Model prediction control method based on hybrid nonlinear Hammerstein model

Abstract

The invention relates to the technical field of motor control, in particular to a model prediction control method based on a hybrid nonlinear Hammerstein model, which comprises the following steps of: sampling three-phase current of a motor, constructing the hybrid nonlinear Hammerstein model, calculating d-axis and q-axis linear component stator current at a k + 1 moment through an external input autoregression model, and calculating a k + 1 moment. D-axis and q-axis non-linear component stator currents at the k + 1 moment are selected through the midline table and the non-linear component table, a first control equation is constructed, a modulation signal is obtained, and the modulation signal is converted into a pulse control signal through a modulation module and controls a motor driver. According to the method, the hybrid nonlinear Hammerstein model is introduced to be applied to the permanent magnet synchronous motor driving system, and nonlinear motion component factors of the motor system are brought into a model prediction process, so that linear and nonlinear motion of the motor system are considered, the motion state of the motor system can be accurately represented, and the description precision is relatively good.

Description

Technical Field

[0001] The present invention relates to the technical field of motor control, and in particular to a model predictive control method based on a hybrid nonlinear Hammerstein model. Background Art

[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 the chemical industry. As a control strategy that has emerged in recent years, MPC, compared to vector control (VOC), does not require a current inner loop or parameter tuning. It directly generates inverter drive signals without pulse modulation, making it easier to handle system constraints or add other control objectives. It has the advantages of simple structure, fast dynamic response, and easy scalability. Compared with direct torque control (DTC), MPC optimizes the selection of the optimal voltage vector by predicting the motor state. This makes vector selection more accurate and effective, and it can more easily account for various nonlinear constraints, including switching frequency reduction. It has the advantages of good steady-state performance and flexible control.

[0003] However, the traditional model predictive control design ARX model realizes the model establishment and prediction process of the linear component, which can only describe the linear motion state of the motor system, but cannot accurately describe the nonlinear motion turntable of the motor system, and the description accuracy is low.

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

[0005] The object of the present invention is to provide a model predictive control method based on a hybrid nonlinear Hammerstein model with better description accuracy.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions: A model predictive control method based on a hybrid nonlinear Hammerstein model comprises the following steps: S1: Sample the three-phase current of the motor and process the sampled three-phase current through Park transformation to obtain the d-axis component of the stator current and the q-axis component of the stator current ,It needs to be stated that the Park transformation is a ,conventional coordinate transformation; S2: Based on the d-axis component of the stator current and the q-axis component of the stator current Construct a hybrid nonlinear Hammerstein model, which includes linear and nonlinear components. An external input autoregressive model is used as the linear component. The linear components of the stator currents of the d-axis and q-axis at time k+1 are calculated by the external input autoregressive model. and , using the midline table and the nonlinear component table as the nonlinear component, the d-axis and q-axis nonlinear component stator currents at time k+1 are selected through the midline table and the nonlinear component table and , where k is the current moment; S3: Based on the linear components of the stator current of the d-axis and q-axis at time k+1 obtained in step 2 and And the stator current of the d-axis and q-axis nonlinear components at time k+1 obtained in step 2 and Constructing a first control equation for mixing linear components and nonlinear components, and obtaining a modulated signal according to the first control equation; S4: The modulation signal is converted into a pulse control signal through a modulation module and controls the motor driver.

