JP6214948B2 - Friction compensation device, friction compensation method, and servo control device - Google Patents

Description

  The present invention relates to a friction compensation device, a friction compensation method, and a servo control device.

In products that require relatively high control accuracy, such as machine tools, it is necessary to compensate for a decrease in control accuracy due to the influence of nonlinear friction inherent in the mechanical system.
Conventionally, feedback or feed-forward compensation using a friction model is known as a nonlinear friction compensation method (see, for example, Patent Document 1).

Since the friction characteristics vary due to aging and individual differences, there is a possibility that the desired control accuracy cannot be maintained only by adjusting the compensation model friction parameters before product shipment.
To solve this problem, online identification methods for friction parameters are being studied.
Most conventional friction identification methods are intended for a classic friction model composed of Coulomb friction, static friction, and viscous friction (see FIG. 13).

International Publication No. 2007/105527

  However, for example, the frictional behavior at the time of speed reversal in the sinusoidal drive of the machine tool table surface cannot be reproduced by the classic friction model. For example, FIG. 14 shows a comparison between a friction characteristic based on a classical friction model and an actual friction characteristic. In FIG. 14, the horizontal axis represents the position, the vertical axis represents the friction force, the characteristic represented by the broken line represents the friction characteristic based on the classical friction model, and the characteristic represented by the solid line represents the actual friction characteristic. From FIG. 14, it is clear that the actual friction characteristics are different from the friction characteristics based on the classical friction model. This is because friction is not only dependent on speed but also on position.

  The present invention has been made in view of such circumstances, and a friction compensation device capable of improving the estimation accuracy of friction by estimating the friction force using a friction model close to actual friction behavior It is another object of the present invention to provide a friction compensation method and a servo control device.

A first aspect of the present invention is a friction compensation device that is applied to a servo control device that performs control such that a control amount such as a position and orientation of a control target follows a target value, and a predetermined parameter included in a friction model is set. Parameter identifying means for identifying, and friction estimating means for estimating the frictional force of the control object using the friction model in which the predetermined parameter is identified by the parameter identifying means , wherein the predetermined parameter is at least coulomb A frictional force and a maximum static frictional force, wherein the parameter identification means uses data acquisition means for acquiring an actual machine friction characteristic indicating a relationship between the position or speed of the control target and the frictional force, and the actual machine friction characteristic. and identifying means for identifying the predetermined parameters, the friction model using the predetermined parameter identified, type the position or velocity By calculating a verification friction characteristic indicating the relationship between the position or speed and the friction force, it is determined whether or not an error between the verification friction characteristic and the actual machine friction characteristic is within a predetermined allowable range, And a parameter adjusting unit that adjusts the Coulomb friction force and the maximum static friction force so that the error is within the allowable range when the error is not within the allowable range.

  According to this aspect, since the actual machine friction characteristic in which the position or velocity and the friction force are associated is acquired, and the parameter of the friction model is identified from the actual machine friction characteristic, more detailed and dynamic than the classic friction model is obtained. A friction model can be constructed. As a result, the friction model can be dynamically adapted in accordance with a change in the characteristics of the control target due to deterioration over time, the surrounding environment, and the like, and a reduction in accuracy due to the influence of friction can be suppressed.

  In the above friction compensator, the actual machine friction characteristic is represented as a hysteresis loop, and the parameter adjusting means uses the Coulomb friction force identified by the identification means as the amplitude ratio of the hysteresis between the verification friction characteristic and the actual machine friction characteristic. The coulomb friction force may be adjusted by dividing by.

  As a result, the verification friction characteristic can be efficiently brought close to the actual machine friction characteristic.

  In the friction compensation apparatus, the data acquisition unit includes a first torque calculation unit that calculates a torque including a disturbance component by inputting a position or speed to the inverse model of the control target, and an operation amount-torque conversion model. And calculating a frictional force by subtracting the torque calculated by the second torque calculating means from the second torque calculating means for calculating the torque from the operation amount and the torque calculated by the first torque calculating means. It is good also as providing a frictional force calculating means.

  By providing such a configuration, the actual machine friction characteristics can be obtained at a desired timing regardless of whether the controlled object is operating or stopped. As a result, it is possible to identify the parameters of the friction model regardless of whether the control target is operating or stopped.

