CN109270455B - Induction motor state monitoring method based on weak-sensitivity ensemble Kalman filtering - Google Patents

Induction motor state monitoring method based on weak-sensitivity ensemble Kalman filtering Download PDF

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CN109270455B
CN109270455B CN201811244773.9A CN201811244773A CN109270455B CN 109270455 B CN109270455 B CN 109270455B CN 201811244773 A CN201811244773 A CN 201811244773A CN 109270455 B CN109270455 B CN 109270455B
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state
induction motor
rotor
equation
stator
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CN109270455A (en
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娄泰山
陈南华
杨存祥
杨小亮
丁国强
王妍
凌丹
王延峰
王磊
张云玲
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Zhengzhou University of Light Industry
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/34—Testing dynamo-electric machines
    • G01R31/343—Testing dynamo-electric machines in operation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/34—Testing dynamo-electric machines
    • G01R31/346—Testing of armature or field windings
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
    • G06F17/12—Simultaneous equations, e.g. systems of linear equations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization

Abstract

The invention discloses an induction motor state monitoring method based on weak-sensitive ensemble Kalman filtering, and aims to solve the technical problem that the existing method is low in accuracy of state monitoring results of an induction motor. The method comprises the following steps: establishing a state equation of the induction motor system, establishing a measurement equation, a discretization state equation and a measurement equation of the induction motor system, adopting weak-sensitive Kalman filtering to the discretization state equation and the measurement equation, and outputting the stator current, the rotor flux linkage and the angular speed of the induction motor. Compared with EnKF, the method uses a weak-sensitive optimal control technology to solve the uncertainty of parameters (such as rotor resistance, stator resistance and the like) in the induction motor system, weakens the sensitivity of state (stator current, rotor flux linkage and angular speed) estimation in the induction motor system to the uncertain parameters, improves the state monitoring precision of the induction motor, and can be applied to the state PID control process of the induction motor.

Description

Induction motor state monitoring method based on weak-sensitivity ensemble Kalman filtering
Technical Field
The invention relates to the technical field of state monitoring of induction motors, in particular to a state monitoring method of an induction motor based on weak-sensitivity ensemble Kalman filtering.
Background
The induction motor has the advantages of simple structure, stable performance, low cost, convenient manufacture and the like, is widely concerned in theoretical research and practical application, and is widely applied to the fields of electric automobiles, transportation, numerical control machines and the like. At present, a practical alternating current speed regulating system of an induction motor generally adopts an indirect method to monitor flux linkage and rotating speed, namely, the flux linkage and the rotating speed are calculated in real time by detecting physical quantities such as voltage, current and the like of a stator end of the motor and utilizing a state estimation method, so that the flux linkage and the rotating speed are accurately controlled, namely, the induction motor is controlled without a speed sensor, and the speed sensor-free control technology is an important research direction of the alternating current speed regulating system of the induction motor. Therefore, the research focus of the induction motor is mainly focused on the speed sensorless control, and the key problems to be solved by the speed sensorless control system of the induction motor are the monitoring of the rotating speed of the induction motor and the monitoring of the rotor flux linkage. An ensemble Kalman filtering (EnKF) is a Kalman filtering method based on Monte Carlo, the calculation of a Jacobian matrix is avoided through ensemble sampling, the method has higher calculation efficiency and the capability of processing a high-dimensional nonlinear system, but a mathematical model established by an induction motor system in engineering practice often contains uncertainty of parameters (such as rotor resistance, stator resistance and the like), and when the EnKF is adopted to monitor the states (stator current, rotor flux linkage and angular speed) of the induction motor, the uncertainty of the parameters can greatly reduce the precision of a monitoring result and even can cause divergence.
Disclosure of Invention
The invention aims to solve the technical problem of providing an induction motor state monitoring method based on weak-sensitivity ensemble Kalman filtering so as to solve the technical problem of low accuracy of the state monitoring result of an induction motor in the conventional method.
