CN114710081A - Online resonance suppression method based on extended state observer and improved trap - Google Patents
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
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- H—ELECTRICITY
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- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
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Abstract
The invention relates to an online resonance suppression method based on an extended state observer and an improved wave trap, which comprises the following steps in sequence: establishing a double-inertia transmission device model; a second-order extended state observer is added on the basis of the double-inertia transmission device model; on the basis of adding a double-inertia transmission device model of a second-order extended state observer, an improved notch filter is added to obtain improved notch central frequency, improved notch bandwidth and notch depth and resonant frequency f0(ii) a Will resonate at a frequency f0And inputting the improved notch filter to perform online resonance suppression. The second-order extended state observer can estimate external interference and uncertainty in real time, compensate control signals and improve the anti-interference capability of a system; the improved notch filter can effectively work in the full frequency band, and avoids the central notch frequencyNear the nyquist frequency, the notch filter becomes inaccurate.
Description
Technical Field
The invention relates to the technical field of alternating current servo control systems, in particular to an online resonance suppression method based on an extended state observer and an improved wave trap.
Background
The servo system is used as a key ring on the intelligent equipment, and the performance improvement of the whole system is directly restricted by the control precision and stability of the servo system. The inherent characteristics of the transmission mechanism of the alternating current servo system can cause mechanical resonance phenomenon, so that the stability of the rotating speed and the torque is seriously reduced, and the control quality is greatly influenced. Therefore, the method for suppressing the vibration of the industrial servo system is researched, and the method has important significance for improving the performance of intelligent equipment.
The traditional disturbance observer restrains external disturbance by observing the disturbance quantity of a loop, acquires electromagnetic torque and rotational speed feedback to realize disturbance compensation, and can play a good role in restraining vibration. However, for the low-frequency vibration phenomenon of the dual-inertia system, due to the influence of the rigidity coefficient and the inertia ratio of the system, the flexibility characteristic of the system is aggravated, the disturbance composition is more complicated, and the rotating speed of the motor is inconsistent with the rotating speed of the load, so that the load has large-amplitude low-frequency oscillation. The structure of the traditional disturbance observer cannot consider the influence caused by the dynamic change of parameters of a servo system, so that the observer cannot adapt to the internal disturbances such as the inertia change of a motor and the like, and the traditional disturbance observer has certain limitation.
Disclosure of Invention
The invention aims to provide an online resonance suppression method based on an extended state observer and an improved trap filter, which can eliminate the influence caused by internal and external disturbance, improve the anti-interference capability of a system, and simultaneously improve the online resonance suppression capability of a servo system and the service life of mechanical equipment.
In order to realize the purpose, the invention adopts the following technical scheme: an on-line resonance suppression method based on an extended state observer and an improved trap comprises the following steps in sequence:
(1) establishing a double-inertia transmission device model;
(2) a second-order extended state observer is added on the basis of the double-inertia transmission device model;
(3) on the basis of adding a double-inertia transmission device model of a second-order extended state observer, an improved notch filter is added to obtain three parameters of the improved notch filter: improved notch center frequency, improved notch bandwidth and notch depth, and resonant frequency f0；
(4) Will resonate at a frequency f0The input improved notch filter performs online resonance suppression.
In step (1), the dual inertia transmission model is:
wherein ,JM、JLInertia of the motor and load, respectively, KsIs the stiffness coefficient of the transmission mechanism, TE、TL、TWRespectively the electromagnetic torque, the load torque and the torsion torque when the rotating shaft is in torsion deformation, bM、bL、bSDamping coefficients of the motor, the load and the transmission mechanism respectively, and angles and angular velocities of the motor and the load respectively are represented by thetaM、wM and θL、wLRepresents; the motor rotating shaft is connected to the load rotating shaft through a transmission mechanism, and the electromagnetic torque of the driver is converted into load torque to drive the load to operate.
