CN111697886A - Permanent magnet synchronous motor speed sensorless control method based on parameter identification - Google Patents

Permanent magnet synchronous motor speed sensorless control method based on parameter identification Download PDF

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CN111697886A
CN111697886A CN202010491480.1A CN202010491480A CN111697886A CN 111697886 A CN111697886 A CN 111697886A CN 202010491480 A CN202010491480 A CN 202010491480A CN 111697886 A CN111697886 A CN 111697886A
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permanent magnet
synchronous motor
magnet synchronous
parameter
model
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张承宁
滕继晖
张硕
李雪萍
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Beijing Institute of Technology BIT
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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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/18—Estimation of position or speed
    • 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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • 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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/0017—Model reference adaptation, e.g. MRAS or MRAC, useful for control or parameter estimation
    • 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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • 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
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/24—Vector control not involving the use of rotor position or rotor speed sensors
    • 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
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/022—Synchronous motors
    • 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
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/05—Synchronous machines, e.g. with permanent magnets or DC excitation

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  • Power Engineering (AREA)
  • Control Of Electric Motors In General (AREA)
  • Control Of Ac Motors In General (AREA)

Abstract

The invention provides a permanent magnet synchronous motor speed sensorless control method based on parameter identification, and provides improvement aiming at the existing model reference self-adaptive method based on a model and combining a parameter identification means. In the prior art, only through the implementation mode of the model reference adaptive method, although the rotor speed can be accurately estimated, the method has the defect of depending on the accuracy of a reference model, including the accuracy of the model and the accuracy of parameters. Therefore, the method combines the model reference self-adaptive method and the parameter identification method, and can improve the accuracy of the model through the identified accurate parameters, so as to improve the accuracy of the rotation speed estimation.