[0007] Furthermore, in step S2, the linear components of the stator currents of the d-axis and q-axis at time k+1 are calculated by the external input autoregressive model. and The process is as follows: S2-1: In step S2, the external input autoregressive model is constructed as follows: (1); Where, is the d-axis component of the stator current at time k in the rotating coordinate system, is the q-axis component of the stator current at time k in the rotating coordinate system, is the d-axis component of the stator voltage at time k in the rotating coordinate system, is the q-axis component of the stator voltage at time k in the rotating coordinate system, and are the d-axis and q-axis current model coefficients, and are the d-axis and q-axis voltage model coefficients, m is the current model order, n is the voltage model order, and z is the discrete time domain operator; S2-2: Substitute the d-axis and q-axis current model coefficients in formula (1) and and the d-axis and q-axis voltage model coefficients and Construct the recursive vector of d-axis and q-axis coefficients at time k and , the recursive vector of 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 the obtained electronic voltage component data and stator current component data into a recursive vector of d-axis and q-axis data at time k and , k moment d-axis and q-axis data recursive vector and The expression is as follows: (3); Where, and They are the d-axis and q-axis stator current components at time k, time k-1, and up to time km, and are the d-axis and q-axis stator voltage components at time k, time k-1, and up to time kn respectively; S2-3: Use the maximum likelihood estimation algorithm to recursively calculate the d-axis and q-axis coefficient vectors at time k and Update so that the d-axis and q-axis coefficients at time k are recursive vectors and Updated to the recursive vector of d-axis and q-axis coefficients at time k+1 and ; S2-4: Calculate the data recursive vector at time k+1 and , where the d-axis and q-axis data recursive vectors at time k are and The d-axis component of the stator current at time k+1 in element and the q-axis component of the stator current at time k+1 Elements are represented by their reference signals and Instead, the Lagrangian method is used to calculate the d-axis and q-axis stator current reference values ​​at time k+1 and , the specific formula is as follows: (4); Where, 、 、 and 、 、 are the d-axis and q-axis stator current reference values ​​at time k, k-1, and k-2 respectively; S2-5: Construct the linear component control equation and recursively transform the d-axis and q-axis coefficients at time k+1 obtained in step S2-3 into the vector and And the data recursive vector at time k+1 obtained in steps S2-4 and Substituting into the control equation, the linear components of the stator current of the d-axis and q-axis at time k+1 are calculated. and , the specific formula is as follows: (5); S2-6: Hyperlocalize the external input autoregressive model to obtain d-axis and q-axis state gains 、 and lumped variables 、 , the specific formula is as follows: (6); (7); in, To control the cycle, and are the d-axis and q-axis stator voltage components, respectively, Accumulate iterative variables for the current part, Accumulate iterative variables for the voltage part; Furthermore, the stator current of the d-axis and q-axis nonlinear components at time k+1 is selected through the neutral line table and the nonlinear component table. and The process is as follows: S3-1: Establish a complex plane in a two-phase stationary coordinate system, divide the complex plane into 6 intervals, and name them SI, S-II, S-III, S-IV, SV, and S-VI respectively, and calculate the midline of each interval. 、 、 、 、 、 The neutral line table is established for the stator current of the two-phase stationary coordinate system, and the nonlinear component table of the same dimension is established at the same time. Each element in the table is recorded as 、 、 、 、 、 ,It should be noted that the complex plane is a plane that conventionally uses a rectangular coordinate system to represent complex numbers; S3-2: The sampled three-phase current is transformed into a two-phase stationary coordinate system through 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 interval centerline and the α-axis and β-axis stator current components , and select the interval Si with the minimum Euclidean distance. The specific formula is as follows: (8); Where i is the loop variable, which takes values ​​in I, II, III, IV, V, and VI; is the rated current; S3-3: Determine nonlinear component table elements Is it a null value? If so, the element corresponding to the interval Si of the minimum Euclidean distance is assigned the value using the stator current reference value at time k+1 and the linear component difference. 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 d-axis and q-axis nonlinear component stator current at time k+1 and , the specific expression is as follows: (10).

[0008] Furthermore, in step S3, the first control equation is constructed as follows: (11); Where, is the proportional gain, is the weight factor.

[0009] Furthermore, in step S2-3, the d-axis and q-axis coefficients at time k are recursively vectored. and The steps to perform the update are as follows: (1) Calculate the stator current component error and recursively transform the d-axis and q-axis coefficients at time k into vectors and And the d-axis and q-axis coefficient recursive vectors at time k+1 and Substituting into formula (12), the expression is as follows: (12); (2) Design the d-axis and q-axis transformation matrices at time k and ,in, ,…, are the d-axis matrix elements from time k to time km, ,…, They are the q-axis matrix elements from time k to time km, the d-axis and q-axis matrix elements at time k and The expression is as follows: (13); in, λ is the error gain, a is the power coefficient; (3) Update the coefficient recursive vector so that the coefficient recursive vector and Updated to and , the specific formula is as follows: (14); in, is the update step size, is the first adjustable coefficient, is the second adjustable coefficient.

[0010] By adopting the above technical solution, the present invention has the following beneficial effects: 1. The present invention introduces a hybrid nonlinear Hammerstein model and applies it to a permanent magnet synchronous motor drive system, incorporating the nonlinear motion component of the motor system into the model prediction process, thereby taking into account both the linear and nonlinear motion of the motor system, and being able to accurately characterize the motion state of the motor system with good description accuracy.

