A model predictive control method based on hybrid nonlinear hammerstein model

Abstract

The application relates to the technical field of motor control, in particular to a model predictive control method based on a hybrid nonlinear Hammerstein model, which comprises the following steps: sampling three-phase currents of a motor, constructing a hybrid nonlinear Hammerstein model, calculating linear component stator currents of d-axis and q-axis at k+1 time through an external input autoregressive model, selecting nonlinear component stator currents of d-axis and q-axis at k+1 time through a neutral line table and a nonlinear component table, constructing a first control equation, obtaining a modulation signal, and converting the modulation signal into a pulse control signal through a modulation module and controlling a motor driver. The application introduces the hybrid nonlinear Hammerstein model into a permanent magnet synchronous motor driving system, and puts nonlinear motion component factors of the motor system into a model prediction process, so that linear and nonlinear motions of the motor system are considered, the motor system motion state can be accurately characterized, and the description precision is good.

Description

Technical Field

[0001] This invention relates to the field of motor control technology, and specifically to a model predictive control method based on a hybrid nonlinear Hammerstein model. Background Technology

[0002] Model predictive control (MPC) is a type of computer control algorithm that emerged in the field of industrial engineering control in the late 1970s and has been widely used in process control industries such as chemical engineering. As a control strategy that has emerged in recent years, MPC, compared with vector control (VOC), eliminates the need for current inner loop and parameter tuning, directly generates inverter drive signals without pulse modulation, and is easier to handle system constraints or add other control objectives. It has advantages such as simple structure, fast dynamic response, and easy expansion. Compared with direct torque control (DTC), MPC optimizes the selection of the optimal voltage vector by predicting the motor state, making it more accurate and effective in vector selection. It is also easier to consider various nonlinear constraints, including reduced switching frequency, and has advantages such as good steady-state performance and flexible control.

[0003] However, the traditional Model Predictive Control (ARX) model, which implements the model building and prediction process for linear components, can only describe the linear motion state of the motor system and cannot accurately describe the nonlinear motion of the turntable, resulting in low description accuracy.

[0004] In view of this, the applicant has conducted in-depth research on the above-mentioned issues, which led to this case. Summary of the Invention

[0005] The purpose of this invention is to provide a model predictive control method based on a hybrid nonlinear Hammerstein model with good descriptive accuracy.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A model predictive control method based on a hybrid nonlinear Hammerstein model includes the following steps:

[0008] S1: Sample the three-phase current of the motor, and process the sampled three-phase current through Park transform to obtain the d-axis component of the stator current. and the q-axis component of the stator current ;

[0009] S2: Based on the d-axis component of the stator current and the q-axis component of the stator current A hybrid nonlinear Hammerstein model is constructed, comprising linear and nonlinear components. An external input autoregressive model is used as the linear component, and the stator currents of the d-axis and q-axis linear components at time k+1 are calculated using this external input autoregressive model. and The external input autoregressive model is constructed as follows:

[0010] (1);

[0011] In the formula, Let be the d-axis component of the stator current at time k in the rotating coordinate system. Let be the q-axis component of the stator current at time k in the rotating coordinate system. Let be the d-axis component of the stator voltage at time k in the rotating coordinate system. Let be the q-axis component of the stator voltage at time k in the rotating coordinate system. and These are the current model coefficients for the d-axis and q-axis, respectively. and , respectively, are the voltage model coefficients for the d-axis and q-axis, m is the order of the current model, n is the order of the voltage model, and z is the discrete-time operator;

[0012] The midline table and the nonlinear component table are used as the nonlinear components, and the stator currents of the d-axis and q-axis nonlinear components at time k+1 are selected through the midline table and the nonlinear component table. and Where k is the current time;

[0013] S3: Stator current based on the linear components of the d-axis and q-axis at time k+1 obtained in step 2. and And the stator currents at time k+1 with nonlinear components along the d-axis and q-axis obtained in step 2. and A first control equation is constructed that combines linear and nonlinear components, and a modulation signal is obtained based on the first control equation.

[0014] S4: The modulation signal is converted into a pulse control signal by the modulation module and used to control the motor driver.