Description

Permanent magnet synchronous motor speed sensorless control method based on parameter identification
Technical Field
The invention belongs to the technical field of permanent magnet synchronous motor control, and particularly relates to a speed-free control technology based on parameter identification and suitable for the condition of inductance mismatch.
Background
In the vector control of the permanent magnet synchronous motor, the rotating speed and the position are very important feedback information and are also the key for realizing closed-loop control. In the prior art, a photoelectric encoder is mostly adopted as a speed sensor, and the rotating speed and the position of a rotor are finally obtained on a light receiving plate through emitting light and transmitting light at intervals of a grating. However, in general, the existence of the mechanical encoder brings some problems to the application of the permanent magnet synchronous motor, for example, for the permanent magnet synchronous motor for vehicles, the existence of the mechanical encoder makes the installation space of the whole motor large, which is not friendly to the originally scarce space on the vehicle; the application scenarios of the motor are limited due to the properties of the mechanical encoder itself, and the motor is not robust in some harsh environments such as cold and bumpy environments; and the mechanical encoder is expensive, so that the cost of the motor control system is increased, and the commercial operation is not facilitated.
The continuously developed speed-free control technology aiming at the permanent magnet synchronous motor can effectively overcome the defects of mechanical speed measurement. At present, a sliding-mode observer method based on back emf, a rotating voltage injection method, a model reference self-adaption method based on a model and the like are widely used, but the methods have certain defects, such as oscillation effect in sliding-mode control, noise introduced in the voltage injection method, model reference method dependence on model accuracy and the like, and the methods need to be combined with other methods for use in practical application.
Disclosure of Invention
In view of this, the present invention provides a method for controlling a permanent magnet synchronous motor without a speed sensor based on parameter identification, which specifically includes the following steps:
firstly, acquiring three-phase current of a permanent magnet synchronous motor in real time on line;
step two, establishing a mathematical model under a d-q coordinate system of the permanent magnet synchronous motor, and identifying equivalent inductance parameters under the coordinate system by using a recursive least square method;
thirdly, obtaining a mathematical model of the permanent magnet synchronous motor under a d-q coordinate system based on a model reference self-adaptive method, and designing a self-adaptive law based on Popov super-stability to obtain a rotor electrical angular velocity expression; obtaining a rotor electrical angular velocity estimation value based on parameter identification by using the equivalent inductance parameter identified in the step two;
and step four, feeding back the rotor electric angular velocity estimated value obtained in the step four and position information obtained by integrating the rotor electric angular velocity estimated value to vector control and realizing the control of the permanent magnet synchronous motor.
Further, the mathematical model under the d-q coordinate system of the permanent magnet synchronous motor established in the second step specifically includes:
sequentially performing Clark conversion and Park conversion on the three-phase current collected in the step one, and establishing the following model:
Figure BDA0002521245100000021
in the formula id、iqD-and q-axis currents, UdAnd UqIs d-axis and q-axis voltage, RsAnd LsIs equivalent resistance and inductance in d-q coordinate system, WeIs the electrical angular velocity of the rotor, /)fIs a permanent magnet flux linkage;
at idIn the vector control method of 0, the vector control method can be expressed as a form of vector multiplication of:
Figure BDA0002521245100000022
further, the identifying the equivalent inductance parameter in the coordinate system by using the recursive least square method in the second step specifically includes:
s2.1, setting initial parameter values, observing to obtain m state equations containing parameters to be estimated and m error equations of real state values and estimated state values, and calculating the square sum of m errors, wherein the formula is as follows:
Figure BDA0002521245100000023
e represents the state estimate and viewMeasuring the error of the value, wherein Y represents the state value vector of the real observation, X represents the state variable matrix theta representing the parameter matrix to be estimated, and X theta is the state estimation value vector;
s2.2, obtaining the optimal parameter estimation by deriving the error sum of squares formula and making the error sum of squares equal to zero:
Figure BDA0002521245100000024
wherein
Figure BDA0002521245100000025
The method comprises the steps of obtaining a parameter estimation value to be estimated, namely an equivalent inductance parameter to be estimated;
s2.3, however, the method is not friendly to the situation of adding new observation equations, and when there is a new observation equation (i.e. the m +1 th observation equation), all matrix operations need to be recalculated, which undoubtedly increases the calculation complexity. Based on this consideration, using the recursive least squares method, when there are m +1 observation equations first, the optimal parameter estimation expression is:
Figure BDA0002521245100000026
in the formula Xm+1Matrix of state variables representing m +1 observation equations, Ym+1Representing a matrix of m +1 observations. In the present invention, this formula is based on the first m observation equations, thus defining two new variables P (m) and P (m + 1):
Figure BDA0002521245100000027
introducing a matrix theorem:
(A+BC)-1＝A-1-A-1B(E+CA-1B)-1CA-1wherein A, B and C represent non-singular matrices, respectively.
Applying matrix theorem to the new variables can obtain
P(m+1)＝[P-1(m)+XT(m+1)X(m+1)]-1
＝P(m)-P(m)XT(m+1)[1+X(m+1)P(m)XT(m+1)]-1X(m+1)P(m)
Wherein X (m +1) represents the m +1 state equation, and P (m) is as defined above;
s2.4, substituting the formula P (m +1) obtained from S2.3 into the optimal parameter obtained from S2.2, and finding out X (m +1) P (m) XTThe (m +1) is a constant, so that the complicated calculation process of an inverse matrix is omitted, and the advantage of the recursive least squares over the traditional least squares is achieved. The final optimal parameter estimate is:
Figure BDA0002521245100000031
in the formula
Figure BDA0002521245100000032
And (3) representing the optimal parameter estimation value obtained after m observation equations, wherein y (m +1) represents the m +1 th observation value, and P (m) is defined as above, and finally the optimal parameter estimation value based on m +1 state equations is obtained.
Further, the mathematical model of the permanent magnet synchronous motor under the d-q coordinate system is obtained based on the model reference adaptive method in the third step, and the mathematical model has the following form:
Figure BDA0002521245100000033
using estimated speed of rotation in the model
Figure BDA0002521245100000034
Replacing the actual speed We。
Designing an adaptive law based on Popov hyperstability to obtain the following rotor electrical angular velocity expression:
Figure BDA0002521245100000035
and substituting the identified equivalent inductance parameters into the formula to obtain the rotor electrical angular velocity estimated value based on parameter identification.