[0011] 2. The present invention also introduces a maximum likelihood estimation algorithm to update the linear components online to obtain more accurate control accuracy and model adaptability. Only 1-2 matrix transformation operations are required during the update and prediction process, and the required processor resources are relatively small. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Figure 1 FIG. 1 is a structural diagram of a model predictive control method based on a hybrid nonlinear Hammerstein model of the present invention. In the figure, is the electrical angular velocity reference value, S is the pulse control signal, θ r Motor rotor position angle; Figure 2 This is a flow chart of a model predictive control method based on a hybrid nonlinear Hammerstein model of the present invention; Figure 3 Create schematics for complex plane decomposition and midline tables of nonlinear components. DETAILED DESCRIPTION

[0013] The invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0014] like Figure 1-Figure 2 As shown, this embodiment provides a model predictive control method based on a hybrid nonlinear Hammerstein model, comprising the following steps: S1: Sample the three-phase current of the motor and transform the sampled three-phase current into the rotating coordinate system through Park 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 Construct a hybrid nonlinear Hammerstein model, which includes linear and nonlinear components. The external input autoregressive model is used as the linear component. The linear components of the stator currents of the d-axis and q-axis at time k+1 are calculated by the external input autoregressive model. and , using the midline table and the nonlinear component table as the nonlinear component, the d-axis and q-axis nonlinear component stator currents at time k+1 are selected through the midline table and the nonlinear component table and , where k is the current moment; In step S2, the linear components of the stator currents of the d-axis and q-axis at time k+1 are calculated by the external input autoregressive model. and The process is as follows: S2-1: In step S2, the external input autoregressive model is constructed as follows: (1); Where, is the d-axis component of the stator current at time k in the rotating coordinate system, is the q-axis component of the stator current at time k in the rotating coordinate system, is the d-axis component of the stator voltage at time k in the rotating coordinate system, is the q-axis component of the stator voltage at time k in the rotating coordinate system, and are the d-axis and q-axis current model coefficients, and are the d-axis and q-axis voltage model coefficients, m is the current model order, n is the voltage model order, and z is the discrete time domain operator; S2-2: Substitute the d-axis and q-axis current model coefficients in formula (1) and and the d-axis and q-axis voltage model coefficients and Construct the recursive vector of d-axis and q-axis coefficients at time k and , the recursive vector of 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 the obtained electronic voltage component data and stator current component data into a recursive vector of d-axis and q-axis data at time k and , k moment d-axis and q-axis data recursive vector and The expression is as follows: (3); Where, and They are the d-axis and q-axis stator current components at time k, time k-1, and up to time km, and are the d-axis and q-axis stator voltage components at time k, time k-1, and up to time kn respectively; S2-3: Use the maximum likelihood estimation algorithm to recursively calculate the d-axis and q-axis coefficient vectors at time k and Update so that the d-axis and q-axis coefficients at time k are recursive vectors and Updated to the recursive vector of d-axis and q-axis coefficients at time k+1 and ; S2-4: Calculate the data recursive vector at time k+1 and , where the d-axis and q-axis coefficient recursive vectors at time k are and The d-axis component of the stator current at time k+1 in element and the q-axis component of the stator current at time k+1 Elements are represented by their reference signals and Instead, the Lagrangian method is used to calculate the d-axis and q-axis stator current reference values ​​at time k+1 and , the specific formula is as follows: (4); Where, 、 、 and 、 、 are the d-axis and q-axis stator current reference values ​​at time k, k-1, and k-2 respectively; S2-5: Use the time-shifting idea to construct the linear component control equation. Specifically, recursively transform the d-axis and q-axis coefficients at time k+1 obtained in step S2-3 into and And the data recursive vector at time k+1 obtained in steps S2-4 and Substituting into the control equation, the linear components of the stator current of the d-axis and q-axis at time k+1 are calculated. and , the specific formula is as follows: (5); S2-6: Hyperlocalize the external input autoregressive model to obtain d-axis and q-axis state gains 、 and lumped variables 、 , the specific formula is as follows: (6); (7); in, To control the cycle, and are the d-axis and q-axis stator voltage components, respectively, Accumulate iterative variables for the current part, Accumulates the iteration variable for the voltage portion.

