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 PDF

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CN111208425B
CN111208425B CN202010039328.XA CN202010039328A CN111208425B CN 111208425 B CN111208425 B CN 111208425B CN 202010039328 A CN202010039328 A CN 202010039328A CN 111208425 B CN111208425 B CN 111208425B
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姜素霞
韩东轩
安小宇
娄泰山
杨小亮
刘一君
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Abstract

本发明公开了一种基于弱敏秩卡尔曼滤波的高精度异步电机系统状态模型的构建方法及异步电机状态检测方法，旨在解决现有技术中异步电机状态检测不准确、精度低的技术问题。本发明使用弱敏最优控制方法来解决异步电机系统中参数的不确定性，并将RKF的均方误差代价函数和弱敏代价函数通过敏感性权重系数联合在一起组成新的代价函数，然后将该代价函数最小化获得弱敏秩卡尔曼滤波的最优增益，减弱异步电机系统中状态估计对不确定参数的敏感性，提高了状态监测精度。

Figure 202010039328

The invention discloses a construction method of a high-precision asynchronous motor system state model based on weakly sensitive rank Kalman filtering and an asynchronous motor state detection method, aiming to solve the technical problems of inaccurate and low-precision asynchronous motor state detection in the prior art . The invention uses the weak-sensitive optimal control method to solve the uncertainty of parameters in the asynchronous motor system, and combines the mean square error cost function of the RKF and the weak-sensitive cost function through the sensitivity weight coefficient to form a new cost function, and then This cost function is minimized to obtain the optimal gain of weakly sensitive rank Kalman filter, which reduces the sensitivity of state estimation to uncertain parameters in asynchronous motor systems and improves the accuracy of state monitoring.

Figure 202010039328

Description

高精度异步电机系统状态模型的构建方法及异步电机状态检 测方法Construction method of high-precision asynchronous motor system state model and asynchronous motor state detection method

技术领域technical field

本发明涉及异步电机状态检测技术领域，具体涉及一种基于弱敏秩卡尔曼滤波的高精度异步电机系统状态模型的构建方法及异步电机状态检测方法。The invention relates to the technical field of asynchronous motor state detection, in particular to a construction method of a high-precision asynchronous motor system state model based on weakly sensitive rank Kalman filtering and an asynchronous motor state detection method.

背景技术Background technique

异步电机有结构简单、坚固耐用、运行可靠、运行效率较高等优点，在理论研究和实际应用领域受到广泛关注。在工业生产领域和农业生产领域均有广泛应用。Asynchronous motors have the advantages of simple structure, sturdiness and durability, reliable operation and high operating efficiency, and have received extensive attention in the field of theoretical research and practical application. It is widely used in the field of industrial production and agricultural production.

由于磁链和转速不易测定，所以目前对异步电机交流调速系统的检测方法是通过检测电机定子端的电压和电流等容易测量的物理量对异步电机交流调速系统进行间接检测。由此产生了异步电机的无速度传感器控制技术，即利用状态估计的方法来实时计算磁链和转速，从而实现磁链和转速的精确控制。因此，无速度传感器的控制是异步电机的研究重点，而对异步电机转速的检测和转子磁链的检测是异步电机无速度传感器控制系统需要解决的关键问题。Because the flux linkage and rotational speed are not easy to measure, the current detection method for the AC speed control system of asynchronous motor is to indirectly detect the AC speed control system of asynchronous motor by detecting the easily measurable physical quantities such as the voltage and current of the stator terminal of the motor. Therefore, the sensorless control technology of the asynchronous motor is produced, that is, the method of state estimation is used to calculate the flux linkage and the rotational speed in real time, so as to realize the precise control of the flux linkage and the rotational speed. Therefore, the speed sensorless control is the research focus of the asynchronous motor, and the detection of the speed of the asynchronous motor and the detection of the rotor flux linkage are the key issues to be solved in the sensorless control system of the asynchronous motor.

秩卡尔曼滤波(RKF)是基于秩统计量相关原理提出一种秩采样方法，并在此基础上进一步提出的一种滤波方法。秩卡尔曼滤波方法不仅适用于高斯分布，也适用于常见的多元t分布、多元极值分布等非高斯分布的非线性滤波。但是工程实践中异步电机系统建立的数学模型往往含有参数(比如定子电阻和转子电阻等)不确定性，当采用RKF对异步电机状态(定子电流、转子磁链和角速度)进行检测时，这些参数不确定性将会极大地降低检测结果的精度，甚至会导致发散。Rank Kalman Filter (RKF) is a rank sampling method based on the correlation principle of rank statistics, and a filtering method further proposed on this basis. The rank Kalman filtering method is not only suitable for Gaussian distribution, but also for nonlinear filtering of non-Gaussian distributions such as common multivariate t distribution and multivariate extreme value distribution. However, the mathematical model established by the asynchronous motor system in engineering practice often contains uncertainties of parameters (such as stator resistance and rotor resistance, etc.) Uncertainty will greatly reduce the accuracy of detection results, and even lead to divergence.

发明内容SUMMARY OF THE INVENTION

本发明要解决的技术问题是提供一种基于弱敏秩卡尔曼滤波的高精度异步电机系统状态模型的构建方法及异步电机状态检测方法，以期解决现有技术中异步电机状态检测不准确、精度低的技术问题。The technical problem to be solved by the present invention is to provide a method for constructing a state model of a high-precision asynchronous motor system based on weakly sensitive rank Kalman filtering and a method for detecting the state of an asynchronous motor, in order to solve the inaccurate and precise detection of the state of an asynchronous motor in the prior art. Low technical issues.

为解决上述技术问题，本发明采用如下技术方案：In order to solve the above-mentioned technical problems, the present invention adopts the following technical solutions:

设计一种高精度异步电机系统状态模型的构建方法，包括以下步骤：A method for constructing a high-precision asynchronous motor system state model is designed, including the following steps:

(1)在待检测异步电机系统中，以第一定子电流x1、第二定子电流x2、第一转子磁链x3、第二转子磁链x4、角速度x5构建状态向量x＝[x1,x2,x3,x4,x5]T，建立异步电机系统的状态方程；(1) In the asynchronous motor system to be detected, the state vector x is constructed with the first stator current x 1 , the second stator current x 2 , the first rotor flux linkage x 3 , the second rotor flux linkage x 4 , and the angular velocity x 5 =[x 1 , x 2 , x 3 , x 4 , x 5 ] T , establish the state equation of the asynchronous motor system;

(2)以采样时间dt测量异步电机系统的第一定子电流

Figure BDA0002364989800000021
和第一转子磁链
Figure BDA0002364989800000022
建立异步电机系统的量测方程；(2) Measure the first stator current of the asynchronous motor system with the sampling time dt
Figure BDA0002364989800000021
and the first rotor flux linkage
Figure BDA0002364989800000022
Establish the measurement equation of the asynchronous motor system;

(3)对所得异步电机系统的状态方程进行离散化处理，获得离散状态方程；(3) Discretize the state equation of the obtained asynchronous motor system to obtain the discrete state equation;

(4)基于步骤(3)的离散状态方程与步骤(2)的量测方程构建立异步电机系统状态模型。(4) Based on the discrete state equation of step (3) and the measurement equation of step (2), a state model of the asynchronous motor system is established.

