CN111208425B - Method for constructing high-precision asynchronous motor system state model and asynchronous motor state detection method - Google Patents
Method for constructing high-precision asynchronous motor system state model and asynchronous motor state detection method Download PDFInfo
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Abstract
The invention discloses a method for constructing a high-precision asynchronous motor system state model based on weak-sensitive rank Kalman filtering and an asynchronous motor state detection method, and aims to solve the technical problems of inaccurate asynchronous motor state detection and low precision in the prior art. The invention uses the weak-sensitive optimal control method to solve the uncertainty of the parameters in the asynchronous motor system, combines the mean square error cost function and the weak-sensitive cost function of the RKF through the sensitivity weight coefficient to form a new cost function, then minimizes the cost function to obtain the optimal gain of the weak-sensitive rank Kalman filtering, weakens the sensitivity of the state estimation in the asynchronous motor system to the uncertain parameters, and improves the state monitoring precision.
Description
Technical Field
The invention relates to the technical field of asynchronous motor state detection, in particular to a method for constructing a high-precision asynchronous motor system state model based on weak-sensitive rank Kalman filtering and an asynchronous motor state detection method.
Background
The asynchronous motor has the advantages of simple structure, firmness, durability, reliable operation, higher operation efficiency and the like, and is widely concerned in the fields of theoretical research and practical application. Has wide application in the industrial production field and the agricultural production field.
Because the magnetic linkage and the rotating speed are not easy to be measured, the current detection method for the alternating current speed regulating system of the asynchronous motor indirectly detects the alternating current speed regulating system of the asynchronous motor by detecting physical quantities which are easy to measure, such as voltage, current and the like at the stator end of the motor. Therefore, a speed sensorless control technology of the asynchronous motor is generated, namely, the flux linkage and the rotating speed are calculated in real time by using a state estimation method, so that the flux linkage and the rotating speed are accurately controlled. Therefore, the control without a speed sensor is the research focus of the asynchronous motor, and the detection of the rotating speed of the asynchronous motor and the detection of the rotor flux linkage are the key problems to be solved by the control system without the speed sensor of the asynchronous motor.
Rank Kalman Filtering (RKF) is a filtering method which is provided based on rank statistic correlation principle and further provided on the basis of the rank sampling method. The rank Kalman filtering method is not only suitable for Gaussian distribution, but also suitable for nonlinear filtering of non-Gaussian distribution such as common multivariate t distribution, multivariate extreme value distribution and the like. However, the mathematical model established by the asynchronous motor system in engineering practice often contains uncertainty of parameters (such as stator resistance and rotor resistance), and when the RKF is adopted to detect the state of the asynchronous motor (stator current, rotor flux linkage and angular velocity), the uncertainty of the parameters will greatly reduce the accuracy of the detection result, and even cause divergence.
Disclosure of Invention
The invention aims to solve the technical problems of inaccurate state detection and low precision of an asynchronous motor in the prior art by providing a method for constructing a high-precision asynchronous motor system state model based on weak-sensitive rank Kalman filtering and a method for detecting the state of the asynchronous motor.
In order to solve the technical problems, the invention adopts the following technical scheme:
a method for constructing a high-precision asynchronous motor system state model is designed, and comprises the following steps:
(1) in the asynchronous motor system to be detected, a first stator current x is used1A second stator current x2First rotor flux linkage x3Second rotor flux linkage x4Angular velocity x5Constructing a state vector x ═ x1,x2,x3,x4,x5]TEstablishing a state equation of the asynchronous motor system;
(2) measuring a first stator current of an asynchronous machine system with a sampling time dt
And a first rotor flux linkage
Establishing a measurement equation of an asynchronous motor system;
(3) discretizing the state equation of the obtained asynchronous motor system to obtain a discrete state equation;
(4) and (3) constructing a state model of the asynchronous motor system based on the discrete state equation in the step (3) and the measurement equation in the step (2).
