CN109713971B - Disturbance suppression method for permanent magnet synchronous motor - Google Patents
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Abstract
The invention provides a disturbance suppression method of a permanent magnet synchronous motor, which aims to solve the defects of the existing disturbance observer design and particularly aims at solving the problems that the output voltage of prediction control deviates from an accurate value and the stable operation of the motor is influenced due to the fact that voltage disturbance is generated due to inductance change in the operation process of the motor. Compared with the traditional method, the method has the advantages of simple design, good dynamic and static following performance and the like.
Description
Technical Field
The invention relates to the field of disturbance suppression in permanent magnet synchronous motor control, in particular to voltage disturbance observation and compensation of a permanent magnet synchronous motor under the condition of inductance mismatch.
Background
In a digital control system applied to permanent magnet synchronous motor control, the dead-beat current predictive control is a widely adopted method, has the characteristics of small calculated amount and good dynamic and static tracking performances, and has a better control effect compared with the traditional PI control. However, since the dead-beat current prediction control depends on an accurate motor model, the calculated reference voltage deviates from an accurate value when the motor parameters are mismatched, and the current and the torque of the motor fluctuate obviously. By combining predictive control and a disturbance observer, the disturbance caused by the mismatch of the motor parameters is observed in real time, so that the control performance can be improved and the influence of system disturbance can be compensated.
The conventional disturbance observers comprise a dimensionality reduction observer and a synovium observer, and can play a role in compensating system disturbance by reasonably adjusting system parameters, but the observers still have some defects. For example, Kyeong-Hwa Kim et al, in a text "a Current Control for a Permanent Magnet Synchronous Motor with Simple Disturbance Estimation Scheme", designs a dimension reduction observer, which is essentially a multi-input multi-output PI controller, and can compensate for the Disturbance of the predicted Control output reference voltage caused by parameter mismatch, but is limited to a small parameter mismatch range (within a 50% increase/decrease range), and when the parameter mismatch amount is large, the observer can generate overshoot to affect the observation accuracy. Zhang Xiaooguang et al in Deadbed Predictive Current Control of Permanent-Magnet Synchronous Motors with Stator Current and DisturbanceObserver have designed a synovial membrane observer based on index approach rate, can real-time observe the voltage disturbance caused by parameter mismatch, but it carries on the design of the observer under d-q coordinate system, the voltage and Current components of the quadrature-direct axis are coupled, influence the precision of observation; meanwhile, the calculation is more complex by adopting a sliding film control algorithm, the calculated amount is far greater than that of linear operation, and the requirement on motor control hardware equipment is higher.
Disclosure of Invention
In order to solve the defects of the existing disturbance observer design and particularly solve the problem that the predicted control output voltage deviates from an accurate value and the stable operation of the motor is influenced due to the fact that voltage disturbance is generated due to inductance change in the motor operation process, the invention provides a disturbance suppression method of a permanent magnet synchronous motor by combining with an extended Kalman filtering theory. The method specifically comprises the following steps:
acquiring online data, namely acquiring three-phase current, rotating speed and rotor position angle of a permanent magnet synchronous motor in real time;
step two, establishing a dead-beat current prediction control model, and calculating the reference voltage at the next moment in real time by using the data acquired in the step one;
establishing a disturbance observer equation based on an Extended Kalman Filter (EKF) algorithm, taking the reference voltage obtained in the second step as a control quantity, taking a voltage disturbance quantity caused by inductance as a state vector, and taking three-phase current, rotating speed and rotor position angle as observed quantities; and updating and calculating the voltage disturbance quantity in real time by using the equation, and performing feedforward compensation on the reference voltage to obtain an updated reference voltage.
Further, the second step specifically comprises the steps of establishing a mathematical model of the permanent magnet synchronous motor under an α - β coordinate system:
in the formula uα、uβIs stator voltage under α - β coordinate system iα、iβStator current phi of α - β coordinate systemrIs a rotor flux linkage; rsIs a stator resistor; l issIs a stator inductance; omegae、ωmThe electrical angular velocity of the rotor and the mechanical angular velocity of the rotor, respectively; theta is a rotor position angle; p is a differential operator; t iseIs an electromagnetic torque; t isLIs the load torque; b is a viscosity coefficient; p is a radical ofmThe number of pole pairs of the motor is shown; psiα、ψβThe current is a stator flux linkage under a α - β coordinate system, t is a time variable, J is load moment of inertia, and under a α - β coordinate system, the voltage and the current are not coupled, so that model errors are reduced to the maximum extent, and the calculation accuracy is improved.
