Permanent magnet synchronous motor control method based on adaptive extended Kalman filter

Abstract

The invention belongs to the field of permanent magnet synchronous motor control, and particularly relates to a permanent magnet synchronous motor control method based on a self-adaptive extended Kalman filter, which comprises the following steps of: inputting voltage on a static coordinate system and current on the static coordinate system into the self-adaptive extended Kalman filter; and estimating the rotor angle and the rotating speed of the permanent magnet synchronous motor through a self-adaptive extended Kalman filter, and updating the system noise covariance of the self-adaptive extended Kalman filter in a self-adaptive manner. The problems that in actual engineering control, the operation condition of a motor is constantly changed, the system noise is not constant, and the fixed system noise covariance Q is difficult to maintain optimal estimation are solved. And the system noise covariance Q can be adaptively updated along with the continuously changing noise of the operation condition of the motor, so that more accurate vector control on the permanent magnet synchronous motor is realized.

Description

Technical Field

[0001] This application belongs to the field of permanent magnet synchronous motor control, and specifically relates to a permanent magnet synchronous motor control method based on an adaptive extended Kalman filter. Background Art

[0002] The permanent magnet synchronous motor (PMSM) has a relatively simple structure, high power density, strong reliability, and high efficiency, and is widely used in the field of motor control. The most commonly used control method for the permanent magnet synchronous motor is vector control. The core of this control method is to perform Clark transformation and Park transformation on voltage and current, and decompose the three-phase current into the quadrature-axis and direct-axis currents on the two-phase rotating coordinate system. In order to achieve vector control, the electrical angle of the rotor needs to be obtained. The traditional method is to use a Hall sensor to detect the electrical angle of the rotor in real time. However, in a harsh environment, the effect of the Hall sensor may be greatly reduced. At the same time, in order to save costs and reduce volume, the current research focus is on predicting the electrical angle by means of algorithms to replace the traditional Hall sensor. Therefore, choosing which algorithm to achieve this goal and how to simplify the algorithm as much as possible have become one of the research hotspots in the current field of motor control. In general, in the permanent magnet synchronous motor control method based on the extended Kalman filter, since the system noise covariance Q and the measurement noise covariance R are default to follow a normal distribution in the EKF algorithm, but in actual engineering control, the operating conditions of the motor are constantly changing, and its system noise is not constant. The fixed system noise covariance Q is difficult to maintain the optimal estimate. Summary of the Invention

[0003] The technical problem to be solved by this application is to provide a permanent magnet synchronous motor control method based on an adaptive extended Kalman filter, and solve the problem that in actual engineering control, the operating conditions of the motor are constantly changing, its system noise is not constant, and the fixed system noise covariance Q is difficult to maintain the optimal estimate.

[0004] The technical solution adopted by this application is as follows:

[0005] A permanent magnet synchronous motor control method based on an adaptive extended Kalman filter, comprising:

[0006] Input the voltage in the stationary coordinate system and the current in the stationary coordinate system into the adaptive extended Kalman filter, estimate the rotor angle and speed of the permanent magnet synchronous motor through the adaptive extended Kalman filter, and adaptively update the system noise and system noise covariance of the adaptive extended Kalman filter.

[0007] Furthermore, the system noise is obtained by obtaining a nonlinear equation of an adaptive extended Kalman filter through a state equation with current as a state vector, discretizing the nonlinear equation to obtain a discretized nonlinear equation, and using the discretized nonlinear equation and the state prediction equation to obtain an expression for the system noise.

[0008] Furthermore, the system estimated noise covariance is defined at time k-1, the system estimated noise covariance is combined with the expression of system noise and the discretized nonlinear equation to obtain a first expression of the estimated noise covariance, the first expression is combined with the system estimated noise covariance, and the prior error covariance expression is used as a correction term to update the system noise covariance.

[0009] Furthermore, the system noise covariance is combined with the state prediction equation, the state estimation equation, the Kalman gain equation, the prior error covariance and the update error covariance to estimate the rotor angle and speed of the permanent magnet synchronous motor.

[0010] Furthermore, the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance and update error covariance are based on the discretized nonlinear equation, Jacobian matrix and the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance equation and update error covariance equation of the extended Kalman filter to obtain the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance and update error covariance in the adaptive extended Kalman filter of the PMSM in the stationary coordinate system.