  In the above friction compensator, the identification unit includes a first frictional force identification unit that identifies a Coulomb frictional force from a frictional force at the time of speed reversal of the actual machine friction characteristic, and a Coulomb friction identified by the first frictional force identification unit. A second frictional force identifying means for identifying the maximum static frictional force from the force; and a rising characteristic of hysteresis in the actual machine frictional characteristic expressed as a hysteresis loop is linearly approximated, and the predetermined parameter is determined from the linearly approximated hysteresis characteristic Among these, an element identifying means for identifying a parameter other than the Coulomb friction force and the maximum static friction force may be provided.

  A second aspect of the present invention is a servo control device including the above friction compensation device.

According to a third aspect of the present invention, there is provided a friction compensation method applied to a servo control device that performs control for causing a control amount such as a position and orientation of a control target to follow a target value, and a predetermined parameter included in the friction model is set. A parameter identification process for identifying, and a friction estimation process for estimating a frictional force of the control target using the friction model in which the predetermined parameter is identified by the parameter identification process , wherein the predetermined parameter is at least Including the Coulomb friction force and the maximum static friction force, the parameter identification process uses the data acquisition process for acquiring the actual machine friction characteristic indicating the relationship between the position or speed of the control object and the friction force, and the actual machine friction characteristic. Te, the identification process for identifying the predetermined parameters, the friction model using the predetermined parameter identified, type the position or velocity By calculating a verification friction characteristic indicating the relationship between the position or speed and the friction force, it is determined whether or not an error between the verification friction characteristic and the actual machine friction characteristic is within a predetermined allowable range, And a parameter adjustment process for adjusting the Coulomb friction force and the maximum static friction force so that the error is within the allowable range when the error is not within the allowable range.

  According to the present invention, it is possible to improve the estimation accuracy of friction, thereby reducing the control error due to the influence of friction.

It is the figure which showed one structural example of the servo control apparatus of the machine tool which concerns on one Embodiment of this invention. It is the figure which showed schematic structure of the parameter identification part which concerns on one Embodiment of this invention. It is the figure which showed one structural example of the data acquisition part shown in FIG. It is the figure which showed an example of the actual machine friction characteristic. It is the figure which showed one structural example of the identification part shown in FIG. It is a figure for demonstrating identification of a Coulomb friction force. Oh Ru a diagram for explaining the calculation procedure of the spring constant of the maximum friction force and each element of each element. Oh Ru a diagram for explaining the calculation procedure of the spring constant of the maximum friction force and each element of each element. Oh Ru a diagram for explaining the calculation procedure of the spring constant of the maximum friction force and each element of each element. It is a figure for demonstrating the adjustment method of an identification parameter . It is the figure which showed the flowchart for demonstrating the procedure of the parameter identification by an identification part. It is the figure shown about an example of the error of the processing track which arises by the influence of friction in a machine tool. It is the figure which showed the characteristic of the classic friction model. It is the figure which compared and showed the friction characteristic based on a classic friction model, and an actual friction characteristic.

  Hereinafter, an embodiment in which a friction compensation device and a friction compensation method of the present invention are applied to a servo control device of a machine tool for machining a mold or the like will be described with reference to the drawings.

  For example, in a machine tool, trajectory tracking control is often required, and not only a single axis but also a plurality of axes such as xyz are often controlled simultaneously. Generally, a drive system of a ball screw or a linear guide is adopted as a drive system of a machine tool. The machining trajectory may be deteriorated due to the nonlinear frictional characteristics inherent in these drive systems and the like.

  For example, if two axes are operated with a sine wave on one axis and a cosine wave on the other axis, an arc can be drawn, and this arc drawing control is often used to verify the controllability of machine tools. It is done. In this machining, as shown in FIG. 12, at the time of speed reversal (quadrant switching) where the speed of one of the axial motions is reversed due to the influence of friction, the machining trajectory (solid line in the figure) becomes the target trajectory (in the figure). Quadrant protrusions that deviate from the broken line are generated. This is because at the time of speed reversal, the speed changes from minute to zero, minute (sign inversion), and the frictional behavior changes in a non-linear region.

In mold processing and the like, since there are many curved surface processing, the speed reversal of the axial motion frequently occurs. If quadrant protrusions are generated at the time of speed reversal, streaks remain on the processed surface, which may degrade the accuracy of the mold. Further, the behavior of nonlinear friction varies depending on temperature, humidity, the weight of the workpiece, and the like.
The friction compensation device and method according to the present embodiment are incorporated in a servo control device of a machine tool in order to reduce a control error due to friction in the machine tool as described above, for example.