The voltage after adding the disturbance term into the model is as follows:
in the formula (f)α、fβIndicating the voltage disturbance in α - β coordinate system.
Wherein the disturbance term is
Where Δ L represents an inductance mismatch amount, and Δ L ═ Ls-Ls0，Ls0And indicating the inductance calibration value.
The two formulas can make clear that the voltage disturbance in the invention is the voltage variation caused by inductance mismatch, and the suppression mode of the voltage disturbance is to superpose the output quantity of the disturbance observer on the reference voltage of the prediction control output.
Further, the step three of updating and calculating the voltage disturbance variable in real time by using the equation specifically includes:
①, initializing the state vector, the covariance of the state vector, the system noise covariance matrix and the measurement noise covariance matrix of the equation;
② prediction, with initialized state vector as tk-1Correction value of time
In the case of (2), the estimated value is predicted
And a priori estimated covariance matrix Pk|k-1On the basis of which the Kalman gain K is determinedk；
③, updating, correcting the prior estimated value according to the observation error and the minimum variance principle to obtain the corrected value of the state vector
Covariance matrix P for simultaneous calculation of correction valuesk；
④, after completing step ③, outputting the state vector correction value, and substituting the state vector correction value and the covariance value of the state vector correction value into step ② to calculate using k as a new sampling time point.
Further, the initialization of the state vector comprises the initialization of three-phase current, rotating speed, rotor position angle and voltage disturbance, and the disturbance observer observes the voltage disturbance in real time, namely starts to work from the starting moment of the motor, so that the initial values of the state vector are all set to be 0.
Further, to improve the accuracy of the disturbance observer, the state vector dimension is set to 6, and the observation vector dimension is set to 4. And in the running process of the disturbance observer, acquiring the current, the rotating speed and the rotor position angle of the permanent magnet synchronous motor in real time, inputting the current, the rotating speed and the rotor position angle into the disturbance observer, and correcting the priori estimation value of the observer. Wherein the state vector x is
x＝[iαiβωeθ fαfβ]TThe observation vector is y ═ iαiβωeθ]T。
Further, the step ⑧ specifically includes:
and (3) solving a Kalman gain matrix at the moment k by using the covariance matrix of the state vector estimation value at the moment k, the measurement transfer matrix and the measurement noise covariance matrix:
in the formula, HkTo measure a transfer matrix; r is a measurement noise covariance matrix;
meanwhile, obtaining a covariance value of a state vector correction value at the moment k by using a Kalman gain matrix at the moment k and a covariance matrix of a state vector estimation value:
Pk＝Pk|k-1-KkHkPk|k-1。
the extended kalman filter employed in the method provided by the present invention is a linear minimum variance estimation. The method has good filtering performance, under the condition that system noise and measurement noise are known, a mathematical model of the signal is established, and the original signal can be well recovered through extended Kalman filtering. Therefore, the method of the present invention has at least the following advantages over conventional methods:
(1) the disturbance observer can be used for observing system disturbance in real time, the disturbance quantity is directly compensated and output of predictive control, the change of motor parameters does not need to be accurately identified, and the system design is simplified.
(2) And the EKF algorithm is used for calculation, and the nonlinear motor model is subjected to linearization treatment, so that the calculation amount is greatly reduced, and the calculation time is shortened.
(3) The EKF algorithm has high robustness, so that when the EKF method is used for disturbance estimation, the EKF algorithm can be quickly converged to a true value when the initial state value is inaccurate (such as 20% error).
Drawings
FIG. 1 is a flow chart of a method provided in connection with the present invention
FIG. 2 flow chart of EKF algorithm of disturbance observer
Fig. 3 inductance mismatch (L ═ 2L)0) Motor dq-axis current profile based on predictive control under circumstances
Fig. 4 inductance mismatch (L ═ 2L)0) Prediction control based motor dq-axis current profile in combination with EKF disturbance observer
Fig. 5 inductance mismatch (L ═ L)0/2) motor dq-axis current profile based on predictive control
Fig. 6 inductance mismatch (L ═ L)0/2) prediction control based motor dq-axis current profile in combination with EKF disturbance observer
Detailed Description
The method provided by the invention is further elaborated with reference to the following drawings.