Preferably, in the step (1), the state equation of the asynchronous motor system is established as follows:
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; t isLIs the load torque, J is the rotor inertia, pnIs the number of pole pairs, TrIs the time constant of the rotor, sigma is the no-load leakage coefficient of the motor; u. of1Is a first stator voltage control input, u2Is a second stator voltage control input; l issIs stator inductance, LrIs rotor inductance, LmIs the stator and rotor mutual inductance; c ═ Rs,Rr]To have uncertain parametersGathering; w is zero-mean white Gaussian noise, x ═ x1,x2,x3,x4,x5]TAnd is the state vector of the asynchronous motor system. c ═ c1 c2]Is an uncertain parameter vector, c1And c2Stator resistance and rotor resistance, respectively; u ═ u1 u2]And is the stator voltage control input.
Preferably, in the equation of state of the asynchronous machine system, the rotor time constant TrAnd the motor no-load magnetic leakage coefficient sigma is obtained by the following formula:
tkfirst stator voltage control input of time
tkSecond stator voltage control input of time of day
The following method was used:
wherein k corresponds to tkThe number of steps of the time; u shapeNBeing three-phase symmetrical power supplyA rated voltage; f is the supply frequency; dt corresponds to the sampling time interval of the step of constructing the metrology equation.
Preferably, in the step (2), the established measurement equation of the asynchronous motor system is as follows:
z＝Hx+v＝h(x,c)+v
wherein,
where v is zero-mean white gaussian noise and H is the observation matrix of the measurement equation.
Preferably, in the step (3), the discrete state equation is:
where dt is the sampling time,
is tkA state matrix of the motor at the moment; t isLIs the load torque, J is the rotor inertia, pnIs the number of pole pairs, TrIs the time constant of the rotor, and sigma is the no-load leakage flux of the motorA coefficient; l issIs stator inductance, LrIs rotor inductance, LmIs the stator and rotor mutual inductance.
Preferably, in the step (4), the established state model equation of the asynchronous motor system is as follows:
xk＝f(xk-1,c,uk-1)+wk-1
zk＝h(xk,c)+vk
wherein, wkAnd vkAre independent zero mean white Gaussian noise sequences, wjAnd vjIs a zero mean Gaussian white noise sequence independent of each other at the j step, and wkHas a variance of Qk，vkHas a variance of RkAnd satisfy
Wherein, deltakjIs a function of Kronecker delta, delta when k is jkj1 is ═ 1; when k ≠ j, δkj＝0。
The method for detecting the state of the high-precision asynchronous motor is characterized in that a discrete state equation and a measurement equation contained in a state model of the asynchronous motor system are subjected to weak-sensitive rank Kalman filtering processing, and state parameters of the asynchronous motor during operation are output.
Preferably, the weak-sensitive rank kalman filtering processing method includes:
(1) separately initializing the discrete equation of state, the state of the metrology equation, and the state error variance matrix of claim 1 using:
wherein, the initial state
Initial error variance matrix
P0、QkAnd RkAre all unrelated; qkAnd RkRespectively are the independent zero mean value Gaussian white noise sequences w of the kth stepkAnd vkThe variance of (a);
(2) calculating rank sampling points and covariance and measurement variance of state and measurement:
setting the state estimation value and the error variance matrix of the step k-1 as
And
the rank sampling point set of the k step is:
where the superscript "+" indicates its posterior estimate,
is an error variance matrix
J-th column of square root of (1), satisfy
n-5 is the dimension of state x;
is composed of
The jth column vector of the square root;
is a standard normal offset, i is the number of uncertain parameters; computing p with median ranki＝(i+2.7)/5.4i＝1,2，p1＝0.6852p2＝0.8704，
Taking 1 as a sampling point correction coefficient r;
and (3) time updating: the state is predicted as:
wherein,
the rank sampling point after nonlinear function transfer is obtained by the following formula:
wherein,
is the mean value of the uncertain parameter, uk-1The stator voltage control input of the step k-1 is input;
variance matrix of one-step prediction error:
wherein the superscript "-" represents a prior estimate of the variable; r is*Taking 1 as a covariance correction coefficient; ω is the covariance weight coefficient:
Qk-1zero mean white Gaussian noise w as the system state equation of step k-1k-1The variance of (a);
measurement updating: and (5) re-rank sampling to obtain a sampling point set:
measuring an average value:
and (3) state estimation:
wherein z iskThe measurement equation in the k step is shown;
variance matrix of estimation error:
wherein,
the variance matrix is estimated a priori at step k,
estimating a variance matrix for the posteriori of the k step;
in the formula:
wherein, Pxz,kIs the covariance of the state and measurements, Pzz,kMeasuring the variance; rkIn the k step system stateZero-mean white gaussian noise v of the equation of statekThe variance of (a);
(3) sensitivity propagation of rank sampling points:
1) the sensitivity of the k-1 step rank sampling points was calculated using the following formula:
wherein,
sensitivity of the posterior state of the k-1 step;
is composed of
The jth column vector of the square root;
is a standard normal offset, i is the number of uncertain parameters; computing p with median ranki＝(i+2.7)/5.4i＝1,2，p1＝0.6852p2＝0.8704，
Taking 1 as a sampling point correction coefficient r;
updating a rank sampling point set:
cifor the i-th uncertain parameter,
is the mean value of the uncertain parameter, uk-1The stator voltage control input of the step k-1 is input;
2) calculating the sensitivity of the prior state estimate and the prior covariance matrix using the following equation
Wherein,
for the sensitivity of the a priori state estimation,
is a prior covariance matrix; r is*Taking 1 as a covariance correction coefficient; ω is the covariance weight coefficient:
3) calculating the re-rank sample set and predicting the sensitivity of the metrology rank samples using the equation
Wherein,
for the sensitivity of the a priori state estimation,
is the mean value of the uncertain parameter, ukStator voltage control input for step k
Is a standard normal offset, i is the number of uncertain parameters; using a central positionRank calculation pi＝(i+2.7)/5.4i＝1,2，p1＝0.6852p2＝0.8704，
Taking 1 as a sampling point correction coefficient r;
the sensitivity of the measured mean was calculated using the following formula:
4) the state and metrology covariance and sensitivity of metrology variance are calculated using the following equations:
wherein,
is a prior measurement matrix, gammai,kSensitivity of the measured mean value;
5) the sensitivities of the state estimate and the state error variance matrix are calculated using the following equation:
in the formula:
in the formula:
wherein
Is an oblique symmetric matrix satisfying gammaTAll of ═ Γ, Ψ, and Θ are nonsingular matrices, and satisfy
KkA Kalman gain for a weakly sensitive rank Kalman filter;
(4) calculating the Kalman gain K of the weak-sensitive rank Kalman filter by adopting the following formulak
Wherein l is the number of uncertain parameters, Wi,kTaking the weight of the ith uncertain parameter as the variance of the uncertain parameter;
sensitivity cost function:
wherein, Tr (P)k) Representative matrix PkThe trace of (2);
(5) the sensitivity matrix was calculated using the following formula:
(6) and (4) carrying out state estimation of the k step by adopting the following formula:
(7) and (5) circularly iterating the steps (1) to (6) to obtain the real-time state parameters of the asynchronous motor.
Compared with the prior art, the invention has the beneficial technical effects that:
the invention uses a weak-sensitive optimal control method to solve the uncertainty of parameters in the asynchronous motor system, combines the mean square error cost function and the weak-sensitive cost function of the RKF through a sensitivity weight coefficient to form a new cost function, minimizes the cost function to obtain the optimal gain of weak-sensitive rank Kalman filtering, weakens the sensitivity of state estimation in the asynchronous motor system to the uncertain parameters, and improves the state monitoring precision of the asynchronous motor system.
Drawings
Fig. 1 is a flow chart of an asynchronous motor state monitoring method based on weak-sensitive rank kalman filtering.
Fig. 2 is a schematic diagram of a weakly sensitive rank kalman filter.
