A Kalman filter-based sensorless control strategy for noise parameter identification

Abstract

Aiming at the problem that the parameters of the noise covariance matrix in the Kalman filtering algorithm are difficult to tune, the present invention proposes a Kalman filter sensorless control strategy based on noise parameter identification. The parameter identification algorithm uses an improved population optimization algorithm, which combines the ideas of particle swarm and beetle antennae, and adds a linearly decreasing weight and a learning factor synchronization formula, so that the convergence speed and search ability of the optimization algorithm are significantly improved. In the vector control system of a brushless DC motor based on the extended Kalman filter, the parameters of the process noise matrix Q and the measurement noise matrix R in the observer are optimized by the improved population algorithm, and the optimal noise matrix parameters are quickly found by testing different fitness functions. The simulation results show that when the rotational speed exceeds the 1000 speed range, the steady-state error decreases and the estimation performance of the observer is significantly improved.

Description

Technical Field

[0001] The present invention relates to the field of sensorless control of motors, and particularly to a Kalman filter sensorless control strategy for noise parameter identification. Background Technique

[0002] Brushless DC motors have significant application value in the fields of industrial automation and renewable energy due to their advantages such as high power, low power consumption, high performance, long life, and low noise. The current popular research fields of brushless DC motors are mainly reflected in the following aspects: researching sensorless control technology to improve the performance and efficiency of motors, including high-precision position control, speed control, and torque control; suppressing torque ripple. Combining technologies such as fuzzy, neural network, active disturbance rejection, and direct torque control, suppressing the commutation torque ripple of brushless DC motors is one of the current research hotspots; field-weakening speed regulation. When a brushless DC motor operates below the base speed, various forms of double-closed-loop control strategies are often used, supplemented by technologies such as PWM and hysteresis control, to obtain good control effects on the system;

[0003] The sensorless technology of brushless DC motors can be divided into two basic types: the high-frequency injection method and the fundamental frequency model method. The high-frequency injection method refers to injecting a high-frequency voltage or high-frequency current, superimposing the high-frequency signal on the base excitation, and estimating the position of the motor even at low speed or stationary by detecting the high-frequency response. However, this method depends on the accuracy of high-frequency signal detection. In addition, the injection of high-frequency excitation is likely to generate high-frequency noise, thereby reducing the system performance. The fundamental frequency model method is mainly used for medium- and high-speed applications. It uses the motor current as the input of the observer and designs an observer to estimate the position of the rotor. The observation methods include the extended Kalman filter (EKF), model reference adaptive control (MRAC), and sliding mode observer (SMO). Among them, compared with SMO and MRAC, EKF has better convergence performance in the low-speed domain. The extended Kalman directly estimates the rotational speed and position of the motor without the need to design filtering technology to process the signal. However, the Kalman observer depends on whether the noise matrix parameters approach the actual system, otherwise it cannot exert good estimation performance. Therefore, an improved scheme is needed to tune the noise matrix parameters. Summary of the Invention

[0004] Object of the Invention: To solve the problem that it is difficult to tune the noise covariance matrix parameters in the Kalman filter algorithm, the present invention provides a Kalman filter sensorless control strategy for noise parameter identification, which improves the anti-interference and estimation accuracy of speed regulation in each speed range of the motor, can reduce chattering under speed or load changes, and obtain high-precision rotor speed and position information.

[0005] Technical Solution: The present invention discloses a Kalman filter sensorless control strategy for noise parameter identification, including the following steps:

[0006] Step 1: Establish the state - space equation of the brushless DC motor in the two - phase stationary coordinate system;

[0007] Step 2: Based on the state - space equation established in Step 1, construct an extended Kalman filter observer. The voltage and current of the brushless DC motor in the two - phase stationary coordinate system are input into the extended Kalman filter observer, and the observed speed is output; Electrical angle

[0008] Step 3: Search for the optimal covariance matrix of the system noise covariance matrix Q and the measurement noise covariance R in the extended Kalman observer constructed in Step 2 through the population algorithm;

[0009] Step 4: The population optimization search algorithm in Step 3 combines the ideas of the particle swarm algorithm and the beetle antennae search algorithm, and adds a linearly decreasing weight and a learning factor synchronization formula.

