阅读说明：本技术 一种高兼容性的非接触式同步电机转子励磁的建模方法 (High-compatibility modeling method for rotor excitation of non-contact synchronous motor ) 是由 蔡峰 李可 孙晓东 陈龙 周剑 邬江陵 于 2021-06-04 设计创作，主要内容包括：本发明公开了一种非接触式同步电机转子励磁的建模方法,包括以下步骤：构建感应型非接触式同步电机转子励磁系统10,形成感应型非接触式同步电机转子励磁系统的辨识模型；建立递推最小二乘法辨识模型,最后实现对初值为估计值的递推最小二乘法辨识建模。本发明所形成的辨识模型不需要知道系统内部的明确谐振补偿网络及变换器拓扑电路,兼容性强。(The invention discloses a modeling method for non-contact synchronous motor rotor excitation, which comprises the following steps: constructing an induction type non-contact synchronous motor rotor excitation system 10 to form an identification model of the induction type non-contact synchronous motor rotor excitation system; and establishing a recursive least square method identification model, and finally realizing recursive least square method identification modeling with an initial value as an estimation value. The identification model formed by the invention does not need to know a definite resonance compensation network and a converter topological circuit in the system, and has strong compatibility.)

1. A modeling method for non-contact synchronous motor rotor excitation is characterized by comprising the following steps: constructing an induction type non-contact synchronous motor rotor excitation system (10) to form an identification model of the induction type non-contact synchronous motor rotor excitation system; and establishing a recursive least square method identification model, and finally realizing recursive least square method identification modeling with an initial value as an estimation value.

2. The modeling method of non-contact synchronous machine rotor excitation according to claim 1, characterized in that the specific process of constructing the induction type non-contact synchronous machine rotor excitation system (10) is as follows: inverting the high frequencyThe variable module (12), the primary side compensation module (13), the PWM modulation module (14), the loose coupling transformer (15), the secondary side compensation module (16), the rectification filter module (17) and the rotor excitation control module (18) are sequentially connected to form an induction type non-contact synchronous motor rotor excitation system (10) as a whole; the system uses the DC voltage U output by the DC power supply (11)_dcAnd PWM control signal d (t) of PWM control modulation module (14) is input, and rotor excitation voltage y (t) is output; the high-frequency inverter module (12), the primary side compensation module (13), the PWM modulation module (14) and the primary side coil of the loose coupling transformer (15) are arranged on a stator of the synchronous motor; a secondary side winding of the loose coupling transformer (15), a secondary side compensation module (16), a rectification filter module (17) and a rotor excitation control module (18) are installed on a synchronous motor rotor.

3. The modeling method of non-contact synchronous machine rotor excitation according to claim 2, characterized in that the loosely coupled transformer (15) is composed of a primary side coil and a secondary side coil of the transformer, which are separated from each other, and the energy transmission is realized through an electromagnetic induction coupling relationship; the primary side compensation module (13) is used for reducing the volt-ampere capacity of the primary side power supply module and improving the power factor of the system; the secondary side compensation module (16) is used for improving the power transmission capability of a system to a load and removing the influence of leakage inductance of a secondary side winding.

4. Method for modelling the excitation of a rotor of a synchronous machine of the type defined in claim 2, characterized in that the high-frequency inverter module (12) supplies the direct current U from the direct current source (11)_dcHigh-frequency alternating current U converted into specified frequency_ac。

5. The modeling method of non-contact synchronous motor rotor excitation according to claim 2, characterized in that the rectification filter module (17) converts high-frequency alternating current I'_acConverted into direct current I'_dcAnd then the rotor excitation control module (18) is used for realizing the excitation of the rotor winding.

6. The modeling method of non-contact synchronous machine rotor excitation according to claim 1, characterized in that in the identification model of the induction type non-contact synchronous machine rotor excitation system, a transfer function G(s) of the system is obtained according to the input signal d (t) and the output signal y (t);

the induction type non-contact synchronous motor rotor excitation system (10) is regarded as a black box model, a measuring module (21) is added to measure an input signal d (t) of the synchronous motor rotor excitation system (10), and r containing noise is obtained₁Input measurement signal d' (t); similarly, the output signal y (t) of the synchronous motor rotor excitation system (10) is measured by adding the measuring module (22) to obtain the signal r containing the noise₂The identification module (23) obtains a transfer function G(s) of the synchronous motor rotor excitation system (10) according to the input and output measurement data; the duty ratio of the input signal D (t) is constant D, and is represented by a step signal D epsilon (t), and the output signal y (t) is a step response signal.