[0015] Furthermore, in step S2, the stator currents of the d-axis and q-axis linear components at time k+1 are calculated using an external input autoregressive model. and The process is as follows:

[0016] S2-1: Construct the external input autoregressive model;

[0017] S2-2: The d-axis and q-axis current model coefficients in formula (1) and and d-axis and q-axis voltage model coefficients and Construct a recursive vector of d-axis and q-axis coefficients at time k. and The recursive vectors of the d-axis and q-axis coefficients at time k and The expression is as follows:

[0018] (2);

[0019] Obtain electronic voltage component data and stator current component data, and construct a recursive vector of d-axis and q-axis data at time k using the obtained electronic voltage component data and stator current component data. and The recursive vectors of d-axis and q-axis data at time k and The expression is as follows:

[0020] (3);

[0021] In the formula, and These represent the d-axis and q-axis stator current components at time k, k-1, and up to time km, respectively. and These are the d-axis and q-axis stator voltage components at time k, k-1, and up to kn, respectively.

[0022] S2-3: The maximum likelihood estimation algorithm is used to recursively calculate the coefficient vectors of the d-axis and q-axis at time k. and Update the recursive vectors of the d-axis and q-axis coefficients at time k. and Updated to the recursive vector of d-axis and q-axis coefficients at time k+1. and ;

[0023] S2-4: Calculate the data recursion vector at time k+1 and Wherein, the recursive vectors of the d-axis and q-axis data at time k. and d-axis component of stator current at time k+1 Elements and the q-axis component of the stator current at time k+1 Each element is determined by its reference signal. and Instead, the Lagrange method is used to calculate the reference values ​​of the stator currents along the d-axis and q-axis at time k+1. and The specific formula is as follows:

[0024] (4);

[0025] In the formula, , , and , , These are the stator current reference values ​​for the d-axis and q-axis at times k, k-1, and k-2, respectively.

[0026] S2-5: Construct the linear component governing equations and recursively vectorize the d-axis and q-axis coefficients at time k+1 obtained in step S2-3. and and the data recursion vector at time k+1 obtained in step S2-4 and Substituting into the governing equations, the linear components of the stator currents along the d-axis and q-axis at time k+1 are calculated. and The specific formula is as follows:

[0027] (5);

[0028] S2-6: Perform hyperlocalization on the external input autoregressive model to obtain the d-axis and q-axis state gains. , and lumped variables , The specific formula is as follows:

[0029] (6);

[0030] (7);

[0031] in, To control the cycle, and These are the stator voltage components along the d-axis and q-axis, respectively. Accumulate iteration variables for the current component. Accumulate iterative variables for the voltage component;

[0032] Furthermore, the stator currents of the d-axis and q-axis nonlinear components at time k+1 are selected using the midline table and the nonlinear component table. and The process is as follows:

[0033] S3-1: Establish a complex plane in a two-phase stationary coordinate system, and divide the complex plane into 6 equal intervals, named SI, S-II, S-III, S-IV, SV, and S-VI respectively, and define the midline of each interval. , , , , , A neutral line table is established for the stator current in the two-phase stationary coordinate system, and a nonlinear component table of the same dimension is also established. Each element in the table is denoted as... , , , , , It should be noted that the complex plane is the plane in which complex numbers are conventionally represented using a rectangular coordinate system;

[0034] S3-2: The sampled three-phase currents are transformed to a two-phase stationary coordinate system using Clark transformation to obtain the α-axis component of the stator current at time k. and the β-axis component of the stator current Calculate the Euclidean distance between the midline of the interval and the stator current components along the α and β axes. And select the interval Si with the minimum Euclidean distance, the specific formula is as follows:

[0035] (8);

[0036] In the formula, i is a loop variable that takes values ​​from I, II, III, IV, V, and VI; Rated current;

[0037] S3-3: Determine the elements of the nonlinear component table If the value is empty, then the elements corresponding to the interval Si with the minimum Euclidean distance are assigned values ​​using the stator current reference value and the difference between the linear components at time k+1. The specific formula is as follows:

[0038] (9);

[0039] Otherwise, proceed to the next step;

[0040] S3-4: Select the element corresponding to the minimum Euclidean distance interval Si in the nonlinear component table as the stator current of the d-axis and q-axis nonlinear components at time k+1. and The specific expression is as follows:

[0041] (10).

[0042] Furthermore, in step S3, the first governing equation is constructed as follows:

[0043] (11);

[0044] In the formula, For proportional gain, This is the weighting factor.

