CN202111566646.2A CN202111566646A CN114785233A CN 114785233 A CN114785233 A CN 114785233A CN 202111566646 A CN202111566646 A CN 202111566646A CN 114785233 A CN114785233 A CN 114785233A
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friction
characteristic curve
speed
servo motor
voltage
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徐声
江涛
喻健
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Wuhan Huazhong Tianqin Defense Technology Co ltd
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/0004—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
    • H02P23/14—Estimation or adaptation of motor parameters, e.g. rotor time constant, flux, speed, current or voltage
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2205/00—Indexing scheme relating to controlling arrangements characterised by the control loops
    • H02P2205/01—Current loop, i.e. comparison of the motor current with a current reference

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Abstract

The invention discloses a parameter identification device and method based on a Lugre friction model. The method comprises the steps of establishing a PID closed-loop control system configured with a Lugre friction model, and drawing an output rotating speed w and a friction torque FfricA first characteristic curve of (a); identifying the friction torque F according to the first characteristic curvefricCoulomb friction and stribeck velocity; acquiring a peak voltage Umax input by a servo motor; inputting an identification voltage with extremely slow change speed at the servo motor, wherein the identification voltage firstly rises from an initial voltage to a peak voltage Umax and then falls from the peak voltage Umax to a negative peak voltage Umax; acquiring 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; identification of the bristle stiffness coefficient sigma from the second characteristic curve0(ii) a Establishing a current loop of a servo motor in a PID closed-loop control system; drawing a third characteristic curve of displacement response in the servo motor; according toThird characteristic curve identification bristle damping coefficient sigma1。

Description

Parameter identification device and method based on Lugre friction model
Technical Field
The invention relates to the field of servo control, in particular to a parameter identification method based on a Lugre friction model.
Background
At present, there are many friction models applied to servo control systems. According to the control object and the requirement, the model is inconsistent, and the corresponding friction compensation method has various modes. According to literature reference, a classical coulomb friction and viscous friction model cannot truly simulate the dynamic process of actual friction, so that friction compensation cannot achieve good effect.
Disclosure of Invention
Based on the above, the embodiment of the invention discloses at least a parameter identification method based on a Lugre friction model. According to the method disclosed by the invention, effective precision identification is carried out on the parameters based on the drawn characteristic curve based on comprehensive analysis on the dynamic characteristic and the static characteristic of the Lugre friction model, the deviation between the identified parameter identification and the initial set value is small, and the precision error caused by friction disturbance is inhibited.
In order to achieve the above, the method includes:
s10, providing at least two input voltages at the servo motor, and obtaining the viscous friction coefficient sigma according to the output of the servo motor at different input voltages2；
S21, creating a PID closed-loop control system configured with a Lugre friction model, and acquiring motor parameters of the PID closed-loop control system and the rotational inertia of a controlled object;
s22, obtaining a transfer function (G) of the input voltage and the output rotating speed of the servo motor, and calculating the friction torque F at the stable speed according to the transfer function (G), the motor parameters and the rotary inertiafric；
S23, drawing the output rotating speed w and the friction torque FfricA first characteristic curve of (a);
s24, analyzing the friction torque F according to the first characteristic curvefricCoulomb friction and stribeck velocity;
s31, acquiring a peak voltage Umax input by the servo motor;
s32, inputting an identification voltage with extremely slow speed change into the servo motor, wherein the identification voltage firstly rises from an initial voltage to the peak voltage Umax and then falls from the peak voltage Umax to the negative peak voltage Umax;
s33, obtaining a displacement S between the servo motor and the controlled object, and drawing a second characteristic curve of the displacement S and the identification voltage;
s34, analyzing the formula of the displacement S when the speed changes very slowly according to the static friction characteristics;
s35, where the rotation speed w is 0 when the speed change of the identification voltage is slow, and according to the known viscous friction coefficient σ2Calculating the bristle stiffness coefficient sigma by using the formulas of the maximum static friction force Fs, the coulomb friction force Fc, the stribeck speed and the displacement S0；
S41, creating a current loop of the servo motor in the PID closed-loop control system;
s42, providing a given expected current loop, and drawing a third characteristic curve of displacement response in the servo motor;
s43, obtaining peak time tm according to the third characteristic curve;
s44, according to the peak time tm and bristle rigidity coefficient sigma0And coefficient of viscous friction σ2Calculating sigma1Is the damping coefficient sigma of the bristles1。
The embodiment of the invention at least discloses a parameter identification device based on a Lugre friction model.