优选的，在所述步骤(1)中，所建立的异步电机系统的状态方程为：Preferably, in the step (1), the established state equation of the asynchronous motor system is:

Figure BDA0002364989800000023
Figure BDA0002364989800000023

其中，x1是第一定子电流，x2是第二定子电流，x3是第一转子磁链，x4是第二转子磁链，x5是角速度；TL是负载转矩，J是转子惯性，pn是极对数，Tr是转子时间常数，σ是电机空载漏磁系数；u1是第一定子电压控制输入，u2是第二定子电压控制输入；Ls是定子电感、Lr是转子电感、Lm是定子和转子互感；c＝[Rs,Rr]为具有不确定的参数集合；w是零均值高斯白噪声，x＝[x1,x2,x3,x4,x5]T，为异步电机系统的状态向量。c＝[c1 c2]，是不确定参数向量，c1和c2分别是定子电阻和转子电阻；u＝[u1 u2]，是定子电压控制输入。where x 1 is the first stator current, x 2 is the second stator current, x 3 is the first rotor flux linkage, x 4 is the second rotor flux linkage, x 5 is the angular velocity; T L is the load torque, J is the rotor inertia, p n is the number of pole pairs, T r is the rotor time constant, σ is the no-load flux leakage coefficient of the motor; u 1 is the first stator voltage control input, u 2 is the second stator voltage control input; L s is the stator inductance, L r is the rotor inductance, L m is the stator and rotor mutual inductance; c=[R s , R r ] is the parameter set with uncertainty; w is the zero-mean Gaussian white noise, x=[x 1 , x 2 , x 3 , x 4 , x 5 ] T , is the state vector of the asynchronous motor system. c=[c 1 c 2 ], is the uncertain parameter vector, c 1 and c 2 are the stator resistance and rotor resistance, respectively; u=[u 1 u 2 ], is the stator voltage control input.

优选的，在所述异步电机系统的状态方程中，转子时间常数Tr、电机空载漏磁系数σ通过下述式而得：Preferably, in the state equation of the asynchronous motor system, the rotor time constant Tr and the motor no-load flux leakage coefficient σ are obtained by the following formula:

Figure BDA0002364989800000024
Figure BDA0002364989800000024

Figure BDA0002364989800000025
Figure BDA0002364989800000025

tk时刻的第一定子电压控制输入

Figure BDA0002364989800000031
tk时刻的第二定子电压控制输入
Figure BDA0002364989800000032
通过下述方法求得：The first stator voltage control input at time t k
Figure BDA0002364989800000031
Second stator voltage control input at time t k
Figure BDA0002364989800000032
Obtained by the following method:

Figure BDA0002364989800000033
Figure BDA0002364989800000033

Figure BDA0002364989800000034
Figure BDA0002364989800000034

Figure BDA0002364989800000035
Figure BDA0002364989800000035

其中，k对应于tk时刻的步数；UN是三相对称电源的额定电压；f是供电频率；dt对应于构建量测方程步骤的采样时间间隔。Among them, k corresponds to the number of steps at time t k ; U N is the rated voltage of the three-phase symmetrical power supply; f is the power supply frequency; dt corresponds to the sampling time interval of the step of constructing the measurement equation.

优选的，在所述步骤(2)中，所建立的异步电机系统的量测方程为：Preferably, in the step (2), the established measurement equation of the asynchronous motor system is:

z＝Hx+v＝h(x,c)+vz=Hx+v=h(x,c)+v

其中，in,

Figure BDA0002364989800000036
Figure BDA0002364989800000036

其中，v是零均值高斯白噪声，H是量测方程的观测矩阵。where v is zero mean Gaussian white noise and H is the observation matrix of the measurement equation.

优选的，在所述步骤(3)中，离散状态方程为：Preferably, in the step (3), the discrete state equation is:

Figure BDA0002364989800000037
Figure BDA0002364989800000037

Figure BDA0002364989800000038
Figure BDA0002364989800000038

Figure BDA0002364989800000039
Figure BDA0002364989800000039

Figure BDA00023649898000000310
Figure BDA00023649898000000310

Figure BDA00023649898000000311
Figure BDA00023649898000000311

其中，dt为采样时间，

Figure BDA00023649898000000312
为tk时刻电机的状态矩阵；TL是负载转矩，J是转子惯性，pn是极对数，Tr是转子时间常数，σ是电机空载漏磁系数；Ls是定子电感、Lr是转子电感、Lm是定子和转子互感。where dt is the sampling time,
Figure BDA00023649898000000312
is the state matrix of the motor at time t k ; T L is the load torque, J is the rotor inertia, p n is the number of pole pairs, T r is the rotor time constant, σ is the no-load leakage flux coefficient of the motor; L s is the stator inductance, L r is the rotor inductance and L m is the stator and rotor mutual inductance.

优选的，在所述步骤(4)中，所建立的异步电机系统状态模型方程为：Preferably, in the step (4), the established state model equation of the asynchronous motor system is:

xk＝f(xk-1,c,uk-1)+wk-1 x k =f(x k-1 ,c,u k-1 )+w k-1

zk＝h(xk,c)+vk z k =h(x k ,c)+v k

其中，wk和vk是相互独立的零均值高斯白噪声序列，wj和vj是第j步相互独立的零均值高斯白噪声序列，且wk的方差为Qk，vk的方差为Rk，且满足Among them, w k and v k are mutually independent zero-mean Gaussian white noise sequences, w j and v j are mutually independent zero-mean Gaussian white noise sequences at the jth step, and the variance of w k is Q k , and the variance of v k be R k , and satisfy

Figure BDA0002364989800000041
Figure BDA0002364989800000041

其中，δkj为Kroneckerδ函数，当k＝j时，δkj＝1；当k≠j时，δkj＝0。Among them, δ kj is the Kroneckerδ function, when k=j, δ kj =1; when k≠j, δ kj =0.