In step (2), the second-order extended state observer is:
wherein u is q-axis current feedback, y is motor speed feedback, and z1As a result of the tracking of the rotational speed, z2The tracking result of the total disturbance is obtained; e is the observation error, b is the observer input gain coefficient,
for the estimated value of b, z is adjusted by adjusting the observer gains β 1, β 21 and z2The tracking effect of (2);
the calculation formula of u is as follows:
wherein ,u0Outputting by a rotating speed loop, and acquiring Kp by a rotating speed loop controller; wr is the expected rotation speed given by the servo system; defining the values of the observer gains beta 1 and beta 2 as follows:
w0is in the range of 2 times wsTo 5 times wsW0For observer bandwidth, wsIs the bandwidth of the speed loop controller;
the observer input gain coefficient is:
wherein ,
Ktis a torque constant, npFor number of pole pairs, psi, of the motorfIs a permanent magnet flux linkage of the motor.
In step (3), the transfer function of the notch filter is:
wherein ,ωbTo trap the center frequency, k1、k2Are all damping coefficients;
in the formula ,bbTo trap the bandwidth, xbThe depth of the trapped wave;
discretizing the double T type by adopting a bilinear transformation method, wherein a discretization expression of the discretization is shown as the following formula:
in the formula ,b1、b2、b3B4 is the discretization coefficient of the notch filter, and z is the mark of the discretization of the transfer function; the corresponding discretization coefficients are shown below:
in the formula ,TsSampling frequency for a speed loop;
the parameters of the notch bandwidth and the notch center frequency are further improved to obtain an improved notch filter:
the discretization coefficients are:
wherein ,
for the purpose of an improved center frequency of the notch,
to an improved notch bandwidth;
where k is a gain factor, and k is Ts/2。
In step (4), the center frequency ω is notchedbCarrying out FFT spectrum analysis on the rotating speed error to obtain the resonant frequency f of the system0Will the resonant frequency f0Inputting an improved notch filter for online resonance suppression; the rotating speed error is the expected rotating speed Wr given by the servo system and the tracking result z of the rotating speed1The difference between them; said notch bandwidth bbThe calculation formula of (2) is as follows: bb＝2max{(f0-f1),(f2-f0) }; let the oscillation reference threshold of the resonance of the servo system be H1I.e. amplitude greater than H1Then a mechanical resonance is considered to have occurred, at f0The amplitude values on the left side and the right side reach H1Respectively, has a system frequency of f1And f2；
Setting the servo system at resonant frequency f0Has an amplitude of HmaxAnd obtaining:
xb＝H1/Hmax
wherein ,H1To a set oscillation reference threshold, HmaxAt a resonance frequency f0The amplitude of (c).
Said notch center frequency ωbObtaining the resonant frequency f of the system after FFT spectrum analysis of the rotating speed error0The method specifically comprises the following steps:
(6a) collecting a difference value between the feedback rotating speed and the given rotating speed, namely a rotating speed error, storing data, and stopping data collection when the number of collected points meets the requirement;
(6b) performing FFT spectrum analysis on the data acquired in the last step, and converting the time domain signal into a frequency domain signal;
(6c) processing the frequency domain signal of the previous step by utilizing a resonant frequency extraction algorithm to obtain a resonant frequency f0。
According to the technical scheme, the invention has the beneficial effects that: firstly, the second-order extended state observer can estimate external interference and uncertainty in real time, compensate control signals and improve the anti-interference capability of a system; secondly, the improved notch filter can effectively work in the full frequency band, and the notch filter is prevented from becoming inaccurate when the central notch frequency is close to the Nyquist frequency; thirdly, a method of combining a second-order extended state observer and an improved notch filter is adopted to carry out secondary suppression on mechanical resonance, so that the stability and the precision of a servo system are improved; fourthly, the method does not depend on an accurate mathematical model, can eliminate the influence caused by internal and external disturbance, and simultaneously improves the online resonance inhibition capability of a servo system and the service life of mechanical equipment.
