CN115313931A - Sensor-free vector control method of permanent magnet synchronous motor based on AEKF - Google Patents
Sensor-free vector control method of permanent magnet synchronous motor based on AEKF Download PDFInfo
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- CN115313931A CN115313931A CN202210788393.1A CN202210788393A CN115313931A CN 115313931 A CN115313931 A CN 115313931A CN 202210788393 A CN202210788393 A CN 202210788393A CN 115313931 A CN115313931 A CN 115313931A
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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
- H02P21/24—Vector control not involving the use of rotor position or rotor speed sensors
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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
- H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
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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
- H02P21/18—Estimation of position or speed
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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
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Abstract
The invention discloses a sensor-free vector control method of a permanent magnet synchronous motor based on AEKF, which adds gross error interference into EKF and analyzes the influence of EKF on observation precision. Secondly, setting a weighting coefficient in innovation covariance calculation, calculating an innovation covariance value by adjusting innovation covariance matrix weight at an approaching moment, importing the innovation covariance value into Kalman gain calculation, establishing an AEKF model, taking current and voltage under a static coordinate system as input values, outputting the rotating speed and the rotor position by a Kalman gain matrix calculation method based on an exponential weighting rule, and enabling the AEKF algorithm to have stronger robustness and higher prediction precision on the rotating speed and the rotor position under gross error interference or noise statistical information interference.
Description
Technical Field
The invention particularly relates to a sensorless vector control strategy of a Permanent Magnet Synchronous Motor (PMSM), and particularly relates to a sensorless vector control method of an AEKF.
Background
Compared with a direct current motor, a Permanent Magnet Synchronous Motor (PMSM) has the advantages of high reliability, low cost, easiness in maintenance and the like, and is widely applied to a high-performance speed regulating system. Conventional motor control systems typically employ sensors to obtain the rotor position and speed of the motor, and the use of sensors raises costs and raises reliability issues. Therefore, the sensorless control system is an important research direction for the motor control system.
Extended Kalman Filter (EKF) is an iterative algorithm based on minimum variance. In recent years, the development of high-speed processors has solved the problem of large EKF calculation amount, and has been widely applied to sensorless vector control systems. As an iterative discrete calculation method, EKF utilizes the state prior estimation and measurement feedback of the system, and then obtains a posterior estimation value infinitely approaching the system state truth value at the moment by adjusting a Kalman gain matrix in real time. Compared with other observation algorithms, the EKF has the advantages of wide applicable rotating speed range, strong interference resistance and the like, thereby becoming a hotspot for motor state estimation research.
However, the accuracy of the EKF estimate is related to the selection of the Kalman gain matrix, the system and the measurement noise covariance matrix.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a sensor-free vector control method for an AEKF permanent magnet synchronous motor.
In order to realize the purpose, the invention provides the following technical scheme:
a sensor-free vector control method of a permanent magnet synchronous motor based on AEKF comprises the following steps:
step one, establishing a state equation and an observation equation of a permanent magnet synchronous motor according to a current equation of the permanent magnet synchronous motor
B is system inputA matrix; h is an output matrix, f (x) is a system state matrix, x is a state variable, u is a stator voltage, w and v are respectively a system error and a measurement error, and the system error and the measurement error are white Gaussian noises which are not related to each other;
step two, introducing coarse difference into an observation equation to obtain
T s For sample time, superscript "^" represents the estimate, k | k-1 represents the state transition from time k-1 to time k, g k Is a gross error interference matrix;
selecting an innovation estimation covariance sequence with the length of N, and when k is greater>Selecting gamma as gamma at moment K i And satisfy
Step four, introducing a weighting coefficient gamma i Obtaining an innovation estimation covariance estimation value at the k moment
Innovation covariance estimate at time k-1 of sum
And obtaining recursion form of exponentially weighted innovation covariance matrix
Wherein epsilon k In order to be an innovation sequence,
step five, substituting the recursion form of the exponentially weighted innovation covariance matrix into the Kalman gain matrix K k And obtaining a Kalman gain matrix calculation method based on the exponential weighting rule, and outputting the rotating speed and the rotor position by using the current and the voltage under the static coordinate system as input values through the Kalman gain matrix calculation method based on the exponential weighting rule.