FIG. 3 is a graph comparing the root mean square error of the state monitoring results of the embodiment method and the RKF for an asynchronous motor during no-load starting of the asynchronous motor;
FIG. 4 is a graph comparing the root mean square error of the state monitoring results of the asynchronous motor during three-phase short circuit and recovery of the asynchronous motor of the method of the embodiment with RKF;
in fig. 3 and 4, perf RKF represents the detection method in the non-interfering ideal state; imp RKF represents an existing conventional detection method; DRKF represents the detection method of the example.
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 instruments and devices referred to in the following examples are conventional instruments and devices unless otherwise specified; the related reagents are all conventional reagents in the market, if not specifically indicated; the test methods involved are conventional methods unless otherwise specified.
Example (b): asynchronous motor state detection method based on weak-sensitivity rank Kalman filtering
The detection method comprises an asynchronous motor no-load starting process, a three-phase short circuit fault and a recovery process thereof. The flow chart is shown in figure 1, and the schematic diagram of the weak-sensitive rank Kalman filtering is shown in figure 2.
The detection method of the no-load starting state of the asynchronous motor comprises the following steps:
the method comprises the following steps: in an asynchronous motor system, a state vector x is taken as [ x ]1,x2,x3,x4,x5]TThen the state equation is:
wherein x is1And x2Is the stator current, x3And x4Is the rotor flux linkage, x5Is the angular velocity; j is rotor inertia; p is a radical ofnIs the number of pole pairs; u. of1And u2Is the stator voltage control input; c ═ c1 c2]Is an uncertain parameter vector, c1And c2Stator resistance and rotor resistance, respectively; w is zero-mean white gaussian noise; other model parameters were:
wherein, the rotor inductance Ls＝0.265[H]Stator inductance Lr＝0.265[H]Mutual inductance Lm＝0.253[H]The rotor inertia J is 0.02[ kg. m ]2]Number of pole pairs pn2, k corresponds to the number of steps at time tk; u shapeNRated voltage of three-phase symmetrical power supply; f is the supply frequency; dt corresponds to the sampling time interval of the step of constructing the measurement equation; u. ofn＝[un1,un2,un3]T。
Step two: establishing a measurement equation for an asynchronous motor system
Stator current to be measured
And rotor flux linkage
Angular velocity
As a measurement value, a corresponding measurement model is established, and then a corresponding measurement equation is:
z＝Hx+v＝h(x,c)+v (4)
wherein,
wherein H is an observation matrix of a measurement equation, and v is zero-mean Gaussian white noise; the state equation of the asynchronous motor system is a nonlinear equation, and the measurement equation is a linear equation, so that the whole asynchronous motor system is a nonlinear system.
Step three: establishing a discretization state equation and a measurement equation
Discretizing the state equation (1) of the asynchronous motor to obtain a discrete state equation:
dt corresponds to the sampling time interval of the step of constructing the metrology equation,
is tk-1The first stator voltage at a time controls the input,
is tk-1A second stator voltage control input at a time;
then the discrete asynchronous motor state equation and the measurement equation can be obtained by the arrangement of the equations (1) and (4):
xk＝f(xk-1,c,uk-1)+wk-1 (7)
zk＝h(xk,c)+vk (8)
wherein, wkAnd vkAre mutually independent zero-mean white Gaussian noise sequences, and wkAnd vkRespectively has a variance of QkAnd RkAnd satisfy
Wherein, deltakjIs a function of Kronecker delta, delta when k is jkj1 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:
wherein, the observation frequency is N-150, and the total sampling time is t-0.15 s
Step four: and (3) performing weak-sensitive rank Kalman filtering on the dispersed state equation and the measurement equation, and outputting the stator current, the rotor flux linkage and the angular speed of the asynchronous motor.