[0010] Step 5: Use the linear weighted combination method to optimize the noise matrix parameters with respect to the stator current on the αβ - axes, speed, and phase - angle error as multi - objectives, and test the weight coefficients corresponding to each objective through experiments. The algorithm convergence feedbacks the optimal noise matrix to the Kalman filter observer;

[0011] The voltage - current equations of the brushless DC motor on the αβ - axes are as follows:

[0012]

[0013] Where: u α is the stator voltage on the α - axis, u β is the stator current on the β - axis, i α is the stator current on the α - axis, i β is the stator current on the β - axis, θ e is the rotor position of the brushless DC motor, R s is the stator resistance of the brushless DC motor, L s is the equivalent inductance of the brushless DC motor, ψ f is the magnetic flux of the permanent magnet, ω e is the electrical angular velocity;

[0014] The state - space equation of the nonlinear system of the brushless DC motor is:

[0015]

[0016] Z = h(x)+v (4)

[0017] Select the input state variables, control variables, and output state variables required for the extended Kalman observer, which are: x = [i α , i β , ω e, θ e T , u = [u α , u β T , Z = [i α , i β T . W is the system noise and v is the measurement noise. f(x) represents the 4×1 function value when the independent variable is the input state variable x, and h(x) represents the 2×1 function value when the independent variable is the output state variable Z. B is the matrix coefficient of the control variable.

[0018] The linearization processes are respectively performed on the f(x) and h(x) functions, and the corresponding Jacobian matrices are as follows:

[0019]

[0020] The prior state equation after discretization of the extended Kalman filter for brushless DC motor state estimation using the linearized Jacobian matrix is as follows:

[0021]

[0022] k represents the current iteration number, respectively represent the α-axis stator current, β-axis stator current, electrical speed, and electrical angle in the input state variable at the k-th iteration.

[0023] Substitute into the extended Kalman filter recursive process,

[0024]

[0025] Among them: is the prior estimate value, T s is the sampling time,

[0026] Φ = I + F(x)T s (9)

[0027] Among them: Φ is the state transition matrix, I is the 4th-order identity matrix, and F(x) is the Jacobian matrix;

[0028]

[0029] Among them: P k - is the prior error covariance matrix, and Q represents the covariance matrix of the system process noise;

[0030]

[0031] Among them: K k is the Kalman filter gain, and R represents the covariance matrix of the system process noise,​​​

[0032] The updated optimal estimated value is:

[0033]

[0034] H - is the inverse matrix of H, and Z k is the output state variable at the k-th iteration.

[0035] The updated optimal covariance matrix is:

[0036]

[0037] The system noise covariance matrix Q and the measurement noise covariance R are defined as:

[0038]

[0039] R = diag{r, r} (15)

[0040] where Q is a 4×4 process noise covariance matrix, and represents four different parameters to be optimized on the main diagonal of matrix Q. The third term q ω has a large error fluctuation affected by the sampling time; R is the covariance matrix of the measurement noise, and r is the parameter to be optimized on the main diagonal of matrix R.

[0041] In the particle swarm optimization search algorithm in step 4, the particle velocity update formula is:

[0042]

[0043] where the subscript i represents the particle number, and d represents the particle swarm space dimension; is the velocity of the i-th particle in the d-th dimension, ω is the inertia weight, c1 and c2 are acceleration factors, rand is a random number in the interval [0, 1], is the individual optimal position of the particle, is the global optimal position, and ω is the inertia weight, The independent variable is a 1×5 array containing the noise matrix parameters.

[0044] Assume that the beetle head moves randomly in any direction. Therefore, the vector direction from the right antenna to the left antenna must also be random. Therefore, for an optimization problem in an n-dimensional space, a random vector can be generated to represent and standardize it.

[0045]

[0046] where: rands is a random function, and d b still represents the space dimension, and θb It is represented as the angle of the particle's forward direction.

[0047] The update formulas for the positions of the left and right whiskers of the particle are as follows:

[0048]

[0049] Where: are the positions of the left and right whiskers of the particle respectively, and d0 represents the distance between the two whiskers;

[0050]

[0051] They are respectively represented as the objective functions selected in step 4, and the independent variables included are sign represents the sign function, step is the step size during the search. norm represents the vector norm used to measure the magnitude or length of a vector.

[0052] The formula for synchronizing the addition of linearly decreasing weights and learning factors is:

[0053]

[0054]

[0055] If the inertia weight and learning factor of the particle swarm algorithm are set as one-dimensional vectors, then equations (21) and (22) are respectively the update iteration formulas for the inertia weight and learning factor, ω max 、ω min 、c max 、c min are the maximum and minimum values of the inertia weight and learning factor; d1, d2 are dynamic error coefficients; t, t max are the current iteration number and the maximum iteration number.