Drawings
FIG. 1 is a control block diagram of a dual inertia transmission model;
FIG. 2 is a schematic structural diagram of a second-order extended state observer;
fig. 3 is a block diagram of an online resonance suppression method based on a second order extended state observer and an improved notch filter.
Detailed Description
An online resonance suppression method based on an extended state observer and an improved wave trap comprises the following steps in sequence:
(1) establishing a double-inertia transmission device model;
(2) a second-order extended state observer is added on the basis of the double-inertia transmission device model;
(3) on the basis of adding a double-inertia transmission device model of a second-order extended state observer, an improved notch filter is added to obtain three parameters of the improved notch filter: improved notch center frequency, improved notch bandwidth and notch depth, and resonant frequency f0；
(4) Will resonate at a frequency f0And inputting the improved notch filter to perform online resonance suppression.
As shown in fig. 1, in step (1), the dual inertia transmission model is:
wherein ,JM、JLInertia of the motor and load, respectively, KsIs the stiffness coefficient of the transmission mechanism, TE、TL、TWRespectively the electromagnetic torque, the load torque and the torsion torque when the rotating shaft is in torsion deformation, bM、bL、bSDamping coefficients of the motor, the load and the transmission mechanism respectively, and angles and angular velocities of the motor and the load respectively are represented by thetaM、wM and θL、wLRepresents; the motor rotating shaft is connected to the load rotating shaft through a transmission mechanism, and the electromagnetic torque of the driver is converted into load torque to drive the load to operate.
A second-order Extended State Observer (ESO) is established to carry out real-time disturbance estimation, and the control signal is compensated to eliminate the influence caused by internal and external disturbance. The suppression method based on the second-order extended state observer has low requirements on model parameters, and can improve the anti-interference capability of a system and reduce the double inertia characteristics in the motion process.
As shown in fig. 2, in step (2), the second-order extended state observer is:
wherein u is q-axis current feedback, y is motor speed feedback, and z1As a result of the tracking of the rotational speed, z2The tracking result of the total disturbance is obtained; e is the observation error, b is the observer input gain coefficient,
for the estimated value of b, z is adjusted by adjusting the observer gains β 1, β 21 and z2The tracking effect of (2);
the second-order extended state observer treats the double inertia links and unknown disturbance in the system as disturbance quantity which can be observed and compensated, and the rigidity and the disturbance rejection capability of the system are improved by estimating the total disturbance. On this basis, the forward path of the system can be redesigned.
The calculation formula of u is as follows:
wherein ,u0Outputting by a rotating speed loop, and acquiring Kp by a rotating speed loop controller; wr is the expected rotation speed given by the servo system;
values of observer gains beta 1 and beta 2 are defined as follows:
w0is in the range of 2 times wsTo 5 times wsW0For observer bandwidth, wsIs the bandwidth of the speed loop controller. Can be in the closed-loop bandwidth w of the systemsBased on the above, w can be set to be a multiple number according to experience0Is in the range of 2 times wsTo 5 times wsMeanwhile, the bandwidth of the observer is ensured to be far less than the sampling frequency.
The observer input gain coefficient is:
wherein ,
Ktis a torque constant, npFor number of pole pairs, psi, of the motorfIs a permanent magnet flux linkage of the motor.
The second-order extended state observer is used, the anti-interference capability of a system can be well improved, the influence of mechanical vibration can be effectively weakened, and in order to further inhibit the mechanical vibration, an improved notch filter is added on the basis, and the on-line inhibition is carried out on the specific resonant frequency of the system.
