CN109713971A - A kind of Disturbance Rejection method of permanent magnet synchronous motor - Google Patents
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Abstract
The present invention is to solve the existing existing deficiency of disturbance observer design, and voltage disturbance is generated because inductance changes especially in motor operation course, PREDICTIVE CONTROL output voltage is caused to deviate exact value, the problem of influencing motor even running, in conjunction with Extended Kalman filter theory, a kind of Disturbance Rejection method of permanent magnet synchronous motor is provided, using the disturbance observer based on Extended Kalman filter, can accurately observe the system disturbance due to caused by parameter mismatch.It is compared with the traditional method, there are many beneficial effects such as design is simple, sound state followability is good.
Description
Technical field
The present invention relates to the Disturbance Rejection fields in permanent magnet synchronous motor control, more particularly to permanent magnet synchronous motor in electricity
Feel voltage disturbance observation and the compensation under mismatch condition.
Background technique
In the numerical control system for being applied to permanent magnet synchronous motor control, dead beat predictive current control is a kind of wide
The method of general use has the characteristics that small calculation amount, dynamic and static tracking performance are good, controls compared to traditional PI, nothing
Beat predictive current control has better control effect.But since dead beat predictive current control depends on accurate motor mould
Type so will lead to calculated reference voltage when parameter of electric machine mismatch deviates exact value, and then makes the electric current of motor and turns
Square generates obvious fluctuation.By combining PREDICTIVE CONTROL and disturbance observer, observation in real time is caused due to parameter of electric machine mismatch
Disturbance, can be improved control performance and compensation system disturbance influence.
Common disturbance observer has reduced dimension observer and synovial membrane observer at present, by reasonable regulating system parameter,
Disturbance observer can play the role of compensation system disturbance, but there are still some defects for these observers.For example, Kyeong-
Hwa Kim et al. is in " A Current Control for a Permanent Magnet Synchronous Motor with
A Simple Disturbance Estimation Scheme " a kind of reduced dimension observer is devised in a text, be substantially
A kind of multiple-input and multiple-output PI controller can compensate the PREDICTIVE CONTROL output reference voltage disturbance generated by parameter mismatch, but
It is only limitted to lesser parameter mismatch range (in 50% increase and decrease range), when parameter mismatch amount is larger, observer can generate overshoot
And influence accuracy of observation.Zhang Xiaoguang et al. is in " Deadbeat Predictive Current Control of
Permanent-Magnet Synchronous Motors with Stator Current and Disturbance
Observer " a kind of synovial membrane observer based on exponential approach rate is devised in a text, observed parameter mismatch it can cause in real time
Voltage disturbance, but its design that device is observed under d-q coordinate system, there is coupling, influences in ac-dc axis voltage and current component
The precision of observation；Simultaneously as complex using the calculating of synovial membrane control algolithm, calculation amount is much larger than linear operation, to motor
It is more demanding to control hardware device.
Summary of the invention
It is existing insufficient to solve the design of existing disturbance observer, and especially in motor operation course because inductance changes
The problem of generating voltage disturbance, causing PREDICTIVE CONTROL output voltage to deviate exact value, influence motor even running, the present invention combine
Extended Kalman filter is theoretical, provides a kind of Disturbance Rejection method of permanent magnet synchronous motor, filters using based on spreading kalman
The disturbance observer of wave can accurately observe the system disturbance due to caused by parameter mismatch.Method specifically includes the following steps:
Step 1: online data obtains, three-phase current, revolving speed, the rotor position angle of permanent magnet synchronous motor are acquired in real time；
Step 2: establishing dead beat predictive current control model, calculated in real time using the data acquired in the step 1
The reference voltage of subsequent time out；
Step 3: the disturbance observer equation for being based on Extended Kalman filter (EKF) algorithm is established, it will be by the step 2
Obtained reference voltage is as control amount, using the voltage disturbance amount as caused by inductance as state vector, with three-phase current, turns
Speed, rotor position angle are as observed quantity；And voltage disturbance amount is calculated using the equation real-time update, and feedforward compensation is described in
On reference voltage, the reference voltage that is updated.