In order to solve the technical problems, the invention adopts the following technical scheme:
an induction motor state monitoring method based on weak-sensitivity ensemble Kalman filtering is designed, and comprises the following steps:
the method comprises the following steps: obtaining a first stator current x of an induction motor system1A second stator current x2First rotor flux linkage x3Second rotor flux linkage x4Angular velocity x5Rotor inertia J, pole pair number p, and rotor time constant TrMotor no-load leakage magnetic coefficient sigma, inverse lambda of instantaneous time constant and first stator voltage control input u1A second stator voltage control input u2Rotor inductance LsStator inductance LrMutual inductance LmFixed parameters
Figure BDA0001840253400000011
In an induction motor system, a first stator current x is taken1A second stator current x2First rotor flux linkage x3Second rotor flux linkage x4Angular velocity x5Constructing a state vector x ═ x1,x2,x3,x4,x5]TThen, the state equation of the induction motor system is established as follows:
Figure BDA0001840253400000021
wherein x is1Is the first stator current, x2Is the second stator current, x3Is the first rotor flux linkage, x4Is the second rotor flux linkage, x5Is the angular velocity; j is rotor inertia, p is pole pair number, TrIs the time constant of the rotor, sigma is the no-load leakage coefficient of the motor, K is a fixed parameter, and lambda is the instantaneous time constantThe reciprocal of the number; u. of1Is a first stator voltage control input, u2Is a second stator voltage control input; c ═ c1 c2]Is an uncertain parameter vector, c1And c2Rotor resistance and stator resistance, respectively; w is zero-mean white gaussian noise;
measuring a first stator current of an induction motor system at constant sampling time intervals h
Figure BDA0001840253400000022
Second stator current
Figure BDA0001840253400000023
And angular velocity
Figure BDA0001840253400000024
Establishing a measurement equation of an induction motor system:
z＝Hx+v＝h(x,c)+v (2)
wherein the content of the first and second substances,
Figure BDA0001840253400000025
wherein H is an observation matrix of a measurement equation, and v is zero-mean Gaussian white noise;
discretizing the state equation (1) of the induction motor system to obtain a discrete state equation of the induction motor system
Figure BDA0001840253400000026
h corresponds to the sampling time interval of the step of constructing the metrology equation,
Figure BDA0001840253400000031
is tk-1The first stator voltage at a time controls the input,
Figure BDA0001840253400000032
is tk-1Second stator voltage at timeA control input;
establishing an induction motor system state model based on the discrete state equation and the measurement equation of the induction motor system:
xk＝f(xk-1,c,uk-1)+wk-1 (5)
zk＝h(xk,c)+vk (6)
wherein, wkAnd vkAre mutually independent zero-mean white Gaussian noise sequences, and wkRespectively has a variance of Qk，vkHas a variance of RkAnd satisfy
Figure BDA0001840253400000033
Wherein, deltakjIs a function of Kronecker delta, delta when k is j kj1 is ═ 1; when k ≠ j, δkj＝0；
System noise variance matrix Q of induction motor system model obtained by statistical methodkSum measure noise variance matrix Rk；
Step two: processing the dispersed state equation and the measurement equation, and outputting the stator current, the rotor flux linkage and the angular speed of the induction motor;
1. initializing a state model matched with the induction motor system
Figure BDA0001840253400000034
Figure BDA0001840253400000035
Wherein, the initial state
Figure BDA0001840253400000036
Initial error variance matrix
Figure BDA0001840253400000037
P0、QkAnd RkAre all unrelated;
2. calculating state and metrology set points and covariance and metrology variance
Setting the state estimation value and the error variance matrix of the step k-1 as
Figure BDA0001840253400000038
And
Figure BDA0001840253400000039
the set point of the k step is:
Figure BDA00018402534000000310
where the superscript "+" indicates its posterior estimate,
Figure BDA00018402534000000311
is an error variance matrix