The method comprises the following steps: model establishment, deadbeat current prediction control and EKF algorithm online disturbance observation. The above three aspects are explained in detail below:
1. model building
When the motor runs, the motor controller can acquire running state information of the motor in real time, wherein the running state information comprises current, rotating speed and rotor position. The controller can obtain a corresponding inverter switching sequence by combining the collected motor running state information with a corresponding control strategy, so that the motor is driven to run.
Mathematical model of permanent magnet synchronous motor under α - β coordinate system:
in the formula uα、uβIs stator voltage under α - β coordinate system iα、iβStator current phi of α - β coordinate systemrIs a rotor flux linkage; rsIs a stator resistor; l issIs a stator inductance; omegae、ωmRespectively being rotorsElectrical angular velocity and mechanical angular velocity of the rotor; theta is a rotor position angle; p is a differential operator; t iseIs an electromagnetic torque; t isLIs the load torque; b is a viscosity coefficient; p is a radical ofmThe number of pole pairs of the motor is shown; psia、ψβThe stator flux linkage is in a α - β coordinate system, t is a time variable, and J is load moment of inertia.
The mathematical model of the permanent magnet synchronous motor under a d-q coordinate system is as follows:
in the formula ud、uqIs the stator voltage under a d-q coordinate system; i.e. id、iqIs the stator current under a d-q coordinate system; psid、ψqIs a stator flux linkage under a d-q coordinate system; l isd、LqThe armature inductances of the d and q axes, respectively.
A permanent magnet synchronous motor model can be built based on a motor mathematical model under a d-q coordinate system, a disturbance suppression control system model under the condition of permanent magnet synchronous motor inductance mismatch can be built based on an SVPWM control theory, an inverter principle, a dead-beat current prediction control principle and an EKF algorithm, and a working flow chart of the model is shown in FIG. 1.
2. Deadbeat current predictive control
The deadbeat current prediction control can output a motor reference voltage at the next moment, i.e. u (k +1), according to the voltage vector, i.e. u (k), applied to the motor at the current moment and the motor parameters. The calculation formula of u (k +1) calculated at the k-th time is as follows:
in the formula TsIs a control period; i.e. iqrefIs a q-axis reference current.
When the calculated reference voltage exceeds the maximum output voltage limit of the SVPWM, the output reference voltage needs to be adjusted to obtain the reference voltage within the SVPWM output range:
in the formula ud *、uq *The stator reference voltage calculated according to the formula (3) in a d-q coordinate system; u. ofd **、u q **The reference voltage within the corrected SVPWM output voltage range under the d-q coordinate system is obtained; u shapedcIs the dc bus voltage.
3. EKF algorithm on-line disturbance observation
The motor is a continuous nonlinear system, and the extended Kalman filter algorithm is well suitable for the calculation processing of motor control. The extended Kalman filtering adopts a recursion algorithm, a filter is designed in a time domain by using a state space method, the method is suitable for estimation of a multidimensional random process, and the calculation process of the method is divided into a priori prediction part and a posterior correction part.
The specific steps of constructing the disturbance observer based on the extended kalman filter algorithm are as follows, as shown in fig. 2:
first, after adding the voltage equation in the formula (1) to the disturbance term, it is rewritten as:
in the formula (f)α、fβIndicating the voltage disturbance in α - β coordinate system.
Wherein the disturbance term is
Where Δ L represents an inductance mismatch amount, and Δ L ═ Ls-Ls0，Ls0And indicating the inductance calibration value.
The formula (6) can show that the voltage disturbance is the voltage variation caused by the inductance mismatch.
Expression of equation (5) as a form of the current state equation
Inductor LsIs slow with respect to the change in current, so it can be considered that the change in voltage perturbation due to the inductance mismatch is slow with respect to the change in current, it remains constant for a time interval as small as one sampling period, and the derivative is 0, i.e. it is a linear derivative
Based on the extended Kalman filtering algorithm, according to the effect of a disturbance observer, the voltage disturbance generated by the mismatch of inductance parameters is observed in real time, and a state vector x is selected as
x＝[iαiβωeθ fαfβ]T(9)
The control variable u is
u＝[uαuβ]T(10)
U hereα、uβFor output reference voltage u of predictive control algorithmd、uqAnd (4) obtaining a voltage value through coordinate transformation. Compared with the method of collecting the voltage value output by the inverter as the control quantity, the method of using the output reference voltage value of the predictive control algorithm as the control quantity of the EKF algorithm is simpler and more direct, and the accuracy of collecting the output voltage value of the inverter is generally difficult to ensure.