[0045] Furthermore, in steps S2-3, the recursive vectors of the d-axis and q-axis coefficients at time k... and The steps to perform the update are as follows:

[0046] (1) Calculate the stator current component error, and recursively vectorize the d-axis and q-axis coefficients at time k. and and the recursive vectors of the d-axis and q-axis coefficients at time k+1. and Substituting into formula (12), the expression is as follows:

[0047] (12);

[0048] (2) Design the transformation matrices of the d-axis and q-axis at time k. and ,in, ,…, These are the d-axis matrix elements from time k to time km. ,…, These represent the q-axis matrix elements from time k to time km, and the d-axis and q-axis matrix elements at time k. and The expression is as follows:

[0049] (13);

[0050] in, λ For error gain, a The power coefficient;

[0051] (3) Update the coefficient recursion vector, thereby making the coefficient recursion vector and Updated to and The specific formula is as follows:

[0052] (14);

[0053] in, To update the step size, The first adjustable coefficient, This is the second adjustable coefficient.

[0054] By adopting the above technical solution, the present invention has the following beneficial effects:

[0055] 1. This invention introduces a hybrid nonlinear Hammerstein model for use in permanent magnet synchronous motor drive systems. By incorporating the nonlinear motion components of the motor system into the model prediction process, it takes into account both the linear and nonlinear motion of the motor system, thus accurately characterizing the motion state of the motor system with good description accuracy.

[0056] 2. This invention also introduces a maximum likelihood estimation algorithm to update linear components online, thereby obtaining more accurate control precision and model fit. Only 1-2 matrix transformation operations are required during the update and prediction process, and the required processor resources are relatively small. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of the structure of a model predictive control method based on a hybrid nonlinear Hammerstein model according to the present invention. Here, S is the electrical angular velocity reference value, θ is the pulse control signal, and θ is the electrical angular velocity reference value. r Motor rotor position angle;

[0058] Figure 2 This is a flowchart of a model predictive control method based on a hybrid nonlinear Hammerstein model according to the present invention;

[0059] Figure 3 A schematic diagram is created for the nonlinear component complex plane splitting and midline table. Detailed Implementation

[0060] The invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0061] like Figures 1-2 As shown, this embodiment provides a model predictive control method based on a hybrid nonlinear Hammerstein model, including the following steps:

[0062] S1: Sample the three-phase current of the motor, and transform the sampled three-phase current into a rotating coordinate system using Park transformation to obtain the d-axis component of the stator current. and the q-axis component of the stator current ;

[0063] S2: d-axis component based on stator current and the q-axis component of the stator current A hybrid nonlinear Hammerstein model is constructed, comprising linear and nonlinear components. An external input autoregressive model is used as the linear component, and the stator currents of the d-axis and q-axis linear components at time k+1 are calculated using this model. and The external input autoregressive model is constructed as follows:

[0064] (1);

[0065] In the formula, Let be the d-axis component of the stator current at time k in the rotating coordinate system. Let be the q-axis component of the stator current at time k in the rotating coordinate system. Let be the d-axis component of the stator voltage at time k in the rotating coordinate system. Let be the q-axis component of the stator voltage at time k in the rotating coordinate system. and These are the current model coefficients for the d-axis and q-axis, respectively. and , respectively, are the voltage model coefficients for the d-axis and q-axis, m is the order of the current model, n is the order of the voltage model, and z is the discrete-time operator;

[0066] The midline table and the nonlinear component table are used as the nonlinear components. The stator current of the d-axis and q-axis nonlinear components at time k+1 is selected through the midline table and the nonlinear component table. and Where k is the current time;

[0067] In step S2, the stator currents of the d-axis and q-axis linear components at time k+1 are calculated using an external input autoregressive model. and The process is as follows:

[0068] S2-1: Construct the external input autoregressive model;

[0069] S2-2: The d-axis and q-axis current model coefficients in formula (1) and and d-axis and q-axis voltage model coefficients and Construct a recursive vector of d-axis and q-axis coefficients at time k. and The recursive vectors of the d-axis and q-axis coefficients at time k and The expression is as follows:

[0070] (2);

[0071] Obtain electronic voltage component data and stator current component data, and construct a recursive vector of d-axis and q-axis data at time k using the obtained electronic voltage component data and stator current component data. and The recursive vectors of d-axis and q-axis data at time k and The expression is as follows:

[0072] (3);

[0073] In the formula, and These represent the d-axis and q-axis stator current components at time k, k-1, and up to time km, respectively. and These are the d-axis and q-axis stator voltage components at time k, k-1, and up to kn, respectively.