The device is applied to a PID closed-loop control system configured with a Lugre friction model;
the device comprises:
a viscous friction coefficient calculation module for providing at least two input voltages at the servo motor and obtaining a viscous friction coefficient sigma according to the output of the servo motor at different input voltages2；
The friction torque calculation module is used for acquiring motor parameters of the PID closed-loop control system and the rotary inertia of the controlled object; obtaining a transfer function (G) of the input voltage and the output rotating speed of the servo motor, and calculating a friction torque F at a stable speed according to the transfer function (G), the motor parameter and the rotational inertiafric；
A first characteristic curve drawing module for drawing the output rotation speed w and the friction torque FfricA first characteristic curve of (1);
a first characteristic curve analysis module for analyzing the friction torque F according to the first characteristic curvefricCoulomb friction and stribeck velocity;
the second characteristic curve drawing module is used for acquiring the peak voltage Umax input by the servo motor; inputting an identification voltage with extremely slow speed change at the servo motor, wherein the identification voltage firstly rises from an initial voltage to the peak voltage Umax and then falls from the peak voltage Umax to the negative peak voltage Umax; acquiring 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;
the second characteristic curve analysis module is used for analyzing the formula of the displacement S when the speed changes very slowly according to the static friction characteristic; the rotation speed w is 0 when the speed of the identification voltage changes slowly, and according to the known viscous friction coefficient sigma2Calculating the bristle stiffness coefficient sigma by using the formulas of the maximum static friction force Fs, the coulomb friction force Fc, the stribeck speed and the displacement S0；
The third characteristic curve drawing module is used for creating a current loop of the servo motor in the PID closed-loop control system; providing a given expected current loop, and drawing a third characteristic curve of displacement response in the servo motor;
the third characteristic curve analysis module is used for acquiring peak time tm according to the third characteristic curve; for bristle stiffness coefficient σ according to peak time tm0And coefficient of viscous friction sigma2Calculating sigma1Is the mane damping coefficient sigma1。
In view of the above, other features and advantages of the disclosed exemplary embodiments will become apparent from the following detailed description of the disclosed exemplary embodiments, which proceeds with reference to the accompanying drawings.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
FIG. 1 is a schematic diagram of a Simulink simulation model of Lugre friction in the example;
FIG. 2 is a graph showing the relationship between the displacement s and the friction force in the analysis of the hysteresis characteristic of static friction according to the embodiment;
FIG. 3 is a graph of transfer function response for an analysis of stiction damping characteristics in an example embodiment;
FIG. 4 is a graph of input and output curves for an embodiment for Stribeck effect analysis;
FIG. 5 is a graph of input and output curves for an embodiment analysis of friction hysteresis characteristics;
FIG. 6 is a diagram of a physical simulation model of an embodiment for a split friction analysis;
FIG. 7 is a graph showing the input and output of the separation friction force in the separation friction force analysis according to the embodiment;
FIG. 8 is a plot of calculated friction torque versus actual friction torque for an open loop of the method of an embodiment;
FIG. 9 is a simulink simulation model diagram of the PID velocity closed loop of the method of the embodiment;
FIG. 10 is a plot of calculated friction torque versus actual friction torque in a closed loop of the method of an embodiment;
FIG. 11 is a graph of output speed and friction torque for the method of the embodiment;
FIG. 12 is a graph of input identification voltage versus displacement for the method of the embodiment;
FIG. 13 is a simulation model diagram of the method of the embodiment with the addition of a current loop in the PID closed loop control system;
FIG. 14 is a graph of current step response for a method according to an embodiment;
FIG. 15 is a graph of step response displacement for the method of the example embodiment.
Detailed Description
In the following discussion, numerous details are set forth to provide a thorough understanding of the present invention. It will be understood by those skilled in the art that the present invention may be practiced without such details. In other instances, well-known elements have been illustrated in schematic or block diagram form in order not to obscure the present invention in unnecessary detail. Additionally, for the most part, details concerning network communications, electromagnetic signaling techniques, user interfaces or input/output techniques, and the like, have been omitted inasmuch as such details are not considered necessary to obtain a complete understanding of the present invention, and are considered to be within the understanding of persons of ordinary skill in the relevant art.