[0011] An embodiment of the present application also provides an adaptive extended Kalman filter for use in permanent magnet synchronous motor control, adaptively updating the system noise covariance of the adaptive extended Kalman filter, and estimating the rotor angle and speed of the permanent magnet synchronous motor through the adaptive extended Kalman filter.

[0012] Furthermore, the adaptive extended Kalman filter is based on the discretized nonlinear equation, the Jacobian matrix, and the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance equation, and update error covariance equation of the extended Kalman filter to obtain the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance, and update error covariance in the adaptive extended Kalman filter of the PMSM in a stationary coordinate system.

[0013] Furthermore, the design method of the adaptive extended Kalman filter includes:

[0014] Establish the voltage equation of the three-phase coordinate system of the permanent magnet synchronous motor PMSM;

[0015] The voltage equation of the permanent magnet synchronous motor in the three-phase coordinate system is simplified to the voltage equation in the stationary coordinate system through Clark transformation;

[0016] Transform the voltage equation in the stationary coordinate system into a state equation with current as the state vector;

[0017] According to the transformation of the voltage equation of the PMSM in the stationary coordinate system into the state equation with the current as the state vector, a state vector x, an input vector u and an output vector y are selected;

[0018] According to the state vector x, the input vector u and the output vector y, the nonlinear equation corresponding to the system is obtained, including the nonlinear term of the nonlinear equation;

[0019] Linearize the nonlinear terms to obtain the Jacobian matrix;

[0020] Let the sampling time be Ts, and discretize the nonlinear equation;

[0021] Based on the discretized nonlinear equations, Jacobian matrix and the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance equation and update error covariance equation of the extended Kalman filter, the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance and update error covariance of the EKF model of PMSM in the stationary coordinate system are obtained;

[0022] The equation obtained by combining the discretized nonlinear equation and the state prediction equation is combined with the state estimation equation again to obtain the expression of system noise;

[0023] The expression of system noise is combined with the discretized nonlinear equation to further expand and improve the expression of system noise;

[0024] Define the system estimated noise covariance at time k-1, and combine it with the discretized nonlinear equation, state prediction equation, prior error covariance equation, and update error covariance equation to obtain the expression of the estimated noise covariance;

[0025] The system estimated noise covariance is combined with the estimated noise covariance expression, and the prior error covariance expression is substituted and a correction term is introduced to obtain the expression for updating the system noise covariance;

[0026] The expression of updating the system noise covariance is combined with the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance and updated error covariance expressions in the EKF model of PMSM in the stationary coordinate system to obtain the equation of the adaptive extended Kalman filter of PMSM in the stationary coordinate system.

[0027] In this application, by using an adaptive extended Kalman filter, the system noise and system noise covariance can be adaptively updated, which can change continuously with the operating conditions of the motor. The system noise covariance Q is adaptively updated, so as to achieve more accurate vector control of the permanent magnet synchronous motor. Description of the Drawings

[0028] Figure 1 is the equivalent circuit diagram of the permanent magnet synchronous motor in the prior art of the embodiment of this application;

[0029] Figure 2 is the control principle block diagram of the permanent magnet synchronous motor based on the adaptive extended Kalman filter provided by the embodiment of this application. Detailed Embodiment

[0032] In order to make the purpose, technical solutions and advantages of this application clearer, the following further details this application in combination with embodiments. It should be understood that the specific embodiments described here are only used to explain this application and are not used to limit this application.

[0033] In the sensorless control method of the permanent magnet synchronous motor, the commonly used method is to use a Kalman filter to replace the traditional Hall sensor. In the control method of the permanent magnet synchronous motor based on the extended Kalman filter, since the system noise covariance Q and the measurement noise covariance R are default to conform to the normal distribution in the Kalman filter (EKF algorithm), and based on the fact that the operating conditions of the motor are constantly changing, the system noise is not constant, and the fixed system noise covariance Q is difficult to maintain the optimal estimate.

[0034] This application uses an adaptive extended Kalman filter to estimate the rotor angle and speed of the permanent magnet synchronous motor through the adaptive extended Kalman filter. The adaptive extended Kalman filter can adaptively update the system noise and system noise covariance of the adaptive extended Kalman filter. And the calculation process of estimating the rotor angle and speed of the permanent magnet synchronous motor by the adaptive extended Kalman filter is updated through the system noise covariance. Thus, more accurate vector control of the permanent magnet synchronous motor is achieved.