Further, the step 2 specifically includes: establish mathematical model of the permanent magnet synchronous motor under alpha-beta coordinate system:
U in formulaα、uβFor stator voltage under alpha-beta coordinate system；iα、iβFor stator current under alpha-beta coordinate system；ψrFor rotor flux；
RsFor stator resistance；LsFor stator inductance；ωe、ωmThe respectively mechanical angular speed of the angular rate of rotor and rotor；θ is to turn
Sub- position angle；P is differential operator；TeFor electromagnetic torque；TLFor load torque；B is the coefficient of viscosity；pmFor the number of pole-pairs of motor；
ψα、ψβFor the stator magnetic linkage under alpha-beta coordinate system；T is time variable；J is load rotating inertia.Under alpha-beta coordinate system, voltage electricity
There is no couplings for flow, maximally reduce model error, improve computational accuracy.
Voltage after disturbance term is added in above-mentioned model are as follows:
In formula, fα、fβIndicate voltage disturbance amount under alpha-beta coordinate system.
Wherein disturbance term is
In formula, △ L indicates inductance mismatch amount, △ L=Ls-Ls0, Ls0Indicate inductance calibration value.
It is because of voltage change caused by inductance mismatch that heretofore described voltage disturbance, which can be specified, with two formula 2
Amount and voltage disturbance suppressor mode be by the output quantity of disturbance observer be added to PREDICTIVE CONTROL output reference voltage
On.
Further, calculating voltage disturbance measurer body using the equation real-time update in the step 3 includes:
1.: by the state vector of the equation, the covariance of state vector, system noise covariance matrix and measure noise
Covariance matrix is initialized；
2.: prediction, using the state vector of initialization as tk-1The correction value at momentIn the case where, predict estimated valueAnd the covariance matrix P of prior estimatek|k-1, kalman gain K is found out on this basisk；
3.: it updates, priori estimates is modified according to observation error and minimum variance principle, to obtain state
The correction value of vectorThe covariance matrix P of correction value is found out simultaneouslyk；
4.: after completing step 3., the correction value of the state vector is exported, while using k as new sampling time point, it will
The covariance value of the state vector correction value and the state vector correction value substitutes into step and is 2. calculated.
Further, the initialization of the state vector, including three-phase current, revolving speed, rotor position angle, voltage disturbance
Initialization, disturbance observer observe voltage disturbance in real time, i.e. disturbance observer is started to work from the electric motor starting moment, therefore will
State vector initial value is disposed as 0.
Further, it is the precision for improving the disturbance observer, sets 6 for state vector dimension, observation vector dimension
Degree is set as 4.In disturbance observer operational process, electric current, revolving speed and the rotor position angle of permanent magnet synchronous motor are acquired in real time
Input disturbance observer is modified observer priori estimates.Wherein, state vector x is
X=[iα iβ ωe θ fα fβ]T, observation vector is y=[iα iβ ωe θ]T。
Further, 3. the step specifically includes:
Using the state vector estimated value covariance matrix at k moment, measurement transfer matrix and measure noise covariance matrix
Find out the kalman gain matrix at k moment:
In formula, HkTo measure transfer matrix；R is to measure noise covariance matrix；
Meanwhile k moment state is obtained using the covariance matrix of k moment kalman gain matrix and state vector estimated value
The covariance value of vector corrected value:
Pk=Pk|k-1-KkHkPk|k-1。
The Extended Kalman filter used in method provided by aforementioned present invention is a kind of linear minimum-variance estimation.It
There is extraordinary filtering performance, in the situation known to system noise and measurement noise, establishes the mathematical model of signal, pass through expansion
Kalman filtering is opened up, original signal can be preferably recovered.Therefore, method of the invention be compared with the traditional method at least have with
Lower advantage:
(1) it observation system can be disturbed in real time using disturbance observer, by the output of disturbance quantity direct compensation PREDICTIVE CONTROL,
Accurate recognition is carried out without the variation to the parameter of electric machine, simplifies system design.