As will be appreciated by one skilled in the art, the present invention may be embodied as a system, method or computer program product. Accordingly, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a "circuit," module "or" system. Furthermore, the present invention may take the form of a computer program product embodied in any tangible medium having computer-usable program code embodied in the medium.
The parameter identification method based on the Lugre friction model disclosed by the embodiment. The steps of the method are implemented at least in a combination of a server and a display device.
The server generally includes a memory and a processor. The memory mainly comprises a program storage area and a data storage area; the storage program area may store an operating system (for example, an android operating system, abbreviated as "android system", or an ios operating system, or another operating system, where the operating system may also be abbreviated as "system"), an application program (for example, a sound playing function, an image playing function, etc.) required by at least one function, a program related to this embodiment, and the like. And, the storage data area may 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, and the like, which are referred to in the present embodiment. In addition, the memory may include high speed random access memory, and may also include non-volatile memory, such as at least one magnetic disk storage device, flash memory device, and other volatile solid state storage devices. The processor provides high speed computing capability and is capable of calling and executing programs stored in the memory.
Among them, the display screen may be used to display information input by or provided to a user and various applications installed in the electronic terminal. The display screen may include a display panel, and optionally, the display panel may be configured in the form of a Liquid Crystal Display (LCD), an organic light-emitting diode (OLED), or the like. Further, the touch panel may cover the display panel, and when the touch panel detects a touch operation thereon or nearby, the touch panel transmits the touch operation 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.
In this embodiment, the Z-representative bristle average deformation in the Lugre friction model is represented by,
Figure BDA0003422045080000071
wherein w is the angular velocity of the servo motor.
Then when the speed is stable, it can be understood
Figure BDA0003422045080000072
At this time, the bristle deformation amount is represented by:
Figure BDA0003422045080000073
where sgn (w) is a sign function and g (w) is a constant positive output function and is not a symmetric function with respect to velocity. The influencing factors of the g (w) function include but are not limited to contact surface materials, whether lubricant is added or not, temperature and the like, and as the speed increases, g (w) shows a monotonically decreasing output trend.
As is known, the Lugre friction model is expressed by,
Figure BDA0003422045080000081
wherein σ0Is the bristle stiffness coefficient, Fc is the coulomb friction, Fs is the maximum static friction, ws is the Stribeck velocity.
Meanwhile, the friction force F in the Lugre friction modelfricThe size of (a) is related to the degree of curvature of the bristles, and indicates,
Figure BDA0003422045080000082
wherein σ1Is the bristle damping coefficient.
Furthermore, friction force F in Lugre friction modelfricIn proportion to the relative speed of the contact surface between the servo motor and the controlled object, that is, the viscous property of dynamic friction exists, the sum of the static friction force and the dynamic friction force is added to indicate that,
Figure BDA0003422045080000083
wherein: sigma2Is the coefficient of viscous friction.
Based on this, the frictional force F at the time of speed stabilizationfricIt is possible to express equally well the components,
Figure BDA0003422045080000084
further, the Simulink simulation model of Lugre friction force is shown in fig. 1. In the present embodiment, the parameter setting is made for the Lugre friction model in the table.
Figure BDA0003422045080000085
Based on this, the present embodiment analyzes the static friction hysteresis characteristic.
When the force applied to the two contact surfaces between the servo motor and the controlled object is smaller than the maximum static friction force, the static friction force is equivalent to a spring in form, and the two contact surfaces cannot slide relatively but have relative displacement.
Then on the average deformation of the bristles, i.e.
Figure BDA0003422045080000091
At w>At the time of 0, the number of the first,
Figure BDA0003422045080000092
at w<At the time of 0, the number of the first,
Figure BDA0003422045080000093
on the basis of this, it is possible to provide,
Figure BDA0003422045080000094
namely, the method has the advantages that,
Figure BDA0003422045080000095
when the force applied is stable, no sliding occurs between the two contact surfaces under the effect of static friction. The angular velocity w of the motor approaches 0; at this point g (w) can be considered constant a and the bristle deformation dz/dt is equal to 0.