[0035] As Figure 1 shown, a design method based on the extended Kalman filter in the embodiment of this application includes,

[0036] 1) Establish the voltage equation of the permanent magnet synchronous motor PMSM in the three-phase coordinate system; the established voltage equation of the permanent magnet synchronous motor in the three-phase coordinate system is:

[0037]

[0038] Among them, U a 、Ub , U c and a , i b , i c and a , E b , E c are the back electromotive forces of the three-phase windings; R s is the phase resistance of the winding, and L is the equivalent inductance; R a , R b , R c are the load resistance values of the three-phase windings.

[0039] 2) Simplify the voltage equation in the three-phase coordinate system of the permanent magnet synchronous motor to the voltage equation in the stationary coordinate system through Clark transformation:

[0040]

[0041] where u α , u β are the voltage components on the α and β axes in the stationary coordinate system; i α , i β are the current components on the α and β axes in the stationary coordinate system; R s is the stator resistance; L s is the stator inductance; ω e is the rotor angular velocity; ψ f is the permanent magnet flux; θ e is the rotor position.

[0042] 3) Transform the voltage equation in the stationary coordinate system into a state equation with current as the state vector;

[0043] The equation is:

[0044]

[0045] where u α , u β are the voltage components on the α and β axes in the stationary coordinate system; i α , i β are the current components on the α and β axes in the stationary coordinate system; R s is the stator resistance; L s is the stator inductance; ω e is the rotor angular velocity; ψ f is the permanent magnet flux; θ e is the rotor position.

[0046] ​​4) Select the state vector, input vector, and output vector according to the mathematical model of PMSM in the two-phase stationary coordinate system; among them, the state vector, input vector, and output vector are respectively: x = [i α , i β , ω e , θ e T , u = [u α , u β T , y = [i α , i β T . T is the transpose.

[0047] 5) Select the state vector, input vector, and output vector according to the mathematical model of PMSM in the two-phase stationary coordinate system, and the corresponding nonlinear equation of the extended Kalman filter is:

[0048]

[0049] Among them, is the first derivative of x, and the continuously differentiable multi-dimensional functions f[x(t)], h[x(t)], and magnetic induction intensity B are respectively:

[0050]

[0051] In the formula, u α , u β are the voltage components on the α and β axes in the stationary coordinate system; i α , i β are the current components on the α and β axes in the stationary coordinate system; R s is the stator resistance; L s is the stator inductance; ω e is the rotor angular velocity; ψ f is the permanent magnet flux linkage; θ e is the rotor position; f1, f2, f3, f4 are continuously differentiable functions.

[0052] 6) Linearize the nonlinear equations f[x(t)] and h[x(t)] to obtain the comparable matrices F[x(t)] and H[x(t)];

[0053]

[0054] 7) Discretize the nonlinear equation in step 5):

[0055] Get:

[0056]

[0057] Among them, x k ​​​is t k the state vector at time t; φ k|k-1 is t k-1 from time t k to the transition matrix at time t; X k-1 is t k-1 the rotor flux linkage at time t; B is the magnetic induction intensity; T s is the sampling time; u k-1 is t k-1 the voltage value of the rotor at time t; ω k-1 is t k-1 the system noise at time t; y k is t k the output vector at time t; H k is t k the gain at time t; v k is t k the measurement noise at time t.

[0058] 8) Based on the discretized non - linear equations, Jacobian matrices F[x(t)], H[x(t)], and the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance equation, and updated error covariance equation of the extended Kalman filter, obtain the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance, and updated error covariance in the EKF model of PMSM in the stationary coordinate system;

[0059] Based on the state prediction equation of the extended Kalman filter, the state prediction equation in the EKF model of PMSM in the stationary coordinate system is obtained as:

[0060]

[0061] where, φ k|k-1 is from time t k-1 to the transition matrix at time t k ; is t k-1 the estimated value of the state vector at time t; B k is t k the magnetic induction intensity at time t; T s is the sampling time; u k-1 is t k-1 the voltage value of the rotor at time t.

[0062] The state estimation equation in the EKF model of PMSM in the stationary coordinate system is obtained as:

[0063]

[0064] where, is t k from time t k-1State prediction equation at a moment; K k is t k Kalman gain at moment; y k is t k Output vector at moment; h[x(t)] is a continuously differentiable multi-dimensional function of the non-linear system.