  FIG. 1 is a diagram showing a configuration example of the above-described servo control device for a machine tool. As shown in FIG. 1, the servo control device is a control system including, for example, a position feedback system 11, a speed feedback system 12, and a feedforward compensator 13, and further compensates for a control error due to the influence of friction. Therefore, the main component of the friction compensation device 20 is as follows.

  The friction compensator 20 uses a friction model to identify a friction estimation unit 21 that estimates a friction force inherent in the machine tool 100 that is a control target, and a predetermined parameter included in the friction model used in the friction estimation unit 21. The parameter identification unit 22 is provided.

  The friction estimation unit 21 estimates the friction force F using, for example, a friction model expressed by the following equations (1) to (4).

  In the above equations (1) to (4), F is the friction force, Fi is the friction force of each element, v is the speed, g (v) is the Stribeck curve, σ is the viscosity coefficient of the lubricating oil, and N is the element Number, ki is the spring constant of each element, αi is the ratio of the maximum frictional force of each element, Fc is the Coulomb frictional force, Fs is the maximum static frictional force, C is the Stribeck effect, and vs is the Stribeck speed.

Of the various parameters included in the above equations (1) to (4), the spring constant ki of each element, the ratio αi of the maximum frictional force of each element, the Coulomb frictional force Fc, and the maximum static frictional force Fs are parameter identifications. Identified by part 22.
As shown in FIG. 2, the parameter identification unit 22 includes a data acquisition unit 31, an identification unit 32, and a parameter adjustment unit 33 as main components.

The data acquisition unit 31 acquires the actual machine friction characteristic indicating the relationship between the position or speed of the machine tool and the frictional force. In the present embodiment, description will be made assuming that the actual machine friction characteristic indicating the relationship between the position of the machine tool and the frictional force is obtained, but speed may be adopted instead of the position.
FIG. 3 shows a configuration example of the data acquisition unit 31. As shown in FIG. 3, the data acquisition unit 31 inputs a position to the inverse model 51 of the control target (machine tool 100), thereby calculating a torque including a disturbance component, and an operation amount. (E.g., current command) -torque conversion model 61 is used to calculate the torque from the manipulated variable, and the second torque calculator 42 calculates the torque calculated by the first torque calculator 41. A frictional force calculation unit 43 that calculates the frictional force by subtracting the torque that has been generated is provided as a main component.

  Here, since the inverse model 51 to be controlled used in the first torque calculation unit 41 includes a differential element, the torque output from the inverse model 51 is rubbed through the filter 52 for performing properization. It is output to the force calculation unit 43. Further, in order to maintain consistency with the torque output from the first torque calculator 41, the torque output from the manipulated variable-torque conversion model 61 is also converted to a proper filter 62 in the second torque calculator 42. Is output to the frictional force calculation unit 43. The proper filters 52 and 62 have low-pass filter characteristics.

  FIG. 4 shows an example of actual machine friction characteristics obtained by the data acquisition unit 31. In FIG. 4, the horizontal axis indicates the position [mm], and the vertical axis indicates the frictional force [Nm]. Further, for example, the current command [%] may be used as a parameter corresponding to the frictional force. As shown in FIG. 4, the actual machine friction characteristic is generally expressed as a hysteresis loop.

  The identification unit 32 uses the actual machine friction characteristics obtained by the data acquisition unit 31 to use the spring constant ki of each element, the maximum frictional force ratio αi of each element, the Coulomb frictional force Fc, and the maximum static frictional force Fs. Is identified.

Specifically, as shown in FIG. 5, the identification unit 32 includes a first friction identification unit 71, a second friction identification unit 72, and an element identification unit 73.
The first friction identification unit 71 identifies the Coulomb friction force from the friction force at the time of speed reversal of the actual machine friction characteristic represented as a hysteresis loop. As shown in FIG. 6, at the time of speed reversal, it corresponds to the lower left point P1 and the upper right point P2 in the actual machine friction characteristic represented as a hysteresis loop. First friction identifying unit 71 identifies the average value of the frictional force _{F P2} of the frictional force _{F P1} and upper right point P2 of the lower left point P1 a _{(= (F P2 -F P1)} / 2) as Coulomb friction Fc.
The second friction identification unit 72 calculates the maximum static friction force Fs by multiplying the Coulomb friction force Fc by one or more coefficients set in advance.