Then there is a change in the number of,
Figure BDA0003422045080000096
therefore, the method has the advantages that,
Figure BDA0003422045080000097
when s is 0, the frictional force FfricIs 0 and b1＝0。
At this point, a slowly varying force is applied, increasing at a ramp-like very slow rate until a maximum static friction force F of 95% is reachedsThen the force application is maintained for a period of time and the force applied is reduced at a very slow rate until the force reaches a maximum static friction force F of-95%sThe cycle is repeated several times. Due to very slow speed of changeSlow, so that the applied force is substantially equal to the friction force, the amount of displacement s and the friction force F shown in fig. 2 can be plottedfricI.e. the first characteristic curve. According to the first characteristic curve, b2＝-Fs/σ0*ln(0.0975)。
Further, the present embodiment analyzes the damping characteristic of the static friction.
A force is applied, i.e. the output torque of the servo motor. If the output torque does not exceed the maximum static friction torque, no sliding occurs between the two contact surfaces, but a small displacement still occurs between the two contact surfaces.
According to the formula of Newton's mechanics,
Figure BDA0003422045080000101
since no slip occurs, it can be approximated that:
x is z and
Figure BDA0003422045080000102
namely, the method comprises the following steps of,
Figure BDA0003422045080000103
thus, F (t) JS2x(t)+(σ1+σ2)Sx(t)+σ0x(t)。
Then, the transfer function g(s) of the applied force to the output minute displacement has,
Figure BDA0003422045080000104
the transfer function g(s) can be approximated as a damped second order system. In general, the bristle stiffness coefficient σ0Large, and a viscous friction coefficient σ2Is very small and cannot provide good damping effect; while the bristle damping coefficient sigma1But provides a better damping effect.
For example, when the applied torque is 1Nm and the applied object moment of inertia J is 1Kg/m 2, the simulated response curve effect is as shown in fig. 3.
Further, the present embodiment analyzes the Stribeck effect.
During the gradual increase of the speed of the two contact surfaces, the friction force FfricFirst, it will decrease and then slowly increase. A slowly increasing speed signal is input to the Lugre friction model, and FIG. 4 shows the friction force FfricTo output (d).
Further, the present embodiment analyzes the frictional hysteresis characteristic.
When a unidirectional sine wave variable speed exists between the two contact surfaces, the friction force FfricThere is a hysteresis characteristic. Friction force F during speed increasefricGreater than the friction force F during speed reductionfric. The faster the speed change, the wider the hysteresis loop curve. Based on the Lugre friction model, the input signal is the sine wave speed, the speed w is variable, the friction force is output, an input curve and an output curve shown in FIG. 5 are drawn, and the result verifies that the Lugre friction model can realize the dynamic friction hysteresis characteristic.
Further, the present embodiment analyzes the variable separating frictional force.
A slowly increasing force is applied, which is the separation friction if the applied force can just slide the object without a minor displacement. It should be noted that the separation friction force is not completely equivalent to the maximum static friction force, the maximum static friction force is a fixed value, and the separation friction force is a variable value.
Generally, the object will slip when the applied force exceeds the maximum static friction force, i.e. the maximum static friction force is equal to the separation friction force, and literature studies show that the greater the rate of increase of the applied force, the greater the slip will occur when the applied force has not yet reached the maximum static friction force, and therefore the magnitude of the separation friction force is related to the rate of increase of the applied force.
Based on the Lugre friction model, the present embodiment can simulate that the separation friction force is variable by applying application forces at different rates of increase.
In simulink Simscape can build a physical simulation model.
A rigid body with a single mass (m 1Kg) is built by using the Simscape, the rigid body is driven to rotate by applying torque, the rotating shaft can output a rotating speed (w), Lugre friction is added on the model, and the simulink simulation is shown in FIG. 6.
The initial value of the applied torque is 0, the torque increasing rate is 1Nm/s, and the oscilloscope observes the friction force and the output rotating speed. As can be seen, there is a significant change in the rigid body output rotational speed when the applied torque is close to 1.415Nm, i.e., the separation friction is 1.415 Nm. The separation friction force was recorded at different rates of change of applied torque, as shown in fig. 7, and the results indicated that the separation friction force was variable at different rates of increase of applied torque.