1. Respectively initializing the state of discrete state equation and measurement equation and state error variance matrix
Wherein, the initial state
Initial error variance matrix
P0、QkAnd RkAre all unrelated;
2. rank sampling points and covariance and metrology variances for computing states and metrology
Setting the state estimation value and the error variance matrix of the step k-1 as
And
the rank sampling point set of the k step is:
where the superscript "+" indicates its posterior estimate,
is an error variance matrix
J-th column of square root of (1), satisfy
n-5 is the dimension of state x;
and (3) time updating: the state is predicted as:
in the formula:
variance matrix of one-step prediction error:
wherein the superscript "-" represents a prior estimate of the variable;
measurement updating: and (5) re-rank sampling to obtain a sampling point set:
measuring an average value:
and (3) state estimation:
variance matrix of estimation error:
in the formula:
wherein, Pxz,kIs the covariance of the state and measurements, Pzz,kMeasuring the variance;
3. sensitivity propagation of rank sampling points
1) Calculating the sensitivity of the rank sampling point of the k-1 step:
updating a rank sampling point set:
2) calculating the sensitivity of the prior state estimate and the prior covariance matrix
3) Calculating re-rank sample set and predicting sensitivity of metrology rank samples
Calculating the sensitivity of the measured mean value:
4) computing the state and metrology covariance and sensitivity of metrology variance:
5) calculating the sensitivity of the state estimate and the state error variance matrix:
in the formula:
in the formula:
wherein
Is an oblique symmetric matrix satisfying gammaTAll of ═ Γ, Ψ, and Θ are nonsingular matrices, and satisfy
4. Kalman gain K for calculating weak-sensitive rank Kalman filteringk
Wherein, Wi,kTaking the weight of the ith uncertain parameter as the variance of the uncertain parameter;
sensitivity cost function:
5. computing sensitivity matrices
6. State estimation of step k
Repeating the above 6 steps to obtainReal-time status monitoring results to the asynchronous machine, the real-time status monitoring results including a first stator current x1A second stator current x2First rotor flux linkage x3Second rotor flux linkage x4Angular velocity x5. The sampling time dt is 0.001[ s ]]When k is 1, the corresponding time is T0.000 [ s ]](ii) a When k is 2, the corresponding time T is 0.001[ s ]]And the corresponding time of each step is analogized.
And (II) the three-phase short-circuit fault and the recovery process thereof are carried out on the basis of the no-load starting to reach the stable state.
The two processes differ only in stator voltage input and sampling time. At t1At time, a three-phase short-circuit fault occurs, at t2And (3) repairing the fault at any moment, wherein the voltage model parameters in the process are as follows:
wherein k corresponds to tkThe number of steps of the time; u shapeNRated voltage of three-phase symmetrical power supply;
is tkA first stator voltage control input at a time,
Is tkA second stator voltage control input at a time; f isThe frequency of the power supply; dt corresponds to the sampling time interval of the step of constructing the measurement equation; u. ofn＝[un1,un2,un3]T。
Test example:
and comparing the detection method of the embodiment with the real-time state monitoring result of the stator current, the rotor flux linkage and the angular speed parameter of the asynchronous motor by using the conventional method RKF in the field.
Modeling and simulation were performed on MATLAB (R2016b) software and run 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, initial data is input (shown in the specific implementation process), and then calculation is carried out through running MATLAB (R2016b) software.
In the specific implementation process, the observation frequency is N equal to 350, the total sampling time is t equal to 0.35s, and the three-phase short-circuit fault occurrence time t is10.15s, fault repair time t2＝0.25s。
The root mean square error of the detection method of the embodiment and the RKF monitoring result is compared as shown in fig. 3 for the state detection of the asynchronous motor during the no-load starting process of the asynchronous motor by obtaining the result through MATLAB (R2016b) simulation calculation.
The root mean square error ratio of the detection method of the embodiment to the RKF monitoring result is shown in fig. 4 for the state monitoring of the asynchronous motor during the three-phase short circuit and the recovery process thereof.