(2) it is calculated using EKF algorithm, nonlinearized motor model is subjected to linearization process, meter is greatly decreased
Calculation amount shortens and calculates the time.
(3) EKF algorithm robustness with higher, so being carried out using EKF method can be at the beginning of state when disturbance is estimated
(such as 20% error) rapidly converges to true value when being worth inaccurate.
Detailed description of the invention
Fig. 1 combines the flow chart of method provided by the present invention
Fig. 2 disturbance observer EKF algorithm flow chart
Fig. 3 inductance mismatch (L=2L0) in the case of the motor dq shaft current curve graph based on PREDICTIVE CONTROL
Fig. 4 inductance mismatch (L=2L0) in the case of combine the motor dq axis electricity based on PREDICTIVE CONTROL of EKF disturbance observer
Flow curve figure
Fig. 5 inductance mismatch (L=L0/ 2) the motor dq shaft current curve graph in the case of based on PREDICTIVE CONTROL
Fig. 6 inductance mismatch (L=L0/ 2) in conjunction with the motor dq axis electricity based on PREDICTIVE CONTROL of EKF disturbance observer in the case of
Flow curve figure
Specific embodiment
Method provided by the present invention is provided with reference to the accompanying drawing and is further illustrated in detail.
Method includes: three model foundation, dead beat predictive current control and the online disturbance observation of EKF algorithm aspects.Under
Face is respectively described in detail above three aspect:
1, model foundation
When motor operation, electric machine controller is capable of the running state information of motor in real time, running state information packet
Include electric current, revolving speed, rotor-position.Controller combines corresponding control strategy according to collected motor operating state information
To obtain corresponding inverter switching device sequence, so that driving motor is run.
Mathematical model of the permanent magnet synchronous motor under alpha-beta coordinate system:
U in formulaα、uβFor stator voltage under alpha-beta coordinate system；iα、iβFor stator current under alpha-beta coordinate system；ψrFor rotor flux；
RsFor stator resistance；LsFor stator inductance；ωe、ωmThe respectively mechanical angular speed of the angular rate of rotor and rotor；θ is to turn
Sub- position angle；P is differential operator；TeFor electromagnetic torque；TLFor load torque；B is the coefficient of viscosity；pmFor the number of pole-pairs of motor；
ψα、ψβFor the stator magnetic linkage under alpha-beta coordinate system；T is time variable；J is load rotating inertia.
Mathematical model of the permanent magnet synchronous motor under d-q coordinate system:
U in formulad、uqFor stator voltage under d-q coordinate system；id、iqFor stator current under d-q coordinate system；ψd、ψqFor d-q seat
Stator magnetic linkage under mark system；Ld、LqThe respectively armature inductance of d, q axis.
Permanent magnet synchronous motor model can be built based on the motor mathematical model under d-q coordinate system, based on SVPWM control reason
By and inverter principle and dead beat predictive current control principle and EKF algorithm, permanent magnet synchronous motor inductance can be built
Disturbance Rejection control system model under mismatch condition, work flow diagram are as shown in Figure 1.
2, dead beat predictive current control
Dead beat predictive current control can act on the voltage vector of motor according to current time, i.e. u (k) and motor are joined
The motor reference voltage of number output subsequent time, i.e. u (k+1).The calculation formula of u (k+1) is calculated at the kth moment are as follows:
T in formulasTo control the period；iqrefFor q axis reference current.