In this embodiment, a method for performing parameter identification based on characteristic curve data is proposed by analyzing the static characteristics and the dynamic characteristics of the Lugre friction model through mathematical modeling.
S10, providing a plurality of input voltages for the servo motor in an open-loop control state, and acquiring a viscous friction coefficient sigma according to the output of the servo motor at different input voltages2。
Wherein the viscous friction coefficient σ is acquired in S102The method comprises the following specific steps.
And S11, providing input voltage for the servo motor in an open-loop control state, wherein the input voltage rises from 0V to 10V, and the input voltage is changed by 1V every time and is kept stable for 10S every time. And recording the rotating speed of the motor corresponding to the input voltage after each change.
And S12, calculating the back electromotive force Ea according to the motor rotating speed.
And S13, calculating friction torque according to the input voltage and the counter electromotive force.
The calculated friction torque and the actual friction torque are compared as shown in fig. 8.
S14, it can be analyzed from FIG. 1 that for every 1V increase in input voltage, the angular velocity of the servomotor increases by about 0.1677rad/S and the friction torque increases by about 0.067 Nm.
S15, calculating the viscous friction coefficient sigma2I.e. sigma2＝0.067/0.1677＝0.3995Nms/rad。
And S21, creating a PID closed-loop control system configured with a Lugre friction model, and acquiring motor parameters of the PID closed-loop control system and the rotational inertia of the controlled object.
In the present embodiment, motor parameters and rotational inertia are shown in the table.
Motor armature inductance L Armature resistance R of motor Coefficient of motor back electromotive force Ce Motor moment coefficient Ck Controlled object moment of inertia J
0.01(H) 3.75(Ω) 5.7(V/(rad/s)) 5.7(Nm/A) 1Kg/m ^2
Wherein, the PID closed loop control system of Lugre friction, simulink simulation is shown in figure 9.
In the figure, the transfer function G(s) of the input voltage and the output rotating speed of the servo motor is shown as follows:
Figure BDA0003422045080000131
s22, obtaining a transfer function (G) of the input voltage and the output rotating speed of the servo motor, and calculating the friction torque F at the stable speed according to the transfer function (G), the motor parameters and the rotary inertiafric。
The desired angular velocity w of the servo motor in this embodiment is initially 0 and then increases by 0.002 degrees per second every 20s of velocity. 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 input voltage of the motor is used for offsetting the friction torque, therefore, the voltage control U output by the PID calculation can be approximated,
Figure BDA0003422045080000141
wherein w is the desired output speed, FfricRepresents the Lugre friction torque, and K represents the motor drive amplification factor, wherein K is 6 in the embodiment.
Then, the control amount U output by the PID calculation is known and the desired angular velocity w is also known at the time of speed stabilization, so that the friction torque can be calculated according to the foregoing equation.
Fig. 10 shows that the friction torque calculated according to the formula is substantially coincident with the friction torque output by the actual friction model, and the simulation result is substantially coincident.
S23, output speed w and friction torque F shown in FIG. 11 are plottedfricThe first characteristic curve of (1), the Stribeck curve.
S24, analyzing the friction torque F according to the first characteristic curvefricCoulomb friction and stribeck velocity.
Wherein the maximum static friction force Fs is determined to be 1.499Nm according to the intersection point of the first characteristic curve and the ordinate in the coordinate system.
In S24, the coulomb frictional force Fc is 1.004Nm and ws is 0.001rad/S based on the stable portion of the first characteristic curve.
And S31, acquiring the peak voltage Umax input by the servo motor.
Wherein, according to the static friction hysteresis characteristic, since Fs is 1.499Nm, 95% of the motor input torque is selected, then the peak voltage of the servomotor input should be calculated as U Fs 0.95/Ck R0.936875V 0.937V.
And S32, inputting an identification voltage with a speed changing very slowly into the servo motor, wherein the identification voltage increases in a slope-shaped very slowly speed, and rises from an initial voltage to 0.9V, and then falls from the peak voltage Umax to-0.9V, and the cycle is repeated for a plurality of times.
S33, since the speed of change is extremely slow, the moment generated by the applied recognition voltage is substantially equal to the friction force, and then the second characteristic curve of the relationship between the displacement amount S and the voltage shown in fig. 12 can be plotted.
