CN111193448A - Surface-mounted permanent magnet synchronous motor load torque observation method based on extended Kalman filter - Google Patents
Surface-mounted permanent magnet synchronous motor load torque observation method based on extended Kalman filter 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
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
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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
- H02P21/20—Estimation of torque
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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
- 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
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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
- 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
- H02P2207/055—Surface mounted magnet motors
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Abstract
The invention provides a surface-mounted permanent magnet synchronous motor load torque observation method based on an extended Kalman filter, which is characterized in that a mathematical model of a permanent magnet synchronous motor for load torque observation is obtained according to a mathematical model under a two-phase rotating coordinate system of the permanent magnet synchronous motor on the basis of vector control, and is substituted into an extended Kalman filter algorithm to realize the observation of the load torque of the permanent magnet synchronous motor. The surface-mounted permanent magnet synchronous motor load torque observation method based on the extended Kalman filter realizes real-time monitoring of the surface-mounted permanent magnet synchronous motor load torque by using the extended Kalman filter algorithm, can realize sensorless monitoring of the permanent magnet synchronous motor load torque, and has the advantages of simple structure, low cost and stronger anti-interference capability.
Description
Technical Field
The invention relates to the technical field of permanent magnet synchronous motors, in particular to a surface-mounted permanent magnet synchronous motor load torque observation method based on an extended Kalman filter.
Background
Permanent Magnet Synchronous Motors (PMSM) have the advantages of high power, high energy density and simple structure, and are increasingly widely applied in numerous industrial fields. In controlling the operation of the motor, the motor is controlled to provide accurate torque control over a full speed range and a full load range. In addition, by comparing the given command torque with the actual torque of the drive motor system, the operation state of the drive motor system can be indirectly reflected, and whether the fault exists or not can be deduced. Therefore, the real-time monitoring of the torque is not only a requirement for ensuring the control performance, but also an important safety index.
The traditional torque measuring method measures the torque through a torque measuring instrument, and has the defects of high measuring cost, large influence of instrument precision, limitation of installation conditions in some occasions, inconvenience in maintenance, incapability of realizing real-time online monitoring of the load torque and the like.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides the surface-mounted permanent magnet synchronous motor load torque observation method based on the extended Kalman filter, overcomes the defects in the prior art, and has the advantages of predictability, self-adaptive capacity, anti-interference performance, simple structure, easiness in software implementation, low cost and the like.
In order to achieve the purpose, the invention adopts the following technical scheme:
the surface-mounted permanent magnet synchronous motor load torque observation method based on the extended Kalman filter comprises the following steps:
step 1: obtaining actual rotation degree of a surface-mounted permanent magnet synchronous motor and three-phase current i of the motorabcThree-phase current iabcObtaining the current i under a static two-phase coordinate system through Clarke transformationαAnd iβObtaining the current i under a rotating two-phase coordinate system through Park transformationdAnd iq;
Step 2: the difference value of the given rotating speed of the motor and the actual rotating speed of the motor is adjusted by a rotating speed Adjuster (ASR) to determine the given current i of the q axisq *D-axis current is given current id *;
And step 3: setting q axis to current iq *And a feedback current iqAnd d-axis given current id *And a feedback current idThe difference value of the d-axis voltage and the q-axis voltage u are obtained after being adjusted by A Current Regulator (ACR)d、uq;
And 4, step 4: d and q axis real time voltage ud、uqα and β axis real-time voltage u is obtained through inverse PARK conversionα、uβ;
Step 5, real-time voltage u of α and β axesα、uβSVPWM modulation is carried out to obtain a pulse width modulation waveform, the pulse width modulation waveform is sent to an inverter to control a permanent magnet synchronous motor, and real-time three-phase current i is obtainedabcAnd three phase voltage uabc;
Step 6: will measure the real-time current id、iqReal time voltage ud、uqAnd real-time electrical angular velocity weAnd sending the load torque to a load torque observer based on an Extended Kalman Filter (EKF) to realize the real-time observation of the load torque of the permanent magnet synchronous motor.
