A robust model predictive control method for motors based on linear fitting

Abstract

The present invention discloses a motor robust model predictive control method based on linear fitting, comprising: (1) establishing a motor current increment prediction model; (2) establishing a stator inductance estimation model to obtain a stator inductance calculation matrix, and calculating an eigenvector corresponding to the minimum eigenvalue of the stator inductance calculation matrix; (3) calculating a stator inductance estimation value based on the eigenvector; (4) establishing a motor current increment prediction model based on the stator inductance estimation value; (5) constructing a cost function from the motor current increment prediction model based on the stator inductance estimation value, the cost function is used to calculate an optimal stator voltage increment, and finally the optimal stator voltage increment is added to the stator voltage applied at the current control moment to obtain the optimal stator voltage at the next control moment. The present invention estimates the stator inductance by using a linear fitting method based on orthogonal regression, thereby improving the robustness of the model predictive control while avoiding excessive calculation amount and complex parameter setting work.

Description

Technical Field

[0001] The invention belongs to the technical field of permanent magnet synchronous motor control, and in particular relates to a motor robust model predictive control method based on linear fitting. Background Art

[0002] Permanent magnet synchronous motors are widely used in robotics, electric vehicles and other fields due to their wide speed regulation range, high efficiency and high power density. Model predictive control has the advantages of multivariable control and fast dynamic response, and has received increasing attention and extensive research in motor drive systems.

[0003] However, MPC is a model-based control method, so motor parameter mismatch will deteriorate the control performance of MPC; unfortunately, motor parameters will change with the operating environment (including motor body temperature, stator current, etc.). Therefore, it is very important to explore the robustness of MPC and improve its ability to resist parameter disturbances.

[0004] At present, common model predictive control robustness methods can be summarized into four categories: cost function optimization method, observer-based robustness method, lookup table-based robustness method and model-free predictive control. Among them, the parameter / model estimation method in the observer-based robustness method (such as the Chinese patent technology application with publication number CN115459660A) uses proportional-integral regulator, sliding film observer, adaptive observer, etc. to estimate motor parameters or motor model coefficients, and compensates the estimation results to the motor drive system prediction model to improve the robustness of the control method. This method will not destroy the control structure of the model predictive control method, thereby maintaining the advantages of multivariable control and fast dynamic response of the model predictive control method; however, the parameter / model estimation method is mostly based on proportional-integral regulator or different observers, but this will bring complex and time-consuming parameter tuning work. In addition, although the robustness method based on the lookup table (such as the Chinese patent technology application with publication number CN116455288A) does not require parameter tuning and has low computational complexity, it has the problem of update stagnation. In order to solve the problem of update stagnation, more complex calculation work will be brought about, and the robustness method based on the lookup table is currently only applicable to finite control set model predictive control. Summary of the invention

[0005] In view of the above, the present invention provides a motor robust model predictive control method based on linear fitting, which estimates the stator inductance by adopting a linear fitting method based on orthogonal regression, thereby improving the robustness of the model predictive control while avoiding excessive calculation amount and complex parameter setting work.

[0006] A motor robust model predictive control method based on linear fitting includes the following steps:

[0007] (1) The motor current increment prediction model is established by taking the motor stator current increment in two adjacent control cycles as the prediction quantity and the motor stator voltage increment in two adjacent control cycles as the control quantity;

[0008] (2) A stator inductance estimation model is established based on the q-axis stator current increment in the motor current increment prediction model, thereby obtaining the stator inductance calculation matrix and calculating the eigenvector corresponding to its minimum eigenvalue;

[0009] (3) calculating an estimated value of the stator inductance according to the eigenvector;

[0010] (4) Substituting the estimated value of stator inductance into the motor current increment prediction model established in step (1) to obtain a motor current increment prediction model based on the estimated value of stator inductance;

[0011] (5) A cost function is constructed based on the motor current increment prediction model obtained in step (4), and the optimal stator voltage increment is obtained by minimizing the cost function. The optimal stator voltage increment is then added to the stator voltage at the current control moment to obtain the stator voltage at the next control moment.