[0056] The fitness function with respect to the stator current, speed, and phase angle error on the αβ axes is:

[0057]

[0058] The method of converting multiple objectives into a single objective function using the linear weighted combination method described in step 5 is to multiply each objective by the corresponding weight coefficient according to its importance and then sum them up to form a single objective function for solution; then the single objective function after unifying the dimensions is:

[0059] F = β1f1(x) + β2f2(x) + β3f3(x) (25)

[0060] Where: β1, β2, β3 are the weights of each fitness function; by testing different fitness functions, the fitness values are solved to quickly find The approaching value. Information in the sampled motor vector control system, including stator current, rotor speed, electrical angle, and magnetic flux of dynamic and steady-state information, is used to form the training data of the optimization algorithm. After optimization, the EKF has better state estimation accuracy.

[0061] Beneficial effects

[0062] The present invention optimizes the process noise matrix Q and measurement noise matrix R parameters in the Kalman filter observer by using an improved population algorithm, combines the ideas of particle swarm and beetle antennae algorithms to solve the problem that the traditional particle swarm algorithm is prone to falling into local optimum, and adds linear decreasing weight and learning factor synchronization to improve the algorithm convergence speed and search ability. For the optimized Kalman filter algorithm, when the motor speed exceeds the 1000 speed range, the steady-state error decreases, and the estimation performance of the observer is significantly improved. And the torque fluctuation error is smaller. Description of the drawings

[0063] Figure 1 It is a schematic diagram of the vector control structure of a brushless DC motor;

[0064] Figure 2 It is a flow chart of noise parameter self-learning;

[0065] Figure 3 It is a performance comparison diagram of the parameter identification algorithm under the f1 fitness function;

[0066] Figure 4 It is a comparison of the speed observation error at the time of speed mutation between the traditional algorithm and after adding parameter identification;

[0067] Figure 5 It is a comparison of the rotor position observation error at the time of speed mutation between the traditional algorithm and after adding parameter identification;

[0068] Figure 6 It is a comparison of the motor torque between the traditional algorithm and after adding parameter identification; Detailed implementation manners

[0069] The present invention will be further described below with reference to the drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be used to limit the protection scope of the present invention.

[0070] The present invention discloses a Kalman filter sensorless control strategy for noise parameter identification, including the following steps:

[0071] In step 1, the state space equation is:

[0072] The voltage and current equations of the αβ axes of the brushless DC motor are as follows:

[0073]

[0074] Where: uα The stator voltage of the α-axis, u α The stator current of the β-axis, i α The stator current of the α-axis, i β The stator current of the β-axis, θ e The rotor position of the brushless DC motor, R s The stator resistance of the brushless DC motor, L s The equivalent inductance of the brushless DC motor, ψ f The magnetic flux linkage of the permanent magnet, ω e The electrical angular velocity;

[0075] The state space equation of the brushless DC motor nonlinear system is:

[0076]

[0077] Z = h(x) + v (4)

[0078] Select the input state variables, control variables, and output state variables required for the extended Kalman observer, which are: x = [i α , i β , ω e , θ e T , u = [u α , u β T , Z = [i α , i β T . W is the system noise and v is the measurement noise. f(x) represents the 4×1 function value when the independent variable is the input state variable x, and h(x) represents the 2×1 function value when the independent variable is the output state variable Z. B is the matrix coefficient of the control variable.

[0079] Linearize the functions f(x) and h(x) respectively to obtain the corresponding Jacobian matrices as:

[0080]

[0081]

[0082] The surface-mounted motor is adopted in this simulation. The parameters refer to the LAO34-040NN07A brushless DC motor, with a weight of 232 grams, a maximum shaft length of 35 MM, and a shaft width of 5 MM. Its rated speed is 1300 RPM. The reference speeds selected for this simulation test are 500, 1000, and 1300 RPM.

[0083] Table 1 BLDC Parameter Table

[0084] ​​​

[0085] In step 2, the extended Kalman filter observer is as follows:

[0086] The Jacobian matrix obtained by linearization in step 1 is used for the prior state equation after discretization of the extended Kalman filter for brushless DC motor state estimation as follows:

[0087]

[0088] k represents the current iteration number, respectively represent the stator current on the α-axis, the stator current on the β-axis, the electrical rotational speed, and the electrical angle in the input state variables at the k-th iteration.

