CN110784149A - Mechanical resonance suppression method and system for alternating current servo system - Google Patents
Mechanical resonance suppression method and system for alternating current servo system Download PDFInfo
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
- H02P23/04—Arrangements or methods for the control of AC motors characterised by a control method other than vector control specially adapted for damping motor oscillations, e.g. for reducing hunting
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
- H02P23/12—Observer control, e.g. using Luenberger observers or Kalman filters
Abstract
The invention relates to the technical field of an alternating current servo control system, and provides a mechanical resonance suppression method of an alternating current servo system, which comprises the following steps: s1, establishing a double-inertia transmission device model; s2, adding an ADRC controller structure for the double-inertia transmission device model; and S3, adding load acceleration feedback compensation on the basis of adding the model of the ADRC controller structure. The mechanical resonance suppression system of the alternating current servo system comprises a double-inertia transmission device model, an ADRC controller structure added on the double-inertia transmission device model, and a load acceleration feedback structure added after the ADRC controller structure is added. Compared with the traditional PI controller, the improved ADRC can generate a certain inhibition effect on the resonance phenomenon, and meanwhile, the high-speed response and high steady-state precision of the system can be realized; the state observer of the ADRC controller architecture is able to observe both the state variables and the disturbances of the system, which can be eliminated by adding compensation.
Description
Technical Field
The invention relates to the technical field of alternating current servo control systems, in particular to a method and a system for inhibiting mechanical resonance of an alternating current servo system.
Background
An alternating current servo system targeting high speed and high precision is widely applied in high-tech fields such as laser processing, robots, high-precision machine tools and the like. The accurate control of the speed ring can reduce the influence of disturbance on the system and reduce the fluctuation of the rotating speed, so that the system works in a stable state. The speed loop control is the most widely applied control mode in the permanent magnet synchronous motor servo system, and the good speed loop control can effectively inhibit uncertain disturbance in a current loop and a speed loop, so that the overall performance of the system is improved.
Suppression of mechanical resonance can be considered from both mechanical and control aspects. From the mechanical aspect, the damping of the system is improved, the load inertia ratio of the system is reduced, the rigidity of a transmission device of the system is improved, and the resonant frequency of the system can be improved and is beyond the normal working bandwidth of the system.
However, the viscosity coefficient between the motor and the transmission, and the viscosity coefficient between the transmission and the load are difficult to increase; the load inertia ratio is determined by a specific control object and cannot be changed randomly; the stiffness of the transmission can be improved by mechanical design, but to a limited extent.
Disclosure of Invention
The invention aims to provide a method and a system for inhibiting mechanical resonance of an alternating current servo system, which can automatically detect the real-time action of a model and external disturbance of the system and compensate the action, can inhibit the resonance to a certain extent, and can better inhibit the resonance after the feedback of load acceleration.
In order to achieve the above purpose, the embodiments of the present invention provide the following technical solutions: a mechanical resonance suppression method for an alternating current servo system comprises the following steps:
s1, establishing a double-inertia transmission device model;
s2, adding an ADRC controller structure for the double-inertia transmission device model;
and S3, adding load acceleration feedback compensation on the basis of adding the model of the ADRC controller structure.
Further, the double inertia transmission model comprises a motor, a transmission and a load,
the mechanical equation of the motor is as follows:
wherein, J
MIs the inertia of the motor, omega
MIs the motor speed, T
eFor electromagnetic torque, T
LAs a load torque, B
MIs a damping coefficient
The model is simplified by the following relation:
the motor side transfer function is collated as:
the transfer function of the load rotating speed and the output electromagnetic torque of the servo motor is as follows:
the transfer function relationship between the rotating speeds is as follows:
the servo system resonance equation is:
wherein
Resonant frequency
ω
MIs the motor speed, omega
LIs the load rotation speed.
Further, the formation of the ADRC controller structure includes the design of a tracking differentiator, the design of a state observer, and the design of a nonlinear error feedback rate.
