Linear motor friction compensation method combining model feedforward with observer

Abstract

This invention discloses a linear motor friction compensation method combining model feedforward and observer, belonging to the field of linear motor friction compensation. The invention addresses the problem of frictional abrupt changes in existing permanent magnet synchronous linear motors during positive and negative velocity crossings, where the Stribeck friction model leads to overcompensation. The method includes: calculating the current static frictional force F based on the current mover velocity v. f Take the current static friction force F f The friction force feedforward compensation is calculated as 0.5 times the current value. Simultaneously, an observer estimates the viscous friction force compensation as an auxiliary compensation for the current static friction force based on the q-axis current command and the current actual position of the mover. The friction force feedforward compensation and viscous friction force compensation are converted into a compensation current and then superimposed with the current control command output by the position loop controller to obtain a compensated current control command, which is then input to the current loop. This invention is used for friction force compensation in linear motors.

Description

Technical Field

[0001] This invention relates to a linear motor friction compensation method combining model feedforward and observer, belonging to the field of linear motor friction compensation. Background Technology

[0002] Permanent magnet synchronous linear motors (PMLSMs) are characterized by high efficiency, high speed, and high precision, and are widely used in precision machining fields such as high-end CNC machine tools and lithography machines. However, the direct-drive structure of the motor makes it more susceptible to disturbances such as friction. Due to the low-speed creeping characteristics and critical static friction of friction, the system will experience position plateau and speed dead zone problems when the motor speed crosses zero. Therefore, it is necessary to compensate for the friction between the mover and the guide rail during motor operation to improve the motion control performance of the linear motor.

[0003] In the Stribeck model of static friction, velocity is the only dependent variable of the friction force function, and its specific expression is as follows:

[0004]

[0005] In the formula F f F is the static friction force, v is the velocity of the moving part, and F is the static friction force. c For Coulomb friction, F s This represents the maximum static friction force; v s Let B be the turning speed, δ be an empirical parameter, and B be the turning speed. v is the coefficient of viscous friction.

[0006] The Stribeck friction model curve can be obtained from the above expression, as shown below. Figure 4 As shown. The expression for Stribeck friction contains a sign function, thus indicating a nonlinear structure. Figure 4 As shown in the Stribeck local details, the sign function causes the derivative of the frictional force at v = 0 to approach infinity.

[0007] In practical industrial applications of PMLSM, reciprocating motion trajectories are frequently encountered. In a periodic cosine trajectory, there are two special velocity zero-crossing points every half-cycle, defined as positive velocity crossing (velocity from 0+→0→0-) and negative velocity crossing (velocity from 0-→0→0+). Both positive and negative crossings involve two motion phases: a stopping phase (0+→0 and 0-→0) and a starting phase (0→0- and 0→0+). From the perspective of the static friction model alone, the mover is not subjected to maximum static friction during the stopping phase; however, it experiences maximum static friction during the starting phase. If the Stribeck friction model is used for compensation, the friction model is continuous during the velocity transition from positive to 0+, and the friction force changes to F...s The process is also continuous, but during the reverse motion, the frictional force changes from positive to negative. s Change to negative F s The process is very brief. Linear motors have electrical and mechanical time constants, as well as control delays and frictional hysteresis at zero crossings. If the driver's output thrust cannot track the feedforward controller command of the nonlinear abrupt change, then the feedforward command and the driver's output thrust are superimposed on the mover, resulting in a thrust greater than F. s This refers to a situation where frictional overcompensation occurs. Summary of the Invention

[0008] To address the issue that existing permanent magnet synchronous linear motors exhibit frictional abrupt changes during positive and negative velocity crossings, and that using the Stribeck friction model for compensation can lead to overcompensation of frictional force, this invention provides a linear motor frictional force compensation method that combines model feedforward with an observer.

[0009] The present invention provides a linear motor friction compensation method combining model feedforward and observer, comprising:

[0010] The current static friction force F is calculated based on the current velocity v of the moving part. f Take the current static friction force F f 0.5 times the frictional force feedforward compensation amount;

[0011] At the same time, the observer estimates the viscous friction compensation amount as an auxiliary compensation amount for the current static friction force based on the q-axis current command and the current actual position of the mover;

[0012] The frictional force feedforward compensation and viscous frictional force compensation are converted into compensation current and then superimposed with the current control command output by the position loop controller to obtain the compensated current control command, which is then input to the current loop.