In the fifth step, the process is carried out,
1) Establishing an extended Kalman State equation
2) Obtaining state prediction value estimates
3) Obtaining error covariance matrix estimates
φ＝I+T s F k|k-1 Wherein
4) Obtaining a Kalman gain matrix K k|k-1 ＝P k|k-1 H T [HP k|k-1 H T +R] -1 Wherein I is a unit matrix, K k|k-1 As Kalman gain matrix, F k|k-1 A jacobian matrix being a state matrix f (x), A = ψ f /L s ，B＝(ψ f ω e )/L s ，C＝(3ψ f n p )/(2J)，D＝-i β sinθ-i α cosθ，R s Is stator resistance, L s Is stator inductance, ω e Is the electrical angular velocity of the rotor psi f Is a permanent magnet flux linkage i α And i β The stator current alpha and beta axis components are respectively, and theta is a rotor position angle;
5) EKF was modified by introducing an innovation sequence, which contains gross interference, represented as
Assuming information estimation covariance matrix
In an observation interval of time length k, the optimal estimated value in the interval
6) The Kalman gain matrix K k|k-1 ＝P k|k-1 H T [HP k|k-1 H T +R] -1 And
integrating to obtain Kalman gain matrix
In the first step, the state equation of the permanent magnet synchronous motor is subjected to linearization and discretization, and an extended Kalman state equation is established by combining a current equation.
The invention has the beneficial effects that: in order to improve the observation performance under the condition of gross error and the condition of statistical information deviation, the adaptive extended Kalman algorithm is designed, and the influence of gross error interference or noise statistical information interference on the performance of the observer is weakened by improving the proportion of an innovation sequence covariance matrix at a recent moment.
Drawings
FIG. 1 is a block diagram of an adaptive EKF control in accordance with the present invention.
Fig. 2 is a schematic diagram of a rotation speed error waveform of two control methods for coping with load sudden change when a 0.5N · m load is suddenly applied at time t =0.2 s.
Fig. 3 is a waveform diagram of rotor position and position error when a 0.5N · m load is suddenly applied at time t =0.2 s.
Fig. 4 is a diagram in which 1A current is suddenly applied to i at time t =0.6s α In the above, the rotational speed error of the two control methods is compared with a curve chart.
Fig. 5 is a diagram showing a 1A current burst applied to i at time t =0.6s α In the above, the rotor position versus position error maps of the two control methods.
Fig. 6 shows that x = [0 10 ] at time t =0.6s] T When the error signal of the two control methods is added to the input end of the observer, the rotating speed error of the two control methods is compared with a curve graph.
Fig. 7 shows that x = [0 10 ] at time t =0.6s] T When the error signal of (2) is added to the input end of the observer, the rotor position and the position error are compared in two control methods.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
It should be noted that all directional indicators (such as up, down, left, right, front, back \8230;) in the embodiments of the present invention are only used to explain the relative positional relationship between the components, the motion situation, etc. in a specific posture (as shown in the attached drawings), and if the specific posture is changed, the directional indicator is changed accordingly.
The invention provides a cascaded unified Self-coupling model-free sliding mode control method (SC-MFSMC) based on an Extended State Observer (ESO) on the basis of a vector control speed regulation system of a permanent magnet synchronous motor. Firstly, in order to solve the influences of parameter change sensitivity, external disturbance and the like, a super-local model of a rotating speed ring and a current ring is established under a traditional mathematical model according to a model-free control idea. Then, considering the problems of dimension conflict and the like of the traditional PI control, the cascade model-free sliding mode controller is designed by selecting a proportional-double-integral sliding mode surface on the basis of the traditional model-free sliding mode controller, so that the steady-state error of the rotating speed is effectively reduced, a current loop and a speed loop are designed in a unified mode in a matrix mode in the design process, and the whole design process is simplified. And PI gains are scientifically set through speed factors, and internal and external disturbance and unmodeled parts of the system are observed by using the ESO with disturbance compensation, so that the robustness of the control system against total disturbance is improved. Finally, the effectiveness of the method is proved through system simulation and experiments.
PMSM is selected as the control object in this application, neglects iron core saturation, vortex and hysteresis loss. In a stationary coordinate system, the current equation can be expressed as:
in the formula, R s Is a stator resistor; l is s A stator inductor; omega e Is the rotor electrical angular velocity; psi f Is a permanent magnet flux linkage; i.e. i α And i β The stator current alpha and beta axis components are respectively; u. u α And u β Stator voltage α, β axis components, respectively, and θ is the rotor position angle.
Combining the formula (1), establishing a PMSM state equation and an observation equation as follows:
in the formula (I), the compound is shown in the specification,
system state matrix
State variable x = [ i ] a ,i β ,ω e ,θ] T And B is a system input matrix; h is an output matrix; w and v are respectively system error and measurement error, and are Gaussian white noise which is irrelevant, and the statistical characteristics of the Gaussian white noise are w to N (0, Q), v to N (0, R)
The EKF is the application of Kalman filtering in a nonlinear system, and is an optimal state estimation method in the minimum variance sense. In an EKF-based vector control system, the state equation of the PMSM needs to be linearized and discretized first. In connection with equation (1), the extended kalman state equation is established as follows.
