CN116107221A - Control method of servo control system - Google Patents
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Abstract
The application provides a control method of a servo control system, which comprises the steps of obtaining an original track signalX ref （t) The method comprises the steps of carrying out a first treatment on the surface of the For the original track signalX ref （t) Performing pre-filtering processing and based on transfer function of the pre-filtering processingG AD （s) Calculating a filtered trajectory signalY ref （t) The pre-filtering process is used for suppressing residual vibration of the servo control system; transfer functionG AD （s) The poles of the equivalent servo control system are offset by introducing the zero point, and meanwhile, poles with high damping ratio are configured for the whole open loop system in the pre-filtering treatment process, so that the open loop system is changed from a low damping state to a high damping state, the amplitude of residual vibration is reduced, and the attenuation of the residual vibration is accelerated.
Description
Technical Field
The present disclosure relates generally to the field of servo control systems, and in particular, to a control method of a servo control system.
Background
Mechanical equipment is the basis for achieving industrial automation, and effective movement of the equipment typically requires planning and adjustment of a servo control system. In order to speed up the tact time and improve the production efficiency, trapezoidal trajectory planning is applied to a large number of sports equipment. However, since the servo control system has flexible components such as a coupler, a speed reducer, a transmission shaft and the like, residual vibration phenomenon is easy to generate on the load side of the mechanical equipment after the rapid positioning movement is finished, and the residual vibration phenomenon has slower attenuation speed and longer duration in a common low damping system (servo control system), so that the quality of the surface of a processed product can be influenced, and the service life and the production efficiency of the part can be reduced.
In the prior art, a shaping technology (i.e. a shaper is introduced to process an input track to inhibit residual vibration of a servo control system) or a track smoothing technology (i.e. a smoother is introduced to process the input track to inhibit residual vibration of the servo control system) is mostly adopted; however, neither the shaping technique nor the track smoothing technique effectively solves the problem of longer duration of residual vibration and larger amplitude of vibration in a low damping system (i.e., a servo control system).
Disclosure of Invention
In view of the foregoing drawbacks or shortcomings in the prior art, it is desirable to provide a control method of a servo control system that can solve the foregoing technical problems.
A first aspect of the present application provides a control method of a servo control system, including:
acquiring an original track signalX ref （t）；
For the original track signalX ref （t) Performing a pre-filter process and based on a transfer function of the pre-filter processG AD （s) Calculating a filtered trajectory signalY ref （t) The pre-filtering process is used for inhibiting residual vibration of the servo control system;
wherein ,
is a natural frequency set value, < >>
Is a damping ratio set value; />
Is a preset value;X ref （s) Representation ofX ref （t) Is a laplace transform of (a),Y ref （s) Representation ofY ref （t) Is a laplace transform of (a);Lthe representation of the laplace transform is made,sin order to be of a complex frequency,ttime is;
with the filtered track signalY ref （t) Controlling the servo control system to move.
According to the technical scheme provided by the embodiment of the application, the natural frequency set value
Damping ratio set point->
The setting method of (2) comprises the following steps:
acquiring a plurality of groups of corresponding system parameters of the servo control system in the motion process of different flexible loads according to the same input track, wherein the system parameters comprise natural frequencies
And damping ratio->
；
Calculating the natural frequency
And takes this as the natural frequency set value +.>
；/>
Calculating the damping ratio
And takes this as damping ratio set value +.>
。
According to the technical scheme provided by the embodiment of the application, the method for acquiring the corresponding multiple groups of system parameters of the servo control system in the motion process of different flexible loads according to the same input track comprises the following steps:
the servo control system of different flexible loads under the same input track is subjected to quick positioning linear motion;
obtaining a residual vibration displacement curve of each flexible load in the rapid positioning linear motion process;
and calculating the system parameters according to the residual vibration displacement curve.
According to the technical scheme provided by the embodiment of the application, according to the residual vibration displacement curve, calculating the system parameter comprises the following steps:
performing fast Fourier transform on the residual vibration displacement curve to obtain vibration frequencyf；
Calculating the natural frequency according to formula (2)
：
According to the technical scheme provided by the embodiment of the application, according to the residual vibration displacement curve, calculating the system parameter further comprises the following steps:
calculating a damping ratio according to formula (3)
：
wherein ,
represent the firstqThe rate of decay of the one cycle,x p represent the firstpAnd a vibration peak.