The nonlinear equation corresponding to the motor control system is:
wherein w is system noise; c is a control quantity gain matrix; f (x) is a state transfer function.
Stator current, rotation speed and rotor position angle in α - β coordinate system are selected as observed quantities, namely
y＝[iαiβωeθ]T(14)
The measurement equation corresponding to the motor control system is:
y＝h(x)+v (15)
wherein v is measurement noise; h (x) is a measurement function.
The EKF disturbance observer has the function of observing voltage disturbance generated by inductance mismatch in real time, and utilizes an EKF algorithm to carry out linearization processing on a nonlinear motor model in the design process, so that the calculated amount in online calculation can be reduced to the greatest extent, and the good dynamic and static following characteristics of current in the motor running process are ensured. Respectively carrying out linearization processing on f (x), h (x) to obtain corresponding Jacobian matrixes as follows:
according to the above formulas, an extended kalman filter equation for disturbance estimation under the condition of permanent magnet synchronous motor inductance mismatch can be constructed as follows:
①, updating and calculating the state vector correction value at the k-1 moment through the state transfer function f and the voltage output quantity of the predictive control algorithm to obtain the estimated value of the state vector at the k moment:
in the formula (I), the compound is shown in the specification,
indicating the state vector correction value at the time k-1;
representing the state vector estimate at time k.
Meanwhile, updating and calculating the covariance matrix of the state vector correction value at the k-1 moment by using the state transition matrix and the system noise covariance matrix to obtain the covariance matrix of the state vector estimation value at the k moment:
in the formula, Pk-1A covariance matrix representing the state vector correction value at the time k-1; pk|k-1A covariance matrix representing the state vector estimation value at the time k; fk-1Representing a state transition matrix; qdRepresenting the system noise covariance matrix.
On the basis, a Kalman gain matrix at the moment k is solved by using a state vector estimation value covariance matrix at the moment k, a measurement transfer matrix and a measurement noise covariance matrix:
in the formula, KkIs a Kalman gain matrix; hkTo measure a transfer matrix; r measures the noise covariance matrix.
②, correcting the prior estimation value according to the observation error and the minimum variance principle, namely correcting the estimation value of the state vector at the time k by using the Kalman gain matrix and the observation vector at the time k to obtain the correction value of the state vector at the time k:
in the formula (I), the compound is shown in the specification,
a state vector correction value representing time k; y iskRepresenting the observation vector at time k.
Meanwhile, obtaining a covariance value of a k-moment Kalman state vector correction value by using a k-moment Kalman gain matrix and a covariance matrix of a Kalman state vector estimation value:
Pk＝Pk|k-1-KkHkPk|k-1(23)
in the formula, PkCovariance matrix representing state vector correction values at time k
Kalman filtering is actually a recursive algorithm, and the whole recursive process needs to be given an initial value
And P0. For a practical system, the characteristics of the initial state of the system are uncertain, and the corresponding initial value
And P0The value of (a) is also difficult. However, if the Kalman filter is consistent and asymptotically stable and the coefficient matrix of the system is a time-invariant matrix, the optimal estimation value increases with the filtering times
And PkWill not be subjected to the initial value selected at will
And P0The effect of (2) to achieve unbiased estimation.
The EKF disturbance observer of the invention sets the initial values as follows:
P0＝[0.1 0.1 500 0.5 10 10](25)
when the EKF disturbance observer is designed, the statistical characteristics of the system random disturbance and the measurement noise are unknown, and the covariance matrix of the system noise and the measurement noise can be determined through simulation experiments. And a proper value is selected, so that the convergence of the algorithm is accelerated, and the estimation precision is improved. In the EKF disturbance observer of the invention, the covariance matrix is selected as follows:
in one example based on the method provided by the present invention, fig. 3-6 respectively show the inductance mismatch (L ═ 2L)0) The current curve of the motor dq axis based on predictive control in the case, and the mismatch state (L ═ 2L)0) Prediction control-based motor dq-axis current curve diagram combined with EKF disturbance observer and inductance mismatch (L ═ L)0/2) motor dq-axis current curve based on predictive control, and the mismatch state (L ═ L)0/2) motor dq-axis current profile based on predictive control in combination with an EKF disturbance observer. It can be seen that the method provided by the invention has good disturbance suppression effect.