提供一种高精度异步电机状态检测方法，对所述异步电机系统状态模型所包含的离散状态方程和量测方程进行弱敏秩卡尔曼滤波处理，输出异步电机运行时的状态参数。Provided is a high-precision asynchronous motor state detection method, which performs weakly sensitive rank Kalman filtering processing on discrete state equations and measurement equations included in the asynchronous motor system state model, and outputs state parameters when the asynchronous motor is running.

优选的，所述弱敏秩卡尔曼滤波处理的方法为：Preferably, the weakly sensitive rank Kalman filter processing method is:

(1)采用下式对权利要求1所述离散的状态方程、量测方程的状态和状态误差方差阵分别进行初始化：(1) Adopt the following formula to initialize the discrete state equation and the state of the measurement equation and the state error variance matrix of claim 1 respectively:

Figure BDA0002364989800000042
Figure BDA0002364989800000042

Figure BDA0002364989800000043
Figure BDA0002364989800000043

其中，初始状态

Figure BDA0002364989800000044
初始误差方差矩阵
Figure BDA0002364989800000045
P0、Qk和Rk均不相关；Qk和Rk分别是第k步相互独立的零均值高斯白噪声序列wk和vk的方差；Among them, the initial state
Figure BDA0002364989800000044
initial error variance matrix
Figure BDA0002364989800000045
P 0 , Q k and R k are all uncorrelated; Q k and R k are the variances of the zero-mean Gaussian white noise sequences w k and v k that are independent of each other in the kth step;

(2)计算状态和量测的秩采样点以及协方差和量测方差：(2) Calculate the rank sampling points of the state and measurement, as well as the covariance and measurement variance:

设第k-1步的状态估计值和误差方差阵分别为

Figure BDA0002364989800000046
和
Figure BDA0002364989800000047
则第k步的秩采样点集为：Let the state estimate and the error variance matrix of the k-1th step be respectively
Figure BDA0002364989800000046
and
Figure BDA0002364989800000047
Then the rank sampling point set of the kth step is:

Figure BDA0002364989800000051
Figure BDA0002364989800000051

其中，上标“+”表示其后验估计，

Figure BDA0002364989800000052
为误差方差矩阵
Figure BDA0002364989800000053
的平方根的第j列，满足
Figure BDA0002364989800000054
n＝5为状态x的维度；
Figure BDA0002364989800000055
为
Figure BDA0002364989800000056
平方根的第j列向量；
Figure BDA0002364989800000057
为标准正态偏量，i为不确定参数个数；用中位秩计算pi＝(i+2.7)/5.4i＝1,2，p1＝0.6852p2＝0.8704，
Figure BDA0002364989800000058
采样点修正系数r取1；Among them, the superscript "+" indicates its posterior estimate,
Figure BDA0002364989800000052
is the error variance matrix
Figure BDA0002364989800000053
The jth column of the square root of , satisfying
Figure BDA0002364989800000054
n=5 is the dimension of state x;
Figure BDA0002364989800000055
for
Figure BDA0002364989800000056
the jth column vector of the square root;
Figure BDA0002364989800000057
is the standard normal deviation, i is the number of uncertain parameters; use the median rank to calculate p i =(i+2.7)/5.4i=1,2, p 1 =0.6852p 2 =0.8704,
Figure BDA0002364989800000058
The sampling point correction coefficient r takes 1;

时间更新：状态一步预测为：Time Update: The state one-step prediction is:

Figure BDA0002364989800000059
Figure BDA0002364989800000059

其中，

Figure BDA00023649898000000510
为经过非线性函数传递后的秩采样点，通过下式求得：in,
Figure BDA00023649898000000510
is the rank sampling point after passing through the nonlinear function, which is obtained by the following formula:

Figure BDA00023649898000000511
Figure BDA00023649898000000511

其中，

Figure BDA00023649898000000512
为不确定参数的均值，uk-1为第k-1步的定子电压控制输入；in,
Figure BDA00023649898000000512
is the mean value of the uncertain parameters, u k-1 is the stator voltage control input of the k-1th step;

一步预测误差的方差阵：Variance matrix of one-step forecast error:

Figure BDA00023649898000000513
Figure BDA00023649898000000513

其中，上标“－”表示变量的先验估计；r*为协方差修正系数，取1；ω为协方差权重系数：

Figure BDA00023649898000000514
Qk-1为第k-1步系统状态方程的零均值高斯白噪声wk-1的方差；Among them, the superscript "-" represents the prior estimation of the variable; r * is the covariance correction coefficient, which is taken as 1; ω is the covariance weight coefficient:
Figure BDA00023649898000000514
Q k-1 is the variance of the zero-mean white Gaussian noise w k-1 of the system state equation of the k-1th step;

量测更新：重新秩采样，得到采样点集：Measurement update: re-rank sampling, get sampling point set:

Figure BDA00023649898000000515
Figure BDA00023649898000000515

量测均值：Measurement mean:

Figure BDA00023649898000000516
Figure BDA00023649898000000516

状态估计：State estimation:

Figure BDA0002364989800000061
Figure BDA0002364989800000061

其中，zk为第k步的量测方程；Among them, z k is the measurement equation of the kth step;

估计误差的方差阵：The variance matrix of the estimated error:

Figure BDA0002364989800000062
Figure BDA0002364989800000062

其中，

Figure BDA0002364989800000063
为第k步的先验估计方差阵，
Figure BDA0002364989800000064
为第k步的后验估计方差阵；in,
Figure BDA0002364989800000063
Estimate the variance matrix for the prior of step k,
Figure BDA0002364989800000064
Estimate the variance matrix for the posterior of step k;

式中：where:

Figure BDA0002364989800000065
Figure BDA0002364989800000065

Figure BDA0002364989800000066
Figure BDA0002364989800000066

其中，Pxz,k为状态和量测的协方差，Pzz,k为量测方差；Rk为第k步系统状态方程的零均值高斯白噪声vk的方差；Among them, P xz,k is the covariance of the state and measurement, Pzz,k is the measurement variance; R k is the variance of the zero-mean Gaussian white noise v k of the system state equation of the kth step;

(3)秩采样点的敏感性传播：(3) Sensitivity propagation of rank sampling points:

1)采用下式计算k-1步秩采样点的敏感性：1) Calculate the sensitivity of the k-1 step rank sampling point using the following formula:

Figure BDA0002364989800000067
Figure BDA0002364989800000067

其中，

Figure BDA0002364989800000068
为第k-1步后验状态的敏感性；
Figure BDA0002364989800000069
为
Figure BDA00023649898000000610
平方根的第j列向量；
Figure BDA00023649898000000611
为标准正态偏量，i为不确定参数个数；用中位秩计算pi＝(i+2.7)/5.4i＝1,2，p1＝0.6852p2＝0.8704，
Figure BDA00023649898000000612
采样点修正系数r取1；in,
Figure BDA0002364989800000068
is the sensitivity of the posterior state of the k-1 step;
Figure BDA0002364989800000069
for
Figure BDA00023649898000000610
the jth column vector of the square root;
Figure BDA00023649898000000611
is the standard normal deviation, i is the number of uncertain parameters; use the median rank to calculate p i =(i+2.7)/5.4i=1,2, p 1 =0.6852p 2 =0.8704,
Figure BDA00023649898000000612
The sampling point correction coefficient r takes 1;

更新秩采样点集：Update the set of rank sampling points:

Figure BDA00023649898000000613
Figure BDA00023649898000000613

ci为第i个不确定参数，

Figure BDA0002364989800000071
为不确定参数的均值，uk-1为第k-1步的定子电压控制输入；c i is the ith uncertain parameter,
Figure BDA0002364989800000071
is the mean value of the uncertain parameters, u k-1 is the stator voltage control input of the k-1th step;

2)采用下式计算先验状态估计和先验协方差矩阵的敏感性2) Calculate the sensitivity of the prior state estimate and prior covariance matrix using the following formula

Figure BDA0002364989800000072
Figure BDA0002364989800000072

Figure BDA0002364989800000073
Figure BDA0002364989800000073

其中，

Figure BDA0002364989800000074
为先验状态估计的敏感性，
Figure BDA0002364989800000075
为先验协方差矩阵；r*为协方差修正系数，取1；ω为协方差权重系数：
Figure BDA0002364989800000076
in,
Figure BDA0002364989800000074
is the sensitivity of the prior state estimate,
Figure BDA0002364989800000075
is the prior covariance matrix; r * is the covariance correction coefficient, which takes 1; ω is the covariance weight coefficient:
Figure BDA0002364989800000076

3)采用下式计算重新秩采样点集和预测量测秩采样点的敏感性3) Use the following formula to calculate the sensitivity of the re-rank sampling point set and the predicted measurement rank sampling point

Figure BDA0002364989800000077
Figure BDA0002364989800000077

Figure BDA0002364989800000078
Figure BDA0002364989800000078

其中，

Figure BDA0002364989800000079
为先验状态估计的敏感性，
Figure BDA00023649898000000710
为不确定参数的均值，uk为第k步的定子电压控制输入
Figure BDA00023649898000000711
为标准正态偏量，i为不确定参数个数；用中位秩计算pi＝(i+2.7)/5.4i＝1,2，p1＝0.6852p2＝0.8704，
Figure BDA00023649898000000712
采样点修正系数r取1；in,
Figure BDA0002364989800000079
is the sensitivity of the prior state estimate,
Figure BDA00023649898000000710
is the mean value of the uncertain parameters, uk is the stator voltage control input of the kth step
Figure BDA00023649898000000711
is the standard normal deviation, i is the number of uncertain parameters; use the median rank to calculate p i =(i+2.7)/5.4i=1,2, p 1 =0.6852p 2 =0.8704,
Figure BDA00023649898000000712
The sampling point correction coefficient r takes 1;

采用下式计算量测均值的敏感性：The sensitivity of the measurement mean is calculated using the following formula:

Figure BDA00023649898000000713
Figure BDA00023649898000000713

4)采用下式计算状态和量测协方差以及量测方差的敏感性：4) Calculate the state and measurement covariance and the sensitivity of the measurement variance using the following formula:

Figure BDA0002364989800000081
Figure BDA0002364989800000081

Figure BDA0002364989800000082
Figure BDA0002364989800000082

其中，

Figure BDA0002364989800000083
为先验量测矩阵，γi,k为量测均值的敏感性；in,
Figure BDA0002364989800000083
is a priori measurement matrix, γ i,k is the sensitivity of the measurement mean;

5)采用下式计算状态估计和状态误差方差阵的敏感性：5) Calculate the sensitivity of state estimation and state error variance matrix using the following formula:

Figure BDA0002364989800000084
Figure BDA0002364989800000084

Figure BDA0002364989800000085
Figure BDA0002364989800000085

式中：where:

Figure BDA0002364989800000086
Figure BDA0002364989800000086

式中：where:

Figure BDA0002364989800000087
Figure BDA0002364989800000087

其中

Figure BDA0002364989800000088
是一个斜对称矩阵，满足ΓT＝-Γ，Ψ和Θ均为非奇异矩阵，且满足
Figure BDA0002364989800000089
Kk为弱敏秩卡尔曼滤波的卡尔曼增益；in
Figure BDA0002364989800000088
is an obliquely symmetric matrix that satisfies Γ T = -Γ, Ψ and Θ are both non-singular matrices, and satisfies
Figure BDA0002364989800000089
K k is the Kalman gain of the weakly sensitive rank Kalman filter;

(4)采用下式计算弱敏秩卡尔曼滤波的卡尔曼增益Kk (4) Calculate the Kalman gain K k of the weakly sensitive rank Kalman filter using the following formula

Figure BDA00023649898000000810
Figure BDA00023649898000000810

其中，l为不确定参数个数，Wi,k为第i个不确定参数的权重，取值为不确定参数的方差；Among them, l is the number of uncertain parameters, W i,k is the weight of the i-th uncertain parameter, and the value is the variance of the uncertain parameter;

敏感性代价函数：Sensitivity cost function:

Figure BDA00023649898000000811
Figure BDA00023649898000000811

其中，Tr(Pk)代表矩阵Pk的迹；Among them, Tr(P k ) represents the trace of the matrix P k ;

(5)采用下式计算敏感性矩阵：(5) Calculate the sensitivity matrix using the following formula:

Figure BDA00023649898000000812
Figure BDA00023649898000000812

(6)采用下式进行第k步的状态测算：(6) Use the following formula to measure the state of the kth step:

Figure BDA0002364989800000091
Figure BDA0002364989800000091

(7)步骤(1)～(6)步循环迭代，即得异步电机的实时状态参数。(7) Steps (1) to (6) are cyclically iterated to obtain the real-time state parameters of the asynchronous motor.