Figure BDA00018402534000000312
J-th column of square root of (1), satisfy
Figure BDA00018402534000000313
m is 40 set points of sampling;
the set points after nonlinear function transfer are:
Figure BDA00018402534000000314
the measurement rendezvous point is calculated by the transmitted state rendezvous point and can be obtained by:
Figure BDA00018402534000000315
then the corresponding prior state estimation and measurement mean value are:
Figure BDA0001840253400000041
Figure BDA0001840253400000042
wherein the superscript "-" represents a prior estimate of the variable;
then covariance of state and measurements
Figure BDA0001840253400000043
And measure variance
Figure BDA0001840253400000044
Figure BDA0001840253400000045
Figure BDA0001840253400000046
Wherein the content of the first and second substances,
Figure BDA0001840253400000047
is a state error matrix, i.e. the state value of each rendezvous point
Figure BDA0001840253400000048
And average value
Figure BDA0001840253400000049
The difference between them;
Figure BDA00018402534000000410
for measuring error matrices, i.e. measured values at each set point
Figure BDA00018402534000000411
And post-transfer average
Figure BDA00018402534000000412
Is defined as:
Figure BDA00018402534000000413
Figure BDA00018402534000000414
3. sensitivity propagation of rendezvous
First, the sensitivity of the set point of step k-1 is calculated:
Figure BDA00018402534000000415
wherein i is the number of uncertain parameters;
second, propagation rendezvous sensitivity:
Figure BDA00018402534000000416
Figure BDA00018402534000000417
then, the prior state and the sensitivity of the measurement are calculated separately:
Figure BDA00018402534000000418
Figure BDA00018402534000000419
4. kalman gain K for calculating weak sensitive ensemble Kalman filteringk
Figure BDA00018402534000000420
Wherein, Wi,kTaking the weight of the ith uncertain parameter as the variance of the uncertain parameter;
5. computing sensitivity matrices
Figure BDA0001840253400000051
6. State estimation of step k
Figure BDA0001840253400000052
Performing loop iteration in the 6 steps to obtain a real-time state monitoring result of the induction motor, wherein the real-time state monitoring result comprises a first stator current x1A second stator current x2First rotor flux linkage x3Second rotor flux linkage x4Angular velocity x5。
Preferably, in the equation of state of the induction motor system, the rotor time constant TrMotor no-load leakage coefficient sigma, reciprocal lambda of instantaneous time constant tkFirst stator voltage control input of time
Figure BDA0001840253400000053
tkSecond stator voltage control input of time of day
Figure BDA0001840253400000054
Are obtained by the following formulas:
Figure BDA0001840253400000055
wherein k corresponds to tkThe number of steps of the time.
Further, the sampling time interval h is 0.0001[ s ]]Rotor inductance Ls＝0.0699[H]Stator inductance Lr＝0.0699[H]Mutual inductance Lm＝0.068[H]The rotor inertia J is 0.0586[ kg m [ ]2]The number of pole pairs p is 1, and is obtained by counting the number of observation times N is 50 and the total sampling time t is 1s
Figure BDA0001840253400000056
Compared with the prior art, the invention has the beneficial technical effects that:
compared with the standard ensemble Kalman filtering (EnKF), the weakly sensitive ensemble Kalman filtering (DEnKF) solves the problem of uncertainty of parameters (such as rotor resistance, stator resistance and the like) in an induction motor system by using a weakly sensitive optimal control method, the weakly sensitive cost function and the mean square error cost function of the EnKF are creatively combined together through sensitivity weight coefficients to form a new cost function, the optimal gain of the weakly sensitive ensemble Kalman filtering is obtained by minimizing the cost function, the sensitivity of state (stator current, rotor flux linkage and angular speed) estimation in the induction motor system to uncertain parameters is weakened, and the state monitoring precision of the induction motor is improved.
Drawings
FIG. 1 is a flow chart of the present invention.