Therefore, the detection method of the embodiment has smaller root mean square error value and 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 (6)
1. A high-precision asynchronous motor state detection method is characterized in that a discrete state equation and a measurement equation contained in an asynchronous motor system state model are subjected to weak-sensitive rank Kalman filtering processing, and state parameters of an asynchronous motor during operation are output;
the method comprises the following steps of:
(1) in the asynchronous motor system to be detected, a first stator current x is used1A second stator current x2First rotor flux linkage x3Second rotor flux linkage x4Angular velocity x5Constructing a state vector x ═ x1,x2,x3,x4,x5]TEstablishing a state equation of the asynchronous motor system;
(2) measuring a first stator current of an asynchronous machine system with a sampling time dt
And a first rotor flux linkage
Establishing a measurement equation of an asynchronous motor system;
(3) discretizing the state equation of the obtained asynchronous motor system to obtain a discrete state equation;
(4) constructing a state model of the asynchronous motor system based on the discrete state equation in the step (3) and the measurement equation in the step (2);
the weakly sensitive rank Kalman filtering processing comprises the following steps:
respectively initializing the state of the discrete state equation and the measurement equation and the state error variance matrix by adopting the following formula:
wherein, the initial state
Initial error variance matrix
P0、QkAnd RkAre all unrelated; qkAnd RkRespectively are the independent zero mean value Gaussian white noise sequences w of the kth stepkAnd vkThe variance of (a);
(II) calculating rank sampling points and covariance and measurement variance of the states and measurements:
setting the state estimation value and the error variance matrix of the step k-1 as
And
the rank sampling point set of the k step is:
wherein the superscript "+" indicates its posterior estimate; chi shapej,k-1Is composed of
The j-th sampling point of (2) has 4n sample points, and n is 5, which is the dimension of the state x;
is composed of
The jth column vector of the square root;
is a standard normal offset, i is the number of uncertain parameters; computing p with median ranki＝(i+2.7)/5.4i＝1,2，p1＝0.6852p2＝0.8704，
Taking 1 as a sampling point correction coefficient r;
and (3) time updating: the state is predicted as:
wherein,
the rank sampling point after nonlinear function transfer is obtained by the following formula:
wherein,
is the mean value of the uncertain parameter, uk-1The stator voltage control input of the step k-1 is input;
variance matrix of one-step prediction error:
wherein the superscript "-" represents a prior estimate of the variable; r is*The covariance correction coefficient can be 1; ω is the covariance weight coefficient:
Qk-1is the zero mean value of the state equation of the k-1 step systemWhite gaussian noise wk-1The variance of (a);
measurement updating: re-rank sampling yields a set of sample points:
measuring an average value:
and (3) state estimation:
wherein z iskThe measurement equation in the k step is shown;
variance matrix of estimation error:
wherein,
the variance matrix is estimated a priori at step k,
estimating a variance matrix for the posteriori of the k step;
in the formula:
wherein, Pxz,kIs the covariance of the state and measurements, Pzz,kMeasuring the variance; wherein R iskZero mean white Gaussian noise v as the k-th system state equationkThe variance of (a);
(iii) sensitivity propagation of rank sampling points:
1) the sensitivity of the k-1 step rank sampling points was calculated using the following formula:
wherein,
sensitivity of the posterior state of the k-1 step;
is composed of
The jth column vector of the square root; u. ofpiIs a standard normal offset, i is the number of uncertain parameters; computing p with median ranki＝(i+2.7)/5.4i＝1,2，p1＝0.6852p2＝0.8704，
Taking 1 as a sampling point correction coefficient r;
updating a rank sampling point set:
wherein, ciFor the i-th uncertain parameter,
is the mean value of the uncertain parameter, uk-1For step k-1A sub-voltage control input;
2) calculating the sensitivity of the prior state estimate and the prior covariance matrix using the following equation
Wherein,
for the sensitivity of the a priori state estimation,
is a prior covariance matrix; r is*The covariance correction coefficient can be 1; ω is the covariance weight coefficient:
3) calculating the re-rank sample set and predicting the sensitivity of the metrology rank samples using the equation
Wherein,
for the sensitivity of the a priori state estimation,
is the mean value of the uncertain parameter, ukStator voltage control input for step k
Is a standard normal offset, i is the number of uncertain parameters; computing p with median ranki＝(i+2.7)/5.4i＝1,2，p1＝0.6852p2＝0.8704，
Taking 1 as a sampling point correction coefficient r;
the sensitivity of the measured mean was calculated using the following formula:
4) the state and metrology covariance and sensitivity of metrology variance are calculated using the following equations:
wherein,
is a prior measurement matrix, gammai,kSensitivity of the measured mean value;
5) the sensitivities of the state estimate and the state error variance matrix are calculated using the following equation:
in the formula:
in the formula:
wherein
Is an oblique symmetric matrix satisfying gammaTAll of ═ Γ, Ψ, and Θ are nonsingular matrices, and satisfy
KkA Kalman gain for a weakly sensitive rank Kalman filter;
(IV) calculating the Kalman gain K of the weak-sensitive rank Kalman filter by adopting the following formulak
Wherein l is the number of uncertain parameters, Wi,kTaking the weight of the ith uncertain parameter as the variance of the uncertain parameter;
sensitivity cost function:
wherein, Tr (P)k) Representative matrix PkThe trace of (2);
(v) calculating the sensitivity matrix using the following formula:
(VI) performing state estimation of the k step by adopting the following formula:
and (VII) circularly iterating the steps (I) to (VI) to obtain the real-time state parameters of the asynchronous motor.