[0015] In step S2, the stator current of the d-axis and q-axis nonlinear components at time k+1 is selected through the neutral line table and the nonlinear component table. and The process is as follows: S3-1: Establish the complex plane in the two-phase stationary coordinate system. It should be stated that the complex plane is a geometric representation of complex numbers established by the horizontal real axis and the vertical imaginary axis. The complex plane is evenly divided into 6 intervals, such as Figure 3 As shown, they are named SI, S-II, S-III, S-IV, SV, and S-VI, and the midline of each interval is 、 、 、 、 、 The neutral line table is established for the stator current of the two-phase stationary coordinate system, and the nonlinear component table of the same dimension is established at the same time. Each element in the table is recorded as 、 、 、 、 、 ; S3-2: The sampled three-phase current is transformed into a two-phase stationary coordinate system through 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 interval centerline and the α-axis and β-axis stator current components , and select the interval Si with the minimum Euclidean distance. The specific formula is as follows: (8); Where i is the loop variable, which takes values ​​in I, II, III, IV, V, and VI; is the rated current; S3-3: Determine nonlinear component table elements Is it a null value? If so, the element corresponding to the interval Si of the minimum Euclidean distance is assigned the value using the stator current reference value at time k+1 and the linear component difference. 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 d-axis and q-axis nonlinear component stator current at time k+1 and , the specific expression is as follows: (10).

[0016] S4: Based on the linear components of the stator current of the d-axis and q-axis at time k+1 obtained in step 2 and And the stator current of the d-axis and q-axis nonlinear components at time k+1 obtained in step 2 and constructing a first control equation for mixing linear components and nonlinear components, and obtaining a modulation signal according to the first control equation; In step S3, the first control equation is constructed as follows: (11); Where, is the proportional gain, is the weight factor.

[0017] S5: The modulation signal is converted into a pulse control signal through the modulation module and controls the motor driver.

[0018] In step S2-3, the d-axis and q-axis coefficients at time k are recursively vectored. and The steps to perform the update are as follows: (1) Calculate the stator current component error, the expression is as follows: (12); (2) Design the d-axis and q-axis transformation matrices at time k and ,in, ,…, are the d-axis matrix elements from time k to time km, ,…, They are the q-axis matrix elements from time k to time km, the d-axis and q-axis matrix elements at time k and The expression is as follows: (13); in, λ is the error gain, a is the power coefficient; (3) Update the coefficient recursive vector so that the coefficient recursive vector and Updated to and , the specific formula is as follows: (14); in, is the update step size, is the first adjustable coefficient, is the second adjustable coefficient.

[0019] Through the online updated external input autoregressive model, the linear motion state of the permanent magnet synchronous motor drive system can be accurately predicted and controlled.

[0020] In summary, the present invention introduces a hybrid nonlinear Hammerstein model and applies it to a permanent magnet synchronous motor drive system, incorporating the nonlinear motion component factors of the motor system into the model prediction process, thereby taking into account both the linear and nonlinear motions of the motor system, and can accurately characterize the motion state of the motor system with good description accuracy. In addition, the present invention also introduces a maximum likelihood estimation algorithm to update the linear components online to obtain more accurate control accuracy and model adaptability. Only 1-2 matrix transformation operations are required in the update and prediction process, and the required processor resources are relatively small.

[0021] 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 existing technology, and all of these modifications fall within the scope of protection of the present invention.

Claims

1. A model predictive control method based on a hybrid nonlinear Hammerstein model, characterized in that: The steps include: S1: Sample the three-phase current of the motor and process the sampled three-phase current through Park transformation 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 Construct a hybrid nonlinear Hammerstein model, which includes linear and nonlinear components. An external input autoregressive model is used as the linear component. The linear components of the stator currents of the d-axis and q-axis at time k+1 are calculated by the external input autoregressive model. and , using the midline table and the nonlinear component table as the nonlinear component, the d-axis and q-axis nonlinear component stator currents at time k+1 are selected through the midline table and the nonlinear component table and , where k is the current moment; S3: Based on the linear components of the stator current of the d-axis and q-axis at time k+1 obtained in step 2 and And the stator current of the d-axis and q-axis nonlinear components at time k+1 obtained in step 2 and Constructing a first control equation for mixing linear components and nonlinear components, and obtaining a modulated signal according to the first control equation; S4: The modulation signal is converted into a pulse control signal through a modulation module and controls the motor driver.