FIG. 2 is a schematic diagram of the weakly-sensitive ensemble Kalman filtering in the present invention.
FIG. 3 is a Matlab/Simulink simulation model for monitoring the state of an induction motor.
FIG. 4 shows the stator current x of the present invention and EnKF in the state monitoring result of the induction motor1Root mean square error of (c) versus plot.
FIG. 5 shows the stator current x of the present invention and EnKF in the state monitoring result of the induction machine2Root mean square error of (c) versus plot.
FIG. 6 shows the rotor flux linkage x of the present invention and EnKF in the state monitoring result of the induction motor3Root mean square error of (c) versus plot.
FIG. 7 shows the rotor flux linkage x of the present invention and EnKF in the state monitoring result of the induction motor4Root mean square error of (c) versus plot.
FIG. 8 shows the angular velocity x of the present invention and EnKF in the monitoring result of the induction machine state5Root mean square error of (c) versus plot.
Detailed Description
The following examples are intended to illustrate the present invention in detail and should not be construed as limiting the scope of the present invention in any way.
The first embodiment is as follows: a method for monitoring the state of an induction motor based on weak-sensitive ensemble Kalman filtering is disclosed, the flow chart of which is shown in figure 1, the schematic diagram of the weak-sensitive ensemble Kalman filtering is shown in figure 2, and the method comprises the following steps:
step (I): establishing a non-linear equation of state for an induction motor system
In an induction motor system, a state vector x is taken as [ x ]1,x2,x3,x4,x5]TThen the state equation is:
Figure BDA0001840253400000061
wherein x is1And x2Is the stator current, x3And x4Is the rotor flux linkage, x5Is the angular velocity; k is a fixed parameter; λ is the inverse of the instantaneous time constant; j is rotor inertia; p is the number of pole pairs; u. of1And u2Is the stator voltage control input; c ═ c1 c2]Is an uncertain parameter vector, c1And c2Rotor resistance and stator resistance, respectively; w is zero-mean white gaussian noise; other model parameters were:
Figure BDA0001840253400000071
wherein, the rotor inductance Ls＝0.0699[H]Stator inductance Lr＝0.0699[H]Mutual inductance Lm＝0.068[H](ii) a Rotor inertia J ═ 0.0586[ kg · m2]The pole pair number p is 1; k corresponds to tkThe number of steps of the time;
step (II): establishing a measurement equation for an induction motor system
Stator current to be measured
Figure BDA0001840253400000072
And
Figure BDA0001840253400000073
angular velocity
Figure BDA0001840253400000074
As a measurement value, a corresponding measurement model is established, and then a corresponding measurement equation is:
z＝Hx+v＝h(x,c)+v (30)
wherein the content of the first and second substances,
Figure BDA0001840253400000075
wherein H is an observation matrix of a measurement equation, and v is zero-mean Gaussian white noise; the state equation of the induction motor system is a nonlinear equation, and the measurement equation is a linear equation, so that the whole induction motor system is a nonlinear system.
Step (three): establishing a discretization state equation and a measurement equation
Discretizing the state equation (28) of the induction motor to obtain a discrete state equation:
Figure BDA0001840253400000076
wherein h is 0.0001[ s ] is the time interval between each step of sampling;
then the discrete induction machine state equation and the measurement equation can be obtained by (28) and (30):
xk＝f(xk-1,c,uk-1)+wk-1 (33)
zk＝h(xk,c)+vk (34)
wherein, wkAnd vkAre mutually independent zero-mean white Gaussian noise sequences, and wkAnd vkRespectively has a variance of QkAnd RkAnd satisfy
Figure BDA0001840253400000081
Wherein, deltakjIs a function of Kronecker delta, delta when k is j kj1 is ═ 1; when k ≠ j, δkj＝0；
Through secret experiment, the system noise variance matrix Q obtained by the inventorkSum measure noise variance matrix RkThe matrix is as follows:
Figure BDA0001840253400000082
the number of observation times is N-50, and the total sampling time is t-1 s.