In the formula, T s For sample time, superscript "^" represents the estimate, k | k-1 represents the time from k-1State transition to time k.
The EKF algorithm is specifically realized by the following steps:
1) State prediction value estimation
2) Error covariance matrix estimation
Wherein
3) Kalman gain matrix calculation
K k|k-1 ＝P k|k-1 H T [HP k|k-1 H T +R] -1 (6)
4) State estimation correction
5) Updating error covariance matrix
P k|k ＝(I-K k|k-1 H)P k|k-1 (8)
In the formula, I is a unit matrix, K k|k-1 Is a Kalman gain matrix, F k|k-1 Jacobian matrix being the state matrix f (x), phi = I + T s F k|k-1 ，A＝ψ f /L s ，B＝(ψ f ω e )/L s ，C＝(3ψ f n p )/(2J)，D＝-i β sinθ-i α cosθ。
The EKF is an optimal observation algorithm established on the basis of accurate modeling of the system. In the actual operation process, the observation module is often interfered by an external variable which is not white gaussian noise. When the observed quantity is interfered, the observation equation of the system can be expressed as
In the formula, g k Is a gross interference matrix.
The AEKF adjusts the weights of innovation sequences based on EKF to eliminate the effect of gross errors on parameter estimation. In the process, an innovation sequence is introduced to improve the EKF. The innovation sequence containing gross interference is represented as
In the formula, epsilon k Is an innovation sequence. As can be seen from equation (10), the existence of gross error directly affects the computation of systematic innovation sequence, and if C is an innovation estimation covariance matrix, then there are
In the observation interval with the time length of k, record
For the optimal estimation value in the interval, there are
The observation equation of the system obeys Gaussian distribution, and the optimal estimation value of the formula (12) is verified based on a maximum likelihood estimation method. Assuming that δ is the noise statistic containing the nonlinear system, the likelihood function is established at time k with parameter δ as follows
Taking the logarithm of each of the formulas (13), the following formula can be obtained
Where m is the measurement matrix dimension, by performing the accumulation calculation of equation (14), the maximum value based on the maximum likelihood estimation can be converted into
Taking the derivative of J (delta) to delta, the following formula can be obtained
The partial derivative with respect to the parameter delta is obtained by calculating the partial derivative with respect to the parameter delta in the formula (16)
As can be seen from equation (17), equation (12) is an optimal estimation value of the information covariance matrix C in the interval of the time length k. Considering the influence of the gross error interference on the Kalman gain calculation, the formula (12) and the formula (6) are re-integrated, and the Kalman gain matrix K is deduced again k As follows
From equation (18), during the rotation speed observation, the gross error affects the kalman gain matrix by changing the innovation process, which affects the state estimation of the whole system, but this method cannot improve the utilization weight of the recent data. In order to improve the observation performance under the condition of gross error and the statistical information deviation, the adaptive extended Kalman algorithm is designed, and the influence of interference on the observer performance is weakened by improving the proportion of an innovation sequence covariance matrix at a recent moment.
Therefore, the invention firstly introduces the coarse difference into the observation equation, and the equation is established as follows:
secondly, selecting an innovation estimation covariance sequence with the length of N, and when k is equal to K>When N is needed, the weighting coefficient of k time is selected as gamma i And satisfy
For estimating covariance matrix of k-time innovation, the weighting coefficient of formula (20) is introduced
Similarly, at time k-1, C k-1 The innovation covariance estimate of
The recursion form of the exponentially weighted innovation covariance matrix obtained from the equations (16) and (17) is
And substituting the formula (23) into the formula (18) to obtain a new Kalman gain matrix calculation method. The method sets an exponential weighting rule on the selection of the innovation covariance matrix, improves the weight of recent data in Kalman gain matrix calculation, and has the advantage of high estimation precision compared with the calculation method of the arithmetic mean value of the formula (12). The AEKF based on the exponential weighting rule can be expressed as follows:
based on the formula (24), an AEKF-based PMSM sensorless vector control system is built, and the system structure is shown in FIG. 1. The control loop consists of a rotating speed outer ring and a current inner ring, wherein a rotating speed error is used as a q-axis current given value through the sliding mode controller; and the error signals of the current and the given current under the static coordinate system are subjected to PI modulation to be used as the given values of the d-axis voltage and the q-axis voltage. The input of the AEKF is current and voltage under a static coordinate system, and the output of the rotation speed and the position of the rotor.
The experiment proves that
The PMSM parameter for simulation and experiment is shown in table 1, the simulation rotating speed n =1200r/min, and the simulation time is 1s. In order to verify the feasibility of the AEKF algorithm, the parameter settings of the PI controller and the sliding-mode controller of the two parties are the same in experimental comparison, and the simulation experiment is as follows.