Furthermore, in the surface-mounted permanent magnet synchronous motor, the magnetic path structure of the rotor is symmetrical, and the magnetic permeability of the permanent magnet material is close to that of the air gap, so that the L-shaped magnetic path structure is L-shapedd=LqUnder a two-phase rotating coordinate system d-q, the voltage equation of the permanent magnet synchronous motor is as follows:
in the formula ud、uq、id、iqVoltages and currents of a d axis and a q axis of the two-phase rotating coordinate system are respectively; rs、L、ψfStator resistance, quadrature-direct axis inductance and rotor permanent magnet flux linkage; w is aeIs the electrical angular velocity of the motor;
transforming equation (1) into a current equation yields:
wherein p isnThe number of pole pairs of the permanent magnet synchronous motor is;
the mechanical equation of motion of the motor is:
wherein wmIs the mechanical angular velocity of the motor, and J is the moment of inertia; b is the damping coefficient, TLIs a load torque, and an electrical angle we=pnwm;
So the mechanical motion equation of the transformed motor is:
in practical situations, the motor load torque fluctuation time is far longer than the motor control system dynamic process time, so that the load torque is calculated by regarding as a steady-state value, and derivation of the load torque can obtain the following equation:
the following can be written by the formulas (2), (5) and (6):
equation (7) can be written as the following equation of state:
wherein x ═ idiqweTL]TIs a state variable, an input variable u ═ uduq]TAnd input variable y ═ idiq]T;
The following formulas (7) and (8) can be obtained:
in order to construct the digital system of the extended Kalman filter state observer, discretization processing can obtain
Finishing to obtain:
where T is the sampling period, the discretized state equation (14) is a deterministic equation, but in practical systems, model parameters are uncertain and variable, measurement noise inevitably exists in stator voltages and currents, and these uncertainties are incorporated into the system noise vector V and measurement noise W, so equation (14) can be changed to:
where V (k) is system noise and W (k) is measurement noise, both of which are zero-mean white noise.
Further, the specific process of step 6 is as follows:
the discretized mathematical model of the EKF algorithm is as follows:
wherein x (k +1) represents a state estimation value at the k +1 moment, x (k) represents a state estimation value at the k moment, V (k) is a system noise vector, and W (k) is measurement noise;
the state estimation of the extended kalman filter observer is mainly divided into two states: prediction and correction
(1) And (3) state prediction:
in the formula (I), the compound is shown in the specification,andindicates the (k +1) -th predicted value,represents the k-th estimated value;
the above equation is mainly based on the input u (k) and last state estimationPredicting a vector at the (k +1) time;
(2) calculating a covariance matrix:
in the formula (I), the compound is shown in the specification,is a covariance matrix, mainly to find the gain matrix K (K +1),an error covariance matrix at the moment k is obtained, and Q is a covariance matrix of system noise V; and the Jacobian matrix F (k) is:
the calculation result is as follows:
(3) calculating a gain matrix:
wherein, K (K +1) is a gain matrix which is mainly used for completing the correction of state vector estimation, and R is a covariance matrix of a measurement noise vector W;
(4) and (3) state vector estimation:
in the formula (I), the compound is shown in the specification,is the state vector estimation value of the (k +1) th time, y (k +1) is the measurement state vector,for the predicted output state vector, the above equation completes the state vector estimation of the (k +1) th;
(5) calculating an estimation error covariance matrix:
in the formula (I), the compound is shown in the specification,the covariance matrix reflects the magnitude of the state estimation error at this time, and is called in the next state estimation, so that iterative operation is performed, and the load torque observed value at each moment is obtained.
Compared with the prior art, the invention has the beneficial technical effects that: according to the observation method for the load torque of the surface-mounted permanent magnet synchronous motor based on the extended Kalman filter, the observer in the form of an algorithm replaces the traditional parameter measurement method in the physical form, the load torque of the surface-mounted permanent magnet synchronous motor is monitored in real time by using the algorithm of the extended Kalman filter, and the observation method has the advantages of low cost, simple structure, easiness in software implementation, strong self-adaption capability and anti-jamming capability and the like.