Step (IV): and (3) performing weak-sensitive Kalman filtering on the dispersed state equation and measurement equation to output the stator current, the rotor flux linkage and the angular speed of the induction motor.
1. Respectively initializing the state of discrete state equation and measurement equation and state error variance matrix
Figure BDA0001840253400000083
Figure BDA0001840253400000084
Wherein, the initial state
Figure BDA0001840253400000085
Initial error variance matrix
Figure BDA0001840253400000086
2. Calculating state and metrology set points and covariance and metrology variance
Let step k-1 (i.e., t)k-1Time of day) state estimateAnd error variance matrix are respectively
Figure BDA0001840253400000087
And
Figure BDA0001840253400000088
then step k (i.e., t)kTime of day) are:
Figure BDA0001840253400000089
where the superscript "+" indicates its posterior estimate,
Figure BDA00018402534000000810
is an error variance matrix
Figure BDA00018402534000000811
J-th column of square root of (1), satisfy
Figure BDA00018402534000000812
m is 40 set points of sampling;
the set points after nonlinear function transfer are:
Figure BDA0001840253400000091
the measurement rendezvous point is calculated by the transmitted state rendezvous point and can be obtained by:
Figure BDA0001840253400000092
then the corresponding prior state estimation and measurement mean value are:
Figure BDA0001840253400000093
Figure BDA0001840253400000094
wherein the superscript "-" represents a prior estimate of the variable;
then covariance of state and measurements
Figure BDA0001840253400000095
And measure variance
Figure BDA0001840253400000096
Figure BDA0001840253400000097
Figure BDA0001840253400000098
Wherein the content of the first and second substances,
Figure BDA0001840253400000099
is a state error matrix, i.e. the state value of each rendezvous point
Figure BDA00018402534000000910
And average value
Figure BDA00018402534000000911
The difference between them;
Figure BDA00018402534000000912
for measuring error matrices, i.e. measured values at each set point
Figure BDA00018402534000000913
And post-transfer average
Figure BDA00018402534000000914
Is defined as:
Figure BDA00018402534000000915
Figure BDA00018402534000000916
3. sensitivity propagation of rendezvous
First, the sensitivity of the set point of step k-1 is calculated:
Figure BDA00018402534000000917
wherein i is the number of uncertain parameters;
second, propagation rendezvous sensitivity:
Figure BDA00018402534000000918
Figure BDA00018402534000000919
then, the prior state and the sensitivity of the measurement are calculated separately:
Figure BDA00018402534000000920
Figure BDA00018402534000000921
4. kalman gain K for calculating weak sensitive ensemble Kalman filteringk
Figure BDA0001840253400000101
Wherein, Wi,kAnd taking the weight of the ith uncertain parameter as the variance of the uncertain parameter.
5. Computing sensitivity matrices
Figure BDA0001840253400000102
6. State estimation of step k
Figure BDA0001840253400000103
And (5) performing loop iteration in the 6 steps to obtain a real-time state monitoring result of the induction motor, wherein the real-time state monitoring result comprises stator current, rotor flux linkage and angular speed. The sampling time is h is 0.0001[ s ], when k is 1, the corresponding time is T is 0.0000[ s ]; when k is 2, the corresponding time is T0.0001 [ s ], the corresponding time of each step, and so on.
The invention is a model and a simulation which are carried out on MATLAB (R2016b) software, and the simulation is carried out on a computer with a CPU of i5-7400 and a memory of 8G. In the simulation process, a simulation model is built on MATLAB (R2016b) software through programming, as shown in FIG. 3, initial data is input (as shown in the above specific implementation process), and then calculation is performed through running MATLAB (R2016b) software. Fig. 4 to 8 are each obtained by MATLAB (R2016b) simulation calculation.