[0013] According to the linear motor friction compensation method combining model feedforward and observer of the present invention, the method for obtaining the current mover velocity v is as follows:

[0014] The current motioner velocity v is obtained by performing a differential operation based on the current reference position of the motioner and the preset desired motioner trajectory.

[0015] According to the linear motor friction compensation method combining model feedforward and observer of the present invention, the current static friction force F f The calculation method is as follows:

[0016]

[0017] In the formula F f F is the current static friction force. c For Coulomb friction, Fs This represents the maximum static friction force; v s Let B be the turning speed, δ be an empirical parameter, and B be the turning speed. v It is the coefficient of viscous friction.

[0018] According to the linear motor friction compensation method combining model feedforward and observer of the present invention, the friction feedforward compensation amount and the viscous friction compensation amount are respectively divided by the thrust coefficient k. f The corresponding compensation current is obtained.

[0019] According to the linear motor friction compensation method combining model feedforward and observer of the present invention, the input of the position loop controller is the difference between the current reference position and the current actual position of the mover.

[0020] According to the linear motor friction compensation method combining model feedforward and observer of the present invention, the current loop obtains the actual control current based on the compensated current control command.

[0021] According to the linear motor friction compensation method combining model feedforward and observer of the present invention, the actual control current and thrust coefficient k are used. f The input thrust of the permanent magnet synchronous linear motor is calculated.

[0022] According to the linear motor friction compensation method combining model feedforward and observer of the present invention, the observer is a disturbance observer, a sliding mode observer, or an extended state observer.

[0023] According to the linear motor friction compensation method combining model feedforward and observer of the present invention, the observer estimates the amount of viscous friction compensation based on the q-axis current command and the current actual position of the mover through the mechanical state equation of the permanent magnet synchronous linear motor.

[0024] According to the linear motor friction compensation method combining model feedforward and observer of the present invention, the current loop adopts PI control; the position loop controller adopts PI controller plus phase lead compensation stage.

[0025] The beneficial effects of this invention are as follows: To suppress the problem of friction overcompensation, the method of this invention divides the Stribeck feedforward compensation by 2, thus solving the overcompensation problem at the zero-crossing velocity point. Furthermore, to address the undercompensation of viscous friction in the non-zero velocity region caused by this, an observer is added to compensate for the remaining viscous friction. Experimental verification shows that the method of this invention achieves simultaneous reduction of position error in both the zero-crossing and non-zero velocity regions, with the position error in the zero-crossing velocity region being only ±10 micrometers. Attached Figure Description

[0026] Figure 1This is a flowchart of the linear motor friction compensation method combining model feedforward and observer as described in this invention; in the figure, 's' represents the differential operation.

[0027] Figure 2 The corresponding variable experimental waveforms are obtained using the Stribeck friction model for feedforward compensation.

[0028] Figure 3 The waveform diagrams of corresponding variables are obtained by compensating for friction using the method of this invention.

[0029] Figure 4 It is a Stribeck curve. Detailed Implementation

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0031] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0032] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0033] Specific Implementation Method 1: Combination Figure 1 As shown, this invention provides a linear motor friction compensation method combining model feedforward and observer, comprising:

[0034] The current static friction force F is calculated based on the current velocity v of the moving part. f Take the current static friction force F f 0.5 times the frictional force feedforward compensation amount;

[0035] At the same time, the observer estimates the viscous friction compensation amount as an auxiliary compensation amount for the current static friction force based on the q-axis current command and the current actual position of the mover;

[0036] The frictional force feedforward compensation and viscous frictional force compensation are converted into compensation current and then superimposed with the current control command output by the position loop controller to obtain the compensated current control command, which is then input to the current loop.

[0037] In this embodiment, if the calculated current static friction force F is used exactly... fFriction compensation can lead to overcompensation at friction jump points during positive and negative velocity crossings. To mitigate this overcompensation, this implementation divides the Stribeck feedforward compensation by 2. While this division resolves the overcompensation at zero velocity crossings, it results in undercompensation of viscous friction in the non-zero velocity region. Therefore, an observer is incorporated into the compensation strategy to compensate for the remaining viscous friction, thus better compensating for nonlinear friction.

[0038] Furthermore, the method for obtaining the current mover velocity v is as follows:

[0039] The current motioner velocity v is obtained by performing a differential operation based on the current reference position of the motioner and the preset desired motioner trajectory.

[0040] Current static friction force F f The calculation method is as follows:

[0041]

[0042] In the formula F f F is the current static friction force. c For Coulomb friction, F s This represents the maximum static friction force; v s Let B be the turning speed, δ be an empirical parameter, and B be the turning speed. v It is the coefficient of viscous friction.