[0089] Substitute into the extended Kalman filter recursive process,

[0090]

[0091] Among them: is the prior estimated value, T s is the sampling time,

[0092] Φ = I + F(x)T s (9)

[0093] Among them: Φ is the state transition matrix, I is the 4th-order identity matrix, and F(x) is the Jacobian matrix;

[0094]

[0095] Among them: is the prior error covariance matrix, and Q represents the covariance matrix of the system process noise;

[0096]

[0097] Among them: K k is the Kalman filter gain, and R represents the covariance matrix of the system process noise,

[0098] Update the optimal estimated value to:

[0099]

[0100] H - is the inverse matrix of H, and Z k is the output state variable at the k-th iteration.

[0101] Update the optimal covariance matrix to:

[0102]

[0103] In step 3, the system noise covariance matrix Q and the measurement noise covariance R are defined as:

[0104]

[0105] R = diag{r, r} (15)

[0106] Among them, Q is a 4×4 process noise covariance matrix, where represents four different parameters to be optimized on the main diagonal of matrix Q. The third term q ω has a large error fluctuation affected by the sampling time; R is the covariance matrix of the measurement noise, where r is the parameter to be optimized on the main diagonal of matrix R. Here, the subscript is used for q to illustrate that the values of these four parameters are not equal. The reason for using i α , i β , ω, θ as subscripts is because these four are affected by the input state variable x = [i α , i β , ω e , θ e T influence. The parameter r to be optimized on the main diagonal of matrix R, and the main diagonal values of the 2×2 measurement noise covariance matrix are equal, so they are all represented by r.

[0107] Preliminarily test the convergence and stability of the observer, and thus set the initial values of the process noise matrix Q and the measurement noise matrix R as follows, which can perform well in each rotational speed range.

[0108]

[0109] In step 4, the particle velocity update formula in the population optimization search algorithm is:

[0110]

[0111] Among them, the subscript i represents the particle number, and d represents the dimension of the particle population space; is the velocity of the i-th particle in the d-th dimension, ω is the inertia weight, c1 and c2 are acceleration factors, rand is a random number in the range of [0, 1], is the individual optimal position of the particle, is the global optimal position, ω is the inertia weight, The independent variable is a 1×5 array containing the noise matrix parameters.

[0112] Assume that the beetle head moves randomly in any direction. Therefore, the vector direction from the right antenna to the left antenna must also be random. Therefore, for the optimization problem in the n-dimensional space, a random vector can be generated to represent and standardize it.

[0113] ​

[0114] where: rands is a random function, d b still represents the spatial dimension, θ b represents the angle of the particle's forward direction.

[0115] The update formulas for the left and right whisker positions of the particle are as follows:

[0116]

[0117] where: are the left and right whisker positions of the particle respectively, and d0 represents the distance between the two whiskers;

[0118]

[0119] respectively represent the objective functions selected in step 4, and the independent variables included are sign represents the sign function, step is the step size during the search. norm represents the vector norm used to measure the size or length of a vector.

[0120] The formula for adding a linearly decreasing weight and synchronizing the learning factor is:

[0121]

[0122] If the inertia weight and learning factor of the particle swarm algorithm are set as one-dimensional vectors, then equations (21) and (22) are the update iteration formulas for the inertia weight and learning factor respectively, ω max 、ω min 、c max 、c min are the maximum and minimum values of the inertia weight and learning factor; d1, d2 are dynamic error coefficients; t, t max are the current iteration number and the maximum iteration number.

[0123] The objective function selected in step 5 is:

[0124]

[0125] The method of converting multiple objectives into a single objective function using the linear weighted combination method described in step 5 is to multiply each objective by the corresponding weight coefficient according to its importance, and finally add them up to form an objective function for solution; then the single objective function after unifying the dimensions is:

[0126] F = β1f1(x) + β2f2(x) + β3f3(x) (28)

[0127] where: β1, β2, β3 are the weights of each fitness function; by testing different fitness functions, the fitness values are solved to quickly find qi , q i , q ω , q θ , the approaching value of r. Information in the sampled motor vector control system, including the stator current, rotor speed, electrical angle, and magnetic flux of dynamic and steady-state information, is used to form the training data of the optimization algorithm. After optimization, the EKF has better state estimation accuracy.

[0128] Figure 1 It is a vector control block diagram based on EKF. The present invention is applied in a motor drive system similar to this. The parameters of the BLDC control system are shown in Table 2. Without changing the system parameters, the process noise matrix Q and the measurement noise matrix R are optimized to improve the estimation accuracy.