2. The model predictive control method based on the hybrid nonlinear Hammerstein model according to claim 1, characterized in that: In step S2, the linear components of the stator currents of the d-axis and q-axis at time k+1 are calculated by the external input autoregressive model. and The process is as follows: S2-1: In step S2, the external input autoregressive model is constructed as follows: （1）； Where, is the d-axis component of the stator current at time k in the rotating coordinate system, is the q-axis component of the stator current at time k in the rotating coordinate system, is the d-axis component of the stator voltage at time k in the rotating coordinate system, is the q-axis component of the stator voltage at time k in the rotating coordinate system, and are the d-axis and q-axis current model coefficients, and are the d-axis and q-axis voltage model coefficients, m is the current model order, n is the voltage model order, and z is the discrete time domain operator; S2-2: Substitute the d-axis and q-axis current model coefficients in formula (1) and and the d-axis and q-axis voltage model coefficients and Construct the recursive vector of d-axis and q-axis coefficients at time k and , the recursive vector of 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 the obtained electronic voltage component data and stator current component data into a recursive vector of d-axis and q-axis data at time k and , k moment d-axis and q-axis data recursive vector and The expression is as follows: （3）； Where, and They are the d-axis and q-axis stator current components at time k, time k-1, and up to time km, and are the d-axis and q-axis stator voltage components at time k, time k-1, and up to time kn respectively; S2-3: Use the maximum likelihood estimation algorithm to recursively calculate the d-axis and q-axis coefficient vectors at time k and Update so that the d-axis and q-axis coefficients at time k are recursive vectors and Updated to the recursive vector of d-axis and q-axis coefficients at time k+1 and ; S2-4: Calculate the data recursive vector at time k+1 and , where the d-axis and q-axis data recursive vectors at time k are and The d-axis component of the stator current at time k+1 in element and the q-axis component of the stator current at time k+1 Elements are represented by their reference signals and Instead, the Lagrangian method is used to calculate the d-axis and q-axis stator current reference values ​​at time k+1 and , the specific formula is as follows: （4）； Where, 、 、 and 、 、 are the d-axis and q-axis stator current reference values ​​at time k, k-1, and k-2 respectively; S2-5: Construct the linear component control equation and recursively transform the d-axis and q-axis coefficients at time k+1 obtained in step S2-3 into the vector and And the data recursive vector at time k+1 obtained in steps S2-4 and Substituting into the control equation, the linear components of the stator current of the d-axis and q-axis at time k+1 are calculated. and , the specific formula is as follows: （5）； S2-6: Hyperlocalize the external input autoregressive model to obtain d-axis and q-axis state gains 、 and lumped variables 、 , the specific formula is as follows: （6）； （7）； in, To control the cycle, and are the d-axis and q-axis stator voltage components, respectively, Accumulate iterative variables for the current part, Accumulates the iteration variable for the voltage portion.

3. The model predictive control method based on the hybrid nonlinear Hammerstein model according to claim 2, characterized in that: The stator currents of the d-axis and q-axis nonlinear components at time k+1 are selected through the neutral line table and the nonlinear component table. and The process is as follows: S3-1: Establish a complex plane in a two-phase stationary coordinate system, divide the complex plane into 6 intervals, and name them SI, S-II, S-III, S-IV, SV, and S-VI respectively, and calculate the midline of each interval. 、 、 、 、 、 The neutral line table is established for the stator current of the two-phase stationary coordinate system, and the nonlinear component table of the same dimension is established at the same time. Each element in the table is recorded as 、 、 、 、 、 ; S3-2: The sampled three-phase current is transformed into a two-phase stationary coordinate system through 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 interval centerline and the α-axis and β-axis stator current components , and select the interval Si with the minimum Euclidean distance. The specific formula is as follows: （8）； Where i is the loop variable, which takes values ​​in I, II, III, IV, V, and VI; is the rated current; S3-3: Determine nonlinear component table elements Is it a null value? If so, the element corresponding to the interval Si of the minimum Euclidean distance is assigned the value using the stator current reference value at time k+1 and the linear component difference. 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 d-axis and q-axis nonlinear component stator current at time k+1 and , the specific expression is as follows: （10）。 4. The model predictive control method based on the hybrid nonlinear Hammerstein model according to claim 3, characterized in that: In step S3, the first control equation is constructed as follows: （11）； Where, is the proportional gain, is the weight factor.

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

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