[0074] S2-3: Recursive vector of d-axis and q-axis coefficients at time k using the maximum likelihood estimation algorithm. and Update the recursive vectors of the d-axis and q-axis coefficients at time k. and Updated to the recursive vector of d-axis and q-axis coefficients at time k+1. and ;

[0075] S2-4: Calculate the data recursion vector at time k+1 and Wherein, at time k, the recursive vectors of the d-axis and q-axis coefficients. and d-axis component of stator current at time k+1 Elements and the q-axis component of the stator current at time k+1 Each element is determined by its reference signal. and Instead, the Lagrange method is used to calculate the reference values ​​of the stator currents along the d-axis and q-axis at time k+1. and The specific formula is as follows:

[0076] (4);

[0077] In the formula, , , and , , These are the stator current reference values ​​for the d-axis and q-axis at times k, k-1, and k-2, respectively.

[0078] S2-5: Construct the linear component governing equations using the time-shifting approach. Specifically, the d-axis and q-axis coefficients obtained at time k+1 in step S2-3 are recursively vectorized. and and the data recursion vector at time k+1 obtained in step S2-4 and Substituting into the governing equations, the linear components of the stator currents along the d-axis and q-axis at time k+1 are calculated. and The specific formula is as follows:

[0079] (5);

[0080] S2-6: Hyperlocalize the external input autoregressive model to obtain the d-axis and q-axis state gains. , and lumped variables , The specific formula is as follows:

[0081] (6);

[0082] (7);

[0083] in, To control the cycle, and These are the stator voltage components along the d-axis and q-axis, respectively. Accumulate iteration variables for the current component. Accumulate iterative variables for the voltage component.

[0084] In step S2, the stator currents of the d-axis and q-axis nonlinear components at time k+1 are selected using the midline table and the nonlinear component table. and The process is as follows:

[0085] S3-1: Establish a complex plane in a two-phase stationary coordinate system. It should be noted that the complex plane is a geometric representation of complex numbers constructed using a horizontal real axis and a vertical imaginary axis. The complex plane is then divided into six equal intervals, as follows: Figure 3 As shown, SI, S-II, S-III, S-IV, SV, and S-VI are named respectively, and the midline of each interval is defined. , , , , , A neutral line table is established for the stator current in the two-phase stationary coordinate system, and a nonlinear component table of the same dimension is also established. Each element in the table is denoted as... , , , , , ;

[0086] S3-2: The sampled three-phase currents are transformed to a two-phase stationary coordinate system using Clark transformation to obtain the α-axis component of the stator current at time k. and the β-axis component of the stator current Calculate the Euclidean distance between the midline of the interval and the stator current components along the α and β axes. And select the interval Si with the minimum Euclidean distance, the specific formula is as follows:

[0087] (8);

[0088] In the formula, i is a loop variable that takes values ​​from I, II, III, IV, V, and VI; Rated current;

[0089] S3-3: Determine the elements of the nonlinear component table If the value is empty, then the elements corresponding to the interval Si with the minimum Euclidean distance are assigned values ​​using the stator current reference value and the difference between the linear components at time k+1. The specific formula is as follows:

[0090] (9);

[0091] Otherwise, proceed to the next step;

[0092] S3-4: Select the element corresponding to the minimum Euclidean distance interval Si in the nonlinear component table as the stator current of the d-axis and q-axis nonlinear components at time k+1. and The specific expression is as follows:

[0093] (10).

[0094] S4: Stator current based on the linear components of the d-axis and q-axis at time k+1 obtained in step 2. and And the stator currents at time k+1 with nonlinear components along the d-axis and q-axis obtained in step 2. and A first governing equation is constructed that combines linear and nonlinear components, and the modulation signal is obtained based on the first governing equation.

[0095] In step S3, the first governing equation is constructed as follows:

[0096] (11);

[0097] In the formula, For proportional gain, This is the weighting factor.

[0098] S5: The modulation signal is converted into a pulse control signal by the modulation module and used to control the motor driver.