与现有技术相比，本发明的有益技术效果在于：Compared with the prior art, the beneficial technical effects of the present invention are:

本发明使用弱敏最优控制方法来解决异步电机系统中参数的不确定性，并将RKF的均方误差代价函数和弱敏代价函数通过敏感性权重系数联合在一起组成新的代价函数，然后将该代价函数最小化获得弱敏秩卡尔曼滤波的最优增益，减弱异步电机系统中状态估计对不确定参数的敏感性，提高了异步电机系统状态监测精度。The invention uses the weak-sensitive optimal control method to solve the uncertainty of parameters in the asynchronous motor system, and combines the mean square error cost function of the RKF and the weak-sensitive cost function through the sensitivity weight coefficient to form a new cost function, and then The optimal gain of weakly sensitive rank Kalman filter is obtained by minimizing the cost function, which reduces the sensitivity of state estimation to uncertain parameters in the asynchronous motor system, and improves the state monitoring accuracy of the asynchronous motor system.

附图说明Description of drawings

图1为基于弱敏秩卡尔曼滤波的异步电机状态监测方法的流程图。Fig. 1 is a flowchart of a state monitoring method of an asynchronous motor based on weakly sensitive rank Kalman filtering.

图2为弱敏秩卡尔曼滤波的原理图。Figure 2 is a schematic diagram of the weakly sensitive rank Kalman filter.

图3为实施例的方法与RKF在异步电机空载启动过程中对于异步电机的状态监测结果的均方根误差对比图；3 is a comparison diagram of the root mean square error of the method of the embodiment and the RKF for the state monitoring result of the asynchronous motor during the no-load start-up process of the asynchronous motor;

图4为实施例的方法与RKF在异步电机三相短路及其恢复过程中对于异步电机的状态监测结果的均方根误差对比图；4 is a comparison diagram of the root mean square error of the state monitoring result of the asynchronous motor in the method of the embodiment and the RKF in the three-phase short circuit of the asynchronous motor and its recovery process;

图3和图4中，perf RKF代表无干扰理想状态下的检测方法；imp RKF代表现有常规的检测方法；DRKF代表实施例的检测方法。In Figures 3 and 4, perf RKF represents the detection method in an ideal state without interference; imp RKF represents the existing conventional detection method; DRKF represents the detection method of the embodiment.

具体实施方式Detailed ways

下面结合附图和实施例来说明本发明的具体实施方式，但以下实施例只是用来详细说明本发明，并不以任何方式限制本发明的范围。The specific embodiments of the present invention will be described below with reference to the accompanying drawings and examples, but the following examples are only used to describe the present invention in detail, and do not limit the scope of the present invention in any way.

在以下实施例中所涉及的仪器设备如无特别说明，均为常规仪器设备；所涉及的试剂如无特别说明，均为市售常规试剂；所涉及的试验方法，如无特别说明，均为常规方法。The instruments and equipment involved in the following examples are conventional instruments and equipment unless otherwise specified; the involved reagents are commercially available conventional reagents unless otherwise specified; the involved test methods, unless otherwise specified, are normal method.

实施例：一种基于弱敏秩卡尔曼滤波的异步电机状态检测方法Embodiment: A state detection method of asynchronous motor based on weakly sensitive rank Kalman filter

该检测方法，包括异步电机空载启动过程和三相短路故障及其恢复过程。其流程图参见图1，弱敏秩卡尔曼滤波的原理图参见图2。The detection method includes a no-load start-up process of an asynchronous motor, a three-phase short-circuit fault and a recovery process thereof. See Figure 1 for its flowchart, and Figure 2 for the principle diagram of the weakly sensitive rank Kalman filter.

(一)异步电机空载启动状态检测步骤如下：(1) The steps for detecting the no-load starting state of the asynchronous motor are as follows:

步骤一：在异步电机系统中，取状态向量x＝[x1,x2,x3,x4,x5]T，则其状态方程为：Step 1: In the asynchronous motor system, take the state vector x=[x 1 , x 2 , x 3 , x 4 , x 5 ] T , then its state equation is:

Figure BDA0002364989800000101
Figure BDA0002364989800000101

其中，x1和x2是定子电流，x3和x4是转子磁链，x5是角速度；J是转子惯性；pn是极对数；u1和u2是定子电压控制输入；c＝[c1 c2]，是不确定参数向量，c1和c2分别是定子电阻和转子电阻；w是零均值高斯白噪声；其他模型参数为：where x 1 and x 2 are the stator currents, x 3 and x 4 are the rotor flux linkage, and x 5 is the angular velocity; J is the rotor inertia; p n is the number of pole pairs; u 1 and u 2 are the stator voltage control inputs; c =[c 1 c 2 ], is the uncertain parameter vector, c 1 and c 2 are the stator resistance and rotor resistance, respectively; w is zero-mean Gaussian white noise; other model parameters are:

Figure BDA0002364989800000102
Figure BDA0002364989800000102

Figure BDA0002364989800000103
Figure BDA0002364989800000103

Figure BDA0002364989800000104
Figure BDA0002364989800000104

Figure BDA0002364989800000105
Figure BDA0002364989800000105

Figure BDA0002364989800000106
Figure BDA0002364989800000106

其中，转子电感Ls＝0.265[H]，定子电感Lr＝0.265[H]，互感Lm＝0.253[H]，转子惯性J＝0.02[kg·m2]，极对数pn＝2，k对应于tk时刻的步数；UN是三相对称电源的额定电压；f是供电频率；dt对应于构建量测方程步骤的采样时间间隔；un＝[un1,un2,un3]T。Among them, rotor inductance L s =0.265[H], stator inductance L r =0.265[H], mutual inductance L m =0.253[H], rotor inertia J=0.02[kg·m 2 ], number of pole pairs p n =2 , k corresponds to the number of steps at time tk; U N is the rated voltage of the three-phase symmetrical power supply; f is the power supply frequency; dt corresponds to the sampling time interval of the step of constructing the measurement equation; u n =[u n1 ,u n2 ,u n3 ] T .

步骤二：建立异步电机系统的量测方程Step 2: Establish the measurement equation of the asynchronous motor system

将测得的定子电流

Figure BDA0002364989800000107
和转子磁链
Figure BDA0002364989800000108
角速度
Figure BDA0002364989800000109
作为量测值，以此建立相应的量测模型，则相应的量测方程为：The measured stator current will be
Figure BDA0002364989800000107
and rotor flux linkage
Figure BDA0002364989800000108
Angular velocity
Figure BDA0002364989800000109
As the measurement value, the corresponding measurement model is established, and the corresponding measurement equation is:

z＝Hx+v＝h(x,c)+v (4)z=Hx+v=h(x,c)+v (4)

其中，in,

Figure BDA0002364989800000111
Figure BDA0002364989800000111

其中，H是量测方程的观测矩阵，v是零均值高斯白噪声；此异步电机系统的状态方程为非线性方程、量测方程为线性方程，因此整个异步电机系统为非线性系统。Among them, H is the observation matrix of the measurement equation, v is the zero-mean Gaussian white noise; the state equation of this asynchronous motor system is a nonlinear equation, and the measurement equation is a linear equation, so the entire asynchronous motor system is a nonlinear system.