As shown in fig. 3, in step (3), the transfer function of the notch filter is:
wherein ,ωbTo trap the center frequency, k1、k2Are damping coefficients;
in the formula ,bbTo trap the bandwidth, xbThe depth of the trapped wave;
discretizing the double T type by a bilinear transformation method, wherein a discretization expression of the discretization is shown as the following formula:
in the formula ,b1、b2、b3B4 is the discretization coefficient of the notch filter, and z is the mark of the discretization of the transfer function;
the corresponding discretization coefficients are shown below:
in the formula ,TsSampling frequency for a speed loop;
in order to make the notch filter work effectively in a full frequency band, the notch filter is prevented from becoming inaccurate when the central notch frequency is close to the Nyquist frequency, the notch bandwidth and notch central frequency parameters are further improved, and the improved notch filter is obtained:
the discretization coefficients are:
wherein ,
for the purpose of an improved center frequency of the notch,
to an improved notch bandwidth;
where k is a gain factor, and k is Ts/2。
In step (4), the center frequency ω is notchedbCarrying out FFT spectrum analysis on the rotating speed error to obtain the resonant frequency f of the system0Will the resonant frequency f0Inputting an improved notch filter for online resonance suppression; the rotating speed error is the expected rotating speed Wr given by the servo system and the tracking result z of the rotating speed1The difference between them; said notch bandwidth bbThe calculation formula of (2) is as follows: bb＝2max{(f0-f1),(f2-f0) }; let the oscillation reference threshold of the resonance of the servo system be H1I.e. amplitude greater than H1Then a mechanical resonance is considered to have occurred, at f0The amplitude values on the left side and the right side reach H1Respectively, has a system frequency of f1And f2；
Setting the servo system at resonant frequency f0Has an amplitude of HmaxObtaining:
xb＝H1/Hmax
wherein ,H1To a set oscillation reference threshold, HmaxAt a resonance frequency f0The amplitude of (c).
Said notch center frequency ωbObtaining the resonant frequency f of the system after FFT spectrum analysis of the rotating speed error0The method specifically comprises the following steps:
(6a) collecting a difference value between the feedback rotating speed and the given rotating speed, namely a rotating speed error, storing data, and stopping data collection when the number of collected points meets the requirement;
(6b) performing FFT spectrum analysis on the data acquired in the last step, and converting the time domain signal into a frequency domain signal;
(6c) processing the frequency domain signal of the previous step by using a resonant frequency extraction algorithm to obtain a resonant frequency f0。
In conclusion, the second-order extended state observer can estimate external interference and uncertainty in real time, compensate control signals and improve the anti-interference capability of a system; the improved notch filter can effectively work in a full frequency band, and the notch filter is prevented from becoming inaccurate when the central notch frequency is close to the Nyquist frequency; a method of combining a second-order extended state observer and an improved notch filter is adopted to carry out secondary suppression on mechanical resonance, and the stability and the precision of a servo system are improved.
Claims (6)
1. An online resonance suppression method based on an extended state observer and an improved trap is characterized in that: the method comprises the following steps in sequence:
(1) establishing a double-inertia transmission device model;
(2) a second-order extended state observer is added on the basis of the double-inertia transmission device model;
(3) on the basis of adding a double-inertia transmission device model of a second-order extended state observer, an improved notch filter is added to obtain three parameters of the improved notch filter: improved notch center frequency, improved notch bandwidth and notch depth, and resonant frequency f0；
(4) Will resonate at a frequency f0And inputting the improved notch filter to perform online resonance suppression.
2. The on-line resonance suppression method based on the extended state observer and the improved trap as claimed in claim 1, wherein: in step (1), the dual inertia transmission model is:
wherein ,JM、JLInertia of the motor and load, respectively, KsIs the stiffness coefficient of the transmission mechanism, TE、TL、TWRespectively the electromagnetic torque, the load torque and the torsion torque when the rotating shaft is in torsion deformation, bM、bL、bSDamping coefficients of the motor, the load and the transmission mechanism respectively, and angles and angular velocities of the motor and the load respectively are represented by thetaM、wM and θL、wLRepresenting; the motor rotating shaft is connected to the load rotating shaft through a transmission mechanism, and the electromagnetic torque of the driver is converted into load torque to drive the load to operate.