[0099] In step S2-3, the recursive vectors of the d-axis and q-axis coefficients at time k and The steps to perform the update are as follows:

[0100] (1) Calculate the stator current component error, the expression is as follows:

[0101] (12);

[0102] (2) Design the transformation matrices of the d-axis and q-axis at time k. and ,in, ,…, These are the d-axis matrix elements from time k to time km. ,…, These represent the q-axis matrix elements from time k to time km, and the d-axis and q-axis matrix elements at time k. and The expression is as follows:

[0103] (13);

[0104] in, λ For error gain, a The power coefficient;

[0105] (3) Update the coefficient recursion vector, thereby making the coefficient recursion vector and Updated to and The specific formula is as follows:

[0106] (14);

[0107] in, To update the step size, The first adjustable coefficient, This is the second adjustable coefficient.

[0108] By using an online-updated external input autoregressive model, the linear motion state of a permanent magnet synchronous motor drive system can be accurately predicted and controlled.

[0109] In summary, this invention introduces a hybrid nonlinear Hammerstein model for use in permanent magnet synchronous motor drive systems. By incorporating the nonlinear motion components of the motor system into the model prediction process, it takes into account both linear and nonlinear motion of the motor system, enabling accurate characterization of the motor system's motion state with good description accuracy. Furthermore, this invention also introduces a maximum likelihood estimation algorithm to update the linear components online, achieving more accurate control precision and model adaptability. Only 1-2 matrix transformation operations are required during the update and prediction process, resulting in lower processor resource requirements.

[0110] The present invention has been described in detail above with reference to the accompanying drawings. However, the embodiments of the present invention are not limited to the above embodiments. Those skilled in the art can make various modifications to the present invention based on the prior art, and these modifications all fall within the protection scope of the present invention.

Claims

1. A model predictive control method based on a hybrid nonlinear Hammerstein model, characterized in that, Includes the following steps: S1: Sample the three-phase current of the motor, and process the sampled three-phase current through Park transform to obtain the d-axis component of the stator current. and the q-axis component of the stator current ; S2: Based on the d-axis component of the stator current and the q-axis component of the stator current A hybrid nonlinear Hammerstein model is constructed, comprising linear and nonlinear components. An external input autoregressive model is used as the linear component, and the stator currents of the d-axis and q-axis linear components at time k+1 are calculated using this external input autoregressive model. and The external input autoregressive model is constructed as follows: （1）； In the formula, Let be the d-axis component of the stator current at time k in the rotating coordinate system. Let be the q-axis component of the stator current at time k in the rotating coordinate system. Let be the d-axis component of the stator voltage at time k in the rotating coordinate system. Let be the q-axis component of the stator voltage at time k in the rotating coordinate system. and These are the current model coefficients for the d-axis and q-axis, respectively. and , respectively, are the voltage model coefficients for the d-axis and q-axis, m is the order of the current model, n is the order of the voltage model, and z is the discrete-time operator; The midline table and the nonlinear component table are used as the nonlinear components, and the stator currents of the d-axis and q-axis nonlinear components at time k+1 are selected through the midline table and the nonlinear component table. and Where k is the current time; S3: Stator current based on the linear components of the d-axis and q-axis at time k+1 obtained in step 2. and And the stator currents at time k+1 with nonlinear components along the d-axis and q-axis obtained in step 2. and A first control equation is constructed that combines linear and nonlinear components, and a modulation signal is obtained based on the first control equation. S4: The modulation signal is converted into a pulse control signal by the modulation module and used to control the motor driver.