7. The modeling method for non-contact synchronous motor rotor excitation according to claim 1, wherein the specific process for establishing the recursive least square method identification model is as follows:

firstly, establishing a difference equation of an induction type non-contact synchronous motor rotor excitation system (10) as follows:

where k is 1,2.3 …, y (k) is the system discretization output, u (k) is the system discretization input, ξ (k) is the system white noise, making it the gaussian white noise with mean equal to zero, a_i、b_jRespectively are differential coefficients;

defining:

data matrix

Parameter matrix theta to be estimated_n＝[a₁...a_n b₁...b_n]^T

Then the simplified formula of formula (1) can be obtained

Taking N groups of data, writing the formula (2) into a matrix form as follows:

Y_N＝φ_Nθ+E_N (3)

in the formula:

n-order output matrix Y_N＝[y(n+1),y(n+2),...,y(n+N)]^T

n-order data matrix

White noise matrix E of n-th order_n＝[ξ(n+1) ξ(n+2).ξ(n+N)]^T

The total number N of the sampled data must be sufficiently large, so that the identification accuracy can be improved, and the influence of noise on the system can be reduced.

u (k) and y (k) are measurable data, and according to the least square criterion, the least square estimation of the parameter theta to be estimated can be obtained by minimizing the index function, as shown in the formula (4):

defining an n-order parameter matrix:

P_N＝(φ^T _Nφ_N)^-1 (5)

equation (4) can be written as:

if a new set of observed values is added, the new parameter estimation value is:

whereinE is an identity matrix;

defining a gain matrixA parameter estimation formula of the recursive least squares algorithm can be obtained:

the method is according to P_NAnd new observation data, directly calculating G_N+1And is thus based onCalculate outDoes not need (phi)^T _Nφ_N)^-1The invention can process larger data volume more quickly and accurately, and provides a recursion least square method identification modeling method of initial value correction according to the recursion least square method identification model in order to improve model precision, save calculation time and calculation amount and improve modeling instantaneity.

8. The modeling method for non-contact synchronous motor rotor excitation according to claim 7, wherein the specific process for realizing the recursive least square method identification model for initial value correction is as follows:

firstly, according to an established recursive least square method identification model, carrying out a simulation experiment on an induction type non-contact synchronous motor rotor excitation system (10) by using an MATLAB/Simulink simulation platform to obtain a simulation result of excitation voltage; reading output excitation voltage data of Simulink simulation by using MATLAB, wherein the simulation time for sampling is 5ms, the sampling period T is 50 mus, sampling input and output signals to obtain a discrete input sequence D epsilon (kT) and an output sequence y (kT), and converting the input sequence D epsilon (kT) and the output sequence y (kT) obtained by sampling into a ramp sequence g (kT) according to an equation (9) so as to enable a data matrix in a least square method to be full-rank:

then, the level of the system (10 model) is obtained by utilizing the red pool information content (AIC) criterion, and the judging formula of the system (10) model level based on the red pool information content criterion is shown as the formula (10):

AIC(n)＝Nlnσ² _ε+2n (10)

wherein n is order, σ² _εA likelihood estimate that is a variance of white noise ξ (k);

substituting the converted slope data into an equation (10) to obtain AIC values of each order of the model, and selecting the order n when the AIC value is minimum and the parameter to be estimated according to the AIC criterionFinally, n is obtained as 3,

in order to improve the accuracy of the model, the recursive least square method identification modeling method is improved by using an initial value correction scheme; firstly, using least square method to make parameter on the collected and transformed front 100 groups of dataNumber estimation, namely taking the obtained parameter to be estimated as an initial value of a recursive least square algorithm to realize initial value correction, and obtaining the parameter to be estimated at the moment through simulation calculationFinally, the discrete transfer function and the continuous transfer function of the obtained model are respectively shown as formula (11) and formula (12):

thus, a dynamic model of the system (10) is obtained.