步骤三：建立离散化状态方程和量测方程Step 3: Establish the discretized state equation and measurement equation

对上述异步电机的状态方程式(1)进行离散化，可得其离散状态方程：By discretizing the state equation (1) of the above asynchronous motor, the discrete state equation can be obtained:

Figure BDA0002364989800000112
Figure BDA0002364989800000112

Figure BDA0002364989800000113
Figure BDA0002364989800000113

Figure BDA0002364989800000114
Figure BDA0002364989800000114

Figure BDA0002364989800000115
Figure BDA0002364989800000115

Figure BDA0002364989800000116
Figure BDA0002364989800000116

dt对应于构建量测方程步骤的采样时间间隔，

Figure BDA0002364989800000117
是tk-1时刻的第一定子电压控制输入，
Figure BDA0002364989800000118
是tk-1时刻的第二定子电压控制输入；dt corresponds to the sampling time interval of the step of constructing the measurement equation,
Figure BDA0002364989800000117
is the first stator voltage control input at time t k-1 ,
Figure BDA0002364989800000118
is the second stator voltage control input at time t k-1 ;

则由式(1)和(4)整理可得离散的异步电机状态方程和量测方程：Then the discrete asynchronous motor state equation and measurement equation can be obtained by sorting out equations (1) and (4):

xk＝f(xk-1,c,uk-1)+wk-1 (7)x k =f(x k-1 ,c,u k-1 )+w k-1 (7)

zk＝h(xk,c)+vk (8)z k =h(x k ,c)+v k (8)

其中，wk和vk是相互独立的零均值高斯白噪声序列，且wk和vk的方差分别为Qk和Rk，且满足Among them, w k and v k are mutually independent zero-mean Gaussian white noise sequences, and the variances of w k and v k are Q k and R k respectively, and satisfy

Figure BDA0002364989800000119
Figure BDA0002364989800000119

其中，δkj为Kroneckerδ函数，当k＝j时，δkj＝1；当k≠j时，δkj＝0；Among them, δ kj is the Kroneckerδ function, when k=j, δ kj =1; when k≠j, δ kj =0;

经保密实验，发明人获取的系统噪声方差阵Qk和量测噪声方差阵Rk矩阵如下：Through confidentiality experiments, the system noise variance matrix Q k and the measurement noise variance matrix R k matrix obtained by the inventor are as follows:

Figure BDA0002364989800000121
Figure BDA0002364989800000121

其中，观测次数为N＝150，总采样时间为t＝0.15sAmong them, the number of observations is N=150, and the total sampling time is t=0.15s

步骤四：对离散后的状态方程和量测方程采用弱敏秩卡尔曼滤波，输出异步电机的定子电流、转子磁链和角速度。Step 4: Weakly sensitive rank Kalman filtering is used for the discrete state equation and measurement equation, and the stator current, rotor flux linkage and angular velocity of the asynchronous motor are output.

1.对离散的状态方程、量测方程的状态和状态误差方差阵分别进行初始化1. Initialize the discrete state equation, the state of the measurement equation and the state error variance matrix respectively

Figure BDA0002364989800000122
Figure BDA0002364989800000122

Figure BDA0002364989800000123
Figure BDA0002364989800000123

其中，初始状态

Figure BDA0002364989800000124
初始误差方差矩阵
Figure BDA0002364989800000125
P0、Qk和Rk均不相关；Among them, the initial state
Figure BDA0002364989800000124
initial error variance matrix
Figure BDA0002364989800000125
P 0 , Q k and R k are all uncorrelated;

2.计算状态和量测的秩采样点以及协方差和量测方差2. Calculate the rank sampling points of the state and measurement, as well as the covariance and measurement variance

设第k-1步的状态估计值和误差方差阵分别为

Figure BDA0002364989800000126
和
Figure BDA0002364989800000127
则第k步的秩采样点集为：Let the state estimate and the error variance matrix of the k-1th step be respectively
Figure BDA0002364989800000126
and
Figure BDA0002364989800000127
Then the rank sampling point set of the kth step is:

Figure BDA0002364989800000128
Figure BDA0002364989800000128

其中，上标“+”表示其后验估计，

Figure BDA0002364989800000129
为误差方差矩阵
Figure BDA00023649898000001210
的平方根的第j列，满足
Figure BDA00023649898000001211
n＝5为状态x的维度；Among them, the superscript "+" indicates its posterior estimate,
Figure BDA0002364989800000129
is the error variance matrix
Figure BDA00023649898000001210
The jth column of the square root of , satisfying
Figure BDA00023649898000001211
n=5 is the dimension of state x;

时间更新：状态一步预测为：Time Update: The state one-step prediction is:

Figure BDA0002364989800000131
Figure BDA0002364989800000131

式中：where:

Figure BDA0002364989800000132
Figure BDA0002364989800000132

一步预测误差的方差阵：Variance matrix of one-step forecast error:

Figure BDA0002364989800000133
Figure BDA0002364989800000133

其中，上标“－”表示变量的先验估计；Among them, the superscript "-" represents the prior estimation of the variable;

量测更新：重新秩采样，得到采样点集：Measurement update: re-rank sampling, get sampling point set:

Figure BDA0002364989800000134
Figure BDA0002364989800000134

量测均值：Measurement mean:

Figure BDA0002364989800000135
Figure BDA0002364989800000135

状态估计：State estimation:

Figure BDA0002364989800000136
Figure BDA0002364989800000136

估计误差的方差阵：The variance matrix of the estimated error:

Figure BDA0002364989800000137
Figure BDA0002364989800000137

式中：where:

Figure BDA0002364989800000138
Figure BDA0002364989800000138

Figure BDA0002364989800000139
Figure BDA0002364989800000139

其中，Pxz,k为状态和量测的协方差，Pzz,k为量测方差；Among them, P xz,k is the covariance of state and measurement, and Pzz,k is the measurement variance;

3.秩采样点的敏感性传播3. Sensitivity propagation of rank sampling points

1)计算k-1步秩采样点的敏感性：1) Calculate the sensitivity of the k-1 step rank sampling point:

Figure BDA0002364989800000141
Figure BDA0002364989800000141

更新秩采样点集：Update the set of rank sampling points:

Figure BDA0002364989800000142
Figure BDA0002364989800000142

2)计算先验状态估计和先验协方差矩阵的敏感性2) Calculate the sensitivity of the prior state estimate and prior covariance matrix

Figure BDA0002364989800000143
Figure BDA0002364989800000143

Figure BDA0002364989800000144
Figure BDA0002364989800000144

3)计算重新秩采样点集和预测量测秩采样点的敏感性3) Calculate the sensitivity of the re-rank sampling point set and predict the measurement rank sampling point

Figure BDA0002364989800000145
Figure BDA0002364989800000145

Figure BDA0002364989800000146
Figure BDA0002364989800000146

计算量测均值的敏感性：Compute the sensitivity of the measurement mean:

Figure BDA0002364989800000147
Figure BDA0002364989800000147

4)计算状态和量测协方差以及量测方差的敏感性：4) Calculate the state and measurement covariance and the sensitivity of the measurement variance:

Figure BDA0002364989800000151
Figure BDA0002364989800000151

Figure BDA0002364989800000152
Figure BDA0002364989800000152

5)计算状态估计和状态误差方差阵的敏感性：5) Calculate the sensitivity of the state estimate and the state error variance matrix:

Figure BDA00023649898000001512
Figure BDA00023649898000001512

Figure BDA0002364989800000153
Figure BDA0002364989800000153

式中：where:

Figure BDA0002364989800000154
Figure BDA0002364989800000154

式中：where:

Figure BDA0002364989800000155
Figure BDA0002364989800000155

其中

Figure BDA0002364989800000156
是一个斜对称矩阵，满足ΓT＝-Γ，Ψ和Θ均为非奇异矩阵，且满足
Figure BDA0002364989800000157
in
Figure BDA0002364989800000156
is an obliquely symmetric matrix that satisfies Γ T = -Γ, Ψ and Θ are both non-singular matrices, and satisfies
Figure BDA0002364989800000157

4.计算弱敏秩卡尔曼滤波的卡尔曼增益Kk 4. Calculate the Kalman gain K k of the weakly sensitive rank Kalman filter

Figure BDA0002364989800000158
Figure BDA0002364989800000158

其中，Wi,k为第i个不确定参数的权重，取值为不确定参数的方差；Among them, Wi ,k is the weight of the i-th uncertain parameter, and the value is the variance of the uncertain parameter;

敏感性代价函数：Sensitivity cost function:

Figure BDA0002364989800000159
Figure BDA0002364989800000159

5.计算敏感性矩阵5. Calculate the sensitivity matrix

Figure BDA00023649898000001510
Figure BDA00023649898000001510

6.第k步的状态估计6. State estimation at step k

Figure BDA00023649898000001511
Figure BDA00023649898000001511

以上6步循环迭代，得到异步电机的实时状态监测结果，所述实时状态监测结果包括第一定子电流x1、第二定子电流x2、第一转子磁链x3、第二转子磁链x4、角速度x5。采样时间为dt＝0.001[s]，当k＝1时，对应的时间为T＝0.000[s]；当k＝2时，对应的时间为T＝0.001[s]，每步的对应时间以此类推。The above 6 steps are cyclically iterated, and the real-time state monitoring results of the asynchronous motor are obtained. The real-time state monitoring results include the first stator current x 1 , the second stator current x 2 , the first rotor flux linkage x 3 , and the second rotor flux linkage x 4 , angular velocity x 5 . The sampling time is dt=0.001[s], when k=1, the corresponding time is T=0.000[s]; when k=2, the corresponding time is T=0.001[s], and the corresponding time of each step is And so on.

(二)三相短路故障及其恢复过程是在空载启动达到稳定状态后的基础上进行的。(2) The three-phase short-circuit fault and its recovery process are carried out on the basis that the no-load startup reaches a stable state.

两过程仅在定子电压输入及采样时间上有区别。在t1时刻，三相短路故障发生，在t2时刻故障修复，此过程的电压模型参数为：The two processes differ only in the stator voltage input and sampling time. At time t 1 , a three-phase short-circuit fault occurs, and the fault is repaired at time t 2. The voltage model parameters of this process are:

Figure BDA0002364989800000161
Figure BDA0002364989800000161

Figure BDA0002364989800000162
Figure BDA0002364989800000162

Figure BDA0002364989800000163
Figure BDA0002364989800000163

Figure BDA0002364989800000164
Figure BDA0002364989800000164

其中，k对应于tk时刻的步数；UN是三相对称电源的额定电压；

Figure BDA0002364989800000165
为tk时刻的第一定子电压控制输入、
Figure BDA0002364989800000166
为tk时刻的第二定子电压控制输入；f是供电频率；dt对应于构建量测方程步骤的采样时间间隔；un＝[un1,un2,un3]T。Among them, k corresponds to the number of steps at time t k ; U N is the rated voltage of the three-phase symmetrical power supply;
Figure BDA0002364989800000165
is the first stator voltage control input at time t k ,
Figure BDA0002364989800000166
is the second stator voltage control input at time tk; f is the power supply frequency; dt corresponds to the sampling time interval of the step of constructing the measurement equation; u n = [u n1 , un2 , un3 ] T .

试验例：Test example:

采用实施例的检测方法与使用本领域常规方法RKF对异步电机的定子电流、转子磁链、角速度参数进行实时状态监测结果对比。The detection method of the embodiment is compared with the real-time state monitoring results of the stator current, rotor flux linkage, and angular velocity parameters of the asynchronous motor using RKF, a conventional method in the art.

在MATLAB(R2016b)软件上进行的建模和仿真，并在CPU为i5-7400、内存为8G的电脑上进行运行。在仿真过程中，本发明在MATLAB(R2016b)软件上通过程序的编写搭建了仿真模型，并进行了初始数据的输入(上面的具体实施过程中已给出)，然后再通过运行MATLAB(R2016b)软件进行计算。The modeling and simulation are carried out on MATLAB (R2016b) software, and run on a computer with a CPU of i5-7400 and a memory of 8G. In the simulation process, the present invention builds a simulation model on the MATLAB (R2016b) software through programming, and inputs the initial data (given in the above specific implementation process), and then runs MATLAB (R2016b) software does the calculation.

具体实施过程中，观测次数为N＝350，总采样时间为t＝0.35s，三相短路故障发生时刻t1＝0.15s，故障修复时刻t2＝0.25s。In the specific implementation process, the number of observations is N=350, the total sampling time is t=0.35s, the three-phase short-circuit fault occurrence time t 1 =0.15s, and the fault repair time t 2 =0.25s.