The results of real-time state monitoring of stator current, rotor flux linkage and angular velocity parameters of the induction motor by using the method of the invention and the EnKF conventional method in the field are compared as follows:
for the state monitoring of the stator current, the root mean square error comparison graph of the EnKF monitoring result and the invention is shown in FIG. 4 and FIG. 5;
for the state monitoring of the rotor flux linkage, the root mean square error comparison graph of the EnKF monitoring result and the invention is shown in FIG. 6 and FIG. 7;
for the state monitoring of the angular velocity, a comparison graph of the root mean square error of the results of the invention and EnKF monitoring is shown in FIG. 8;
it can be seen from the above figures that the root mean square error value of the present invention is smaller and has better accuracy.
While the present invention has been described in detail with reference to the drawings and the embodiments, those skilled in the art will understand that various specific parameters in the above embodiments can be changed without departing from the spirit of the present invention, and a plurality of specific embodiments are formed, which are common variation ranges of the present invention, and will not be described in detail herein.

Claims (3)

1. A method for monitoring the state of an induction motor based on weak-sensitive ensemble Kalman filtering is characterized by comprising the following steps:
(1) obtaining a first stator current x of an induction motor system1A second stator current x2First rotor flux linkage x3Second rotor flux linkage x4Angular velocity x5Rotor inertia J, pole pair number p, and rotor time constant TrMotor no-load leakage magnetic coefficient sigma, inverse lambda of instantaneous time constant and first stator voltage control input u1A second stator voltage control input u2Rotor inductance LsStator inductance LrMutual inductance LmFixed parameters
Figure FDA0002608003670000011
In an induction motor system, a first stator current x is taken1A second stator current x2First rotor flux linkage x3Second rotor flux linkage x4Angular velocity x5Constructing a state vector x ═ x1,x2,x3,x4,x5]TThen, the state equation of the induction motor system is established as follows:
Figure FDA0002608003670000012
wherein x is1Is the first stator current, x2Is the second stator current, x3Is the first rotor flux linkage, x4Is the second rotor flux linkage, x5Is the angular velocity; j is rotor inertia, p is pole pair number, TrIs the rotor time constant, σIs the no-load leakage coefficient of the motor, K is a fixed parameter, and lambda is the reciprocal of the instantaneous time constant; u. of1Is a first stator voltage control input, u2Is a second stator voltage control input; c ═ c1 c2]Is an uncertain parameter vector, c1And c2Rotor resistance and stator resistance, respectively; w is zero-mean white gaussian noise;
measuring a first stator current of an induction motor system at constant sampling time intervals h
Figure FDA0002608003670000013
Second stator current
Figure FDA0002608003670000014
And angular velocity
Figure FDA0002608003670000015
Establishing a measurement equation of an induction motor system:
z＝Hx+v＝h(x,c)+v (2)
wherein the content of the first and second substances,
Figure FDA0002608003670000016
wherein H is an observation matrix of a measurement equation, and v is zero-mean Gaussian white noise;
discretizing the state equation (1) of the induction motor system to obtain a discrete state equation of the induction motor system
Figure FDA0002608003670000021
h corresponds to the sampling time interval of the step of constructing the metrology equation,
Figure FDA0002608003670000022
is tk-1The first stator voltage at a time controls the input,
Figure FDA0002608003670000023
is tk-1A second stator voltage control input at a time;
establishing an induction motor system state model based on the discrete state equation and the measurement equation of the induction motor system:
xk＝f(xk-1,c,uk-1)+wk-1 (5)
zk＝h(xk,c)+vk (6)
wherein, wkAnd vkAre mutually independent zero-mean white Gaussian noise sequences, and wkRespectively has a variance of Qk，vkHas a variance of RkAnd satisfy
Figure FDA0002608003670000024
Wherein, deltakjIs a function of Kronecker delta, delta when k is jkj1 is ═ 1; when k ≠ j, δkj＝0；