The element identification unit 73 linearly approximates the rising characteristic of the hysteresis of the actual machine friction characteristic, and calculates the spring constant ki of each element and the ratio αi of the maximum frictional force of each element from the approximate line. Specifically, as shown in FIG. 7, the coulomb friction force −Fc and + Fc are equally divided by a predetermined division number N (for example, initial value N = 5). Next, the slope Ki (i = 1 to N) in each section is calculated by linearly approximating the hysteresis characteristics in each section (element). Here, when direct linear approximation is difficult from the hysteresis in each section, first, the hysteresis to be linearly approximated is cut out, and then the cut-out portion is approximated to a polynomial whose position is a variable (for example, a fourth-order polynomial). Furthermore, this approximate expression may be approximated to a linear expression.
Next, the sections having the same slope are integrated into one section. For example, in FIG. 7, when the slope K1 of the first section and the slope K2 of the second section are the same, the first section and the second section are integrated. In this way, by integrating the sections, the number of sections can be reduced, and the subsequent arithmetic processing can be simplified.

FIG. 8 shows the hysteresis characteristic after such section integration is performed. As shown in FIG. 8, by integrating the first section and the second section, the number of divisions is changed to N = 4, and the slopes K1 to K4 in each section are calculated.
Subsequently, the maximum frictional force ratio αi (i = 1 to N, αi <1) in each section (element) is calculated. Here, since αi is the ratio of the maximum frictional force, αi (i = 1 to N) is set so that the sum of αi (i = 1 to N) is 1. In the present embodiment, it is set as follows.
α1 = 0.4
α2 = α3 = α4 = 0.2

  Next, the spring constant ki in each section is calculated using the slope Ki (i = 1 to N) of the linear linear approximation in each section and the maximum frictional force ratio αi (i = 1 to N) in each section. The spring constant ki is given by the following equations (7) and (8).

That is, the spring constants k1 to k4 in the present embodiment are as follows.
k4 = K4
k3 = K3-k4
k2 = K2- (k3 + k4)
k1 = K1- (k2 + k3 + k4)

Here, FIG. 9 shows the concept of the spring constant ki. In FIG. 9, for convenience of explanation, the value of the maximum frictional force αi in each section is shown as being different.
As shown in FIG. 9, the range position x is 0 <x ≦ x _1, consider the inclination K1 is generated from the first section by superposition of the components of the spring constant k1~k4 in the fourth section, the position When x is in the range of x ₁ <x ≦ x ₂ , the slope K2 is generated by superimposing the components of the spring constants k2 to k4 in the second interval to the fourth interval. In the range of x ₂ <x ≦ x ₃ , considered inclination K3 is generated from the third section by superposition of the components of the spring constant k3~k4 in the fourth period, the range of x 3 _<x ≦ x _4, components of the spring constant k4 in the fourth section It is assumed that the slope K4 is generated only by the above.

  In this way, the spring constant ki of each section (element), the maximum frictional force ratio αi of each section (element), the Coulomb friction force Fc, and the maximum static friction force Fs are identified.

  The parameter adjustment unit 33 calculates the Coulomb friction force Fc, the maximum static friction force Fs, the spring constant ki of each element, and the ratio αi of the maximum friction force of each section (element) identified by the identification unit 32 from the equation (1). Employed in the friction model given by equation (4) and inputting the speed into this friction model, the verification friction characteristic indicating the relationship between the position (integrated value of the speed) and the frictional force is calculated. Subsequently, an error between the verification friction characteristic and the actual machine friction characteristic is calculated, and when the error is within an allowable range, the various parameters identified by the identification unit 32 are output to the friction estimation unit 21. . Specifically, the parameter adjustment unit 33 calculates the ratio between the friction force of the verification friction characteristic and the friction force of the actual machine friction characteristic at each position, and the average value of the ratio is within an allowable range (for example, 1.05). Or less), it is determined to be within the allowable range.