2. The model predictive control method based on a hybrid nonlinear Hammerstein model according to claim 1, characterized in that, In step S2, the stator currents of the d-axis and q-axis linear components at time k+1 are calculated using an external input autoregressive model. and The process is as follows: S2-1: Construct the external input autoregressive model; S2-2: The d-axis and q-axis current model coefficients in formula (1) and and d-axis and q-axis voltage model coefficients and Construct a recursive vector of d-axis and q-axis coefficients at time k. and The recursive vectors of the d-axis and q-axis coefficients at time k and The expression is as follows: （2）； Obtain electronic voltage component data and stator current component data, and construct a recursive vector of d-axis and q-axis data at time k using the obtained electronic voltage component data and stator current component data. and The recursive vectors of d-axis and q-axis data at time k and The expression is as follows: （3）； In the formula, and These represent the d-axis and q-axis stator current components at time k, k-1, and up to time km, respectively. and These are the d-axis and q-axis stator voltage components at time k, k-1, and up to kn, respectively. S2-3: The maximum likelihood estimation algorithm is used to recursively calculate the coefficient vectors of the d-axis and q-axis at time k. and Update the recursive vectors of the d-axis and q-axis coefficients at time k. and Updated to the recursive vector of d-axis and q-axis coefficients at time k+1. and ; S2-4: Calculate the data recursion vector at time k+1 and Wherein, the recursive vectors of the d-axis and q-axis data at time k. and d-axis component of stator current at time k+1 Elements and the q-axis component of the stator current at time k+1 Each element is determined by its reference signal. and Instead, the Lagrange method is used to calculate the reference values ​​of the stator currents along the d-axis and q-axis at time k+1. and The specific formula is as follows: （4）； In the formula, , , and , , These are the stator current reference values ​​for the d-axis and q-axis at times k, k-1, and k-2, respectively. S2-5: Construct the linear component governing equations and recursively vectorize the d-axis and q-axis coefficients at time k+1 obtained in step S2-3. and and the data recursion vector at time k+1 obtained in step S2-4 and Substituting into the governing equations, the linear components of the stator currents along the d-axis and q-axis at time k+1 are calculated. and The specific formula is as follows: （5）； S2-6: Perform hyperlocalization on the external input autoregressive model to obtain the d-axis and q-axis state gains. , and lumped variables , The specific formula is as follows: （6）； （7）； in, To control the cycle, and These are the d-axis and q-axis stator voltage components, respectively. Accumulate iteration variables for the current component. Accumulate iterative variables for the voltage component.

3. The model predictive control method based on a hybrid nonlinear Hammerstein model according to claim 2, characterized in that, The stator current at time k+1 is selected using the midline table and the nonlinear component table, representing the d-axis and q-axis nonlinear components. and The process is as follows: S3-1: Establish a complex plane in a two-phase stationary coordinate system, and divide the complex plane into 6 equal intervals, named SI, S-II, S-III, S-IV, SV, and S-VI respectively, and define the midline of each interval. , , , , , A neutral line table is established for the stator current in the two-phase stationary coordinate system, and a nonlinear component table of the same dimension is also established. Each element in the table is denoted as... , , , , , ; S3-2: The sampled three-phase currents are transformed to a two-phase stationary coordinate system using Clark transformation to obtain the α-axis component of the stator current at time k. and the β-axis component of the stator current Calculate the Euclidean distance between the midline of the interval and the stator current components along the α and β axes. And select the interval Si with the minimum Euclidean distance, the specific formula is as follows: （8）； In the formula, i is a loop variable that takes values ​​from I, II, III, IV, V, and VI; Rated current; S3-3: Determine the elements of the nonlinear component table If the value is empty, then the elements corresponding to the interval Si with the minimum Euclidean distance are assigned values ​​using the stator current reference value and the difference between the linear components at time k+1. The specific formula is as follows: （9）； Otherwise, proceed to the next step; S3-4: Select the element corresponding to the minimum Euclidean distance interval Si in the nonlinear component table as the stator current of the d-axis and q-axis nonlinear components at time k+1. and The specific expression is as follows: （10）。 4. The model predictive control method based on a hybrid nonlinear Hammerstein model according to claim 3, characterized in that, In step S3, the first governing equation is constructed as follows: （11）； In the formula, For proportional gain, This is the weighting factor.

5. The model predictive control method based on a hybrid nonlinear Hammerstein model according to claim 2, characterized in that, In step S2-3, the recursive vectors of the d-axis and q-axis coefficients at time k and The steps to perform the update are as follows: (1) Calculate the stator current component error, and recursively vectorize the d-axis and q-axis coefficients at time k. and and the recursive vectors of the d-axis and q-axis coefficients at time k+1. and Substituting into formula (12), the expression is as follows: （12）； (2) Design the transformation matrices of the d-axis and q-axis at time k. and ,in, ,…, These are the d-axis matrix elements from time k to time km. ,…, These represent the q-axis matrix elements from time k to time km, and the d-axis and q-axis matrix elements at time k. and The expression is as follows: （13）； in, λ For error gain, a The power coefficient; (3) Update the coefficient recursion vector, thereby making the coefficient recursion vector and Updated to and The specific formula is as follows: （14）； in, To update the step size, The first adjustable coefficient, This is the second adjustable coefficient.

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