Further, the design of the tracking differentiator is specifically,
the trace differential stage of the velocity command is processed, and the fastest discrete trace differentiator can be expressed as:
The fst () function is the fastest control synthesis function, described as follows:
wherein d ═ δ h; d
0＝hd；y＝x
1+hx
2；
Input signal is omega
r(k) R can be realized by adopting a differentiator
1(k)→ω
r(k)，
The differentiator may simultaneously implement the filtering.
Finally, the following is obtained:
further, the state observer is designed specifically such that,
the state observer is an extended state observer and is used for observing the rotating speed value z of the motor
1Known disturbance (load torque T)
L) And the unknown disturbance is uniformly regarded as the total disturbance, and the total disturbance is regarded as the expansion state z
2：
For an established current inner loop, perturb the compensation factor
β when the extended state observer is designed to satisfy the stability condition
1、β
2And ω
0Satisfies the following relation:
s
2+β
1s+β
2＝(s+ω
0)
2，
solved β
1＝2ω
0，β
2＝ω
0 2Wherein, ω is
0Is the bandwidth of a state observer, having
Further, the design of the nonlinear error feedback rate,
the method adopts direct error to replace nonlinear function, directly calculates the error of two state variables, utilizes the gain of the observer to adjust the observation speed of the observer, and the state feedback control law in the forward channel is as follows:
Further, after load acceleration feedback compensation is added, the transfer function of the load rotating speed and the output electromagnetic torque of the servo motor is as follows:
the resonance frequency at this time is:
The embodiment of the invention provides another technical scheme: the mechanical resonance suppression system of the alternating current servo system comprises a double-inertia transmission device model, an ADRC controller structure added on the double-inertia transmission device model, and a load acceleration feedback structure added after the ADRC controller structure is added.
Further, the double-inertia transmission device model comprises a motor, a transmission device and a load, wherein the transmission device transmits the motion and the power of the motor to the load, so that the motion of the load is controlled to meet the requirements of a system.
Compared with the prior art, the invention has the beneficial effects that:
1. compared with the traditional PI controller, the improved ADRC can generate a certain inhibition effect on the resonance phenomenon, and meanwhile, the high-speed response and high steady-state precision of the system can be realized.
2. The state observer with the ADRC controller structure can observe state variables and disturbances of the system at the same time, the disturbances can be eliminated by adding compensation, the influence of parameter change and load disturbance on the system is remarkably reduced, and the characteristic of strong load disturbance resistance is highlighted.
3. The method can realize the resonance suppression of the servo system without depending on an accurate system model, and has the advantages of independent controller parameters and simple configuration.
4. The present invention may be implemented by varying the load acceleration feedback factor α
1The mechanical resonance can be further suppressed by adjusting the equivalent resonance frequency of the system.
Drawings
Fig. 1 is a model block diagram of a dual inertia transmission device of an ac servo system mechanical resonance suppression method according to an embodiment of the present invention;
FIG. 2 is a structural diagram of a feedback compensation resonance suppression structure of a loading acceleration of a conventional PI controller;
fig. 3 is a structural diagram of an ADRC controller of an ac servo system mechanical resonance suppression method according to an embodiment of the present invention;
fig. 4 is a structural diagram of an ADRC load acceleration feedback compensation resonance suppression method for an ac servo system according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The first embodiment is as follows:
the embodiment of the invention provides a mechanical resonance suppression method for an alternating current servo system, which comprises the following steps: s1, establishing a double-inertia transmission device model; s2, adding an ADRC controller structure for the double-inertia transmission device model; and S3, adding load acceleration feedback compensation on the basis of adding the model of the ADRC controller structure. Mechanical resonance suppression can be classified into the following two categories in the prior art: one is an active inhibition method, such as based on PID structure pole configuration, based on observer observation load rotation speed, load torque and the like, based on model reference self-adaptation, fuzzy control, genetic algorithm and other advanced control algorithms, and a mechanical resonance acceleration feedback method based on a PI controller servo system is proposed in documents (Min Overlong, King ceramic quan, three-axis stable satellite scanning mirror servo system resonance inhibition [ J ] control theory and application, 2018,35(9):1250-1259.DOI: 10.7641/CTA.2018.70588.). The method can well inhibit mechanical resonance, but has the defects of over-harmonic delay in response and insufficient load disturbance resistance. The other is a passive suppression method, which mainly suppresses mechanical resonance by designing a notch filter, and the literature (Wook Bahn, Tae-Il Kim, Sang-Hoon Lee, Dong-Il "Dan" cho. resource frequency calibration for adaptive notch filters in industrial servo systems [ J ] mechanics, 2017,41(15):45-52) proposes a method for estimating the resonant frequency of an adaptive notch filter in an industrial servo system. The model-based resonance suppression method is simple in algorithm and good in stability, but depends on the identification precision of the structure and parameters of the controlled model. The analytic method for the second-order system integral resonance control is complex in design and difficult to realize. The invention adopts an ADRC-based mechanical resonance load acceleration feedback inhibition method for an alternating current servo system, the method is simple and easy to realize in design, the resonance inhibition is obvious, the system has fast speed response, high stability and precision and strong load disturbance resistance.
