CN112968643B - Based on self-adaptation extension H ∞ Filtering brushless direct current motor parameter identification method - Google Patents

Based on self-adaptation extension H ∞ Filtering brushless direct current motor parameter identification method Download PDF

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CN112968643B
CN112968643B CN202110140453.4A CN202110140453A CN112968643B CN 112968643 B CN112968643 B CN 112968643B CN 202110140453 A CN202110140453 A CN 202110140453A CN 112968643 B CN112968643 B CN 112968643B
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covariance matrix
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motor
direct current
brushless direct
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CN112968643A (en
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丁洁
陈丽娟
林金星
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Nanjing University of Posts and Telecommunications
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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
    • 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
    • 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
    • H02P21/16—Estimation of constants, e.g. the rotor time constant
    • 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
    • H02P21/22—Current control, e.g. using a current control loop
    • 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
    • H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
    • H02P6/14—Electronic commutators
    • H02P6/16—Circuit arrangements for detecting position
    • H02P6/18—Circuit arrangements for detecting position without separate position detecting elements
    • H02P6/182—Circuit arrangements for detecting position without separate position detecting elements using back-emf in windings
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/40—Arrangements for reducing harmonics

Abstract

The invention discloses a method based on self-adaptive expansion H ∞ The parameter identification method of the brushless direct current motor of the filter algorithm comprises the following steps: (1) describing the internal dynamic characteristics of the brushless direct current motor by using a current equation under a static coordinate system, and establishing a motor dynamic model according to the internal dynamic characteristics; (2) parameters needing to be identified, such as inductance of the motor, are expanded to be in a state, and a continuous state space expression is discretized; (3) the simulation motor adopts a double closed-loop control mode, and phase current and phase voltage are obtained from a current detection unit and a voltage detection unit; (4) establishing H in Krein space ∞ Combining a performance constant and a measurement noise covariance matrix to form a new measurement noise covariance matrix, and iteratively estimating a state estimation error covariance matrix and the new noise covariance matrix by utilizing an expectation maximization idea; (5) by combining the obtained phase current and phase voltage, using the extension H ∞ The filter algorithm estimates motor parameters such as back electromotive force. The method improves the estimation precision of the motor parameters.

Description

Based on self-adaptation extension H ∞ Filtering brushless direct current motor parameter identification method
Technical Field
The invention relates to a motor parameter identification method, in particular to a method based on self-adaptive expansion H ∞ Provided is a method for identifying parameters of a brushless direct current motor with filtering.
Background
The brushless direct current motor is widely applied to the fields of robots, medical equipment and the like due to the advantages of long service life, simplicity in control, high operation efficiency and the like. The brushless direct current motor is a nonlinear multivariable controlled object, and motor parameters need to be accurately detected in order to achieve the optimal performance. At present, the traditional method is to acquire the rotor position information through a position sensor, but the cost and the volume of the system are increased. The key of most realizing sensorless control and torque control is to obtain accurate and real-time back electromotive force of the motor, generally, the back electromotive force of the motor is considered to be ideal trapezoidal wave, but the control precision is low; or calculating the back emf value in the control scheme by looking up the table, but increasing the amount of calculation.
When the motor back emf is taken as the state variable, the estimation can be done with a state observer or filter. The problem is that the state estimation method relies on accurate motor parameters. For a brushless direct current motor, the current change is large in the commutation process, and the deviation of inductance and resistance parameters has great influence on back electromotive force estimation.
Common identification methods include kalman filtering, least square method, sliding mode identification, model reference adaptive algorithm, and the like. For a linear system with accurate model and Gaussian distribution-compliant noise, Kalman filtering can obtain an optimal solution, and a derivative algorithm of the optimal solution is widely applied to motor parameter identification. However, due to the influence of unknown parameters, an accurate motor model is not easy to obtain; while unknown noise is present. When the model or noise of the system is not accurate, expand H ∞ The filtering algorithm has better robustness, but in the estimation process, the covariance matrix of the process noise and the measurement noise is usually set to be a constant artificially, and the change of the covariance matrix with the time is not considered. In addition, in the method, a limited upper bound of model uncertainty needs to be artificially set, the setting process is complicated, and if the parameter selection is unreasonable, the estimation performance of the system is affected.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems, the invention provides a method based on adaptive expansion H ∞ The method for identifying the parameters of the filtered brushless direct current motor can quickly identify the parameters of the motor on line in real time, accurately estimate the parameters in a motor system, including winding back electromotive force, stator resistance, stator inductance and the like, and ensure the convergence of the algorithm while improving the accuracy of the algorithm.