[0065] The Kalman gain equation in the EKF model of PMSM in the stationary coordinate system is obtained as:

[0066]

[0067] where, P k|k-1 is the prior error covariance in the EKF model; H k is t k Gain at moment; R is the measurement noise covariance.

[0068] The prior error covariance in the EKF model of PMSM in the stationary coordinate system is obtained as:

[0069]

[0070] where, φ k|k-1 is t k-1 from moment to t k moment's transition matrix; P k is the updated error covariance in the EKF model; Q k-1 is t k-1 System noise covariance at moment.

[0071] The updated error covariance in the EKF model of PMSM in the stationary coordinate system is obtained as:

[0072] P k =(E - K k H k )P k|k-1

[0073] where, E is the magnetic induction intensity; K k is t k Kalman gain at moment; H k is t k System gain at moment; P k|k-1 is the prior error covariance in the EKF model.

[0074] 9) Combine the discretized non-linear equation in 7) and the state prediction equation in 8), and for the convenience of simplification, let System noise and combine the changed expression with the state estimation equation in 8) to obtain the system noise expression.

[0075] The statistical characteristics of system noise and measurement noise are:

[0076]

[0077] Among them, ω k t k System noise at time; ω i t i System noise at time v k t k The measurement noise at the moment v i t i The measurement noise at the moment.

[0078] The resulting system noise The expression is:

[0079]

[0080] Among them, K k t k Kalman gain at time y k t k The output vector at the moment; H is the system gain; t k Time to t k-1 The state prediction equation at time φ k|k-1 t k-1 Time to t k The transfer matrix at time x k-1 t k-1 The state vector at the moment; t k-1 The estimated value of the state vector at time .

[0081] 10) The system noise in 9) The expression of is combined with the discretized nonlinear equation in 7) to convert the system noise The expression is further expanded and improved.

[0082] The resulting equation is:

[0083]

[0084] Among them, K k t k Kalman gain at time H k t k System gain at time x k t k The state vector at the moment; t k Time to t k-1State prediction equation at a moment; v k is t k Measurement noise at the moment; φ k|k-1 is t k-1 From the moment t k to the moment t k-1 is t k-1 State vector at the moment; is t k-1 Estimated value of the state vector at the moment.

[0085] 11) Define the system estimation noise covariance at the (k - 1) moment as Combine it with the discretized nonlinear equation in 7), the state prediction equation, the prior error covariance equation, and the updated error covariance equation in 8) to further obtain the expression of the estimation noise covariance of.

[0086] 12) Take the system estimation noise covariance in 11) as Combine it with the expression of the estimation noise covariance obtained after combination, and substitute the expression of the prior error covariance in 8) and introduce a correction term to obtain the expression of the updated system noise covariance. The system estimation noise covariance The expression of is:

[0087]

[0088] where, Q k-1 is t k-1 System noise covariance at the moment; H is the system gain; K k is t k Kalman gain at the moment.

[0089] The expression of the updated system noise covariance is:

[0090]

[0091] where, α is the proportionality coefficient; Q0 is the system noise covariance at the t0 moment; Q k-1 is t k-1 System noise covariance at the moment; H is the system gain; K k is t k Kalman gain at the moment.

[0092] 13) Combine the expression of the updated system noise covariance of PMSM in the stationary coordinate system obtained in 12) with the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance, and updated error covariance expressions in the EKF model of PMSM in the stationary coordinate system obtained in 8) to obtain the equation of the adaptive extended Kalman filter of PMSM in the stationary coordinate system.

[0093]

[0094] Combined with the adaptive extended Kalman filter model of PMSM in the stationary coordinate system, the voltage u in the stationary coordinate system is α with u β and the current i in the stationary coordinate system α with i β Input into the extended Kalman filter, and the rotor angle θ of the permanent magnet synchronous motor is estimated by the adaptive extended Kalman filter e and speed ω e , a permanent magnet synchronous motor position sensorless control method using an adaptive extended Kalman filter replaces the traditional position sensor to achieve vector control of the permanent magnet synchronous motor.