FIG. 1 is a block diagram of a model of a dual inertia transmission of the present invention. Wherein, J
MIs the inertia of the motor, T
eFor electromagnetic torque, T
LAs a load torque, B
MTo be damping coefficient, T
sIs an elastic damping moment, omega
MIs the motor speed, omega
LIs the load rotation speed. The mechanical part of the motor with the elastic load mainly comprises the motor, a transmission device and the load, wherein the transmission device transmits the motion and the power of the motor to the load, so that the motion of the load is controlled to meet the requirements of the system. The transmission device has a certain elastic coefficient, and when the system bandwidth continuously rises, the system bandwidth reaches or even exceeds the transmission shaftThe servo motor drives the load to generate mechanical resonance at the natural frequency.
The mechanical equation of the motor is as follows:
wherein P is PMSM pole pair number psi
fIs a motor rotor flux linkage.
Fig. 1 is a simplified system model of a servo motor driving a flexible load into a dual inertia model, and the relationship between the motor and the load is as follows:
simplifying the system model, and arranging the motor side transfer function as:
the transfer function of the load rotating speed and the output electromagnetic torque of the servo motor is as follows:
the transfer function relationship between the rotating speeds is as follows:
the servo system resonance equation is:
wherein
Resonant frequency
The ADRC-based method for suppressing the acceleration feedback of the mechanical resonance load of the alternating current servo system can realize the resonance suppression of the servo system without depending on an accurate system model, and has the advantages of independent controller parameters, simple configuration, no overshoot and delay phenomena and strong load disturbance resistance. The designed ADRC can generate primary inhibition on mechanical resonance, and after load acceleration feedback is added, the inhibition effect on the mechanical resonance is further enhanced.
As an optimization scheme of the embodiment of the invention, the formation of the ADRC controller structure comprises the design of a tracking differentiator, the design of a state observer and the design of a nonlinear error feedback rate.
The design of ADRC is divided into the following three steps:
(1) design of tracking differentiator
Tracking differentiator processing of velocity commands: arranging the transition process for the speed command and providing a differential signal with a high signal-to-noise ratio, the fastest discrete tracking differentiator can be represented as:
where h is the sampling period, ω
r(k) Is the input speed signal at the k-th time, r
1Is omega
r(k) Of the tracking signal r
2Can be approximated as omega
r(k) δ is a parameter that determines how fast the tracking is. The fst () function is the fastest control synthesis function, described as follows:
wherein d ═ δ h; d
0＝hd；y＝x
1+hx
2；
Input signal is omega
r(k) By means of differentiatorsCan realize r
1(k)→ω
r(k)，
The differentiator may simultaneously implement the filtering.