3. The extended state observer and improved trap-based online resonance suppression method according to claim 1, wherein: in step (2), the second-order extended state observer is:
wherein u is q-axis current feedback, y is motor speed feedback, and z1As a result of the tracking of the rotational speed, z2The tracking result of the total disturbance is obtained; e is the observation error, b is the observer input gain coefficient,
for the estimated value of b, z is adjusted by adjusting the observer gains β 1, β 21 and z2The tracking effect of (2);
the calculation formula of u is as follows:
wherein ,u0Outputting by a rotating speed loop, and acquiring Kp by a rotating speed loop controller; wr is the expected rotation speed given by the servo system;
defining the values of the observer gains beta 1 and beta 2 as follows:
w0is in the range of 2 times wsTo 5 times wsW0For observer bandwidth, wsIs the bandwidth of the speed loop controller;
the observer input gain coefficient is:
wherein ,
Ktis a torque constant, npFor number of pole pairs, psi, of the motorfIs a permanent magnet flux linkage of the motor.
4. The on-line resonance suppression method based on the extended state observer and the improved trap as claimed in claim 1, wherein: in step (3), the transfer function of the notch filter is:
wherein ,ωbTo trap the center frequency, k1、k2Are all damping coefficients;
in the formula ,bbTo trap the bandwidth, xbThe depth of the trapped wave;
discretizing the double T type by a bilinear transformation method, wherein a discretization expression of the discretization is shown as the following formula:
in the formula ,b1、b2、b3B4 is the discretization coefficient of the notch filter, and z is the mark of the discretization of the transfer function;
the corresponding discretization coefficients are shown below:
in the formula ,TsSampling frequency for a speed loop;
the parameters of the notch bandwidth and the notch center frequency are further improved to obtain an improved notch filter:
the discretization coefficients are:
wherein ,
in order to improve the center frequency of the notch,
to an improved notch bandwidth;
where k is a gain factor, Ts/2。
5. The on-line resonance suppression method based on the extended state observer and the improved trap as claimed in claim 1, wherein: in step (4), the center frequency ω is notchedbCarrying out FFT spectrum analysis on the rotating speed error to obtain the resonant frequency f of the system0Will resonate at a frequency f0Inputting an improved notch filter for online resonance suppression; the rotating speed error is the expected rotating speed Wr given by the servo system and the tracking result z of the rotating speed1The difference between them; said notch bandwidth bbThe calculation formula of (2) is as follows: bb＝2max{(f0-f1),(f2-f0) }; let the oscillation reference threshold of the resonance of the servo system be H1I.e. amplitude greater than H1Then a mechanical resonance is assumed to occur, at f0The amplitude values on the left side and the right side reach H1Respectively, has a system frequency of f1And f2；
Setting the servo system at resonant frequency f0Has an amplitude of HmaxAnd obtaining:
xb＝H1/Hmax
wherein ,H1To a set oscillation reference threshold, HmaxAt a resonance frequency f0The amplitude of (c).
6. The extended state observer and improved trap-based online resonance suppression method according to claim 5, wherein: said notch center frequency ωbObtaining the resonant frequency f of the system after FFT spectrum analysis of the rotating speed error0The method specifically comprises the following steps:
(6a) collecting a difference value between the feedback rotating speed and the given rotating speed, namely a rotating speed error, storing data, and stopping data collection when the number of collected points meets the requirement;
(6b) performing FFT spectrum analysis on the data acquired in the last step, and converting the time domain signal into a frequency domain signal;
(6c) processing the frequency domain signal of the previous step by utilizing a resonant frequency extraction algorithm to obtain a resonant frequency f0。
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| CN116505810A (en) * | 2023-06-30 | 2023-07-28 | 苏州铼钠克信息技术有限公司 | Method, device, equipment and medium for suppressing oscillation of wave trap and servo system |
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| CN116300476B (en) * | 2023-05-16 | 2023-09-05 | 成都微精电机股份公司 | Resonance suppression method based on rotating speed loop LADRC controller |
| CN116505810A (en) * | 2023-06-30 | 2023-07-28 | 苏州铼钠克信息技术有限公司 | Method, device, equipment and medium for suppressing oscillation of wave trap and servo system |
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