TABLE 1 PMSM parameters
In the motor loading experiment, a 0.5N · m load is suddenly applied at the time t =0.2s, fig. 2 shows a rotation speed error waveform corresponding to sudden load change by two control methods under the condition of sudden load application, and fig. 3 shows a rotor position and position error waveform. According to the simulation waveform, when the AEKF suddenly changes the load, the error of the rotation speed estimation is lower, and the rotor position observation has stronger stability.
At time t =0.6s, a 1A current is suddenly added to i α In the above, the external gross error interference occurring at the time of the rotational speed estimation is simulated. Fig. 4 is a comparison curve of the rotation speed error of the two methods under the condition of gross error interference, and fig. 5 is a comparison graph of the rotor position and the position error of the two methods. As can be seen from the figure, the rotation speed waveforms appear in both the two methods when the AEKF meets external interference, but the fluctuation of the AEKF is lower when the AEKF meets the external interference, the observation performance of the rotor position is more stable, and the rotor position has stronger immunity.
To verify the immunity of the algorithm to internal error disturbances, x = is applied at time t =0.6s[0 1 0 0] T Is added to the input of the observer. The experimental result is shown in fig. 6 and 7, under the interference of the internal error signal, the fluctuation range of the AEKF is smaller than that of the EKF, the error curve of the rotor position does not have a relatively obvious waveform, and the following performance of the rotating speed and the rotor position of the AEKF is better.
The examples should not be construed as limiting the present invention, but any modifications made based on the spirit of the present invention should be within the scope of protection of the present invention.
Claims (3)
1. A sensor-free vector control method of a permanent magnet synchronous motor based on AEKF is characterized in that: which comprises the following steps:
step one, establishing a state equation and an observation equation of a permanent magnet synchronous motor according to a current equation of the permanent magnet synchronous motor
B is a system input matrix; h is an output matrix, f (x) is a system state matrix, x is a state variable, u is a stator voltage, w and v are respectively a system error and a measurement error, and the system error and the measurement error are mutually uncorrelated white Gaussian noise;
step two, introducing coarse difference into an observation equation to obtain
T s For sample time, superscript "^" represents the estimate, k | k-1 represents the state transition from time k-1 to time k, g k Is a gross error interference matrix;
selecting an innovation estimation covariance sequence with the length of N, and when k is larger than N, selecting a weighting coefficient gamma at the moment of k i And satisfy
Step four, introducing a weighting coefficient gamma i Obtaining the innovation estimation covariance estimation value at the time k
Innovation covariance estimate at time k-1 of sum
And obtaining recursion form of exponentially weighted innovation covariance matrix
Wherein epsilon k In order to be an innovation sequence,
step five, substituting the recursion form of the exponentially weighted innovation covariance matrix into the Kalman gain matrix K k And obtaining a Kalman gain matrix calculation method based on the exponential weighting rule, and outputting the rotating speed and the rotor position by using the current and the voltage under the static coordinate system as input values through the Kalman gain matrix calculation method based on the exponential weighting rule.
2. The AEKF-based permanent magnet synchronous motor sensorless vector control method of claim 1, wherein: in the fifth step, the process is carried out,
1) Establishing an extended Kalman State equation
2) Obtaining state prediction value estimates
3) Obtaining error covariance matrix estimates
φ＝I+T s F k|k-1 In which
4) Obtaining a Kalman gain matrix K k|k-1 ＝P k|k-1 H T [HP k|k-1 H T +R] -1 Wherein I is a unit matrix, K k|k-1 Is a Kalman gain matrix, F k|k-1 A jacobian matrix being the state matrix f (x), A = ψ f /L s ，B＝(ψ f ω e )/L s ，C＝(3ψ f n p )/(2J)，D＝-i β sinθ-i α cosθ，R s Is stator resistance, L s Is stator inductance, ω e For the electrical angular velocity, psi, of the rotor f Is a permanent magnet flux linkage i α And i β The stator current alpha and beta axis components are respectively, and theta is a rotor position angle;
5) The EKF is improved by introducing an innovation sequence, and the innovation sequence containing gross interference is shown as
Covariance matrix of hypothetical innovation estimation
In an observation interval with the duration of k, the optimal estimation value in the interval
6) The Kalman gain matrix K k|k-1 ＝P k|k-1 H T [HP k|k-1 H T +R] -1 And
integrating to obtain Kalman gain matrix
3. The AEKF-based permanent magnet synchronous motor sensorless vector control method of claim 1, wherein: in the first step, the state equation of the permanent magnet synchronous motor is subjected to linearization and discretization, and an extended Kalman state equation is established by combining a current equation.
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| CN116165885B (en) * | 2022-11-29 | 2023-11-14 | 华东交通大学 | Model-free adaptive robust control method and system for high-speed train |
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Application publication date: 20221108 |