Obtained by the formulas (1) and (2):
(2) design of state observer
ADRC controller As shown in figure 3, the core of ADRC is an extended state observer, which is used for observing the rotating speed z of the motor
1Known disturbance (load torque T)
L) And the unknown disturbance is uniformly regarded as the total disturbance, and the total disturbance is regarded as the expansion state z
2。
Wherein e is a tracking feedback signal z of the motor rotating speed
1And the observed motor speed omega
MError of β
1、β
2Is the observer gain, u is the controlled quantity i
q。
For an established current inner loop, perturb the compensation factor
β when the extended state observer is designed to satisfy the stability condition
1、β
2And ω
0Satisfies the following relation:
s
2+β
1s+β
2＝(s+ω
0)
2(11)
solved β
1＝2ω
0，β
2＝ω
0 2Wherein, ω is
0Is the bandwidth of a state observer, having
(3) Design of nonlinear error feedback rate
In order to facilitate parameter adjustment and structure simplification of the ADRC controller, direct errors are adopted to replace nonlinear functions, errors of two state variables are directly calculated, and the observer gain is used for adjusting the observation speed of the observer. The state feedback control law in the forward channel is:
wherein K is a proportional control coefficient, and is generally taken
The influence and change of the servo system on the original system can be regarded as a disturbance which can be modeled and compensated due to the fact that the form of an error feedback control law in the forward channel is kept unchanged, and the influence and change of the servo system on the original system are due to the fact that z in a state observer in the ADRC
2The estimation accuracy of the disturbance is high, the influence of the resonance cannot be accurately compensated, and the effect of the resonance suppression needs to be further improved. The ADRC parameters can be simply adjusted through an actual system, so that the system has good robustness, disturbance resistance and control precision.
FIG. 2 is a schematic diagram of a prior art AC servo system mechanical resonance load acceleration feedback suppression method based on a PI controller, i.e. a proportional-integral controller, K
PIs a proportionality coefficient, τ
iFor the integration time constant, both of which are adjustable, the transfer function of the PI controller is:
it can be seen that the PI controller not only introduces a pure integration element to the system, but also introduces an open-loop zero. The introduction of the zero point causes a large overshoot of the response, and each integration element brings about a phase delay of minus ninety degrees from the frequency domain perspective, which reduces the phase margin. The PI controller-based AC servo system mechanical resonance load acceleration feedback suppression method also has the defect of insufficient load disturbance resistance.
As an optimization scheme of the embodiment of the invention, in order to suppress mechanical resonance in a minimum state, a method of load acceleration feedback is added. Since the equivalent gain of the servo system changes after the addition, the gain of the servo system needs to be compensated in order not to affect the system performance. After load acceleration feedback compensation is added, the transfer function of the load rotating speed and the output electromagnetic torque of the servo motor is as follows:
wherein, α
2As gain compensation factor, α
1Is the load acceleration feedback coefficient. The resonance frequency at this time is:
system bandwidth of
With servo systems fed back by load acceleration, it is desirable to add a gain compensated system
The amplitude-frequency characteristic of the time is the same as that of equation (5), the gain compensation coefficient
If it is desired to add gain compensation, the servo system is
Amplitude-frequency characteristic of time and ideal rigid system
Same, when the gain compensation coefficient is
By varying the loadAcceleration feedback coefficient α
1The mechanical resonance can be further suppressed by adjusting the equivalent resonance frequency of the servo system by the value of (a).
The ADRC compensates the forward channel of the whole system, the compensation effect is that the anti-interference capability of the servo system can be enhanced, and an ADRC-based AC servo system load acceleration feedback resonance inhibition principle diagram is shown in figure 4.
Example two:
the embodiment of the invention provides a mechanical resonance suppression system of an alternating current servo system, which comprises a double-inertia transmission device model, an ADRC controller structure added on the double-inertia transmission device model, and a load acceleration feedback structure added after the ADRC controller structure is added. Preferably, the double inertia transmission model comprises a motor, a transmission device and a load, wherein the transmission device transmits the motion and the power of the motor to the load, so as to control the motion of the load to meet the requirements of the system. This embodiment is the same as the above embodiment, and will not be described herein again.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.
Claims (9)
1. A mechanical resonance suppression method of an alternating current servo system is characterized by comprising the following steps:
s1, establishing a double-inertia transmission device model;
s2, adding an ADRC controller structure for the double-inertia transmission device model;
and S3, adding load acceleration feedback compensation on the basis of adding the model of the ADRC controller structure.