Drawings
FIG. 1 is a schematic diagram of a vector control system according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a load torque observation process based on EKF algorithm according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the drawings of the embodiments of the present invention. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the described embodiments of the invention, are within the scope of the invention.
The technical scheme of the invention is further explained in detail by combining the drawings in the specification.
As shown in fig. 1, the method for observing the load torque of the surface-mounted permanent magnet synchronous motor based on the extended kalman filter comprises the following steps:
step 1: obtaining actual rotation degree of a surface-mounted permanent magnet synchronous motor and three-phase current i of the motorabcThree-phase current iabcObtaining the current i under a static two-phase coordinate system through Clarke transformationαAnd iβObtaining the current i under a rotating two-phase coordinate system through Park transformationdAnd iq;
Step 2: the difference value of the given rotating speed of the motor and the actual rotating speed of the motor is adjusted by a rotating speed Adjuster (ASR) to determine the given current i of the q axisq *D-axis current is given current id *;
And step 3: setting q axis to current iq *And contrary toCurrent feed iqAnd d-axis given current id *And a feedback current idThe difference value of the d-axis voltage and the q-axis voltage u are obtained after being adjusted by A Current Regulator (ACR)d、uq;
And 4, step 4: d and q axis real time voltage ud、uqα and β axis real-time voltage u is obtained through inverse PARK conversionα、uβ;
Step 5, real-time voltage u of α and β axesα、uβSVPWM modulation is carried out to obtain a pulse width modulation waveform, the pulse width modulation waveform is sent to an inverter to control a permanent magnet synchronous motor, and real-time three-phase current i is obtainedabcAnd three phase voltage uabc;
Step 6: will measure the real-time current id、iqReal time voltage ud、uqAnd real-time electrical angular velocity weAnd sending the load torque to a load torque observer based on an Extended Kalman Filter (EKF) to realize the real-time observation of the load torque of the permanent magnet synchronous motor.
In the surface-mounted permanent magnet synchronous motor, the rotor magnetic circuit structure is symmetrical, and the magnetic conductivity of the permanent magnet material is close to that of the air gap, so that the L-shaped magnetic circuit structure is L-shapedd=LqUnder a two-phase rotating coordinate system d-q, the voltage equation of the permanent magnet synchronous motor is as follows:
in the formula ud、uq、id、iqVoltages and currents of a d axis and a q axis of the two-phase rotating coordinate system are respectively; rs、L、ψfStator resistance, quadrature-direct axis inductance and rotor permanent magnet flux linkage; w is aeIs the electrical angular velocity of the motor;
transforming equation (1) into a current equation yields:
wherein p isnThe number of pole pairs of the permanent magnet synchronous motor is;
the mechanical equation of motion of the motor is:
wherein wmIs the mechanical angular velocity of the motor, and J is the moment of inertia; b is the damping coefficient, TLIs a load torque, and an electrical angle we=pnwm;
So the mechanical motion equation of the transformed motor is:
in practical situations, the motor load torque fluctuation time is far longer than the motor control system dynamic process time, so that the load torque is calculated by regarding as a steady-state value, and derivation of the load torque can obtain the following equation:
the following can be written by the formulas (2), (5) and (6):
equation (7) can be written as the following equation of state:
wherein x ═ idiqweTL]TIs a state variable, an input variable u ═ uduq]TAnd input variable y ═ idiq]T;
The following formulas (7) and (8) can be obtained:
in order to construct the digital system of the extended Kalman filter state observer, discretization processing can obtain
Finishing to obtain:
where T is the sampling period, the discretized state equation (14) is a deterministic equation, but in practical systems, model parameters are uncertain and variable, measurement noise inevitably exists in stator voltages and currents, and these uncertainties are incorporated into the system noise vector V and measurement noise W, so equation (14) can be changed to:
where V (k) is system noise and W (k) is measurement noise, both of which are zero-mean white noise.