The technical scheme is as follows: the technical scheme adopted by the invention is based on self-adaptive expansion H ∞ The method for identifying the parameters of the filtered brushless direct current motor comprises the following steps:
step 1, providing a state space model of the brushless direct current motor according to a current equation of a static coordinate system.
Wherein, the current equation of the stationary coordinate system in the step 1 is:
Figure BDA0002927209540000021
wherein i α ，i β Is the stator current in the α β coordinate system, e α ，e β Is the winding back electromotive force, u, in the α β coordinate system α ，u β Is the stator voltage in the α β coordinate system, R is the stator resistance, and L is the stator inductance.
Step 2, expanding the stator inductance and the stator resistance of the brushless direct current motor into a state space model, and discretizing a state space equation; the discretized state space equation is obtained as:
x k ＝F k-1 x k-1 +w k-1
y k ＝Hx k +v k
Figure BDA0002927209540000022
Figure BDA0002927209540000023
wherein x is [ x ] 0 T ，L，R] T ，x 0 ＝[i α ，i β ，e α ，e β ] T ，i α ，i β Is the stator current in the α β coordinate system, e α ，e β The winding back electromotive force in an alpha beta coordinate system, R is stator resistance, L is stator inductance, w and v are system noise and measurement noise respectively, Ts is sampling time, and k represents the kth moment.
And 3, collecting phase current and phase voltage of the brushless direct current motor. The phase current and the phase voltage are obtained from a current detection unit and a voltage detection unit.
Step 4, providing H under the Krein space ∞ Filtering algorithm with minimum variance (Q (theta, theta) i ) Approximate log-likelihood function (L) θ (x k ，z 1∶k ))，Estimating to obtain an error covariance matrix and a noise covariance matrix according to an expectation maximization algorithm; step 4 comprises the following processes:
(1) design H ∞ Cost function J of filtering 2 And satisfies the following conditions:
Figure BDA0002927209540000024
in the formula, J 2 As a cost function, x k Is a state variable at the time point k,
Figure BDA0002927209540000025
is an estimate of the state variable at time k, y k Is an observation vector; x ═ x 0 T ，L，R] T ，x 0 ＝[i α ，i β ，e α ，e β ] T Wherein i is α ，i β Is the stator current in the α β coordinate system, e α ，e β Is the winding back electromotive force in the alpha beta coordinate system, R is the stator resistance, L is the stator inductance, H is the system observation matrix; n is the measurement time, S k For custom weight matrices, the same dimensional unit matrix, P, is chosen here k Is an error noise covariance matrix, Q k Is a process noise covariance matrix, R k Measuring a noise covariance matrix, wherein gamma is a performance boundary, and I is a 6-dimensional unit matrix;
the state expression in the Krein space is:
x k ＝F k-1 x k-1 +w k-1
z k ＝Cx k +e k
in the formula, F k-1 The system state transition matrix at time k-1,
Figure BDA0002927209540000031
w k ～ N(w k |0，Q k )，e k ～N(e k |0，W k ) (ii) a Wherein w k-1 Is the system noise at the time point k-1,
Figure BDA0002927209540000032
v k is the measurement noise at the k-th time,
Figure BDA0002927209540000033
qk is a process noise covariance matrix;
Figure BDA0002927209540000034
Figure BDA0002927209540000035
R k measuring a noise covariance matrix, wherein gamma is a performance boundary, and I is a unit matrix;
(2) given the log-likelihood function of the complete data: l is θ (x k ，z 1∶k )＝arg max log p θ (x k ，z 1∶k ) And using the minimum variance Q (theta ) i ) And (3) approximately calculating a log-likelihood function according to the following calculation formula:
Figure BDA0002927209540000036
wherein
Figure BDA0002927209540000037
θ i Denotes the estimated value of θ at the i-th iteration, p θ (x k ，z 1∶k ) Represents x k And z 1∶k In conjunction with the probability density function,
Figure BDA00029272095400000316
denotes x k A posterior probability density function of (a);