According to the technical scheme provided by the embodiment of the application, the transfer function based on the pre-filtering processingG AD （s) Calculating a filtered trajectory signalY ref （t) The method of (1) comprises: calculated according to formula (1)Y ref （s) The method comprises the steps of carrying out a first treatment on the surface of the For a pair ofY ref （s) Inverse Laplace transform is carried out to obtain a filtered track signalY ref （t）；
With the filtered track signalY ref （t) The method for controlling the motion of the servo control system comprises the following steps: the filtered track signalY ref （t) Conversion to a filtered discrete trackY ref [n]；Y ref [n]=Y ref （t=nT s ）；T S Is the sampling period;Y ref [n]representing an nth filtered discrete trace; with the filtered discrete tracksY ref [n]Controlling the servo control system to move.
A second aspect of the present application provides a control method of a servo control system, including:
acquiring an original track signalX ref （t）；
For the original track signalX ref （t) Performing a pre-filter process and based on a transfer function of the pre-filter processG AD （s) Calculating a filtered discrete trajectoryY ref [n]The prefilterWave processing for suppressing residual vibration of the servo control system;
with the filtered discrete tracksY ref [n]Controlling the servo control system to move;
wherein the transfer functionG AD （s) The method comprises the following steps:
Y ref （t) In order to filter the track signal,
is a natural frequency set value, < >>
Is a damping ratio set value; />
Is a preset value;X ref （s) Representation ofX ref （t) Is a laplace transform of (a),Y ref （s) Representation ofY ref （t) Is a laplace transform of (a);Lthe representation of the laplace transform is made,sin order to be of a complex frequency,ttime is;
wherein the transfer function based on the pre-filter processingG AD （s) Calculating a filtered discrete trajectoryY ref [n]The method comprises the following steps:
for transfer functionG AD （s) Performing bilinear transformation to obtain a transformed transfer functionG AD （z）：
wherein ,X ref （z) Representation pairX ref （s) The z-transform is performed and,Y ref （z) Representation pairY ref （s) Performing z transformation;a 1 、a 2 、b 0 、b 1 、b 2 is a coefficient;
transfer function after transformationG AD （z) Converting into a differential equation to obtain a formula (5);
wherein ,X ref [n]=X ref （t=nT s ），Y ref [n]=Y ref （t=nT s ）；T S is the sampling period;X ref [n]representing the nth original discrete track;Y ref [n]representing an nth filtered discrete trace;w[n]representing an intermediate quantity; when n=k<At the time of 0, the temperature of the liquid,X ref [k]=0、w[k]=0、Y ref [k]=0；
calculating a filtered discrete trajectory according to equation (5)Y ref [n]。
According to the technical scheme provided by the embodiment of the application, the natural frequency set value
Damping ratio set point->
The setting method of (2) comprises the following steps:
acquiring a plurality of groups of corresponding system parameters of the servo control system in the motion process of different flexible loads according to the same input track, wherein the system parameters comprise natural frequencies
And damping ratio->
；
Calculating the natural frequency
And takes this as the natural frequency set value +.>
；
Calculating the damping ratio
And takes this as damping ratio set value +.>
。
According to the technical scheme provided by the embodiment of the application, the method for acquiring the corresponding multiple groups of system parameters of the servo control system in the motion process of different flexible loads according to the same input track comprises the following steps:
the servo control system of different flexible loads under the same input track is subjected to quick positioning linear motion;
obtaining a residual vibration displacement curve of each flexible load in the rapid positioning linear motion process;
and calculating the system parameters according to the residual vibration displacement curve.
According to the technical scheme provided by the embodiment of the application, according to the residual vibration displacement curve, calculating the system parameter comprises the following steps:
performing fast Fourier transform on the residual vibration displacement curve to obtain vibration frequencyf；
Calculating the natural frequency according to formula (2)
：
The beneficial effects of this application lie in: the application is realized by the method for the original track signalX ref （t) Performing pre-filtering, introducing zero point during pre-filtering, and canceling the equivalent poles of the servo control system by the zero point, which is the same as that of the servo control systemWhen the method is used, the pole with high damping ratio is configured for the whole open loop system in the pre-filtering treatment process, so that the open loop system is changed from a low damping state to a high damping state, the amplitude of residual vibration is reduced, the attenuation of the residual vibration is accelerated, meanwhile, the combination test can also show that the robustness is better, the lag time is lower, and the method is beneficial to improving the production efficiency.