The method provided by the invention provides improvement aiming at a model reference self-adaptive method based on a model and combining a parameter identification means. In the prior art, only through the implementation mode of the model reference adaptive method, although the rotor speed can be accurately estimated, the method has the defect of depending on the accuracy of a reference model, including the accuracy of the model and the accuracy of parameters. Therefore, the method combines the model reference self-adaptive method and the parameter identification method, and can improve the accuracy of the model through the identified accurate parameters, so as to improve the accuracy of the rotation speed estimation. By executing the method, the obtained rotating speed and the position information obtained by integration are fed back to the vector control, and the speed-sensor-free control process with certain robustness of a double closed loop of a parameter closed loop and a rotating speed closed loop can be finally realized.
Drawings
FIG. 1 is a general framework of a control system corresponding to the method of the present invention;
FIG. 2 is a speed estimate without a closed loop of parameters when the inductance parameters are mismatched;
FIG. 3 position estimation without a closed loop of parameters when the inductance parameters mismatch;
FIG. 4 is a recursive least squares identified inductance parameter;
FIG. 5 rotation speed estimation with closed loop parameters for inductance mismatch;
fig. 6 is a position estimate with a parametric closed loop for inductive mismatch.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. 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 invention provides a permanent magnet synchronous motor speed sensorless control method based on parameter identification, which specifically comprises the following steps as shown in figure 1:
firstly, acquiring three-phase current of a permanent magnet synchronous motor in real time on line;
step two, establishing a mathematical model under a d-q coordinate system of the permanent magnet synchronous motor, and identifying equivalent inductance parameters under the coordinate system by using a recursive least square method;
thirdly, obtaining a mathematical model of the permanent magnet synchronous motor under a d-q coordinate system based on a model reference self-adaptive method, and designing a self-adaptive law based on Popov super-stability to obtain a rotor electrical angular velocity expression; obtaining a rotor electrical angular velocity estimation value based on parameter identification by using the equivalent inductance parameter identified in the step two;
and step four, feeding back the rotor electric angular velocity estimated value obtained in the step four and position information obtained by integrating the rotor electric angular velocity estimated value to vector control and realizing the control of the permanent magnet synchronous motor.
In a preferred embodiment of the present invention, the mathematical model under the d-q coordinate system of the permanent magnet synchronous motor established in the second step specifically includes:
sequentially performing Clark conversion and Park conversion on the three-phase current collected in the step one, and establishing the following model:
Figure BDA0002521245100000041
in the formula id、iqD-and q-axis currents, UdAnd UqIs d-axis and q-axis voltage, RsAnd LsIs equivalent resistance and inductance in d-q coordinate system, WeIs the electrical angular velocity of the rotor, /)fIs a permanent magnet flux linkage;
at idIn the vector control method of 0, the vector control method can be expressed as a form of vector multiplication of:
Figure BDA0002521245100000042
in a preferred embodiment of the present invention, the identifying the equivalent inductance parameter in the coordinate system by using a recursive least square method in the second step specifically includes:
s2.1, setting initial parameter values, observing to obtain m state equations containing parameters to be estimated and m error equations of real state values and estimated state values, and calculating the square sum of m errors, wherein the formula is as follows:
Figure BDA0002521245100000051
e represents the error between the state estimation value and the observed value, Y represents the state value vector of the real observation, X represents the state variable matrix theta represents the parameter matrix to be estimated, and X theta is the state estimation value vector;
s2.2, obtaining the optimal parameter estimation by deriving the error sum of squares formula and making the error sum of squares equal to zero:
Figure BDA0002521245100000052
wherein
Figure BDA0002521245100000053
The method comprises the steps of obtaining a parameter estimation value to be estimated, namely an equivalent inductance parameter to be estimated;
s2.3, using a recursive least square method, wherein when m +1 observation equations exist, the optimal parameter estimation expression is as follows:
Figure BDA0002521245100000054
in the formula Xm+1Matrix of state variables representing m +1 observation equations, Ym+1Representing a matrix consisting of m +1 observations; establishing this equation on the basis of the first m observation equations, two new variables P (m) and P (m +1) are defined:
Figure BDA0002521245100000055
introducing a matrix theorem:
(A+BC)-1＝A-1-A-1B(E+CA-1B)-1CA-1wherein A, B and C represent non-singular matrices, respectively.
Applying matrix theorem to the new variables can obtain
P(m+1)＝[P-1(m)+XT(m+1)X(m+1)]-1
＝P(m)-P(m)XT(m+1)[1+X(m+1)P(m)XT(m+1)]-1X(m+1)P(m)
In the formula, X (m +1) represents the (m +1) th equation of state;
s2.4, substituting the formula P (m +1) obtained by S2.3 into S2.2 to obtain the optimal parameter estimation:
Figure BDA0002521245100000056
in the formula
Figure BDA0002521245100000057
And the optimal parameter estimation value obtained after the m observation equations is shown, y (m +1) represents the m +1 th observation value, and the optimal parameter estimation value based on the m +1 state equations is finally obtained.
In a preferred embodiment of the present invention, the step three is to obtain a mathematical model of the permanent magnet synchronous motor in a d-q coordinate system based on a model reference adaptive method, and the mathematical model has the following form:
Figure BDA0002521245100000058
using estimated speed of rotation in the model
Figure BDA0002521245100000061
Replacing the actual speed We。
Designing an adaptive law based on Popov hyperstability to obtain the following rotor electrical angular velocity expression:
Figure BDA0002521245100000062
and substituting the identified equivalent inductance parameters into the formula to obtain the rotor electrical angular velocity estimated value based on parameter identification.
Fig. 2 and 3 show the conventional estimation of the rotor electrical angular velocity and position in the case of inductance mismatch, and it can be seen that there is a large deviation from the actual value without the improvement of the present invention. Fig. 4-6 show the identification of inductance and the estimation of electronic angular velocity and position based on an example of the present invention, which can be seen to have a significant improvement in the estimation.
It should be understood that, the sequence numbers of the steps in the embodiments of the present invention do not mean the execution sequence, and the execution sequence of each process should be determined by the function and the inherent logic of the process, and should not constitute any limitation on the implementation process of the embodiments of the present invention.
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 (4)