[0012] Furthermore, the expression of the motor current increment prediction model in step (1) is as follows:

[0013] ;

[0014]

[0015] in: and Respectively represent the motor in the k +1 control cycle and k The d-axis stator current increment of a control cycle (relative to the previous moment), and Respectively represent the motor in the k +1 control cycle and k The q-axis stator current increment of a control cycle, and Respectively represent the motor in the k The d-axis stator voltage increment and q-axis stator voltage increment of a control cycle, T s Indicates the duration of the control cycle, L s represents the stator inductance, Indicates k The angular velocity of the motor rotor at each control moment, k An integer greater than or equal to 0.

[0016] Furthermore, the stator inductance estimation model is expressed as follows:

[0017] ;

[0018]

[0019] in: M is a variable coefficient greater than 0 so that ( MT s ) 2 +( ML s ) 2 =1, and Respectively represent the motor in the k - d-axis stator current increment and q-axis stator current increment of 1 control cycle, Indicates that the motor is k -D-axis stator voltage increment for 1 control cycle, Indicates k The lumped dependent variable of the q-axis stator current increment during each control cycle.

[0020] Furthermore, in step (2), the stator inductance calculation matrix is ​​calculated based on the stator inductance estimation model by the following expression:

[0021]

[0022] in: S is the stator inductance calculation matrix, , Indicates that the motor is k - n The q-axis stator voltage increment of a control cycle, , Indicates k - n The lumped dependent variable of the q-axis stator current increment in +1 control cycle, =AVERAGE( x 1, x 2,…, x n ), =AVERAGE( y 1, y 2,…, y n ), AVERAGE( ) means to find the average, N The number of sampling control points is set.

[0023] Furthermore, in step (3), the estimated value of the stator inductance is calculated by the following formula:

[0024]

[0025] in: is the estimated value of stator inductance, [ a , b ] T Calculate the eigenvector corresponding to the minimum eigenvalue of the matrix for the stator inductance.

[0026] Furthermore, in step (5), the cost function is minimized by the following formula:

[0027]

[0028] in: J is the cost function, and Respectively represent the motor in the k +2 control cycles of d-axis stator current increment and q-axis stator current increment, and They represent the d-axis stator current increment reference value and the q-axis stator current increment reference value respectively, Indicates that the motor is k The stator voltage increment of +1 control cycle is the optimal stator voltage increment (which is given by and composition).

[0029] Furthermore, in step (5), the optimal stator voltage increment is added to the stator voltage applied at the current control moment to obtain the stator voltage at the next control moment, that is, ,in and Respectively represent the motor in the k The control moment and k +1 stator voltage at a control moment (which consists of the d-axis stator voltage and the q-axis stator voltage).

[0030] A computer device comprises a memory and a processor, wherein the memory stores a computer program, and the processor is used to execute the computer program to implement the above-mentioned motor robust model predictive control method based on linear fitting.

[0031] A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the motor robust model predictive control method based on linear fitting is implemented.

[0032] The present invention designs a motor robust model predictive control method based on linear fitting. By adopting orthogonal regression linear fitting technology, it can not only estimate the stator inductance of the motor in real time, but also eliminate the need for complex gain coefficient setting. This method does not destroy the structure of the model predictive control algorithm, and can greatly enhance the anti-parameter disturbance capability of the model predictive control algorithm, obtain strong robustness, and maintain good steady-state performance of the model predictive control. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 Schematic diagram of the flow of the motor robust model predictive control method in an embodiment of the present invention.

[0034] Figure 2 Schematic diagram of a fitted straight line for stator inductance estimation in an embodiment of the present invention.

[0035] Figure 3 This is the steady-state simulation waveform of the traditional model predictive control based on the current increment prediction model when the speed is 200r / min.

[0036] Figure 4 It is the steady-state simulation waveform diagram of the robust model predictive control of the present invention when the rotation speed is 200r / min.

[0037] Figure 5 This is the steady-state simulation waveform of the traditional model predictive control based on the current increment prediction model when the speed is 2000r / min.

[0038] Figure 6 It is the steady-state simulation waveform diagram of the robust model predictive control of the present invention when the rotation speed is 2000r / min.