Drawings
Other features, objects and advantages of the present application will become more apparent upon reading of the detailed description of non-limiting embodiments, made with reference to the following drawings, in which:
FIG. 1 is a flow chart of a control method of a servo control system provided in the present application;
FIG. 2 is a control system provided herein;
FIG. 3 is a graph showing frequency as a function of gain (amplitude) using the control method of the servo control system of the present application;
FIG. 4 is a plot of frequency versus gain (amplitude) for residual vibration suppression using a smoother;
FIG. 5 is a plot of frequency as a function of gain (amplitude) for residual vibration suppression using a shaper;
FIG. 6 is a graph showing the phase frequency characteristics of the present application;
FIG. 7 is a graph showing the phase frequency characteristics under suppression using a smoother;
FIG. 8 is a graph of phase frequency characteristics under suppression using a shaper;
FIG. 9 is a graph comparing load side displacement over time without the suppression method, with the shaper suppression method, with the method of the present application, and with the smoother suppression method;
FIG. 10 is an absolute value of the difference between the first pair of peaks and valleys of the residual vibration displacement after the end of the positioning motion without the suppression method, with the shaper suppression method, with the method of the present application, and with the smoother suppression methodhWith vibration frequencyfIs a graph of the change fold line contrast;
reference numerals in the drawings:
100. a pre-filter; 200. a motor; 300. an equivalent flexible system.
Detailed Description
The present application is described in further detail below with reference to the drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting of the invention. It should be noted that, for convenience of description, only the portions related to the invention are shown in the drawings.
It should be noted that, in the case of no conflict, the embodiments and features in the embodiments may be combined with each other. The present application will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.
Example 1
Referring to fig. 1, a flowchart of a control method of a servo control system provided in the present application includes:
s100: acquiring an original track signalX ref （t）；
S200: for the original track signalX ref （t) Performing a pre-filter process and based on a transfer function of the pre-filter processG AD （s) Calculating a filtered trajectory signalY ref （t) The pre-filtering process is used for inhibiting residual vibration of the servo control system;
wherein ,
is a natural frequency set value, < >>
Is a damping ratio set value; />
Is a preset value;X ref （s) Representation ofX ref （t) Is a laplace transform of (a),Y ref （s) Representation ofY ref （t) Is a laplace transform of (a);Lrepresenting the laplace transform, s is the complex frequency,ttime is;
s300: with the filtered track signalY ref （t) Controlling the servo control system to move.
Specifically, the servo control system is a flexible servo control system with a low damping ratio; typically, when the damping ratio is less than 0.1, then it is a low damping ratio; when the damping ratio is greater than 0.1, then a high damping ratio is obtained. For servo control systems, the damping ratio is typically less than 0.1, i.e., the damping ratio of the present servo control system is less than 0.1.
It should be further noted that, the control method of the servo control system provided in the present application suppresses residual vibration of the servo control system on the whole by introducing "zero" and configuring two dimensions of "high damping pole", based on the pre-filtering process. In order to facilitate understanding to those skilled in the art, a specific description will be given below about the inventive concept of the present application.
First, for the input of the flexible servo control system, i.e. the raw track signalX ref （t) The track (commonly referred to as a trapezoidal track) used in any industry;
considering that the driving mechanism (e.g., motor 200) of the flexible servo control system reaches an ideal state, the flexible servo control system can be equivalently: base and mass in equivalent flexible system 300mDynamic relationship between them, namely constant coefficient linear differential equation with respect to time, and Laplace transformation is performed on the dynamic relationship to obtain frequency information, and the dynamic relationship is converted from time domaintConversion to the frequency domainsObtaining a transfer functionG 12 ：
Wherein, in the formulax 2 (t) For the position of the mass relative to the base,x 1 (t) Is the absolute position of the base;
is the natural frequency of the undamped,ζfor the damping ratio (which is related to the damping speed of the residual vibration, the smaller the damping ratio, the slower the damping, the lower the production efficiency), both can be obtained by analyzing the vibration displacement signal in the laser vibrometer.
In order to suppress the residual vibration of the servo control system, therefore, an open loop system in which the pre-filter 100 and the equivalent flexible system 300 are cascaded is obtained by cascading the pre-filter 100 on the basis of the equivalent flexible system 300; in this process, in order to suppress the residual vibration of the servo control system, the inventor introduces a "zero point" into the pre-filter 100, and counteracts a "pole" in the equivalent flexible system 300 through the "zero point", and simultaneously configures a pole with a high damping ratio for the whole open loop system in the pre-filter 100, so that the system is changed from a low damping state to a high damping state, thereby reducing the amplitude of the residual vibration and accelerating the attenuation of the residual vibration; setting the transfer function of the pre-filter 100 as formula (1);
it should be further described that, the zero is obtained by making the molecule of the transfer function zero, and the addition of the zero causes the change of the system response, namely the change of the output phase; the transfer function denominator is made zero to obtain a pole, the pole comprises a damping ratio and a natural frequency parameter, and the pole with a low damping ratio is a main reason for causing the system to generate residual vibration.