The specific process of step 6 is as follows:
the discretized mathematical model of the EKF algorithm is as follows:
wherein x (k +1) represents a state estimation value at the k +1 moment, x (k) represents a state estimation value at the k moment, V (k) is a system noise vector, and W (k) is measurement noise;
the state estimation of the extended kalman filter observer is mainly divided into two states: prediction and correction
(1) And (3) state prediction:
in the formula (I), the compound is shown in the specification,andindicates the (k +1) -th predicted value,represents the k-th estimated value;
the above equation is mainly based on the input u (k) and last state estimationPredicting a vector at the (k +1) time;
(2) calculating a covariance matrix:
in the formula (I), the compound is shown in the specification,is a covariance matrix, mainly to find the gain matrix K (K +1),an error covariance matrix at the moment k is obtained, and Q is a covariance matrix of system noise V; and the Jacobian matrix F (k) is:
the calculation result is as follows:
(3) calculating a gain matrix:
wherein, K (K +1) is a gain matrix which is mainly used for completing the correction of state vector estimation, and R is a covariance matrix of a measurement noise vector W;
(4) and (3) state vector estimation:
in the formula (I), the compound is shown in the specification,is the state vector estimation value of the (k +1) th time, y (k +1) is the measurement state vector,for the predicted output state vector, the above equation completes the state vector estimation of the (k +1) th;
(5) calculating an estimation error covariance matrix:
in the formula (I), the compound is shown in the specification,the covariance matrix reflects the magnitude of the state estimation error at this time, and is called in the next state estimation, so that iterative operation is performed, and the load torque observed value at each moment is obtained.
According to the observation method for the load torque of the surface-mounted permanent magnet synchronous motor based on the extended Kalman filter, the observer in the form of an algorithm replaces the traditional parameter measurement method in the physical form, the load torque of the surface-mounted permanent magnet synchronous motor is monitored in real time by using the algorithm of the extended Kalman filter, and the observation method has the advantages of low cost, simple structure, easiness in software implementation, strong self-adaption capability and anti-jamming capability and the like.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention as defined in the appended claims.
Claims (3)
1. The surface-mounted permanent magnet synchronous motor load torque observation method based on the extended Kalman filter is characterized by comprising the following steps:
step 1: obtaining actual rotation degree of a surface-mounted permanent magnet synchronous motor and three-phase current i of the motorabcThree-phase current iabcObtaining the current i under a static two-phase coordinate system through Clarke transformationαAnd iβObtaining the current i under a rotating two-phase coordinate system through Park transformationdAnd iq;
Step 2: the difference value of the given rotating speed of the motor and the actual rotating speed of the motor is adjusted by a rotating speed Adjuster (ASR) to determine the given current i of the q axisq *D-axis current is given current id *;
And step 3: setting q axis to current iq *And a feedback current iqAnd d-axis given current id *And a feedback current idThe difference value of the d-axis voltage and the q-axis voltage u are obtained after being adjusted by A Current Regulator (ACR)d、uq;
And 4, step 4: d and q axis real time voltage ud、uqα and β axis real-time voltage u is obtained through inverse PARK conversionα、uβ;
Step 5, real-time voltage u of α and β axesα、uβSVPWM modulation is carried out to obtain a pulse width modulation waveform, and the pulse width modulation waveform is sent to the inverseThe transformer controls the permanent magnet synchronous motor to obtain real-time three-phase current iabcAnd three phase voltage uabc;
Step 6: will measure the real-time current id、iqReal time voltage ud、uqAnd real-time electrical angular velocity weAnd sending the load torque to a load torque observer based on an Extended Kalman Filter (EKF) to realize the real-time observation of the load torque of the permanent magnet synchronous motor.