Technical Field

The invention relates to a modeling method for non-contact synchronous motor rotor excitation, belonging to the technical field of vehicle motor control application.

Background

Under the support of national policies, new energy automobiles in China are developing vigorously. As a core component of a new energy automobile, whether the performance of a vehicle-mounted motor meets requirements or not is particularly important. The electrically excited synchronous motor is a common alternating current motor, has the outstanding advantages of adjustable power factor, small loss, high efficiency, simple structure, high reliability and the like, and has great potential as a vehicle-mounted driving motor. However, the conventional electrically excited synchronous motor has a structure of an electric brush and a slip ring for commutation, and the friction between the electric brush and a commutator can cause sparks, thereby bringing potential safety hazards to new energy automobiles. In addition, the brush motor has the defects of relatively low efficiency, high noise, easy heating, short service life, difficult maintenance and the like. Therefore, brushless electric field synchronous motors have been inevitably developed.

In response to this problem, the conventional method is to implement brushless operation by adding an exciter or an additional winding; the brushless motor is realized by adopting a permanent magnet material; the brushless electric excitation and permanent magnet hybrid excitation mode is utilized to realize the brushless operation. In general, the conventional brushless scheme needs to add an additional winding or an additional device, so that the motor has a complex structure, the volume is increased, and the utilization rate of the motor is reduced. The invention provides a novel excitation method for a rotor of a non-contact synchronous motor by utilizing an induction type non-contact energy transmission technology. In addition, the invention provides a recursive least square identification modeling method with high compatibility for initial value correction for the problems of poor compatibility among functional modules of a non-contact synchronous motor rotor excitation system, low transportability and the like.

The patent applications published in the same technical field at home are as follows: the name is 'a synchronous motor rotor excitation method and device', application number: CN 107104613A, which adopts a resonant wireless power transmission mode to transmit the electric energy of the dc or ac power supply to the rotor excitation winding in a non-contact manner, so as to realize rotor excitation or hybrid excitation. The invention adopts a resonant wireless electric energy transmission type technology, the transmission power of the technology is lower, the technology is not suitable for being applied to a vehicle-mounted driving system needing high-power transmission, and the invention does not solve the problems of poor compatibility among functional modules of a non-contact excitation system, low transportability and the like.

Disclosure of Invention

The invention aims to provide a non-contact synchronous motor rotor excitation method by utilizing an induction type non-contact energy transmission technology aiming at the problem that potential safety hazards are brought to a new energy automobile by an electric brush and slip ring structure of an electrically excited synchronous motor, so that brushless operation is realized. Compared with other brushless technologies, the method does not need to add additional windings or additional devices, and is simple in structure and high in motor utilization rate. In addition, for the problems of poor compatibility and low transportability among functional modules of the non-contact synchronous motor rotor excitation system, the invention provides a recursive least square identification modeling method with high compatibility and initial value correction, and the transfer function of the non-contact synchronous motor rotor excitation system, namely the transfer relation between input and output is obtained.

The technical scheme adopted by the invention comprises the following steps: a modeling method for non-contact synchronous motor rotor excitation comprises the following steps: constructing an induction type non-contact synchronous motor rotor excitation system 10 to form an identification model of the induction type non-contact synchronous motor rotor excitation system; and establishing a recursive least square method identification model, and finally realizing recursive least square method identification modeling with an initial value as an estimation value.

Further, the specific process of constructing the rotor excitation system 10 of the induction type non-contact synchronous motor is as follows: the high-frequency inversion module 12, the primary side compensation module 13, the PWM modulation module 14, the loose coupling transformer 15, the secondary side compensation module 16, the rectification filter module 17 and the rotor excitation control module 18 are sequentially connected to form an induction type non-contact synchronous motor rotor excitation system 10 as a whole; the system uses the DC voltage U output by the DC power supply 11_dcAnd PWM control signal d (t) of PWM control modulation module 14 is input, and rotor excitation voltage y (t) is output; wherein, the high frequency inversion module 12, the primary side compensation module 13, and the PWM modulationThe module 14 and the primary side coil of the loose coupling transformer 15 are mounted on the stator of the synchronous machine; the secondary side winding of the loose coupling transformer 15, the secondary side compensation module 16, the rectification filter module 17 and the rotor excitation control module 18 are installed on the synchronous motor rotor.