In order to intuitively highlight the effect generated in the present application, that is, the pre-filtering treatment according to the formula (1) reduces the amplitude of the residual vibration and accelerates the attenuation of the residual vibration, the pre-filtering treatment (hereinafter referred to as the present case) and the pre-filtering treatment (hereinafter referred to as the prior art) are compared and described.
In the prior art, a servo control system is taken as a whole, and the formula (1-1) can know that the poles of the system are as follows:
the damping ratio of the system is +.>
And->
Less than 0.1;
in this case, the prefilter 100 and the servo control system are cascaded to be an open loop system, and the transfer function of the overall system is as follows:
considering that there is a deviation between the actual model and the nominal model of the equivalent flexible system 300, the relationship between the two can be expressed as follows
wherein ,
、/>
is the deviation coefficient; when the natural frequency is set to->
Equal to the natural frequency of the equivalent flexible system 300, damping ratio set point +.>
When the damping ratio is equal to that of the equivalent flexible system 300, i.e. coefficient of deviation +.>
，/>
=0, the zero introduced by the pre-filter 100 cancels the pole of the equivalent flexible system 300, thisNew pole introduced by the temporal pre-filter 100
Becomes the actual pole of the system; due to->
Therefore, the pole of the open loop system is in a high damping state;
and as will be appreciated by those skilled in the art, item iqDamping rate and damping ratio of each cycle
The relation of (2) is:
compared with the prior art, the damping ratio is relatively improved, so that the damping rate is improved, and the damping of residual vibration is accelerated.
Meanwhile, in the prior art, a servo control system is taken as a whole, and the system output of unit pulse is as follows:
Arepresenting the amplitude;
compared with the prior art, the damping ratio is relatively improved, so that the amplitude of residual vibration is reduced.
It should be noted that when the deviation coefficient
，/>
When not equal to 0 and the deviation coefficient value is small (the variation here is not large in engineering), the zero introduced by the pre-filter can largely cancel the effect of the pole of the equivalent flexible system 300, the new pole introduced by the pre-filter is ≡>
Still can be the actual pole of the system.
In some embodiments, the preset value is therefore used to increase the damping ratio of the open loop system
The range of the values is as follows: />
；
Preferably, in order to accelerate the damping of the residual vibration of the system, the damping ratio of the open loop system is configured to be maximum, namely in a critical damping state; thus making the lead
Obtaining a transfer functionG AD ( S )：
In some embodiments, the control method of the servo control system may be applied to the pre-filter 100, as shown in fig. 2, where the output end of the pre-filter 100 is connected to a servo control system, and the servo control system includes a motor 200 and an equivalent flexible system 300 connected to the output end of the motor 200.
Example 2
Based on embodiment 1, in some embodiments, the natural frequency set point
Damping ratio set point->
The setting method of (2) comprises the following steps:
acquiring a plurality of groups of corresponding system parameters of the servo control system in the motion process of different flexible loads according to the same input track, wherein the system parameters comprise natural frequencies
And damping ratio->
；
Calculating the natural frequency
And takes this as the natural frequency set value +.>
；
Calculating the damping ratio
And takes this as damping ratio set value +.>
。
In particular, different flexible loads refer to weight and position changes of the load, and by controlling the movement of the different flexible loads with the same input trajectory, multiple sets of system parameters are obtained, thereby obtaining natural frequencies
And damping ratio->
To determine the design value of the pre-filter.
Specifically, the servo control system comprises a motion control card, a motor 200, an equivalent flexible system 300 and the like, the input track is only written in upper computer software, and then the upper computer, the motor 200 and the motion control card are in communication to realize the motions of different tracks;
specifically, by combining the natural frequencies
Is taken as the natural frequency set value +.>
Damping ratio->
Is taken as the damping ratio set value +.>
So that the purpose of fully utilizing the robustness of the designed pre-filter can be achieved.
In some embodiments, obtaining the corresponding plurality of sets of system parameters of the servo control system in the process of controlling different flexible loads to move according to the same input track comprises the following steps:
the servo control system of different flexible loads under the same input track is subjected to quick positioning linear motion;
obtaining a residual vibration displacement curve of each flexible load in the rapid positioning linear motion process;
and calculating the system parameters according to the residual vibration displacement curve.