通过MATLAB(R2016b)仿真计算获取结果，在异步电机空载启动过程中对于异步电机的状态检测，实施例的检测方法与RKF监测结果的均方根误差对比如图3所示。The results are obtained through MATLAB (R2016b) simulation calculation. For the state detection of the asynchronous motor during the no-load start-up process of the asynchronous motor, the comparison between the root mean square error of the detection method of the embodiment and the RKF monitoring result is shown in Figure 3.

在异步电机三相短路及其恢复过程中对于异步电机的状态监测，实施例的检测方法与RKF监测结果的均方根误差对比如图4所示。For the state monitoring of the asynchronous motor during the three-phase short-circuit of the asynchronous motor and its recovery process, the comparison between the root mean square error of the detection method of the embodiment and the RKF monitoring result is shown in FIG. 4 .

可知，实施例检测方法的均方根误差值较小，具有更好的精确度。It can be seen that the root mean square error value of the detection method of the embodiment is smaller and has better accuracy.

上面结合附图和实施例对本发明作了详细的说明，但是，所属技术领域的技术人员能够理解，在不脱离本发明宗旨的前提下，还可以对上述实施例中的各个具体参数进行变更，形成多个具体的实施例，均为本发明的常见变化范围，在此不再一一详述。The present invention has been described in detail above in conjunction with the accompanying drawings and the embodiments, but those skilled in the art can understand that, without departing from the purpose of the present invention, each specific parameter in the above-mentioned embodiments can also be changed, Forming a plurality of specific embodiments is the common variation range of the present invention, and will not be described in detail here.

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
Figure FDA0003403301650000016
And a first rotor flux linkage
Figure FDA0003403301650000015
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:
Figure FDA0003403301650000011
Figure FDA0003403301650000012
wherein, the initial state
Figure FDA0003403301650000013
Initial error variance matrix
Figure FDA0003403301650000014
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
Figure FDA0003403301650000021
And
Figure FDA0003403301650000022
the rank sampling point set of the k step is:
Figure FDA0003403301650000023
wherein the superscript "+" indicates its posterior estimate; chi shapej,k-1Is composed of
Figure FDA0003403301650000024
The j-th sampling point of (2) has 4n sample points, and n is 5, which is the dimension of the state x;
Figure FDA0003403301650000025
is composed of
Figure FDA0003403301650000026
The jth column vector of the square root;
Figure FDA0003403301650000027
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，
Figure FDA0003403301650000028
Taking 1 as a sampling point correction coefficient r;
and (3) time updating: the state is predicted as:
Figure FDA0003403301650000029
wherein,
Figure FDA00034033016500000210
the rank sampling point after nonlinear function transfer is obtained by the following formula:
Figure FDA00034033016500000211
wherein,
Figure FDA00034033016500000212
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:
Figure FDA00034033016500000213
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:
Figure FDA00034033016500000214
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:
Figure FDA0003403301650000031
measuring an average value:
Figure FDA0003403301650000032
and (3) state estimation:
Figure FDA0003403301650000033
wherein z iskThe measurement equation in the k step is shown;
variance matrix of estimation error:
Figure FDA0003403301650000034
wherein,
Figure FDA0003403301650000035
the variance matrix is estimated a priori at step k,
Figure FDA0003403301650000036
estimating a variance matrix for the posteriori of the k step;
in the formula:
Figure FDA0003403301650000037
Figure FDA0003403301650000038
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:
Figure FDA0003403301650000041
wherein,
Figure FDA0003403301650000042
sensitivity of the posterior state of the k-1 step;
Figure FDA0003403301650000043
is composed of
Figure FDA0003403301650000044
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，
Figure FDA0003403301650000045
Taking 1 as a sampling point correction coefficient r;
updating a rank sampling point set:
Figure FDA0003403301650000046
wherein, ciFor the i-th uncertain parameter,
Figure FDA0003403301650000047
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
Figure FDA0003403301650000048
Figure FDA0003403301650000049
Wherein,
Figure FDA00034033016500000410
for the sensitivity of the a priori state estimation,
Figure FDA00034033016500000411
is a prior covariance matrix; r is*The covariance correction coefficient can be 1; ω is the covariance weight coefficient:
Figure FDA00034033016500000412
3) calculating the re-rank sample set and predicting the sensitivity of the metrology rank samples using the equation
Figure FDA0003403301650000051
Figure FDA0003403301650000052
Wherein,
Figure FDA0003403301650000053
for the sensitivity of the a priori state estimation,
Figure FDA00034033016500000512
is the mean value of the uncertain parameter, ukStator voltage control input for step k
Figure FDA00034033016500000511
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，
Figure FDA0003403301650000054
Taking 1 as a sampling point correction coefficient r;
the sensitivity of the measured mean was calculated using the following formula:
Figure FDA0003403301650000055
4) the state and metrology covariance and sensitivity of metrology variance are calculated using the following equations:
Figure FDA0003403301650000056
Figure FDA0003403301650000057
wherein,
Figure FDA0003403301650000058
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:
Figure FDA0003403301650000059
Figure FDA00034033016500000510
in the formula:
Figure FDA0003403301650000061
in the formula:
Figure FDA0003403301650000062
wherein
Figure FDA0003403301650000063
Is an oblique symmetric matrix satisfying gammaTAll of ═ Γ, Ψ, and Θ are nonsingular matrices, and satisfy
Figure FDA0003403301650000064
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
Figure FDA0003403301650000065
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:
Figure FDA0003403301650000066
wherein, Tr (P)k) Representative matrix PkThe trace of (2);
(v) calculating the sensitivity matrix using the following formula:
Figure FDA0003403301650000067
(VI) performing state estimation of the k step by adopting the following formula:
Figure FDA0003403301650000068
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:
Figure FDA0003403301650000071
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:
Figure FDA0003403301650000072
tkfirst stator voltage control input of time
Figure FDA0003403301650000074
tkSecond stator voltage control input of time of day
Figure FDA0003403301650000073
The following method was used:
Figure FDA0003403301650000081
Figure FDA0003403301650000082
Figure FDA0003403301650000083
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,
Figure FDA0003403301650000084
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:
Figure FDA0003403301650000085
Figure FDA0003403301650000089
Figure FDA0003403301650000086
Figure FDA00034033016500000810
Figure FDA0003403301650000087
where dt is the sampling time,
Figure FDA0003403301650000088
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;
Figure FDA0003403301650000091
is tk-1The first stator voltage at a time controls the input,
Figure FDA0003403301650000092
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
Figure FDA0003403301650000093
Wherein, deltakjIs a function of Kronecker delta, delta when k is jkj1 is ═ 1; when k ≠ j, δkj＝0。
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