[0129] Table 2 BLDC control system parameter table

[0130]

[0131] Figure 2 It is a flowchart of the self-learning of noise parameters. Figure 3 It is a performance comparison chart of the parameter identification algorithm under the f1 fitness function. As shown in the figure, combining PSO particles and BAS longhorn beetle antennae can prevent the particles from falling into local optima. The convergence speed of the LinWPSO linear decreasing weight optimized particle swarm algorithm is significantly improved. The LnCPSO learning factor synchronization optimized particle swarm algorithm further enhances the local and global search capabilities. The IFPSO combines the above optimization algorithms and has good search performance and convergence speed.

[0132] The process noise matrix Q and the measurement noise matrix R parameters in the observer are optimized by an improved population algorithm. Six different fitness functions are tested as shown in Table 3. The population size and iteration parameters are set to 100. The optimization algorithm has a fast convergence speed, and the best noise parameters are quickly searched through the algorithm tool. Through testing, the best noise parameters are shown in the last row of Table 3. β1, β2, and β3 in the multi-objective optimization are 0.55, 0.35, and 0.1.

[0133] Table 3 Noise matrix parameter identification

[0134]

[0135]

[0136] Figure 4For the comparison of the rotational speed observation error at the speed mutation between the traditional algorithm and the algorithm with parameter identification added, when the motor rotational speed reaches 500 RPM, the steady-state error is basically zero, and the waveform distortion phenomenon is alleviated after optimization. When the motor rotational speed reaches 1000 RPM, the steady-state error is about 3 RPM, and the performance is improved by about 50% compared with that before optimization. Finally, when the motor rotational speed enters 1350 RPM, the steady-state error is about 5.5 RPM, and the performance is improved by about 45% compared with that before optimization.

[0137] Figure 5 For the comparison of the rotor position observation error at the speed mutation between the traditional algorithm and the algorithm with parameter identification added, the estimation accuracy of the rotor position can be controlled within 0.0001 rad at different rotational speeds.

[0138] Figure 6 For the comparison of the motor torque between the traditional algorithm and the algorithm with parameter identification added, it can be seen from the figure that the fluctuation range of the torque error decreases.

[0139] The above embodiments are only for illustrating the technical concept and features of the present invention, and the purpose is to enable those skilled in the art to understand the content of the present invention and implement it accordingly. It should not be used to limit the protection scope of the present invention. Any equivalent transformation or modification made according to the spirit of the present invention should be covered within the protection scope of the present invention.