2. The extended Kalman filter-based surface-mounted permanent magnet synchronous motor load torque observation method according to claim 1, characterized in that:
in the surface-mounted permanent magnet synchronous motor, the magnetic path structure of the rotor is symmetrical, and the magnetic conductivity of the permanent magnet material is close to that of the air gap, so that the L-shaped magnetic flux path structure is L-shapedd=LqUnder a two-phase rotating coordinate system d-q, the voltage equation of the permanent magnet synchronous motor is as follows:
in the formula ud、uq、id、iqVoltages and currents of a d axis and a q axis of the two-phase rotating coordinate system are respectively; rs、L、ψfStator resistance, quadrature-direct axis inductance and rotor permanent magnet flux linkage; w is aeIs the electrical angular velocity of the motor;
transforming equation (1) into a current equation yields:
wherein p isnThe number of pole pairs of the permanent magnet synchronous motor is;
the mechanical equation of motion of the motor is:
wherein wmIs the mechanical angular velocity of the motor, and J is the moment of inertia; b is the damping coefficient, TLIs a load torque, and an electrical angular velocity we=pnwm;
So the mechanical motion equation of the transformed motor is:
in practical situations, the motor load torque fluctuation time is far longer than the motor control system dynamic process time, so that the load torque is calculated by regarding as a steady-state value, and derivation of the load torque can obtain the following equation:
the following can be written by the formulas (2), (5) and (6):
equation (7) can be written as the following equation of state:
wherein x ═ idiqweTL]TIs a state variable, an input variable u ═ uduq]TAnd input variable y ═ idiq]T;
The following formulas (7) and (8) can be obtained:
in order to construct the digital system of the extended Kalman filter state observer, discretization processing can obtain
Finishing to obtain:
where T is the sampling period, the discretized state equation (14) is a deterministic equation, but in practical systems, model parameters are uncertain and variable, measurement noise inevitably exists in stator voltages and currents, and these uncertainties are incorporated into the system noise vector V and measurement noise W, so equation (14) can be changed to:
where V (k) is system noise and W (k) is measurement noise, both of which are zero-mean white noise.
3. The extended Kalman filter-based surface-mounted permanent magnet synchronous motor load torque observation method according to claim 1, characterized in that: the specific process of step 6 is as follows:
the discretized mathematical model of the EKF algorithm is as follows:
wherein x (k +1) represents a state estimation value at the k +1 moment, x (k) represents a state estimation value at the k moment, V (k) is a system noise vector, and W (k) is measurement noise;
the state estimation of the extended kalman filter observer is mainly divided into two states: prediction and correction
(1) And (3) state prediction:
in the formula (I), the compound is shown in the specification,andindicates the (k +1) -th predicted value,represents the k-th estimated value;
the above equation is mainly based on the input u (k) and last state estimationPredicting a vector at the (k +1) time;
(2) calculating a covariance matrix:
in the formula (I), the compound is shown in the specification,is a covariance matrix, mainly to find the gain matrix K (K +1),an error covariance matrix at the moment k is obtained, and Q is a covariance matrix of system noise V; and the Jacobian matrix F (k) is:
the calculation result is as follows:
(3) calculating a gain matrix:
wherein, K (K +1) is a gain matrix which is mainly used for completing the correction of state vector estimation, and R is a covariance matrix of a measurement noise vector W;
(4) and (3) state vector estimation:
in the formula (I), the compound is shown in the specification,is the state vector estimation value of the (k +1) th time, y (k +1) is the measurement state vector,for the predicted output state vector, the above equation completes the state vector estimation of the (k +1) th;
(5) calculating an estimation error covariance matrix:
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CN112865642A (en) * | 2021-01-18 | 2021-05-28 | 南京航空航天大学 | Harmonic suppression system and method for line-controlled steering permanent magnet synchronous motor |
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CN113315439A (en) * | 2021-06-02 | 2021-08-27 | 江苏科技大学 | Improved control method of ship propulsion motor |
CN113708684A (en) * | 2021-08-31 | 2021-11-26 | 哈尔滨理工大学 | Permanent magnet synchronous motor control method and device based on extended potential observer |
CN116101364A (en) * | 2022-12-23 | 2023-05-12 | 吉林大学 | Control method of power-assisted steering motor |
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Cited By (6)
Publication number | Priority date | Publication date | Assignee | Title |
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CN112865642A (en) * | 2021-01-18 | 2021-05-28 | 南京航空航天大学 | Harmonic suppression system and method for line-controlled steering permanent magnet synchronous motor |
CN112910328A (en) * | 2021-01-22 | 2021-06-04 | 绍兴敏动科技有限公司 | Permanent magnet synchronous motor acceleration arrangement method based on torque observation compensation |
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CN116101364A (en) * | 2022-12-23 | 2023-05-12 | 吉林大学 | Control method of power-assisted steering motor |
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