2. A method for detecting the state of a high-precision asynchronous motor according to claim 1, wherein in the step (1), the state equation of the asynchronous motor system is established as follows:
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; t isLIs the load torque, J is the rotor inertia, pnIs the number of pole pairs, TrIs the time constant of the rotor, sigma is the no-load leakage coefficient of the motor; u. of1Is a first stator voltage control input, u2Is a second stator voltage control input; l issIs stator inductance, LrIs rotor inductance, LmIs the stator and rotor mutual inductance; c ═ Rs,Rr]As having an uncertain parameter set; w is zero-mean white gaussian noise; x ═ x1,x2,x3,x4,x5]TThe state vector is the state vector of the asynchronous motor system; c ═ c1 c2]Is an uncertain parameter vector, c1And c2Stator resistance and rotor resistance, respectively; u ═ u1 u2]And is the stator voltage control input.
3. A high accuracy asynchronous machine state detection method according to claim 2, characterized in that in the state equation of said asynchronous machine system, the rotor time constant TrAnd the motor no-load magnetic leakage coefficient sigma is obtained by the following formula:
tkfirst stator voltage control input of time
tkSecond stator voltage control input of time of day
The following method was used:
wherein k corresponds to tkThe number of steps of the time; u shapeNRated voltage of three-phase symmetrical power supply; f is the supply frequency; dt corresponds to the sampling time interval of the step of constructing the metrology equation.
4. A method for detecting the state of a high-precision asynchronous motor according to claim 1, wherein in the step (2), the measurement equation of the asynchronous motor system is established as follows:
z＝Hx+v＝h(x,c)+v
wherein,
where v is zero-mean white gaussian noise and H is the observation matrix of the measurement equation.
5. A high accuracy asynchronous motor state detection method according to claim 1, characterized in that in said step (3), the discrete state equation is:
where dt is the sampling time,
is tkA state matrix of the motor at the moment; t isLIs the load torque, J is the rotor inertia, pnIs the number of pole pairs, TrIs the time constant of the rotor, and sigma is the no-load leakage flux of the motorA coefficient;
is tk-1The first stator voltage at a time controls the input,
is tk-1A second stator voltage control input at a time; l issIs stator inductance, LrIs rotor inductance, LmIs the stator and rotor mutual inductance.
6. A method for detecting the state of a high-precision asynchronous motor according to claim 1, wherein in the step (4), the established state model equation of the asynchronous motor system is as follows:
xk＝f(xk-1,c,uk-1)+wk-1
zk＝h(xk,c)+vk
wherein, wkAnd vkIs a k-th independent zero mean Gaussian white noise sequence, wjAnd vjIs a zero mean Gaussian white noise sequence independent of each other at the j step, and wkHas a variance of Qk，vkHas a variance of RkAnd satisfy
Wherein, deltakjIs a function of Kronecker delta, delta when k is jkj1 is ═ 1; when k ≠ j, δkj＝0。
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