Claims

1. A Kalman filter-based sensorless control method for noise parameter identification, characterized in that: It includes the following steps: Step 1: Establish the state - space equation of the brushless DC motor in the two - phase stationary coordinate system; The state - space equation is: The voltage - current equations of the αβ axes of the brushless DC motor are as follows: where: u α is the stator voltage of the α-axis, u β is the stator voltage of the β-axis, i α is the stator current of the α-axis, i β is the stator current of the β-axis, θ e is the rotor position of the brushless DC motor, R s is the stator resistance of the brushless DC motor, L s is the equivalent inductance of the brushless DC motor, ψ f is the magnetic flux linkage of the permanent magnet, ω e is the electrical angular velocity; The state - space equation of the non - linear system of the brushless DC motor is: Z = h(x)+v (4) Select the input state variables, control variables, and output state variables required for the extended Kalman observer, which are: x = [i α , i β , ω e , θ e T , u = [u α , u β T , Z = [i α , i β T , W is the system noise, v is the measurement noise, B is the matrix coefficient of the control variable, f(x) represents the 4×1 function value when the independent variable is the input state variable x, and h(x) represents the 2×1 function value when the independent variable is the output state variable Z;​​​ Step 2: On the basis of Step 1, construct an extended Kalman filter observer. The observed speed output after the voltage and current in the two-phase stationary coordinate system of the brushless DC motor pass through the extended Kalman filter observer Electrical angle The corresponding Jacobian matrices are obtained by linearizing the functions f(x) and h(x) respectively: For f(x) Derivation needs to consider time t, so x = x(t). After linearization, the Jacobian matrix is obtained. The prior state equation after discretization of the extended Kalman filter for brushless DC motor state estimation is as follows: where k represents the current iteration number, respectively represent the α-axis stator current, β-axis stator current, electrical rotational speed, and electrical angle in the input state variables at the k-th iteration; represent the α-axis stator voltage and β-axis stator voltage at the (k - 1)-th iteration; Substitute into the extended Kalman filter recursive process: Wherein: is the prior estimated value, is the prior estimated value at the previous moment, T s is the sampling time; Φ = I + F(x)T s (9) Where: Φ is the state - transition matrix, I is the 4 - order identity matrix, F(x) is the Jacobian matrix. When solving the state - transition matrix Φ, the F(x) Jacobian matrix is equivalent to a constant and is not affected by time t; Wherein: is the prior error covariance matrix, P k-1 is the optimal covariance matrix at the previous moment, and Q represents the covariance matrix of the system process noise; Where: K k is the Kalman filter gain, and R represents the covariance matrix of the system process noise, Update the optimal estimated value as: Among them, H - is the inverse matrix of H, Z k is the output state variable at the k-th iteration; Update the optimal covariance matrix as: Step 3: Obtain the system noise covariance matrix Q and the measurement noise covariance matrix R in the extended Kalman observer constructed in Step 2, and search for the optimal covariance matrix through the group optimization search algorithm; the group optimization search algorithm combines the particle swarm algorithm and the beetle antennae search algorithm and adds a linear decreasing weight and learning factor synchronization method; The system noise covariance matrix Q and the measurement noise covariance matrix R are defined as: R = diag{r,r} (15) where Q is a 4×4 process noise covariance matrix, q ω ,q θ represent the four different parameters to be optimized on the main diagonal of matrix Q. The third item q ω has a large error fluctuation affected by the sampling time; R is the covariance matrix of the measurement noise, where r is the parameter to be optimized on the main diagonal of matrix R; The population optimization search algorithm is: The particle velocity update formula is: where the subscript i represents the particle number, and d represents the dimensionality of the particle population space; is the velocity of the i-th particle in the d-th dimension, ω is the inertia weight, c1 and c2 are acceleration factors, rand is a random number in the interval [0, 1], is the individual optimal position of the particle, is the global optimal position, ω is the inertia weight, The independent variable is a 1×5 array containing the parameters of the noise matrix; Assume that the beetle head moves randomly in any direction. Therefore, the vector direction from the right antenna to the left antenna must also be random. For the optimization problem in the n - dimensional space, a random vector is generated to represent and standardize it; where: rands is a random function, d b still represents the spatial dimension, θ b represents the angle of the particle's forward direction; The update formulas for the left and right antenna positions of the particle are as follows: Wherein: are respectively the positions of the left whisker and the right whisker of the particle, and d0 represents the distance between the two whiskers; The particle position update formula is: Among them, respectively represent the selected objective functions, and the independent variables included therein are respectively sign represents the sign function, step is the step size during the search, and norm represents the vector norm used to measure the magnitude or length of a vector; The formula for adding a linear decreasing weight and learning factor synchronization is: If the inertia weight and learning factors of the particle swarm algorithm are set as one-dimensional vectors, then Equations (21) and (22) are the update iteration formulas for the inertia weight and learning factors, respectively, ω max 、ω min 、c max 、c min are the maximum and minimum values of the inertia weight and learning factors; d1 and d2 are dynamic error coefficients; t and t max are the current iteration number and the maximum iteration number; Step 4: Use the linear weighted combination method to perform multi - objective optimization on the noise matrix parameters with respect to the stator current of the αβ axes, speed, and phase - angle error. Through experimental tests, the weight coefficients corresponding to each objective are obtained, and the algorithm convergence feedbacks the optimal noise matrix to the Kalman filter observer; Use the linear weighted combination method to perform multi - objective optimization on the noise matrix parameters with respect to the stator current of the αβ axes, speed, and phase - angle error, and select the objective function as: The multi - objective is transformed into a single - objective function by the linear weighted combination method. According to the importance of each objective, it is multiplied by the corresponding weight coefficient respectively, and finally added to form a single - objective function for solution; then the single - objective function after unifying the dimensions is: F = β1f1(x)+β2f2(x)+β3f3(x) (25) Wherein: β1, β2, and β3 are the weights of the fitness functions; by testing different fitness functions, the fitness values are solved to quickly find q ω ,q θ , the approaching values of r, q ω ,q θ represent four different parameters to be optimized on the main diagonal of matrix Q, Q is a 4×4 process noise covariance matrix, r is the parameter to be optimized on the main diagonal of matrix R, and R is the covariance matrix of measurement noise; sample the information in the motor vector control system, including the stator current, rotor speed, electrical angle, and magnetic flux of dynamic and steady-state information, so as to form the training data of the optimization algorithm. After optimization, the EKF has better state estimation accuracy.

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