S34, analyzing the formula of the displacement S when the speed changes very slowly according to the static friction characteristics; wherein, according to the static friction characteristics, there may be
Figure BDA0003422045080000151
Among them, since the speed change is extremely slow, the output speed is almost 0.
Therefore, the method has the advantages that,
Figure BDA0003422045080000152
in this way, there is a possibility that,
Figure BDA0003422045080000153
wherein, b1＝0，
Figure BDA0003422045080000161
At S35, b2 is 3.478e-5 according to the second characteristic curve. The rotational speed w is 0 when the speed of the identification voltage changes slowly, and according to the known viscous friction coefficient σ2Maximum static friction force Fs, Coulomb friction force Fc, striCalculating bristle rigidity coefficient sigma by using beck speed and displacement S0。
Wherein the identified parameter σ20.3995Nms/rad, Fs 1.499Nm, Fc 1.004Nm, ws 0.001rad/s, then σ0＝-Fs*ln(0.0975)/b2＝10033。
This embodiment is based on the static friction damping characteristic, and inputs a torque, if there is friction torque, which is not enough to rotate the motor, and a certain displacement occurs due to the deformation of the bristles. Therefore, the current loop shown in fig. 13 must be added to the inner ring of the motor to be able to observe a minute displacement output for a step torque.
S41, creating a current loop of the servo motor in the PID closed-loop control system;
s42, the motor will not rotate given the desired current loop of 0.1A. The step response of the current is shown in fig. 14 below. At this time, a third characteristic curve of the servo motor displacement step response in fig. 15 is plotted.
And S43, acquiring the peak time tm equal to 0.01465S according to the third characteristic curve.
S44, J is 1, theta0 is 10033, and theta2 is 0.4.
Then σ can be calculated according to the following equation1I.e. have
Figure BDA0003422045080000162
Figure BDA0003422045080000171
Figure BDA0003422045080000172
Figure BDA0003422045080000173
The following can be obtained:
Figure BDA0003422045080000174
Figure BDA0003422045080000175
σ1＝2δJwn-σ2；
therefore, the method has the advantages that,
Figure BDA0003422045080000176
δ＝0.734923；σ1＝318.53。
based on this, the identification parameter and the actual parameter of the present embodiment based on the above characteristic curve and features are shown in the following table.
Figure BDA0003422045080000177
Then, the method of this embodiment first performs static characteristic and dynamic characteristic analysis of friction through mathematical modeling of the Lugre model, and proposes a method for performing corresponding parameter identification based on characteristic curve data through mathematical model analysis. The deviation of the identified parameter precision and a set value is small, and the precision mathematical model can be controlled to be optimized after being obtained, so that the precision error caused by friction disturbance is inhibited.
Further, the present embodiment is based on a parameter identification device of the Lugre friction model. The device is applied to a PID closed-loop control system configured with a Lugre friction model.
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.
The viscous friction coefficient calculation module is used for servoThe motor provides at least two input voltages, and a viscous friction coefficient sigma is obtained according to the output of the servo motor at different input voltages2。
The friction torque calculation module is used for acquiring motor parameters of the PID closed-loop control system and the rotary inertia of the controlled object; obtaining a transfer function (G) of the input voltage and the output rotating speed of the servo motor, and calculating a friction torque F at a stable speed according to the transfer function (G), the motor parameters and the rotational inertiafric。
The first characteristic curve drawing module is used for drawing the output rotating speed w and the friction torque FfricThe first characteristic curve of (1).
A first characteristic curve analysis module for analyzing the friction torque F according to the first characteristic curvefricCoulomb friction and stribeck velocity.
The second characteristic curve drawing module is used for obtaining the peak voltage Umax input by the servo motor; inputting an identification voltage with extremely slow speed change at the servo motor, wherein the identification voltage firstly rises from an initial voltage to the peak voltage Umax and then falls from the peak voltage Umax to the negative peak voltage Umax; and obtaining a displacement S between the servo motor and a controlled object, and drawing the displacement S and a second characteristic curve of the identification voltage.