1. A permanent magnet synchronous motor speed sensorless control method based on parameter identification is characterized in that: the method specifically comprises the following steps:
firstly, acquiring three-phase current of a permanent magnet synchronous motor in real time on line;
step two, establishing a mathematical model under a d-q coordinate system of the permanent magnet synchronous motor, and identifying equivalent inductance parameters under the coordinate system by using a recursive least square method;
thirdly, obtaining a mathematical model of the permanent magnet synchronous motor under a d-q coordinate system based on a model reference self-adaptive method, and designing a self-adaptive law based on Popov super-stability to obtain a rotor electrical angular velocity expression; obtaining a rotor electrical angular velocity estimation value based on parameter identification by using the equivalent inductance parameter identified in the step two;
and step four, feeding back the rotor electric angular velocity estimated value obtained in the step four and position information obtained by integrating the rotor electric angular velocity estimated value to vector control and realizing the control of the permanent magnet synchronous motor.
2. The method of claim 1, wherein: the mathematical model under the d-q coordinate system of the permanent magnet synchronous motor established in the second step specifically comprises the following steps:
sequentially performing Clark conversion and Park conversion on the three-phase current collected in the step one, and establishing the following model:
Figure FDA0002521245090000011
in the formula id、iqD-and q-axis currents, UdAnd UqIs d-axis and q-axis voltage, RsAnd LsIs equivalent resistance and inductance in d-q coordinate system, WeIs the electrical angular velocity of the rotor, /)fIs a permanent magnet flux linkage;
at idIn the vector control method of 0, the vector control method can be expressed as a form of vector multiplication of:
Figure FDA0002521245090000012
3. the method of claim 2, wherein: identifying the equivalent inductance parameter under the coordinate system by using a recursive least square method in the second step specifically comprises the following steps:
s2.1, setting initial parameter values, observing to obtain m state equations containing parameters to be estimated and m error equations of real state values and estimated state values, and calculating the square sum of m errors, wherein the formula is as follows:
Figure FDA0002521245090000013
e represents the error between the state estimation value and the observed value, Y represents the state value vector of the real observation, X represents the state variable matrix theta represents the parameter matrix to be estimated, and X theta is the state estimation value vector;
s2.2, obtaining the optimal parameter estimation by deriving the error sum of squares formula and making the error sum of squares equal to zero:
Figure FDA0002521245090000021
wherein
Figure FDA0002521245090000022
The method comprises the steps of obtaining a parameter estimation value to be estimated, namely an equivalent inductance parameter to be estimated;
s2.3, using a recursive least square method, wherein when m +1 observation equations exist, the optimal parameter estimation expression is as follows:
Figure FDA0002521245090000023
in the formula Xm+1Matrix of state variables representing m +1 observation equations, Ym+1Representing a matrix consisting of m +1 observations; on the basis of the first m observation equations, two new variables P (m) and P (m +1) are defined:
Figure FDA0002521245090000024
introducing a matrix theorem:
(A+BC)-1＝A-1-A-1B(E+CA-1B)-1CA-1wherein A, B and C represent non-singular matrices, respectively;
applying matrix theorem to the new variables can obtain
P(m+1)＝[P-1(m)+XT(m+1)X(m+1)]-1
＝P(m)-P(m)XT(m+1)[1+X(m+1)P(m)XT(m+1)]-1X(m+1)P(m)
In the formula, X (m +1) represents the (m +1) th equation of state;
s2.4, substituting the formula P (m +1) obtained by S2.3 into S2.2 to obtain the optimal parameter estimation:
Figure FDA0002521245090000025
in the formula
Figure FDA0002521245090000026
Expressed in m observation equationsAnd finally, obtaining the optimal parameter estimation value based on m +1 state equations, wherein y (m +1) represents the m +1 th observation value.
4. The method of claim 3, wherein: the third step is to obtain a mathematical model of the permanent magnet synchronous motor under a d-q coordinate system based on a model reference self-adaptive method, and the mathematical model has the following form:
Figure FDA0002521245090000027
will be W in the modeleBy estimating the speed of rotation
Figure FDA0002521245090000028
Alternatively, the following form is obtained:
Figure FDA0002521245090000029
designing an adaptive law based on Popov hyperstability to obtain the following rotor electrical angular velocity expression:
Figure FDA0002521245090000031
and substituting the identified equivalent inductance parameters into the formula to obtain the rotor electrical angular velocity estimated value based on parameter identification.
CN202010491480.1A 2020-06-02 2020-06-02 Permanent magnet synchronous motor speed sensorless control method based on parameter identification Pending CN111697886A (en)

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Application publication date: 20200922