  On the other hand, when the error is not within the allowable range, the Coulomb friction force Fc identified by the identification unit 32 is corrected, and the maximum static friction force Fs is corrected based on the corrected Coulomb friction force Fc. Then, by using the corrected Coulomb friction force Fc and the maximum static friction force Fs in the friction model, the verification friction characteristic is calculated again, and the verification friction characteristic and the actual machine friction characteristic are compared again (see FIG. 10). . Then, the value of the above-described Coulomb friction force Fc is repeatedly adjusted until this error falls within the allowable range. Thus, the parameters are adjusted only for the Coulomb friction force Fc and the maximum static friction force Fs, and the values identified by the identification unit 32 are used for the spring constant ki of each element and the ratio αi of the maximum friction force of each element. Since it is employed, parameter adjustment can be performed efficiently.

Next, the operation of the servo control device including the above-described friction compensation device 20 will be described with reference to FIG.
For example, during normal control, the position and speed of the object to be controlled are detected, and the detected position signal and speed signal information are fed back to the position / speed feedback systems 11 and 12, and the feedforward compensator 13 is used. Thus, a current command i ^* for causing the actual position to follow the position command is generated.
Note that, as described above, the speed signal may be obtained by calculation by differentiating (approximate differentiation) the detected position signal without detecting the actual speed, and this speed signal may be used for control.

The speed signal is input to the friction compensator 20, and the speed signal is input to the friction model of the friction estimation unit 21, whereby the friction force F is estimated. The estimated frictional force F is converted into a current command in the current command conversion unit 14 and output as a current compensation command i _dis . This current compensation command i _dis is subtracted from the current command value i ^* generated by the position / velocity feedback system, whereby the current command i ^* is corrected, and the corrected current command i _C ^* is sent to the drivers 90. Entered. By controlling the drivers 90 in accordance with the current command i _C ^* , position / speed control of the machine tool 100 is performed, and machining by the machine tool 100 along the target locus becomes possible.

  When such normal control is performed or when a parameter identification instruction is input when the operation of the machine tool 100 is stopped, the parameter identification unit 22 performs parameter identification. The parameter identification timing may be performed every time the machine tool 100 is started, or may be performed at predetermined time intervals such as several weeks or months. Further, it may be performed when an operator operates an input device such as a button for instructing parameter identification, or may be performed sequentially during operation of the machine tool. Thus, the parameter identification timing is not particularly limited.

At the time of parameter identification, the position signal, speed signal, and current command i _C ^* of the machine tool 100 are input to the parameter identification unit 22. The data acquisition unit 31 (see FIG. 2) of the parameter identification unit 22 acquires the actual machine friction characteristics from these pieces of information, and outputs the actual machine friction characteristics to the identification unit 32 (step SA1 in FIG. 11). The identification unit 32 specifies the Coulomb friction force Fc and the maximum static friction force Fs from the actual machine friction characteristics (step SA2 in FIG. 11), and further, by linear approximation of the hysteresis loop, the ratio of the maximum friction force αi of each element and each The spring constant ki of the element is determined (steps SA3 and SA4 in FIG. 11), and these identification parameters are output to the parameter adjustment unit 33.

The parameter adjustment unit 33 employs the identification parameter from the identification unit 32 in the friction model, and inputs a speed corresponding to the actual machine to the friction model, thereby calculating a verification friction characteristic indicating the relationship between the position and the friction force. (Step SA5 in FIG. 11). Subsequently, an error between the verification friction characteristic and the actual machine friction characteristic is calculated, and the Coulomb friction force Fc and the maximum static friction force Fs are adjusted until the error falls within the allowable range (step SA6 in FIG. 11) ( In step SA7 in FIG. 11, the identification parameter when the error falls within the allowable range is output to the friction estimation unit 21.
As a result, the friction estimation unit 21 estimates the frictional force using the latest identification parameter.

  As described above, according to the friction compensation device 20, the friction compensation method, and the servo control device according to the present embodiment, an actual machine friction characteristic represented by a hysteresis loop in which a position or speed and a friction force are associated is acquired. Since the parameters of the friction model are identified from the actual machine friction characteristics, a more detailed and dynamic friction model than the classical friction model can be constructed. As a result, the friction model can be dynamically adapted according to a change in the characteristics of the controlled object due to deterioration over time, the surrounding environment, and the like, and a reduction in control accuracy due to the influence of friction can be suppressed.