System noise variance matrix Q of induction motor system model obtained by statistical methodkSum measure noise variance matrix Rk；
(2) Processing the dispersed state equation and the measurement equation, and outputting the stator current, the rotor flux linkage and the angular speed of the induction motor;
initializing a state model matched with the induction motor system
Figure FDA0002608003670000025
Figure FDA0002608003670000026
Wherein, the initial state
Figure FDA0002608003670000027
Initial error variance matrix
Figure FDA0002608003670000028
P0、QkAnd RkAre all unrelated;
second, calculate the set point of the state and measurement and the covariance and measurement variance
Setting the state estimation value and the error variance matrix of the step k-1 as
Figure FDA0002608003670000031
And
Figure FDA0002608003670000032
the set point of the k step is:
Figure FDA0002608003670000033
where the superscript "+" indicates its posterior estimate,
Figure FDA0002608003670000034
is an error variance matrix
Figure FDA0002608003670000035
J-th column of square root of (1), satisfy
Figure FDA0002608003670000036
m is 40 set points of sampling;
the set points after nonlinear function transfer are:
Figure FDA0002608003670000037
the measurement rendezvous point is calculated by the transmitted state rendezvous point and can be obtained by:
Figure FDA0002608003670000038
then the corresponding prior state estimation and measurement mean value are:
Figure FDA0002608003670000039
Figure FDA00026080036700000310
wherein the superscript "-" represents a prior estimate of the variable;
then covariance of state and measurements
Figure FDA00026080036700000311
And measure variance
Figure FDA00026080036700000312
Figure FDA00026080036700000313
Figure FDA00026080036700000314
Wherein the content of the first and second substances,
Figure FDA00026080036700000315
is a state error matrix, i.e. the state value of each rendezvous point
Figure FDA00026080036700000316
And average value
Figure FDA00026080036700000317
The difference between them;
Figure FDA00026080036700000318
for measuring error matrices, i.e. measured values at each set point
Figure FDA00026080036700000319
And post-transfer average
Figure FDA00026080036700000320
Is defined as:
Figure FDA00026080036700000321
Figure FDA00026080036700000322
sensitive propagation of rendezvous
First, the sensitivity of the set point of step k-1 is calculated:
Figure FDA00026080036700000323
wherein i is the number of uncertain parameters;
second, propagation rendezvous sensitivity:
Figure FDA00026080036700000324
Figure FDA0002608003670000041
then, the prior state and the sensitivity of the measurement are calculated separately:
Figure FDA0002608003670000042
Figure FDA0002608003670000043
fourthly, calculating the Kalman gain K of the weak sensitive ensemble Kalman filteringk
Figure FDA0002608003670000044
Wherein, Wi,kTaking the weight of the ith uncertain parameter as the variance of the uncertain parameter;
calculating sensitivity matrix
Figure FDA0002608003670000045
State estimation of the k step
Figure FDA0002608003670000046
Performing loop iteration in the 6 steps to obtain a real-time state monitoring result of the induction motor, wherein the real-time state monitoring result comprises a first stator current x1A second stator current x2First rotor flux linkage x3Second rotor flux linkage x4Angular velocity x5。
2. The method of claim 1 in which the rotor time constant T is in the equation of state of the induction machine systemrMotor no-load leakage coefficient sigma, reciprocal lambda of instantaneous time constant tkFirst stator voltage control input of time
Figure FDA0002608003670000047
tkSecond stator voltage control input of time of day
Figure FDA0002608003670000048
Are obtained by the following formulas:
Figure FDA0002608003670000049
wherein k corresponds to tkThe number of steps of the time.
3. The method of claim 1 in which the sampling interval h is 0.0001[ s ]]Rotor inductance Ls＝0.0699[H]Stator inductance Lr＝0.0699[H]Mutual inductance Lm＝0.068[H]The rotor inertia J is 0.0586[ kg m [ ]2]The number of pole pairs p is 1, and is obtained by counting the number of observation times N is 50 and the total sampling time t is 1s
Figure FDA0002608003670000051
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