Further, the loosely coupled transformer 15 is composed of a primary side coil and a secondary side coil of the transformer, which are separated from each other, and realizes energy transmission through an electromagnetic induction coupling relationship; the primary side compensation module 13 is used for reducing the volt-ampere capacity of the primary side power supply module and improving the power factor of the system; the secondary side compensation module 16 is used for improving the power transmission capability of the system to the load and removing the influence of the leakage inductance of the secondary side winding.

Further, the high frequency inversion module 12 outputs the direct current U from the direct current power supply 11_dcHigh-frequency alternating current U converted into specified frequency_ac。

Further, the rectification filter module 17 converts the high-frequency alternating current I'_acConverted into direct current I'_dcAnd then the rotor excitation control module 18 is used for realizing the excitation of the rotor winding.

Further, in the identification model of the rotor excitation system of the induction type non-contact synchronous motor, a transfer function G(s) of the system is obtained according to an input signal d (t) and an output signal y (t);

the induction type non-contact synchronous motor rotor excitation system 10 is regarded as a black box model, and the measurement module 21 is added to measure an input signal d (t) of the synchronous motor rotor excitation system 10 to obtain a signal containing noise r₁Input measurement signal d' (t); similarly, the measurement module 22 is added to measure the output signal y (t) of the synchronous motor rotor excitation system 10 to obtain the signal containing the noise r₂The identification module 23 obtains a transfer function g(s) of the synchronous motor rotor excitation system 10 according to the input and output measurement data; the duty ratio of the input signal D (t) is constant D, and is represented by a step signal D epsilon (t), and the output signal y (t) is a step response signal.

Further, the specific process of establishing the recursive least square method identification model is as follows:

firstly, a difference equation of an induction type non-contact synchronous motor rotor excitation system 10 is established as follows:

where k is 1,2.3 …, y (k) is the system discretization output, u (k) is the system discretization input, ξ (k) is the system white noise, making it the gaussian white noise with mean equal to zero, a_i、b_jRespectively are differential coefficients;

defining:

data matrix

Parameter matrix theta to be estimated_n＝[a₁...a_n b₁...b_n]^T

Then the simplified formula of formula (1) can be obtained

Taking N groups of data, writing the formula (2) into a matrix form as follows:

Y_N＝φ_Nθ+E_N (3)

in the formula:

n-order output matrix Y_N＝[y(n+1),y(n+2),...,y(n+N)]^T

n-order data matrix

White noise matrix E of n-th order_n＝[ξ(n+1)ξ(n+2).ξ(n+N)]^T

The total number N of the sampled data must be sufficiently large, so that the identification accuracy can be improved, and the influence of noise on the system can be reduced.

u (k) and y (k) are measurable data, and according to the least square criterion, the least square estimation of the parameter theta to be estimated can be obtained by minimizing the index function, as shown in the formula (4):

defining an n-order parameter matrix:

P_N＝(φ^T _Nφ_N)^-1 (5)

equation (4) can be written as:

if a new set of observed values is added, the new parameter estimation value is:

whereinE is an identity matrix;

defining a gain matrixA parameter estimation formula of the recursive least squares algorithm can be obtained:

the method is according to P_NAnd new observation data, directly calculating G_N+1And is thus based onCalculate outDoes not need (phi)^T _Nφ_N)^-1The invention can process larger data volume more quickly and accurately, and provides a recursion least square method identification modeling method of initial value correction according to the recursion least square method identification model in order to improve model precision, save calculation time and calculation amount and improve modeling instantaneity.

Further, the specific process for realizing the identification model by the recursive least square method of initial value correction is as follows:

firstly, according to an established recursive least square method identification model, a simulation experiment is carried out on an induction type non-contact synchronous motor rotor excitation system 10 by utilizing an MATLAB/Simulink simulation platform, and a simulation result of excitation voltage is obtained. Reading output excitation voltage data of Simulink simulation by using MATLAB, wherein the simulation time for sampling is 5ms, the sampling period T is 50 mus, sampling input and output signals to obtain a discrete input sequence D epsilon (kT) and an output sequence y (kT), and converting the input sequence D epsilon (kT) and the output sequence y (kT) obtained by sampling into a ramp sequence g (kT) according to an equation (9) so as to enable a data matrix in a least square method to be full-rank:

then, the order of the system 10 model is obtained by using the information content of akage pool (AIC) criterion, and the judging formula of the system 10 model order based on the information content of akage pool is shown as the formula (10):