2. The method of claim 1, wherein the method further comprises: the double-inertia transmission device model comprises a motor, a transmission device and a load,
the mechanical equation of the motor is as follows:
wherein, J
MIs the inertia of the motor, omega
MIs the motor speed, T
eFor electromagnetic torque, T
LAs a load torque, B
MIs a damping coefficient
The model is simplified by the following relation:
the motor side transfer function is collated as:
the transfer function of the load rotating speed and the output electromagnetic torque of the servo motor is as follows:
the transfer function relationship between the rotating speeds is as follows:
the servo system resonance equation is:
wherein
Resonant frequency
ω
MIs the motor speed, omega
LIs the load rotation speed.
3. An ac servo system mechanical resonance suppression method as claimed in claim 1, wherein said ADRC controller structure formation comprises a tracking differentiator design, a state observer design and a nonlinear error feedback rate design.
4. An AC servo mechanical resonance suppression method as claimed in claim 3, wherein said tracking differentiator is designed in particular,
the trace differential stage of the velocity command is processed, and the fastest discrete trace differentiator can be expressed as:
The fst () function is the fastest control synthesis function, described as follows:
wherein d ═ δ h; d
0＝hd；y＝x
1+hx
2；
Input signal is omega
r(k) R can be realized by adopting a differentiator
1(k)→ω
r(k)，
The differentiator may simultaneously implement the filtering.
Finally, the following is obtained:
5. an AC servo mechanical resonance suppression method as claimed in claim 3, wherein said state observer is designed in particular,
the state observer is an extended state observer and is used for observing the rotating speed value z of the motor
1Known disturbance (load torque T)
L) And the unknown disturbance is uniformly regarded as the total disturbance, and the total disturbance is regarded as the expansion state z
2：
For an established current inner loop, perturb the compensation factor
β when the extended state observer is designed to satisfy the stability condition
1、β
2And ω
0Satisfies the following relation:
s
2+β
1s+β
2＝(s+ω
0)
2，
solved β
1＝2ω
0，β
2＝ω
0 2Wherein, ω is
0Is the bandwidth of a state observer, having
6. The AC servo system mechanical resonance suppression method of claim 3, wherein the nonlinear error feedback rate is designed,
the method adopts direct error to replace nonlinear function, directly calculates the error of two state variables, utilizes the gain of the observer to adjust the observation speed of the observer, and the state feedback control law in the forward channel is as follows:
wherein K is a proportional control coefficient, and is generally taken
7. The method for suppressing mechanical resonance of an alternating current servo system as claimed in claim 1, wherein after adding load acceleration feedback compensation, the transfer function of the load rotation speed and the output electromagnetic torque of the servo motor is as follows:
the resonance frequency at this time is:
8. An alternating current servo mechanical resonance suppression system is characterized in that: the system comprises a double-inertia transmission device model, an ADRC controller structure added on the double-inertia transmission device model, and a load acceleration feedback structure added after the ADRC controller structure is added.
9. The ac servo mechanical resonance suppression system of claim 8, wherein: the double-inertia transmission device model comprises a motor, a transmission device and a load, wherein the transmission device transmits the motion and the power of the motor to the load, so that the motion of the load is controlled to meet the requirements of a system.
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| CN111464098B (en) * | 2020-04-28 | 2022-02-11 | 广州鸿威技术有限公司 | Resonance characteristic off-line identification method for servo system |
| CN112039395A (en) * | 2020-07-09 | 2020-12-04 | 苏州绿控传动科技股份有限公司 | Method and device for restraining resonance of flexible load driven by permanent magnet synchronous motor |
| CN114185370A (en) * | 2020-08-24 | 2022-03-15 | 广东博智林机器人有限公司 | Servo system and rotating speed compensation method thereof |
| CN114710081A (en) * | 2022-03-18 | 2022-07-05 | 合肥工业大学 | Online resonance suppression method based on extended state observer and improved trap |
| CN114710081B (en) * | 2022-03-18 | 2023-08-22 | 合肥工业大学 | Online resonance suppression method based on extended state observer and improved wave trap |
| CN116300476A (en) * | 2023-05-16 | 2023-06-23 | 成都微精电机股份公司 | Resonance suppression method based on rotating speed loop LADRC controller |
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