When maximum output voltage limitation of the reference voltage being calculated beyond SVPWM, need to output reference voltage
It is adjusted, obtains the reference voltage in SVPWM output area:
U in formulad *、uq *For under d-q coordinate system according to the calculated reference stator voltage of formula (3)；ud **、uq **For d-q coordinate
Reference voltage under system in revised SVPWM output voltage range；UdcFor DC bus-bar voltage.
3, the online disturbance observation of EKF algorithm
Motor is a continuous nonlinear system, and expanded Kalman filtration algorithm is perfectly suitable for motor control
Calculation processing.Extended Kalman filter uses recursive algorithm, and use state space law designs filter in time domain, is suitable for more
The estimation of random process is tieed up, calculating process is divided into priori prediction and posteriority corrects two parts.
Based on expanded Kalman filtration algorithm building disturbance observer, specific step is as follows, as shown in Figure 2:
Firstly, being rewritten after disturbance term is added in the voltage equation in formula (1) are as follows:
In formula, fα、fβIndicate voltage disturbance amount under alpha-beta coordinate system.
Wherein disturbance term is
In formula, △ L indicates inductance mismatch amount, △ L=Ls-Ls0, Ls0Indicate inductance calibration value.
It is because of voltage variety caused by inductance mismatch that voltage disturbance described in this patent, which can be specified, by formula (6)；
By formula (7) can specify voltage disturbance suppressor mode be by the output quantity of disturbance observer be added to PREDICTIVE CONTROL output
Reference voltage on.
Formula (5) is expressed as to the form of current status equation
Inductance LsVariation relative to the variation of electric current be slow, it is possible to voltage caused by thinking because of inductance mismatch
Shock wave is slowly, to remain unchanged in a sampling period small in this way time interval relative to the variation of electric current,
Derivative is 0, i.e.,
Based on expanded Kalman filtration algorithm, the effect according to disturbance observer is real-time observation because inductance parameters mismatch produces
Raw voltage disturbance, select state vector x for
X=[iα iβ ωe θ fα fβ]T (9)
Controlling variable u is
U=[uα uβ]T (10)
U hereinα、uβFor the output reference voltage u of predictive control algorithmd、uqThe voltage value obtained through coordinate transform.Make
Use the output reference voltage value of predictive control algorithm as the control amount of EKF algorithm compared to the voltage value that acquisition inverter exports
It is more simple direct as control amount, and the output voltage values for acquiring inverter are generally difficult to guarantee precision.
The then corresponding nonlinear equation of electric machine control system are as follows:
In formula, w is system noise；C is control amount gain matrix；F (x) is state transition function.
Select stator current, revolving speed and rotor position angle under alpha-beta coordinate system as observed quantity, i.e.,
Y=[iα iβ ωe θ]T (14)
The then corresponding measurement equation of electric machine control system are as follows:
Y=h (x)+v (15)
In formula, v is measurement noise；H (x) is measurement functions.
EKF disturbance observer in the present invention has the function of observing the voltage disturbance generated by inductance mismatch in real time, sharp
Linearization process is carried out to nonlinear motor model in the design process with EKF algorithm, can be reduced to the greatest extent online
Calculation amount when calculating guarantees that the sound state following feature of electric current in motor operation course is good.F (x), h (x) are carried out respectively
Linearization process obtains corresponding Jacobian matrix are as follows:
According to the above various expansion card that can be constructed for disturbing estimation in the case of permanent magnet synchronous motor inductance mismatch
Kalman Filtering equation are as follows:
1. being corrected by state vector of the voltage output amount of state transition function f and predictive control algorithm to the k-1 moment
Value is updated calculating, obtains the estimated value of k moment state vector:
In formula,Indicate the state vector correction value at k-1 moment；Indicate the state vector estimated value at k moment.
Meanwhile the state vector correction value at k-1 moment is assisted using state-transition matrix and system noise covariance matrix
Variance matrix is updated calculating, obtains the covariance matrix of the state vector estimated value at k moment:
In formula, Pk-1Indicate the covariance matrix of k-1 moment state vector correction value；Pk|k-1Indicate the state vector at k moment
The covariance matrix of estimated value；Fk-1Indicate state-transition matrix；QdIndicate system noise covariance matrix.