[0043] Combination Figure 1 As shown, the frictional force feedforward compensation and the viscous frictional force compensation are respectively divided by the thrust coefficient k. f The corresponding compensation current is obtained.

[0044] The input to the position loop controller is the difference between the current reference position and the current actual position of the mover.

[0045] The current loop obtains the actual control current based on the compensated current control command.

[0046] Based on the actual control current and thrust coefficient k f The input thrust of the permanent magnet synchronous linear motor is calculated, which includes the actual control current and the thrust coefficient k. f Multiplying these together yields the input thrust of the permanent magnet synchronous linear motor.

[0047] As an example, the term "observer" generally refers to a disturbance observer (DOB), sliding mode observer, or extended state observer, etc.

[0048] Furthermore, based on the q-axis current command and the current actual position of the mover, the observer estimates the viscous friction compensation amount in real time through the mechanical state equation of the permanent magnet synchronous linear motor, and feeds the compensation to the current command.

[0049] In general, nonlinear friction can be better compensated by adding the friction feedforward to the observer's output.

[0050] The current loop uses PI control; the position loop controller uses a PI controller with phase lead compensation.

[0051] Figure 1 In the process, the desired trajectory of the mover is generated by trajectory planning to produce the current position command of the mover; the permanent magnet synchronous linear motor uses a double integral element for equivalence, and the current actual position of the mover of the motor can be obtained by measuring with a grating ruler.

[0052] In this invention, friction compensation includes a friction feedforward compensation section and an observer section. The current reference position of the mover is used to obtain the current mover velocity v through a differential element, and the friction feedforward value is calculated using a friction function. To suppress the problem of friction overcompensation at the zero-crossing velocity point, a coefficient of 0.5 is added before the friction output value; combined with the observer, this achieves comprehensive suppression of Coulomb friction and viscous friction.

[0053] Experimental verification:

[0054] A linear motor experimental platform was built, and the waveforms were verified experimentally as follows: Figure 2 and Figure 3 As shown, from Figure 2 As can be seen, the overcompensation problem of the Stribeck friction model causes the position error to increase instead of decrease in the zero-crossing velocity region, with the peak position error reaching ±100 micrometers in the zero-crossing region; furthermore... Figure 3 As shown, the method of the present invention can achieve synchronous reduction of position error in both the zero-velocity region and the non-zero-velocity region, with the position error in the zero-velocity region being only ±10 micrometers.

[0055] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for compensating friction in a linear motor by combining model feedforward and observer, characterized in that... include, Based on the current mover velocity Calculate the current static friction force Take the current static friction force 0.5 times the frictional force feedforward compensation amount; At the same time, the observer estimates the viscous friction compensation amount as an auxiliary compensation amount for the current static friction force based on the q-axis current command and the current actual position of the mover; The frictional force feedforward compensation and viscous frictional force compensation are converted into compensation current and then superimposed with the current control command output by the position loop controller to obtain the compensated current control command, which is then input to the current loop. The current mover velocity The method to obtain it is as follows: The current motioner velocity is obtained by performing a differential operation based on the preset desired motioner trajectory from the current reference position of the motioner. ; Current static friction force The calculation method is as follows: ， In the formula Given the current static friction force, For Coulomb friction, This is the maximum static friction force; For turning speed, These are empirical parameters. It is the coefficient of viscous friction; The observer estimates the viscous friction compensation amount based on the q-axis current command and the current actual position of the mover through the mechanical state equation of the permanent magnet synchronous linear motor. The current loop uses PI control; The position loop controller uses a PI controller with a phase lead compensation circuit.

2. The linear motor friction compensation method combining model feedforward and observer as described in claim 1, characterized in that, The frictional feedforward compensation and the viscous frictional compensation are respectively divided by the thrust coefficient. The corresponding compensation current is obtained.

3. The linear motor friction compensation method combining model feedforward and observer as described in claim 2, characterized in that, The input to the position loop controller is the difference between the current reference position and the current actual position of the mover.

4. The linear motor friction compensation method combining model feedforward and observer as described in claim 3, characterized in that, The current loop obtains the actual control current based on the compensated current control command.

5. The linear motor friction compensation method combining model feedforward and observer as described in claim 4, characterized in that, Based on actual control current and thrust coefficient The input thrust of the permanent magnet synchronous linear motor is calculated.

6. The linear motor friction compensation method combining model feedforward and observer as described in claim 1, characterized in that, The observer is a disturbance observer, a sliding mode observer, or an extended state observer.

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