the joint probability density function is calculated as:
Figure BDA0002927209540000038
wherein the content of the first and second substances,
Figure BDA0002927209540000039
and P k|k-1 Are respectively an extension H ∞ A priori estimated state and error covariance matrix at time k of filtering, z 1∶k The measured value at the moment of 1: k, and c is a constant;
(3) finding theta according to the maximum expectation algorithm i So that Q (theta ) i ) The method can be used for the maximization,
Figure BDA00029272095400000310
finally obtaining the estimation formula of the covariance of the state variables and the covariance of the noise:
Figure BDA00029272095400000311
wherein the content of the first and second substances,
Figure BDA00029272095400000312
for an a-priori estimation of the time instant k,
Figure BDA00029272095400000313
the prior estimate error covariance matrix for the i +1 th iteration at time k,
Figure BDA00029272095400000314
for the a posteriori estimate and error covariance for the (i + 1) th iteration at time k,
Figure BDA00029272095400000315
the noise covariance matrix for the i +1 th iteration at time k.
Step 5, according to the phase voltage, the phase current and the error covariance matrix and the noise covariance matrix obtained by estimation, utilizing the expansion H ∞ The filtering algorithm estimates the internal dynamic characteristic parameters of the brushless DC motor.
Extension H used in step 5 ∞ The filter algorithm estimates the internal dynamic characteristic parameters of the brushless DC motor by iterative cycleAnd taking a loop variable i from 0 to M-1, wherein M is the iteration number:
Figure BDA0002927209540000041
Figure BDA0002927209540000042
Figure BDA0002927209540000043
Figure BDA0002927209540000044
in the formula (I), the compound is shown in the specification,
Figure BDA0002927209540000045
and P k|k-1 Are respectively an extension H ∞ A priori estimated state and error covariance matrix at time k of filtering, W k ＝diag(R k -γ 2 I)，R k A measured noise covariance matrix at the moment k, gamma is a performance boundary, and I is a unit matrix;
Figure BDA0002927209540000046
the prior estimate error covariance matrix for the ith iteration at time k,
Figure BDA0002927209540000047
a noise covariance matrix of the ith iteration at the time k; y is k Is an observation vector;
Figure BDA0002927209540000048
h is a system observation matrix, and I is a 6-dimensional unit matrix;
wherein
Figure BDA0002927209540000049
And P k|k-1 The calculation formula of (A) is as follows:
Figure BDA00029272095400000410
Figure BDA00029272095400000411
in the formula, F k-1 Is the system state transition matrix at time k-1, P k-1 The covariance matrix of the error at the moment of k-1, and Q is a process noise covariance matrix; f (-) is the expanded system state transition matrix,
Figure BDA00029272095400000412
for a posteriori estimation of the time k-1, u k-1 Is the system input at time k-1; wherein u ═ u α ，u β ] T ，u α ，u β Is the stator voltage in the α β coordinate system;
after each iteration is completed, updating
Figure BDA00029272095400000413
Figure BDA00029272095400000414
Figure BDA00029272095400000415
Wherein the content of the first and second substances,
Figure BDA00029272095400000416
the prior estimate error covariance matrix for the i +1 th iteration at time k,
Figure BDA00029272095400000417
the a posteriori estimate and error covariance for the (i + 1) th iteration at time k,
Figure BDA00029272095400000418
a noise covariance matrix of i +1 th iteration at the time k;
the final iteration to the Mth time outputs are:
Figure BDA00029272095400000419
wherein the content of the first and second substances,
Figure BDA00029272095400000420
respectively the a posteriori estimate at time k and the error covariance matrix,
Figure BDA00029272095400000421
for the estimation error covariance matrix at time k,
Figure BDA00029272095400000422
the noise covariance matrix estimated for time k,
Figure BDA00029272095400000423
is the state variable of the mth iteration at time k.