On this basis, the state vector estimated value covariance matrix at k moment, measurement transfer matrix and measurement noise are utilized
Covariance matrix finds out the kalman gain matrix at k moment:
In formula, KkFor kalman gain matrix；HkTo measure transfer matrix；R measures noise covariance matrix.
2. being modified according to observation error and minimum variance principle to priori estimates, that is, utilize kalman gain square
The observation vector at battle array and k moment is modified the estimated value of k moment state vector, obtains the correction value of k moment state vector:
In formula,Indicate the state vector correction value at k moment；ykIndicate the observation vector at k moment.
Meanwhile when obtaining k using the covariance matrix of k moment kalman gain matrix and Kalman state vector estimated value
Carve the covariance value of Kalman state vector corrected value:
Pk=Pk|k-1-KkHkPk|k-1 (23)
In formula, PkIndicate the covariance matrix of k moment state vector correction value
Kalman filtering is actually a kind of recursive algorithm, and entire recursive process needs given initial valueAnd P0.For
For one real system, the characteristic of system initial state is uncertain, corresponding initial valueAnd P0Value it is also relatively difficult.
But if Kalman filter is Uniformly asymptotic stadbility, and when coefficient matrix of system is constant matrix, then with filter
The increase of wave number, optimal estimation valueAnd PkThe initial value that finally will not arbitrarily be chosenAnd P0Influence, realize zero deflection
Estimation.
Initial value is arranged in EKF disturbance observer of the invention are as follows:
P0=[0.1 0.1 500 0.5 10 10] (25)
In the design of EKF disturbance observer, the statistical property of system random disturbances and measurement noise is unknown, system noise
The covariance matrix of sound and measurement noise can be determined by emulation experiment.Suitable numerical value is selected, algorithm is helped speed up
Convergence and raising estimated accuracy.In EKF disturbance observer of the invention, covariance matrix selection is as follows:
In an example based on method provided by the present invention, Fig. 3-6 respectively illustrates inductance mismatch (L=2L0) feelings
Motor dq shaft current curve and this mismatch Conditions (L=2L under condition based on PREDICTIVE CONTROL0) under combine EKF disturbance observer
The motor dq shaft current curve graph and inductance mismatch (L=L based on PREDICTIVE CONTROL0/ 2) based on the electricity of PREDICTIVE CONTROL in the case of
Machine dq shaft current curve and this mismatch Conditions (L=L0/ 2) motor based on PREDICTIVE CONTROL of EKF disturbance observer is combined under
Dq shaft current curve graph.It can be seen that there is good Disturbance Rejection effect using method provided by the present invention.
It although an embodiment of the present invention has been shown and described, for the ordinary skill in the art, can be with
A variety of variations, modification, replacement can be carried out to these embodiments without departing from the principles and spirit of the present invention by understanding
And modification, the scope of the present invention is defined by the appended.
Claims (6)
1. a kind of Disturbance Rejection method of permanent magnet synchronous motor, which is characterized in that specifically includes the following steps:
Step 1: online data obtains, three-phase current, revolving speed, the rotor position angle of permanent magnet synchronous motor are acquired in real time；
Step 2: establishing dead beat predictive current control model, calculated down in real time using the data acquired in the step 1
The reference voltage at one moment；
Step 3: establishing the disturbance observer equation for being based on Extended Kalman filter (EKF) algorithm, will be obtained by the step 2
Reference voltage as control amount, using the voltage disturbance amount as caused by inductance as state vector, with three-phase current, revolving speed, turn
Sub- position angle is observed quantity；And voltage disturbance amount is calculated using the equation real-time update, and feedforward compensation is electric to the reference
In pressure, the reference voltage that is updated.