The second characteristic curve analysis module is used for analyzing the calculation formula of the displacement S when the speed changes very slowly according to the static friction characteristic and according to the known viscous friction coefficient sigma2Calculating the bristle rigidity coefficient sigma according to the formula of the maximum static friction force Fs, the coulomb friction force Fc, the stribeck speed and the displacement S0。
The third characteristic curve drawing module is used for creating a current loop of the servo motor in the PID closed-loop control system; a given desired current loop is provided and a third characteristic curve of the displacement response in the servo motor is plotted.
The third characteristic curve analysis module is used for acquiring peak time tm according to the third characteristic curve; for measuring the peak time tm,Coefficient of bristle stiffness σ0And coefficient of viscous friction sigma2Calculating sigma1Is the damping coefficient sigma of the bristles1。
The present invention has been described in terms of the preferred embodiment, and it is not intended to be limited to the embodiment. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (10)

1. A parameter identification method based on a Lugre friction model is characterized in that,
the method comprises the following steps:
s10, providing at least two input voltages at the servo motor, and obtaining the viscous friction coefficient sigma according to the output of the servo motor at different input voltages2；
S21, creating a PID closed-loop control system configured with a Lugre friction model, and acquiring motor parameters of the PID closed-loop control system and the rotational inertia of a controlled object;
friction torque F of the Lugre friction modelfricIs configured in such a way that,
Figure FDA0003422045070000011
fc is coulombic friction, Fs is maximum static friction, sgn (w) is a step function, w is the angular speed of the motor, and ws is stribeck speed;
s22, obtaining a transfer function (G) of the input voltage and the output rotating speed of the servo motor, and calculating the friction torque F at the stable speed according to the transfer function (G), the motor parameter and the rotational inertiafric；
S23, drawing the output rotating speed w and the friction torque FfricA first characteristic curve of (1);
s24, analyzing the friction torque F according to the first characteristic curvefricCoulomb friction and stribeck velocity;
s31, acquiring a peak voltage Umax input by the servo motor;
s32, inputting an identification voltage with extremely slow speed change into the servo motor, wherein the identification voltage firstly rises from an initial voltage to the peak voltage Umax and then falls from the peak voltage Umax to the negative peak voltage Umax;
s33, 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;
s34, analyzing the formula of the displacement S when the speed changes very slowly according to the static friction characteristic;
Figure FDA0003422045070000021
s35, where the rotation speed w is 0 when the speed change of the identification voltage is slow, and according to the known viscous friction coefficient σ2Calculating the bristle rigidity coefficient sigma according to the formula of the maximum static friction force Fs, the coulomb friction force Fc, the stribeck speed and the displacement S0；
S41, creating a current loop of the servo motor in the PID closed-loop control system;
s42, providing a given expected current loop, and drawing a third characteristic curve of displacement response in the servo motor;
s43, obtaining peak time tm according to the third characteristic curve;
s44, according to the peak time tm and bristle rigidity coefficient sigma0And coefficient of viscous friction σ2Calculating sigma1Is the mane damping coefficient sigma1。
2. The Lugre friction model-based parameter identification method of claim 1, wherein,
obtaining the viscous friction coefficient sigma2Configured to:
s11, providing at least two input voltages at the servo motor, and recording the motor rotating speed corresponding to the input voltages;
s12, calculating the counter electromotive force according to the motor speed;
s13, calculating friction torque according to the input voltage and the counter electromotive force;
s14, acquiring the friction torque corresponding to the increment of the input voltage and the increment of the motor rotating speed;
s15, calculating the viscous friction coefficient sigma according to the friction torque and the increment of the motor rotating speed2。
3. The Lugre friction model-based parameter identification method of claim 1, wherein,
the transfer function (G) is configured such that,
Figure FDA0003422045070000031
l is armature inductance of the motor, R is armature resistance R, Ce of the motor is counter electromotive force coefficient of the motor, Ck motor is moment coefficient, and J is rotational inertia of the controlled object;
the voltage control U is configured such that when the speed is stable,
Figure FDA0003422045070000032
Firiclugre friction torque and K is a driving amplification coefficient of the servo motor;
in S22, a friction torque F is calculated according to the voltage control U when the speed is stable, the expected output rotating speed of the servo motor, a transfer function (G), the motor parameter and the rotational inertiafric。
4. The Lugre friction model-based parameter identification method of claim 1, wherein,
at S24, a maximum static friction force Fs is determined from an intersection of the first characteristic curve and the ordinate in the coordinate system.