Has the advantages that: compared with the prior art, the invention has the following advantages: the method comprises the steps of firstly establishing a state space expression according to a current equation of a static coordinate system, then establishing H in a Krein space by taking inductance and other parameters needing to be identified as an augmentation vector and a discrete state model ∞ And the filtering algorithm is used for forming a new covariance matrix by the noise covariance matrix and the performance boundary, and realizing real-time estimation of the new covariance matrix based on the idea of expectation maximization. The invention combines expectation maximization and expansion H according to the observed value of the current moment ∞ The filtering algorithm realizes the online estimation of the error and noise covariance matrix, improves the accuracy of the algorithm and ensures the convergence of the algorithm.
Drawings
FIG. 1 is a diagram of the adaptive extension H-based method of the present invention ∞ A flow chart of a filtered brushless direct current motor parameter identification method;
FIG. 2 is a block diagram of a control circuit for dual closed-loop control of a brushless DC motor;
FIG. 3 is a comparison graph of the result of back electromotive force estimation and the true value using the method of the present invention and the EKF algorithm in the simulation of the brushless DC motor by the dual closed-loop control method;
FIG. 4 is a comparison graph of inductance estimation results and actual values obtained by the method and the EKF algorithm of the present invention in a simulation of a brushless DC motor in a dual closed-loop control manner;
fig. 5 is a comparison graph of the resistance estimation result and the true value by the method and the EKF algorithm of the present invention in the simulation of the brushless dc motor by the double closed-loop control method.
Detailed Description
The technical solution of the present invention is further described below with reference to the accompanying drawings and examples.
The invention relates to a method based on self-adaptive expansion H ∞ Referring to fig. 1, a flow chart of the method for identifying the parameters of the filtered brushless direct current motor is shown, a dynamic estimation model of the brushless direct current motor in a static coordinate system is established, and the parameters of the motor are estimated by adopting the self-adaptive extended H-infinity filtering method according to the dynamic estimation model of the motor. The method specifically comprises the following steps:
step 1, describing the internal dynamic characteristics of the motor by using a current equation under an alpha beta static reference coordinate system as a continuous state space expression of the motor.
The current equation in the α β stationary reference frame is as follows:
Figure BDA0002927209540000051
wherein i α ，i β Is the stator current in the α β coordinate system, e α ，e β Is the winding back electromotive force, u, in the α β coordinate system α ，u β Is the stator voltage in the α β coordinate system, R is the stator resistance, and L is the stator inductance. Assuming that the derivative of the back emf is 0, the state space expression is now:
Figure BDA0002927209540000052
y 0 ＝H 0 x 0
wherein x is 0 ＝[i α ，i β ，e α ，e β ] T Is a system state vector, y ═ i α ，i β ] T For system output, u ═ u α ，u β ] T Is the system input.
Figure BDA0002927209540000053
Step 2, the stator inductance L and the stator resistance R are expanded into a system state vector to obtain a continuous six-order state space model:
x k ＝f k-1 (x k-1 ，u k-1 )+w k-1
y k ＝Hx k +v k
wherein x is [ x ] 0 T ，L，R] T ，
Figure BDA0002927209540000061
Figure BDA0002927209540000062
Discretizing the continuous spatial expression yields:
x k ＝F k-1 x k-1 +w k-1
y k ＝Hx k +v k
Figure BDA0002927209540000063
wherein, w k And v k Is the system noise and the measurement noise, and Ts is the sampling time.
And 3, adopting a surface-mounted permanent magnet brushless direct current motor as the experimental motor of the permanent magnet synchronous direct current motor in the simulation system, adopting a two-by-two 120-degree conduction mode for control, and using a double closed-loop control mode, wherein the difference between the given value of the motor rotating speed and the actual rotating speed value calculated by the Hall signal is used as the input of the input speed controller as shown in figure 2. The difference between the output of the speed controller and the current feedback quantity acquired by the current detection unit is the input of the current controller. And the PWM control signal generator can interpret the current position of the motor rotor according to the Hall sensor and then is connected to a power tube to be opened so as to finish the speed regulation of the motor. Meanwhile, the phase current and the phase voltage are obtained by obtaining them from the current detection unit and the voltage detection unit.