2. the method as described in claim 1, it is characterised in that: the step 2 specifically includes: establishing permanent magnet synchronous motor and exist
Mathematical model under alpha-beta coordinate system:
U in formulaα、uβFor stator voltage under alpha-beta coordinate system；iα、iβFor stator current under alpha-beta coordinate system；ψrFor rotor flux；RsFor
Stator resistance；LsFor stator inductance；ωe、ωmThe respectively mechanical angular speed of the angular rate of rotor and rotor；θ is rotor position
Angle setting；P is differential operator；TeFor electromagnetic torque；TLFor load torque；B is the coefficient of viscosity；pmFor the number of pole-pairs of motor；ψα、ψβFor
Stator magnetic linkage under alpha-beta coordinate system；T is time variable；J is load rotating inertia；
Voltage after disturbance term is added in above-mentioned model are as follows:
In formula, fα、fβIndicate voltage disturbance amount under alpha-beta coordinate system；
Wherein disturbance term are as follows:
In formula, △ L indicates inductance mismatch amount, △ L=Ls-Ls0, Ls0Indicate inductance calibration value.
3. method according to claim 2, it is characterised in that: calculate electricity using the equation real-time update in the step 3
Pressure disturbance quantity specifically includes:
1.: by the state vector of the equation, the covariance of state vector, system noise covariance matrix and measure noise association side
Poor matrix is initialized；
2.: prediction, using the state vector of initialization as tk-1The correction value at momentIn the case where, predict estimated value
And the covariance matrix P of prior estimatek|k-1, kalman gain K is found out on this basisk；
3.: it updates, priori estimates is modified according to observation error and minimum variance principle, to obtain state vector
Correction valueThe covariance matrix P of correction value is found out simultaneouslyk；
4.: after completing step 3., the correction value of the state vector is exported, while using k as new sampling time point, it will be described
The covariance value of state vector correction value and the state vector correction value substitutes into step and is 2. calculated.
4. the method as described in claim 1, it is characterised in that: the initialization of the state vector, including three-phase current, turn
The initialization of speed, rotor position angle, voltage disturbance, disturbance observer observe voltage disturbance in real time, i.e. disturbance observer is from motor
Startup time is started to work, therefore state vector initial value is disposed as 0.
5. the method as described in claim 1, it is characterised in that: the state vector x is 6 dimensional vectors
X=[iα iβ ωe θ fα fβ]T, observation vector is 4 dimensional vector y=[iα iβ ωe θ]T, in formula, iα、iβFor alpha-beta seat
Mark is lower stator current, ωeFor the angular rate of rotor, θ is rotor position angle, fα、fβIt is disturbed for voltage under motor alpha-beta coordinate system
Momentum.
6. method as claimed in claim 3, it is characterised in that: 3. the step specifically includes:
K is found out using the state vector estimated value covariance matrix at k moment, measurement transfer matrix and measurement noise covariance matrix
The kalman gain matrix at moment:
In formula, HkTo measure transfer matrix；R is to measure noise covariance matrix；
Meanwhile k moment state vector is obtained using the covariance matrix of k moment kalman gain matrix and state vector estimated value
The covariance value of correction value:
Pk=Pk|k-1-KkHkPk|k-1。
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN110086395A (en) * | 2019-05-08 | 2019-08-02 | 哈尔滨理工大学 | A kind of permanent magnet synchronous motor parameter identification method |
| CN110504880A (en) * | 2019-07-24 | 2019-11-26 | 东南大学盐城新能源汽车研究院 | A kind of magnetic flux switching permanent-magnetism linear motor disturbance-observer Front feedback control method |
| CN112072981A (en) * | 2020-08-14 | 2020-12-11 | 上大电气科技(嘉兴)有限公司 | PMSM current prediction control method based on SD-MPM |
| CN112422002A (en) * | 2020-10-09 | 2021-02-26 | 北京理工大学 | Robust permanent magnet synchronous motor single current sensor prediction control method |
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