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 (5)
1. A disturbance suppression method for a permanent magnet synchronous motor is characterized by comprising the following steps:
acquiring online data, namely acquiring three-phase current, rotating speed and rotor position angle of a permanent magnet synchronous motor in real time;
step two, establishing a dead-beat current prediction control model, and calculating the reference voltage at the next moment in real time by using the data acquired in the step one;
establishing a disturbance observer equation based on an Extended Kalman Filter (EKF) algorithm, taking the reference voltage obtained in the second step as a control quantity, taking a voltage disturbance quantity caused by inductance as a state vector, and taking three-phase current, rotating speed and a rotor position angle as observed quantities; updating and calculating the voltage disturbance quantity in real time by using the equation, and performing feedforward compensation on the reference voltage to obtain an updated reference voltage;
establishing a mathematical model of the permanent magnet synchronous motor under an α - β coordinate system:
in the formula uα、uβIs stator voltage under α - β coordinate system iα、iβStator current phi of α - β coordinate systemrIs a rotor flux linkage; rsIs a stator resistor; l issIs a stator inductance; omegae、ωmThe electrical angular velocity of the rotor and the mechanical angular velocity of the rotor, respectively; theta is a rotor position angle; p is a differential operator; t iseIs an electromagnetic torque; t isLIs the load torque; b is a viscosity coefficient; p is a radical ofmThe number of pole pairs of the motor is shown; psiα、ψβIs a stator flux linkage under a α - β coordinate system, t is a time variable, J is a load moment of inertia;
the voltage after adding the disturbance term into the model is as follows:
in the formula (f)α、fβRepresenting the voltage disturbance quantity under α - β coordinate system;
wherein the perturbation term is:
in the formula, △ L represents an inductance mismatch amount, △ L ═Ls-Ls0，Ls0And indicating the inductance calibration value.
2. The method of claim 1, wherein: the step three of updating and calculating the voltage disturbance variable in real time by using the equation specifically comprises the following steps:
①, initializing the state vector, the covariance of the state vector, the system noise covariance matrix and the measurement noise covariance matrix of the equation;
② prediction, with initialized state vector as tk-1Correction value of time
In the case of (2), the estimated value is predicted
And a priori estimated covariance matrix Pk|k-1On the basis of which the Kalman gain K is determinedk；
③, updating, correcting the prior estimated value according to the observation error and the minimum variance principle to obtain the corrected value of the state vector
Covariance matrix P for simultaneous calculation of correction valuesk；
④, after completing step ③, outputting the state vector correction value, and substituting the state vector correction value and the covariance value of the state vector correction value into step ② to calculate using k as a new sampling time point.
3. The method of claim 1, wherein: the initialization of the state vector comprises the initialization of three-phase current, rotating speed, rotor position angle and voltage disturbance, and the disturbance observer observes the voltage disturbance in real time, namely starts to work from the starting moment of the motor, so that the initial values of the state vector are all set to be 0.
4. The method of claim 1, wherein: the state vector x is a 6-dimensional vector
x＝[iαiβωeθ fαfβ]TThe observation vector is 4-dimensional vector y ═ iαiβωeθ]TIn the formula, iα、iβIs stator current, omega, in α - β coordinate systemeIs the electrical angular velocity of the rotor, theta is the rotor position angle, fα、fβThe voltage disturbance quantity under the coordinate system of the motor α - β.
5. The method according to claim 2, wherein said step ③ specifically comprises:
and (3) solving a Kalman gain matrix at the moment k by using the covariance matrix of the state vector estimation value at the moment k, the measurement transfer matrix and the measurement noise covariance matrix:
in the formula, HkTo measure a transfer matrix; r is a measurement noise covariance matrix;
meanwhile, obtaining a covariance value of a state vector correction value at the moment k by using a Kalman gain matrix at the moment k and a covariance matrix of a state vector estimation value:
Pk＝Pk|k-1-KkHkPk|k-1。
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