Specifically, in the rapid positioning rectilinear motion: fast means that the values of the speed and acceleration parameters of the input trajectory are large (the value in the test is speed 400mm/sAcceleration 5000mm/s 2 ) This meets the requirement of high productivity and also easily causes residual vibration on the load side; positioning linear motion refers to the process of inputting a track to a motion control card for discrete processing, and then driving a load to move from one point to another point by the motor 200, wherein the process can be completed in hundreds of milliseconds.
Specifically, after the rapid positioning linear motion is finished, the load can generate a small-amplitude vibration phenomenon, the vibration is called residual vibration, and a displacement curve of the vibration is obtained through a laser vibration meter. The laser vibration meter can obtain the displacement (including residual vibration displacement) of a load from the beginning of movement to a certain time by beating laser on reflective foil paper and utilizing Doppler effect, and can obtain time-displacement data of different data amounts (for example, 500 ten thousand) on upper computer software of the laser vibration meter by adjusting sampling rate, so as to draw a residual vibration displacement curve;
in some embodiments, calculating the system parameter from the residual vibration displacement curve comprises the steps of:
performing fast Fourier transform on the residual vibration displacement curve to obtain vibration frequencyf；
Calculating the natural frequency according to formula (2)
：
Specifically, the vibration frequency can be obtained through the self-contained fast Fourier transform of the upper computer softwarefThe method comprises the steps of carrying out a first treatment on the surface of the Considering that the system is in a low damping state mostly, the natural frequency of the system can be obtained through
Obtained.
In some embodiments, deriving the system parameter from the residual vibration displacement curve further comprises the steps of:
calculating a damping ratio according to formula (3)
：
wherein ,
represent the firstqThe rate of decay of the one cycle,x p represent the firstpAnd a vibration peak.
In some embodiments, a transfer function based on the pre-filter processG AD （s) Calculating a filtered trajectory signalY ref （t) The method of (1) comprises: calculated according to formula (1)Y ref （s) The method comprises the steps of carrying out a first treatment on the surface of the For a pair ofY ref （s) Inverse Laplace transform is carried out to obtain a filtered track signalY ref （t）；
In the way describedFiltering trajectory signalsY ref （t) The method for controlling the motion of the servo control system comprises the following steps: the filtered track signalY ref （t) Conversion to a filtered discrete trackY ref [n]；Y ref [n]=Y ref （t=nT s ）；T S Is the sampling period;Y ref [n]representing an nth filtered discrete trace; with the filtered discrete tracksY ref [n]Controlling the servo control system to move.
In the above steps, by continuously filtering the track signalY ref （t) Converting into discrete filtered discrete tracksY ref [n]To meet different application environments and different use requirements.
Example 3
The present embodiment provides a control method of a servo control system, whose core principle is the same as that of the servo control system in embodiment 1, in which zero is introduced into the pre-filter to cancel out the pole of the equivalent flexible system, and at the same time, a new pole is introduced into the pre-filter
Becomes the actual pole of the system; due to->
The pole of the open loop system is therefore in a highly damped state; thereby accelerating the attenuation of the residual vibration and reducing the amplitude of the residual vibration.