Step 4, giving H ∞ Filtering the cost function and converting it into H in Krein space ∞ And (3) filtering algorithm:
Figure BDA0002927209540000064
rearranging the above formula to obtain
Figure BDA0002927209540000071
Where J is the cost function, N is the measurement time, S k For custom weight matrices, the same dimensional unit matrix, P, is chosen here k Is an error noise covariance matrix, Q k Is a process noise covariance matrix, R k To measure the noise covariance matrix, gamma is the performance boundary, I k Is an identity matrix of dimension k.
Order to
Figure BDA0002927209540000072
Figure BDA0002927209540000073
Then the state expression in the Krein space is available:
x k ＝F k-1 x k-1 +w k-1
z k ＝Cx k +e k
wherein, w k ～N(w k |0，Q k )，e k ～N(e k |0，W k )。
To achieve real-time estimation of an inaccurate noise covariance matrix, a minimum variance is approximated to a log-likelihood function according to an expectation-maximization algorithm:
Figure BDA0002927209540000074
wherein
Figure BDA0002927209540000075
θ i Representing the estimated value of theta at the ith iteration,
Figure BDA0002927209540000076
to relate to x k The mathematical expectation of (2).
Figure BDA0002927209540000077
Denotes x k A posterior probability density function of.
Giving a joint probability density function:
Figure BDA0002927209540000078
wherein the content of the first and second substances,
Figure BDA0002927209540000079
and P k|k-1 Are respectively an extension H ∞ A priori estimated state and error covariance matrix at time k of filtering, z 1∶k The measured value at time 1: k, c represents a constant with respect to θ.
Finding theta according to the maximum expectation algorithm i So that Q (theta ) i ) The intensity of the light beam is maximized,
Figure BDA00029272095400000710
finally, the estimation formula of the error variable covariance and the noise covariance is obtained:
Figure BDA00029272095400000711
Figure BDA00029272095400000712
wherein the content of the first and second substances,
Figure BDA00029272095400000713
for an a-priori estimation of the time instant k,
Figure BDA00029272095400000714
the prior estimate error covariance matrix for the i +1 th iteration at time k,
Figure BDA00029272095400000715
for the posterior estimate and error covariance for the i +1 th iteration at time k,
Figure BDA00029272095400000716
the noise covariance matrix for the i +1 th iteration at time k.
Step 5, according to the measured phase voltage, phase current and the noise covariance matrix obtained by estimation, utilizing the expansion H ∞ The filtering algorithm estimates parameters such as back electromotive force. The estimation process is as follows:
Figure BDA0002927209540000081
Figure BDA0002927209540000082
initial values of the iterations:
Figure BDA0002927209540000083
fori is 0: m-1, wherein M is the iteration number,
Figure BDA0002927209540000084
Figure BDA0002927209540000085
Figure BDA0002927209540000086
after each step of the iterative process is completed, updating
Figure BDA0002927209540000087
Figure BDA0002927209540000088
Figure BDA0002927209540000089
The final output is:
Figure BDA00029272095400000810
setting the sampling period T s ＝2×10 -6 ，N＝4，γ 2 Each initial value is x 50 0 ＝[0，0，0，0，0.01，0.5] T ， P 0 ＝diag[1，1，1，1，1，1] T ，Q 0 ＝diag(10 -6 ，10 -6 ，10 -4 ，10 -4 ，0，0)，R＝diag(3×10 -3 ，3× 10 -3 ). Respectively using an extended Kalman filter algorithm and an adaptive extension H through the obtained phase current and phase voltage ∞ And the filtering algorithm is used for estimating the back electromotive force of the motor and identifying the motor parameters at the same time. As can be seen from FIG. 3, the adaptive extension H ∞ The filtering algorithm is obviously superior to an extended Kalman filtering algorithm (EKF algorithm), the precision of the estimated winding back electromotive force is higher than that of the extended Kalman filtering algorithm, and FIG. 4 shows that the adaptive extension H is realized ∞ The stator inductance of the filter estimation is more accurate than the inductance value of the Kalman filter estimation, the stabilization time is shorter, the convergence speed is faster, and as can be seen from FIG. 5, the adaptive expansion H is used ∞ Compared with the extended Kalman filtering method, the precision of the stator resistance estimation by the filtering algorithm is greatly improved, and the convergence speed is higher. From this, adaptive extension H ∞ The filtering algorithm is greatly improved in the aspects of accuracy, stability, robustness and the like.