AIC(n)＝Nlnσ² _ε+2n (10)

wherein n is order, σ² _εA likelihood estimate that is a variance of white noise ξ (k);

substituting the converted slope data into an equation (10) to obtain AIC values of each order of the model, and selecting the order n when the AIC value is minimum and the parameter to be estimated according to the AIC criterionFinally, n is obtained as 3,

in order to improve the accuracy of the model, the recursive least square method identification modeling method is improved by using an initial value correction scheme; firstly, carrying out parameter estimation on the collected and transformed front 100 groups of data by using a least square method, taking the obtained parameter to be estimated as an initial value of a recursive least square algorithm so as to realize initial value correction, and then obtaining the parameter to be estimated at the moment through simulation calculationFinally, the discrete transfer function and the continuous transfer function of the obtained model are respectively shown as formula (11) and formula (12):

at this point, a dynamic model of the system 10 is obtained.

1) The high-frequency inversion module, the primary side compensation module, the modulation module, the loose coupling transformer, the secondary side compensation module, the rectification filter module and the rotor excitation control module are taken as a whole to form an induction type non-contact synchronous motor rotor excitation system; 2) regarding an induction type non-contact synchronous motor rotor excitation system as a black box model, and forming an identification model of the induction type non-contact synchronous motor rotor excitation system; 3) establishing a recursive least square method identification model; 4) and (5) identification modeling realization of a recursive least square method with an initial value as an estimated value.

The invention has the advantages that:

1. the non-contact transformer is used for replacing an electric brush and a slip ring in a traditional excitation system, and the brushless excitation target without increasing the complexity of an excitation device and a motor is realized.

2. The resonance compensation module is utilized to reduce the problems of small coupling coefficient and large leakage inductance caused by the air gap between the primary side coil and the secondary side coil, reduce the volt-ampere capacity of the primary side power supply module, improve the power factor of a system and transfer power to a load.

3. The induction type non-contact synchronous motor rotor excitation system is regarded as a black box model, a definite resonance compensation network and a converter topological circuit in the system do not need to be considered, compatibility is high, and simplified processing of a complex system is achieved.

4. And the transfer relation between the input and the output of the system is obtained by utilizing the initial value corrected recursive least square method identification model, and the obtained result is good in coincidence with the simulation result.

The modeling method of the non-contact synchronous motor rotor excitation with high compatibility only needs input and output variables which can be measured and are easy to measure, and does not need to add an additional excitation device; in addition, the identification model formed by the method does not need to know a definite resonance compensation network and a converter topology circuit in the system, and the compatibility is strong.

Drawings

Fig. 1 is a rotor excitation system of an induction type non-contact synchronous motor according to the present invention.

Fig. 2 is an identification model of the rotor excitation system of the induction type non-contact synchronous motor according to the invention.

Fig. 3 is a simulation result of the excitation voltage of the rotor excitation system of the induction type non-contact synchronous motor and a step response output sequence obtained according to sampling in the invention. (a) Simulation results of excitation voltage of the motor rotor excitation system; (b) a step response output sequence;

fig. 4 is a ramp response output sequence after a step data transition as described in the present invention.

Fig. 5 is a comparison between data obtained from the initial value-corrected recursive least square method identification model and a simulation output excitation voltage curve.

FIG. 6 is a flow chart of the implementation of the recursive least square method identification modeling of initial value correction described in the present invention.

Detailed Description

The specific implementation of the invention comprises the following 4 steps:

1. as shown in fig. 1, an induction type non-contact synchronous motor rotor excitation system 10 is constructed. The invention takes a high-frequency inversion module 12, a primary side compensation module 13, a PWM modulation module 14, a loose coupling transformer 15, a secondary side compensation module 16, a rectification filter module 17 and a rotor excitation control module 18 as a whole to form an induction type non-contact synchronous motor rotor excitation system 10. The system uses the DC voltage U output by the DC power supply 11_dcAnd a PWM control signal d (t) of the PWM control modulation module 14 as an input, and a rotor excitation voltage y (t) as an output. The loosely coupled transformer 15 is composed of a primary side coil and a secondary side coil of the transformer, which are separated from each other, and realizes energy transmission by an electromagnetic induction coupling relationship. The primary side compensation module 13 is used to reduce the volt-ampere capacity of the primary side power module and improve the power factor of the system. Similarly, the secondary side compensation module 16 is used to improve the power transmission capability of the system to the load and remove the influence of the leakage inductance of the secondary side winding. The high-frequency inversion module 12 outputs the direct current U from the direct current power supply 11_dcHigh-frequency alternating current U converted into specified frequency_ac. The rectification filter module 17 converts the high-frequency alternating current I'_acConverted into direct current I'_dcAnd then the rotor excitation control module 18 is used for realizing the excitation of the rotor winding. The high-frequency inversion module 12, the primary side compensation module 13, the PWM modulation module 14 and the primary side coil of the loose coupling transformer 15 are mounted on the stator of the synchronous motor; the secondary side winding of the loose coupling transformer 15, the secondary side compensation module 16, the rectification filter module 17 and the rotor excitation control module 18 are installed on the synchronous motor rotor. The power transfer process of the system 10 is as follows:

the PWM modulation module 14 controls the high frequency inverter module 12 under the power supply of the dc power supply 11 according to the PWM control signal d (t) input by the system, outputs corresponding PWM signals to control each switching tube of the inverter, and outputs the dc power U output by the dc power supply 11_dcConverted into high-frequency alternating current U_acAnd outputs U 'after resonance compensation by the primary side compensation module 13'_acAnd applied to the primary winding of the loosely coupled transformer 15. High-frequency alternating current signal U'_acA high-frequency alternating magnetic field is generated on the primary coil and energy is coupled to the secondary coil via an air gap, so that an alternating excitation current I is generated_ac. Excitation current I_acOutputs I 'after resonance compensation of the secondary side compensation module 16'_acAnd then the direct current I 'is output after being rectified and filtered by a rectification and filtering module 17'_dcFinally, the field voltage y (t) is applied to the rotor field winding via the rotor field control module 18.

The input of the primary side compensation module 13 is a high-frequency alternating current U_acThe output is a compensated high-frequency alternating current U'_acThe input/output relationship of the primary side compensation module 13 is as follows:

in the formula, ω₁Is the angular frequency, L, of the power supply₁To compensate for the self-inductance of the winding at the primary side, R₁Is the resistance of the primary side compensation circuit.

The input of the loose coupling transformer 15 is a compensated high-frequency alternating current U'_acThe output is alternating exciting current I_acThe input-output relationship of the loosely coupled transformer 15 is:

in the formula, Z_inIs the input impedance of the transformer, Z₁₁Is the loop impedance of the primary winding, Z₂₂Is the loop impedance of the secondary winding, and M is the mutual inductance between the primary and secondary windings.

The input of the secondary side compensation module 16 is an exciting current I_acThe output is the compensation exciting current I' ac, and the input and output relationship of the secondary side compensation module 16 is as follows:

in the formula, ω₂Is the angular frequency of the current, L₂For self-inductance of the secondary side compensation winding, R₂Is the resistance of the secondary side compensation circuit.

2. As shown in fig. 2, an identification model of the rotor excitation system of the induction type non-contact synchronous motor is formed. It derives the transfer function G(s) of the system from the input signal d (t) and the output signal y (t). The specific process is as follows:

the induction type non-contact synchronous motor rotor excitation system 10 is regarded as a black box model, namely, a clear resonance compensation network and a converter topological circuit in the system are not considered, and the simplified processing of a complex system is realized. Considering that the actual system is affected by noise at the input end and the output end, the measuring module 21 is added to measure the input signal d (t) of the system 10 to obtain the signal r containing the noise₁Input measurement signal d' (t). Similarly, the measurement module 22 is added to measure the output signal y (t) of the system 10 to obtain the signal containing the noise r₂Output measurement signal y' (t). The recognition module 23 obtains the transfer function g(s) of the system 10 according to the input and output measurement data. The duty ratio of the input signal D (t) is constant D, and is represented by a step signal D epsilon (t), and the output signal y (t) is a step response signal. The establishment of the recognition module 23 and the process of obtaining the transfer function g(s) will be described in detail below.