5. The Lugre friction model-based parameter identification method of claim 1, wherein,
at S24, the coulomb friction Fc and the stribeck velocity are determined from the stable portion of the first characteristic curve.
6. The Lugre friction model-based parameter identification method of claim 1, wherein,
the peak voltage Umax is configured such that,
Umax＝Fs*0.95/Ck*R。
7. the Lugre friction model-based parameter identification method of claim 1, wherein,
the formula of the displacement S when the speed changes very slowly is configured as follows:
Figure FDA0003422045070000041
in S35, b1 and b2 are obtained according to the second characteristic curve;
the rotation speed w is 0 when the speed of the identification voltage changes slowly, and according to the known viscous friction coefficient sigma2Obtaining a bristle rigidity coefficient sigma through the maximum static friction force Fs, the coulomb friction force Fc, the stribeck speed, the calculated coefficient b1 and the calculated coefficient b20。
8. The Lugre friction model-based parameter identification method of claim 1, wherein,
in S44, the bristle damping coefficient σ is calculated1And is configured to be, in use,
Figure FDA0003422045070000051
Figure FDA0003422045070000052
Figure FDA0003422045070000053
Figure FDA0003422045070000054
9. a parameter identification device based on a Lugre friction model is characterized in that,
the device is applied to a PID closed-loop control system configured with a Lugre friction model;
wherein, the friction torque F of the Lugre friction modelfricIs configured in such a way that,
Figure FDA0003422045070000055
fc is coulombic friction, Fs is maximum static friction, sgn (w) is a step function, w is the angular speed of the motor, and ws is stribeck speed;
the device comprises:
a viscous friction coefficient calculation module for providing at least two input voltages at the servo motor and obtaining a viscous friction coefficient sigma according to the output of the servo motor at different input voltages2；
The friction torque calculation module is used for acquiring motor parameters of the PID closed-loop control system and the rotational inertia of a controlled object; obtaining a transfer function (G) of the input voltage and the output rotating speed of the servo motor, and calculating a friction torque F at a stable speed according to the transfer function (G), the motor parameters and the rotational inertiafric；
A first characteristic curve drawing module for drawing the output rotation speedw and friction torque FfricA first characteristic curve of (1);
the first characteristic curve analysis module is used for analyzing the coulomb friction force and the stribeck speed of the friction torque Ffric according to the first characteristic curve;
the second characteristic curve drawing module is used for acquiring the peak voltage Umax input by the servo motor; inputting an identification voltage with extremely slow speed change at the servo motor, wherein the identification voltage firstly rises from an initial voltage to the peak voltage Umax and then falls from the peak voltage Umax to the negative peak voltage Umax; acquiring 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;
the second characteristic curve analysis module is used for analyzing an equation of the displacement S when the speed changes very slowly according to the static friction characteristic;
Figure FDA0003422045070000061
the rotational speed w is 0 when the speed of the identification voltage changes slowly, and according to the known viscous friction coefficient σ2Calculating the bristle rigidity coefficient sigma according to the formula of the maximum static friction force Fs, the coulomb friction force Fc, the stribeck speed and the displacement S0。
10. A parameter identification device based on a Lugre friction model is characterized in that,
the device comprises a plurality of devices which are connected with each other,
the third characteristic curve drawing module is used for creating a current loop of the servo motor in the PID closed-loop control system; providing a given expected current loop, and drawing a third characteristic curve of displacement response in the servo motor;
the third characteristic curve analysis module is used for acquiring peak time tm according to the third characteristic curve; for bristle stiffness coefficient σ according to peak time tm0And coefficient of viscous friction σ2Calculating sigma1Is the mane damping coefficient sigma1。
CN202111566646.2A 2021-12-20 2021-12-20 Parameter identification device and method based on Lugre friction model Pending CN114785233A (en)

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116276922A (en) * 2023-05-22 2023-06-23 佛山科学技术学院 Friction force identification method for five-axis parallel device

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116276922A (en) * 2023-05-22 2023-06-23 佛山科学技术学院 Friction force identification method for five-axis parallel device

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