The present embodiment is different from embodiment 1 in that in order to directly acquire a discrete filter trajectory (i.e., a filter discrete trajectoryY ref [n]) In this embodiment, the formula (1) is transformed to directly output the filtered discrete trackY ref [n]Namely, the present embodiment provides a control method of a servo control system, including:
acquiring an original track signalX ref （t）；
For the original track signalX ref （t) The pre-filtering process is carried out and the filter is carried out,and based on the transfer function of the pre-filter processingG AD （s) Calculating a filtered discrete trajectoryY ref [n]The pre-filtering process is used for inhibiting residual vibration of the servo control system;
with the filtered discrete tracksY ref [n]Controlling the servo control system to move;
wherein the transfer functionG AD （s) The method comprises the following steps:
Y ref （t) In order to filter the track signal,
is a natural frequency set value, < >>
Is a damping ratio set value; />
Is a preset value;X ref （s) Representation ofX ref （t) Is a laplace transform of (a),Y ref （s) Representation ofY ref （t) Is a laplace transform of (a);Lrepresenting the laplace transform, s is the complex frequency,ttime is;
wherein the transfer function based on the pre-filter processingG AD （s) Calculating a filtered discrete trajectoryY ref [n]The method comprises the following steps:
for transfer functionG AD （s) Performing bilinear transformation to obtain a transformed transfer functionG AD （z）：
wherein ,X ref （z) Representation pairX ref （s) The z-transform is performed and,Y ref （z) Representation pairY ref （s) Performing z transformation;a 1 、a 2 、b 0 、b 1 、b 2 is a coefficient;
transfer function after transformationG AD （s) Converting into a differential equation to obtain a formula (5);
wherein ,X ref [n]=X ref （t=nT s ），Y ref [n]=Y ref （t=nT s ）；T S is the sampling period;X ref [n]representing the nth original discrete track;Y ref [n]representing an nth filtered discrete trace;w[n]representing an intermediate quantity; when n=k<At the time of 0, the temperature of the liquid,X ref [k]=0、w[k]=0、Y ref [k]=0；
calculating a filtered discrete trajectory according to equation (5)Y ref [n]。
In some embodiments, the natural frequency set point
Damping ratio set point->
The setting method of (2) comprises the following steps:
acquiring a plurality of groups of corresponding system parameters of the servo control system in the motion process of different flexible loads according to the same input track, wherein the system parameters comprise natural frequencies
And damping ratio->
；
Calculating the solidWith frequency
And takes this as the natural frequency set value +.>
；
Calculating the damping ratio
And takes this as damping ratio set value +.>
。
In some embodiments, obtaining the corresponding plurality of sets of system parameters of the servo control system in the process of controlling different flexible loads to move according to the same input track comprises the following steps:
the servo control system of different flexible loads under the same input track is subjected to quick positioning linear motion;
obtaining a residual vibration displacement curve of each flexible load in the rapid positioning linear motion process;
and calculating the system parameters according to the residual vibration displacement curve.
In some embodiments, calculating the system parameter from the residual vibration displacement curve comprises the steps of:
performing fast Fourier transform on the residual vibration displacement curve to obtain vibration frequencyf；
Calculating the natural frequency according to formula (2)
：
In some embodiments, deriving the system parameter from the residual vibration displacement curve further comprises the steps of:
calculating a damping ratio according to formula (3)
：
wherein ,
represent the firstqThe rate of decay of the one cycle,x p represent the firstpAnd a vibration peak.
In some embodiments, the preset value is therefore used to increase the damping ratio of the open loop system
The range of the values is as follows: />
；
Preferably, in order to accelerate the damping of the residual vibration of the system, the damping ratio of the open loop system is configured to be maximum, namely in a critical damping state; thus making the lead
Obtaining a transfer functionG AD （s）：
Example 4
To further illustrate the technical effects of the present application, the present embodiment is described in terms of theoretical simulation.
Experiment 1:
as shown in fig. 3, 4 and 5, the solid curve with downward opening represents the bode diagram (bode diagram) of the system model, and the gain at the peak is the largest, which means that the load resonance around this frequency is intense, and the residual vibration suppression method is needed for attenuation; the dashed curves shown in fig. 3, 4 and 5 with downward openings represent that the frequency parameters of the actual system deviate somewhat from the parameters of the system model, resulting in frequencies at the peaks that may be on the left side of the model or on the right side of the model.
The graph with upward opening in fig. 3 shows the frequency as a function of gain (amplitude) in a manner employing the control method of the servo control system of the present application;
the curve with the opening up in fig. 4 shows the frequency as a function of gain (amplitude) in the manner of residual vibration suppression using a smoother;
the graph in fig. 5 with the opening up shows the frequency as a function of gain (amplitude) in the manner of residual vibration suppression using a shaper;
it should be noted that, as can be seen from fig. 3 to fig. 5, the negative gain is brought to the system by adopting various modes, and the suppression effect is achieved for the residual vibration; wherein, when the deeper the peak is concave, the better the residual vibration suppression effect is when the parameter has no deviation; the width of two sides at the peak value represents the degree of tolerance deviation of model parameters of each inhibition method, and the wider the tolerance deviation is, the better residual vibration inhibition capability of the inhibition method is still achieved at the larger deviation, namely the better robustness is;
therefore, under the same phase lag condition, the peak value is deeper in the downward recess relative to the shaper by adopting the control method of the servo control system in the application, and the residual vibration suppression effect is better; the width of two sides at the peak is wider, and the robustness is better.