Claims (5)

1. Based on self-adaptation extension H ∞ The method for identifying the parameters of the filtered brushless direct current motor is characterized by comprising the following steps of:
step 1, providing a state space model of the brushless direct current motor according to a current equation of a static coordinate system;
step 2, expanding the stator inductance and the stator resistance of the brushless direct current motor into a state space model, and discretizing a state space equation;
step 3, collecting phase current and phase voltage of the brushless direct current motor;
step 4, adopting H in Krein space ∞ Filtering algorithm using minimum variance Q (theta ) i ) Approximate log-likelihood function L θ (x k ，z 1：k ) Estimating to obtain an error covariance matrix and a noise covariance matrix according to an expectation maximization algorithm; step 4 comprises the following processes:
(1) design H ∞ Cost function J of filtering 2 And satisfies the following conditions:
Figure FDA0003694703400000011
in the formula, J 2 As a cost function, x k ，
Figure FDA0003694703400000012
The state variable at time k and its estimated value, y k Is an observation vector; x ═ x 0 T ，L，R] T ，x 0 ＝[i α ，i β ，e α ，e β ] T Wherein i α ，i β Is the stator current in the α β coordinate system, e α ，e β Winding back electromotive force in an alpha beta coordinate system, R is stator resistance, L is stator inductance, and H is a system observation matrix; n is the measurement time, S k For custom weight matrices, the same dimensional unit matrix, P, is chosen here k Is an error noise covariance matrix, Q k Is the process noise covariance matrix at time k, R k Measuring a noise covariance matrix, wherein gamma is a performance boundary, and I is a 6-dimensional unit matrix;
the state expression in the Krein space is:
x k ＝F k-1 x k-1 +w k-1
z k ＝Cx k +e k
in the formula, F k-1 The system state transition matrix at time k-1,
Figure FDA0003694703400000013
w k ～N(w k |0，Q k )，e k ～N(e k |0，W k )；w k-1 is the system noise at the time point k-1,
Figure FDA0003694703400000014
v k is the measurement noise at the k-th time,
Figure FDA0003694703400000015
(2) given the log-likelihood function of the complete data: l is a radical of an alcohol θ (x k ，z 1：k )＝arg max logp θ (x k ，z 1：k ) And using the minimum variance Q (theta ) i ) And (3) approximately calculating a log-likelihood function according to the following calculation formula:
Figure FDA0003694703400000016
wherein
Figure FDA0003694703400000017
θ i Denotes the estimated value of θ at the i-th iteration, p θ (x k ，z 1：k ) Denotes x k And z 1：k In conjunction with the probability density function,
Figure FDA0003694703400000018
denotes x k A posterior probability density function of (a);
the joint probability density function is calculated as:
Figure FDA0003694703400000021
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003694703400000022
and P k|k-1 Are respectively an extension H ∞ A priori estimated state and error covariance matrix at time k of filtering, z 1：k Is 1: c is a constant value;
(3) finding theta according to the maximum expectation algorithm i So that Q (theta ) i ) The intensity of the light beam is maximized,
Figure FDA0003694703400000023
finally obtaining the estimation formula of the covariance of the state variables and the covariance of the noise:
Figure FDA0003694703400000024
Figure FDA0003694703400000025
wherein the content of the first and second substances,
Figure FDA0003694703400000026
the prior estimate error covariance matrix for the i +1 th iteration at time k,
Figure FDA0003694703400000027
the a posteriori estimate and the error covariance matrix for the i +1 th iteration at time k,
Figure FDA0003694703400000028
a noise covariance matrix of i +1 th iteration at the time k;
step 5, according to the phase voltage, the phase current and the error covariance matrix and the noise covariance matrix obtained by estimation, utilizing the expansion H ∞ The filtering algorithm estimates the internal dynamic characteristic parameters of the brushless DC motor.