[0095] The embodiment of the present application provides a permanent magnet synchronous motor control method based on an adaptive extended Kalman filter, comprising:

[0096] The voltage and current on the stationary coordinate system are input into the adaptive extended Kalman filter, the rotor angle and speed of the permanent magnet synchronous motor are estimated by the adaptive extended Kalman filter, and the system noise covariance of the adaptive extended Kalman filter is adaptively updated.

[0097] The system noise is obtained by obtaining a nonlinear equation of an adaptive extended Kalman filter through a state equation with current as a state vector, discretizing the nonlinear equation to obtain a discretized nonlinear equation, and using the discretized nonlinear equation and the state prediction equation to obtain an expression for the system noise.

[0098] The system estimated noise covariance is defined at time k-1, and the system estimated noise covariance is combined with the expression of system noise and the discretized nonlinear equation to obtain the first expression of the estimated noise covariance. The first expression is combined with the system estimated noise covariance, and the prior error covariance expression is used as a correction term to update the system noise covariance.

[0099] The system noise is obtained by obtaining a nonlinear equation of an adaptive extended Kalman filter through a state equation with current as a state vector, discretizing the nonlinear equation to obtain a discretized nonlinear equation, and using the discretized nonlinear equation and the state prediction equation to obtain an expression for the system noise.

[0100] The rotor angle and speed of the permanent magnet synchronous motor are estimated by combining the system noise covariance with the state prediction equation, the state estimation equation, the Kalman gain equation, the prior error covariance and the update error covariance.

[0101] The state prediction equation, state estimation equation, Kalman gain equation, prior error covariance, and updated error covariance are based on the discretized non-linear equations, Jacobian matrix, and the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance equation, and updated error covariance equation of the extended Kalman filter. The state prediction equation, state estimation equation, Kalman gain equation, prior error covariance, and updated error covariance in the adaptive extended Kalman filter of the PMSM in the stationary coordinate system are obtained.

[0102] Figure 2 As shown, Figure 2(a) shows the electrical angle value detected by the Hall sensor, and Figure 2(b) shows the electrical angle value estimated by the algorithm. It can be obtained that the error between the value estimated by the algorithm and the electrical angle value measured by the Hall sensor is within one degree, indicating that the permanent magnet synchronous motor control method based on the extended Kalman filter is effective.

[0103] In the embodiment of the present application, a mathematical model of the PMSM in the three-phase coordinate system is established, and the voltage equation of the permanent magnet synchronous motor in the three-phase coordinate system is simplified to the voltage equation in the αβ two-phase stationary coordinate system through the Clark transformation. The voltage equation in the αβ two-phase stationary coordinate system is transformed into a state equation with the current as the state vector. According to the mathematical model of the PMSM in the two-phase stationary coordinate system, the state vector, input vector, and output vector are selected, and the corresponding non-linear equation of the system is obtained based on the mathematical model of the PMSM in the two-phase stationary coordinate system. The non-linear equation is linearized to obtain the Jacobian matrix. Based on the discretized non-linear equations, Jacobian matrices F[x(t)], H[x(t)], and the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance equation, and updated error covariance equation of the extended Kalman filter, the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance, and updated error covariance in the EKF model of the PMSM in the stationary coordinate system are obtained. Subsequently, an adaptive algorithm is introduced to obtain the system noise and the system estimation noise covariance is Finally, combined with the adaptive extended Kalman filter model of the PMSM in the stationary coordinate system, the voltage u α and u β in the stationary coordinate system and the current i α and i β in the stationary coordinate system are input into the adaptive extended Kalman filter. The rotor angle θ e and speed ω e of the permanent magnet synchronous motor are estimated through the adaptive extended Kalman filter.

[0104] The above are only the preferred embodiments of the present application and are not intended to limit the present application. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present application shall be included within the protection scope of the present application.

Claims

1. A permanent magnet synchronous motor control method based on an adaptive extended Kalman filter, characterized in that include: The voltage and current on the stationary coordinate system are input into the adaptive extended Kalman filter, the rotor angle and speed of the permanent magnet synchronous motor are estimated by the adaptive extended Kalman filter, and the system noise covariance of the adaptive extended Kalman filter is adaptively updated.

2. The permanent magnet synchronous motor control method based on the adaptive extended Kalman filter according to claim 1 is characterized in that: The system noise is obtained by obtaining a nonlinear equation of an adaptive extended Kalman filter through a state equation with current as a state vector, discretizing the nonlinear equation to obtain a discretized nonlinear equation, and using the discretized nonlinear equation and the state prediction equation to obtain an expression for the system noise.