As shown in fig. 6, 7 and 8, the phase frequency characteristic curves of the present application, the smoothing device suppression, and the shaping device suppression residual vibration modes are shown, respectively, as a function of frequency and phase; the more downward the tip position in the plot, the more phase lag is indicated;
it should be noted that, as can be seen from fig. 6 to 8, the tip position is the lowest and the phase lag is the largest in the mode of smoothing device suppression (i.e., the curve shown in fig. 7); in fig. 6, the tip positions are equal to each other and higher than those of fig. 7 in the suppression mode of the present application and the suppression mode of the shaper shown in fig. 8;
therefore, by adopting the control method of the servo control system, the phase lag time is smaller than that of the smoother inhibition mode, the system response is faster, and the production efficiency is improved.
Example 5
To further illustrate the technical effects of the present application, the present embodiment is illustrated in terms of experimental conclusion.
Experiment 3
To further verify the effect of the present application on residual vibration suppression, the original trajectory signal is setX ref （t) The motion parameter of (a) is the maximum displacementx g =80mmMaximum speedv g =400mm/sMaximum accelerationa g =5000mm/sIs (are) provided; vibration frequency of flexible servo control systemf=17.68Hz；
As shown in fig. 9, each curve from left to right shows a graph comparing load side displacement with time without adopting a suppression method, adopting a shaper suppression method, adopting the method in the application and adopting a smoother suppression method; wherein the horizontal axis represents time; the left vertical axis represents absolute displacement of vibration response after suppression by a shaper, the application and a smoother method; the right vertical axis indicates that the absolute displacement of the vibration response is not suppressed without employing the suppressing method.
As is apparent from the figure, under the control method of the servo control system of the present application (solid line), the residual vibration displacement is significantly reduced, and the vibration suppression capability is superior to that of the smoother suppression method and the shaper suppression method.
Experiment 4
In order to verify the robustness of the proposed method, keeping the experimental known conditions unchanged, an additional small magnet is attached to the end of the cantilever of the flexible servo control system. Thus, the vibration frequencyfCan be found in [15.17, 22.76 ]]Adjusting the Hz;
as shown in FIG. 10, the absolute values of the differences between the first pair of peaks and valleys of the residual vibration displacement after positioning the moving structure without the present application method, the smoother suppression method, the shaper suppression method, and the suppression methodhWith vibration frequencyfIs a graph of the change fold line contrast; wherein the horizontal axis representsFrequency and flexible vibration frequency perturbation ratio; the left vertical axis represents absolute displacement of the post-suppression vibration response using the shaper suppression, the present application, and the smoother approach; the right vertical axis represents absolute displacement of the vibration response without the suppression method.
As can be seen from the figure, residual vibration displacement is effectively reduced after the control method of the servo control system is adopted in a wide frequency variation range.
The foregoing description is only of the preferred embodiments of the present application and is presented as a description of the principles of the technology being utilized. It will be appreciated by persons skilled in the art that the scope of the invention referred to in this application is not limited to the specific combinations of features described above, but it is intended to cover other embodiments in which any combination of features described above or equivalents thereof is possible without departing from the spirit of the invention. Such as the above-described features and technical features having similar functions (but not limited to) disclosed in the present application are replaced with each other.
Claims (10)
1. A control method of a servo control system, comprising:
acquiring an original track signalX ref （t）；
For the original track signalX ref （t) Performing a pre-filter process and based on a transfer function of the pre-filter processG AD （s) Calculating a filtered trajectory signalY ref （t) The pre-filtering process is used for inhibiting residual vibration of the servo control system;
wherein ,
is a natural frequency set value, < >>
Is a damping ratio set value; />
Is a preset value;X ref （s) Representation ofX ref （t) Is a laplace transform of (a),Y ref （s) Representation ofY ref （t) Is a laplace transform of (a);Lthe representation of the laplace transform is made,sin order to be of a complex frequency,ttime is;
with the filtered track signalY ref （t) Controlling the servo control system to move.
2. The method according to claim 1, wherein the natural frequency set value
Damping ratio set point->
The setting method of (2) comprises the following steps:
acquiring a plurality of groups of corresponding system parameters of the servo control system in the motion process of different flexible loads according to the same input track, wherein the system parameters comprise natural frequencies
And damping ratio->
；
Calculating the natural frequency
And takes this as the natural frequency set value +.>
；
Calculating the damping ratio
And takes this as damping ratio set value +.>
。
3. The method for controlling a servo control system according to claim 2, wherein obtaining a plurality of sets of system parameters corresponding to the servo control system in the process of controlling different flexible loads in the same input track comprises the following steps:
the servo control system of different flexible loads under the same input track is subjected to quick positioning linear motion;
obtaining a residual vibration displacement curve of each flexible load in the rapid positioning linear motion process;
and calculating the system parameters according to the residual vibration displacement curve.