The configuration of the servo control device to which the friction compensation device 20 of the present invention is applied is not limited to the configuration shown in FIG. 1, and is widely applied to the servo control device to be controlled in which position and orientation control is performed. Is possible.
Further, in the present embodiment, the machine tool 100 is a control target, but the control target is not limited to this. Any machine may be used as long as its position, posture (for example, pitch angle, roll angle, yaw angle) is controlled to follow the target value.
For example, in the flying body, the frictional force in the flying nozzle that injects fuel becomes a problem. For example, the nozzle converts the rotational driving force of the motor into a linear motion system via a ball screw or the like, and is angle-controlled using a linear motion actuator. For this reason, the drive system has nonlinear friction. In order to reduce such a control error due to friction, the friction compensation device of the present invention is employed.

20 friction compensator 21 friction estimation unit 22 parameter identification unit 31 data acquisition unit 32 identification unit 33 parameter adjustment unit 41 first torque calculation unit 42 second torque calculation unit 43 friction force calculation unit 51 inverse models 52 and 62 to be controlled Filter 61 Operation amount-torque conversion model 71 First friction identification unit 72 Second friction identification unit 73 Element identification unit 100 Machine tool

Claims (6)

A friction compensation device that is applied to a servo control device that performs control to cause a control amount such as a position and orientation of a control target to follow a target value,
Parameter identifying means for identifying a predetermined parameter included in the friction model ;
Friction estimation means for estimating the friction force of the control object using the friction model in which the predetermined parameter is identified by the parameter identification means ,
The predetermined parameters include at least a Coulomb friction force and a maximum static friction force,
The parameter identification means includes
Data acquisition means for acquiring actual machine friction characteristics indicating the relationship between the position or speed of the control object and the friction force;
And identification means for using the actual friction characteristics to identify the predetermined parameter,
By inputting a position or speed into the friction model using the identified predetermined parameter, a verification friction characteristic indicating a relationship between the position or speed and the friction force is calculated, and the verification friction characteristic and the actual machine are calculated. It is determined whether or not the error from the friction characteristic is within a predetermined allowable range. When the error is not within the allowable range, the Coulomb friction force and the maximum static friction force are set so that the error is within the allowable range. And a parameter adjusting means for adjusting the friction compensation device. The actual machine friction characteristic is expressed as a hysteresis loop,
The said parameter adjustment means adjusts a Coulomb friction force by dividing the Coulomb friction force identified by the said identification means by the amplitude ratio of the hysteresis of the said friction characteristic for verification and the said actual machine friction characteristic. Friction compensator. The data acquisition means includes
First torque calculation means for calculating a torque including a disturbance component by inputting a position or speed to the inverse model of the control object;
Second torque calculation means for calculating torque from the operation amount using an operation amount-torque conversion model;
The frictional force calculating means for calculating a frictional force by subtracting the torque calculated by the second torque calculating means from the torque calculated by the first torque calculating means. Friction compensation device. The identification means includes
First friction force identification means for identifying the Coulomb friction force from the friction force at the time of speed reversal of the actual machine friction characteristics;
Second friction force identification means for identifying a maximum static friction force from the Coulomb friction force identified by the first friction force identification means;
The rise characteristic of hysteresis in the actual machine friction characteristic expressed as a hysteresis loop is linearly approximated, and parameters other than the Coulomb friction force and the maximum static friction force among the predetermined parameters are calculated from the linearly approximated hysteresis characteristic. The friction compensation apparatus according to any one of claims 1 to 3, further comprising element identification means for identifying.   A servo control device comprising the friction compensation device according to claim 1. A friction compensation method applied to a servo control device that performs control to cause a control amount such as a position and orientation of a control target to follow a target value,
A parameter identification process for identifying predetermined parameters included in the friction model ;
A friction estimation step of estimating the frictional force of the control object using the friction model in which the predetermined parameter is identified by the parameter identification step ,
The predetermined parameters include at least a Coulomb friction force and a maximum static friction force,
The parameter identification process includes:
A data acquisition process for acquiring actual machine friction characteristics indicating the relationship between the position or speed of the control object and the friction force;
Using the actual friction characteristics, and identifying step of identifying said predetermined parameters,
By inputting a position or speed into the friction model using the identified predetermined parameter, a verification friction characteristic indicating a relationship between the position or speed and the friction force is calculated, and the verification friction characteristic and the actual machine are calculated. It is determined whether or not the error from the friction characteristic is within a predetermined allowable range. When the error is not within the allowable range, the Coulomb friction force and the maximum static friction force are set so that the error is within the allowable range. And a parameter adjustment process for adjusting the friction compensation method.

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