3. And establishing a recursive least square method identification model. Firstly, a difference equation of an induction type non-contact synchronous motor rotor excitation system 10 is established as follows:

where k is 1,2.3 …, y (k) is the system discretization output, u (k) is the system discretization input, ξ (k) is the system white noise, making it the gaussian white noise with mean equal to zero, a_i、b_jRespectively are differential coefficients;

defining:

data matrix

Parameter matrix theta to be estimated_n＝[a₁...a_n b₁...b_n]^T

Then the simplified formula of formula (1) can be obtained

Taking N groups of data, writing the formula (2) into a matrix form as follows:

Y_N＝φ_Nθ+E_N (3)

in the formula:

n-order output matrix Y_N＝[y(n+1),y(n+2),...,y(n+N)]^T，

n-order data matrix

White noise matrix E of n-th order_n＝[ξ(n+1)ξ(n+2).ξ(n+N)]^T

The total number N of the sampled data must be sufficiently large to ensure the accuracy of the identification and reduce the influence of noise on the system.

u (k) and y (k) are measurable data, and the least square estimation of the parameter theta to be estimated can be obtained by minimizing the index function according to the least square criterionAs shown in formula (4):

defining an n-order parameter matrix:

P_N＝(φ^T _Nφ_N)^-1 (5)

equation (4) can be written as:

if a new set of observed values is added, the new parameter estimation value is:

in the formulaE is an identity matrix.

Defining a gain matrixA parameter estimation formula of the recursive least squares algorithm can be obtained:

the method is according to P_NAnd new observation data, directly calculating G_N+1And is thus based onCalculate outDoes not need (phi)^T _Nφ_N)^-1And a larger data volume can be processed more quickly and accurately. In order to improve the model precision, save the calculation time and the calculation amount and improve the modeling instantaneity, the invention provides an initial value correction recursive least square method identification modeling method according to the recursive least square method identification model. The specific implementation is described in section 4.

4. And (5) realizing identification modeling by using a recursive least square method for initial value correction. Firstly, according to the established recursive least square method identification model, a simulation experiment is carried out on the induction type non-contact synchronous motor rotor excitation system 10 by utilizing an MATLAB/Simulink simulation platform, and the simulation result of the excitation voltage is obtained and is shown in fig. 3 (a). The output excitation voltage data of the Simulink simulation is read by using MATLAB, wherein the simulation time for sampling is 5ms, the sampling period T is 50 μ s, the input sequence D epsilon (kT) obtained by sampling the input and output signals is obtained, and the output sequence y (kT) is shown in fig. 3 (b). In order to make the data matrix full in the least square method, the sampled input sequence D epsilon (kT) and output sequence y (kT) are transformed into ramp sequence g (kT) according to equation (9).

The transformed response data is shown in fig. 4.

The order of the system 10 model is then obtained using the Akage Information Content (AIC) criterion. The decision formula of the model order of the system 10 based on the akage pool information amount criterion is shown as the formula (10):

AIC(n)＝Nlnσ² _ε+2n (10)

wherein n is order, σ² _εIs a likelihood estimate of the variance of white noise ξ (k).

And (5) substituting the converted slope data into an equation (10) to obtain AIC values of each order of the model. According to the AIC criterion, selecting the order n when the AIC value is minimum and the parameter to be estimated at the momentFinally, n is obtained as 3,

in order to improve the accuracy of the model, the invention utilizes the scheme of initial value correction to recurThe least square method identification modeling method is improved. Firstly, using least square method to make parameter estimation on the collected and converted front 100 groups of data, using the obtained parameter to be estimated as initial value of recursive least square algorithm to implement initial value correction, then utilizing simulation to calculate the parameter to be estimated at this momentFinally, the discrete transfer function and the continuous transfer function of the obtained model are respectively shown as a formula (11) and a formula (12).

At this point, a dynamic model of the system 10 is obtained. The comparison between the obtained data and the simulation output excitation voltage curve according to the recursive least square method identification model corrected by the established initial value is shown in fig. 5.

Combining the above implementation process of the recursive least square method identification modeling of initial value correction, an identification modeling flowchart is formed, as shown in fig. 6. FIG. 6 shows an implementation of the recognition module 23 in FIG. 2.