2. The adaptive extension-based H of claim 1 ∞ The method for identifying the parameters of the filtered brushless direct current motor is characterized in that a current equation of a static coordinate system in the step 1 is as follows:
Figure FDA0003694703400000029
wherein i α ，i β Is alpha beta sittingStator current in the system, e α ，e β Is the winding back electromotive force, u, in the α β coordinate system α ，u β Is the stator voltage in the α β coordinate system, R is the stator resistance, and L is the stator inductance.
3. The adaptive extension-based H of claim 1 ∞ The method for identifying the parameters of the filtered brushless direct current motor is characterized in that the discretization state space equation in the step 2 is as follows:
x k ＝F k-1 x k-1 +w k-1
y k ＝Hx k +v k
Figure FDA00036947034000000210
Figure FDA0003694703400000031
wherein x is [ x ] 0 T ，L，R] T ，x 0 ＝[i α ，i β ，e α ，e β ] T Wherein i α ，i β Is the stator current in the α β coordinate system, e α ，e β Is the winding back electromotive force in the alpha beta coordinate system, R is the stator resistance, L is the stator inductance, w and v are the system noise and the measurement noise, respectively, T s For the sampling time, k denotes the kth time instant.
4. The adaptive extension-based H of claim 1 ∞ The method for identifying the parameters of the filtered brushless direct current motor is characterized by comprising the following steps: and (4) acquiring the phase current and the phase voltage of the brushless direct current motor in the step (3), wherein the phase current and the phase voltage are acquired through a current detection unit and a voltage detection unit.
5. The adaptive extension-based H of claim 1 ∞ The method for identifying the parameters of the filtered brushless direct current motor is characterized by comprising the following steps: extension H utilization as described in step 5 ∞ The filter algorithm estimates the internal dynamic characteristic parameters of the brushless direct current motor, the estimation process is an iterative loop, a loop variable i is taken from 0 to M-1, and M is the iteration frequency:
Figure FDA0003694703400000032
Figure FDA0003694703400000033
Figure FDA0003694703400000034
Figure FDA0003694703400000035
in the formula (I), the compound is shown in the specification,
Figure FDA0003694703400000036
the prior estimate error covariance matrix for the ith iteration at time k,
Figure FDA0003694703400000037
a noise covariance matrix of the ith iteration at the time k;
wherein
Figure FDA0003694703400000038
And P k|k-1 The calculation formula of (A) is as follows:
Figure FDA0003694703400000039
Figure FDA00036947034000000310
in the formula, P k-1 The covariance matrix of the error at the moment of k-1, and Q is a process noise covariance matrix; f (-) is the expanded system state transition matrix,
Figure FDA00036947034000000311
is a posterior estimate of the time k-1, u k-1 Is the system input at the time of k-1; wherein u ═ u α ，u β ] T ，u α ，u β Is the stator voltage in the α β coordinate system;
after each iteration is completed, updating
Figure FDA00036947034000000312
Figure FDA00036947034000000313
Figure FDA00036947034000000314
The final iteration to the Mth time outputs are:
Figure FDA00036947034000000315
wherein, P k|k Respectively the error covariance matrix at time k,
Figure FDA00036947034000000316
for the estimation error covariance matrix at time k,
Figure FDA00036947034000000317
the noise covariance matrix estimated for time k,
Figure FDA00036947034000000318
is the state variable of the mth iteration at time k.
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CN106487297A (en) * 2016-11-24 2017-03-08 北京邮电大学 A kind of PMSM parameter identification method based on covariance matching Unscented kalman filtering algorithm
CN108134549A (en) * 2017-12-25 2018-06-08 西安理工大学 A kind of method for improving permanent magnet synchronous motor speed estimate stability

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