4. A control method of a servo control system according to claim 3, wherein calculating the system parameter from the residual vibration displacement curve comprises the steps of:
performing fast Fourier transform on the residual vibration displacement curve to obtain vibration frequencyf；
Calculating the natural frequency according to formula (2)
：
5. The method of controlling a servo control system according to claim 4, wherein calculating the system parameter from the residual vibration displacement curve further comprises the steps of:
calculating a damping ratio according to formula (3)
：
wherein ,
represent the firstqThe rate of decay of the one cycle,x p represent the firstpAnd a vibration peak.
6. The control method of a servo control system according to any one of claims 1 to 5, characterized in that a transfer function based on the pre-filter processingG AD （s) Calculating a filtered trajectory signalY ref （t) The method of (1) comprises: calculated according to formula (1)Y ref （s) The method comprises the steps of carrying out a first treatment on the surface of the For a pair ofY ref （s) Inverse Laplace transform is carried out to obtain a filtered track signalY ref （t）；
With the filtered track signalY ref （t) The method for controlling the motion of the servo control system comprises the following steps: the filtered track signalY ref （t) Conversion to a filtered discrete trackY ref [n]；Y ref [n]=Y ref （t=nT s ）；T S Is the sampling period;Y ref [n]representing an nth filtered discrete trace; with the filtered discrete tracksY ref [n]Controlling the servo control system to move.
7. A control method of a servo control system, comprising:
acquiring an original track signalX ref （t）；
Signal the original trackNumber (number)X ref （t) Performing a pre-filter process and based on a transfer function of the pre-filter processG AD （s) Calculating a filtered discrete trajectoryY ref [n]The pre-filtering process is used for inhibiting residual vibration of the servo control system;
with the filtered discrete tracksY ref [n]Controlling the servo control system to move;
wherein the transfer functionG AD （s) The method comprises the following steps:
Y ref （t) In order to filter the track signal,
is a natural frequency set value, < >>
Is a damping ratio set value; />
Is a preset value;X ref （s) Representation ofX ref （t) Is a laplace transform of (a),Y ref （s) Representation ofY ref （t) Is a laplace transform of (a);Lthe representation of the laplace transform is made,sin order to be of a complex frequency,ttime is;
wherein the transfer function based on the pre-filter processingG AD （s) Calculating a filtered discrete trajectoryY ref [n]The method comprises the following steps:
for transfer functionG AD （s) Performing bilinear transformation to obtain a transformed transfer functionG AD （z）：
wherein ,X ref （z) Representation pairX ref （s) The z-transform is performed and,Y ref （z) Representation pairY ref （s) Performing z transformation;a 1 、a 2 、b 0 、b 1 、b 2 is a coefficient;
transfer function after transformationG AD （z) Converting into a differential equation to obtain a formula (5);
wherein ,X ref [n]=X ref （t=nT s ），Y ref [n]=Y ref （t=nT s ）；T S is the sampling period;X ref [n]representing the nth original discrete track;Y ref [n]representing an nth filtered discrete trace;w[n]representing an intermediate quantity; when n=k<At the time of 0, the temperature of the liquid,X ref [k]=0、w[k]=0、Y ref [k]=0；
calculating a filtered discrete trajectory according to equation (5)Y ref [n]。
8. The method according to claim 7, wherein the natural frequency set value
Damping ratio set point->
The setting method of (2) comprises the following steps:
acquiring corresponding multiple groups of system parameters of the servo control system in the motion process of different flexible loads according to the same input trackNumber, the system parameters include natural frequency
And damping ratio->
；
Calculating the natural frequency
And takes this as the natural frequency set value +.>
；
Calculating the damping ratio
And takes this as damping ratio set value +.>
。/>
9. The method of claim 8, wherein obtaining the corresponding plurality of sets of system parameters of the servo control system during the movement of different flexible loads on the same input track comprises the steps of:
the servo control system of different flexible loads under the same input track is subjected to quick positioning linear motion;
obtaining a residual vibration displacement curve of each flexible load in the rapid positioning linear motion process;
and calculating the system parameters according to the residual vibration displacement curve.
10. The method of controlling a servo control system according to claim 9, wherein calculating the system parameter from the residual vibration displacement curve comprises the steps of:
performing fast Fourier transform on the residual vibration displacement curve to obtain vibration frequencyf；
Calculating the natural frequency according to formula (2)
：
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