3. The permanent magnet synchronous motor control method based on an adaptive extended Kalman filter according to claim 1, characterized in that The system estimated noise covariance is defined at time k-1, and the system estimated noise covariance is combined with the expression of system noise and the discretized nonlinear equation to obtain the first expression of the estimated noise covariance. The first expression is combined with the system estimated noise covariance, and the prior error covariance expression is used as a correction term to update the system noise covariance.

4. The permanent magnet synchronous motor control method based on the adaptive extended Kalman filter according to claim 1 is characterized in that: The system noise is obtained by obtaining a nonlinear equation of an adaptive extended Kalman filter through a state equation with current as a state vector, discretizing the nonlinear equation to obtain a discretized nonlinear equation, and using the discretized nonlinear equation and the state prediction equation to obtain an expression for the system noise.

5. The permanent magnet synchronous motor control method based on the adaptive extended Kalman filter according to claim 4 is characterized in that: The rotor angle and speed of the permanent magnet synchronous motor are estimated by combining the system noise covariance with the state prediction equation, the state estimation equation, the Kalman gain equation, the prior error covariance and the update error covariance.

6. The permanent magnet synchronous motor control method based on an adaptive extended Kalman filter according to claim 5, wherein The state prediction equation, state estimation equation, Kalman gain equation, prior error covariance and update error covariance are based on discretized nonlinear equations, Jacobian matrix and the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance equation and update error covariance equation of an extended Kalman filter, so as to obtain the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance and update error covariance in the adaptive extended Kalman filter of the PMSM in a stationary coordinate system.

7. An adaptive extended Kalman filter for permanent magnet synchronous motor control, characterized in that, The system noise covariance of the adaptive extended Kalman filter is adaptively updated, and the rotor angle and speed of the permanent magnet synchronous motor are estimated by the adaptive extended Kalman filter.

8. An adaptive extended Kalman filter according to claim 7, characterized in that, The adaptive extended Kalman filter is based on discretized nonlinear equations, Jacobian matrix and the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance equation and update error covariance equation of the extended Kalman filter to obtain the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance and update error covariance in the adaptive extended Kalman filter of the PMSM in a stationary coordinate system.

9. An adaptive extended Kalman filter according to claim 8, wherein, The design method of the adaptive extended Kalman filter includes: Establish the voltage equation of the three-phase coordinate system of the permanent magnet synchronous motor PMSM; The voltage equation of the permanent magnet synchronous motor in the three-phase coordinate system is simplified to the voltage equation in the stationary coordinate system through Clark transformation; Transform the voltage equation in the stationary coordinate system into a state equation with current as the state vector; According to the transformation of the voltage equation of the PMSM in the stationary coordinate system into the state equation with the current as the state vector, a state vector x, an input vector u and an output vector y are selected; According to the state vector x, the input vector u and the output vector y, the nonlinear equation corresponding to the system is obtained, including the nonlinear term of the nonlinear equation; Linearize the nonlinear terms to obtain the Jacobian matrix; Let the sampling time be Ts, and discretize the nonlinear equation; Based on the discretized nonlinear equations, Jacobian matrix and the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance equation and update error covariance equation of the extended Kalman filter, the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance and update error covariance of the EKF model of PMSM in the stationary coordinate system are obtained; The equation obtained by combining the discretized nonlinear equation and the state prediction equation is combined with the state estimation equation again to obtain the expression of system noise; The expression of system noise is combined with the discretized nonlinear equation to further expand and improve the expression of system noise; Define the system estimated noise covariance at time k-1, and combine it with the discretized nonlinear equation, state prediction equation, prior error covariance equation, and update error covariance equation to obtain the expression of the estimated noise covariance; The system estimated noise covariance is combined with the estimated noise covariance expression, and the prior error covariance expression is substituted and a correction term is introduced to obtain the expression for updating the system noise covariance; The expression of updating the system noise covariance is combined with the state prediction equation, state estimation equation, Kalman gain equation, prior error covariance and updated error covariance expressions in the EKF model of PMSM in the stationary coordinate system to obtain the equation of the adaptive extended Kalman filter of PMSM in the stationary coordinate system.

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