[0039] Figure 7 This is a simulation waveform diagram of the traditional model predictive control based on the current increment prediction model when the speed is 2000r / min, the torque is 15N·m, and the stator inductance changes suddenly.

[0040] Figure 8 The figure is a simulation waveform diagram of the robust model predictive control of the present invention when the speed is 2000 r / min, the torque is 15 N·m and the stator inductance changes suddenly. DETAILED DESCRIPTION

[0041] In order to describe the present invention more specifically, the technical solution of the present invention is described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0042] The robust model predictive control method based on the current increment prediction model in this embodiment includes the following steps:

[0043] Step 1: Taking the current increment of the motor stator current in two adjacent control cycles as the prediction quantity and the voltage increment of the motor stator voltage in two adjacent control cycles as the control quantity, a corresponding motor current increment prediction model is established. Specifically:

[0044] First, a two-phase rotating coordinate system oriented by the rotor flux is established. The stator voltage equation of the surface-mounted permanent magnet synchronous motor on the d and q axes is:

[0045] (1)

[0046] Where: u d , u q , i d and i q They represent the stator voltage vector u s With the stator current vector i s The components on the d and q axes, R s is the stator resistance, L d , L q represents the d and q axis stator inductance, ω r represents the angular velocity of the rotor, ψ f Represents the flux linkage of a permanent magnet.

[0047] Since the control cycle is short enough, equation (1) can be discretized to obtain the d and q axis stator currents in k The predicted value at time +1 is:

[0048] (2)

[0049] Where: and Respectively represent k +1 The predicted values ​​of d and q axis currents at the control time, and Respectively represent k The d and q axis current measurement values ​​at the control moment, , Respectively represent k Control the d and q axis voltages applied at the moment.

[0050] In the motor drive system, since the control cycle is very short, it can be considered ω rIt is constant in two adjacent control cycles, so the The term can be considered unchanged in two adjacent control cycles. Since the stator resistance voltage drop in the surface-mounted permanent magnet synchronous motor system is usually small, especially when the motor is running at high speed, the stator resistance can usually be ignored. Subtracting the predicted current at two adjacent control moments calculated by formula (2), the current increment prediction model suitable for the surface-mounted permanent magnet synchronous motor can be obtained as follows:

[0051] (3)

[0052] Where: , , , , , .

[0053] Step 2: Based on the q-axis current increment prediction equation in the motor current increment prediction model, a stator inductance estimation model is established to obtain a stator inductance calculation matrix and calculate the eigenvector corresponding to the minimum eigenvalue of the stator inductance calculation matrix.

[0054] It can be seen from formula (3) that the current increment prediction model of the surface-mounted permanent magnet synchronous motor only uses the stator inductance L s This is a motor parameter, so only real-time estimation is required L s The actual value of can realize the strong anti-parameter disturbance ability of MPC.

[0055] The q-axis current increment prediction equation in equation (3) can be transformed into the following form:

[0056] (4)

[0057] It can be seen from equation (4) that the current increment prediction equation of the q-axis of the surface-mounted permanent magnet synchronous motor can be written as a first-order linear equation ( y = ax ) form, that is , , a = T s / L s Therefore, we can x and y The measured value of L s The coefficient of a , thus achieving L s Real-time estimation.

[0058] At present, the commonly used linear fitting methods are least squares method and orthogonal regression method, but the least squares method only considers the dependent variable y There is an error in the independent variable x When there is a measurement error, the fitted straight line is inaccurate, and the orthogonal regression method can solve this problem. Therefore, this embodiment adopts a linear fitting method based on orthogonal regression to design a stator inductance estimation method. x and the dependent variable y to obtain more accurate fitting results.

[0059] The standard equation of the fitted straight line based on the linear fitting method of orthogonal regression is in the form of a ( xx 0)+ b ( yy 0)=0, x and y are the independent variable on the horizontal axis and the dependent variable on the vertical axis, x 0 and y 0 are the horizontal and vertical coordinates of a point on the fitting line.

[0060] Multiply both sides of the q-axis current increment prediction equation in equation (3) by M And transform it and rewrite it into a ( x- x 0)+ b ( yy 0)=0, that is, the stator inductance estimation model is as follows:

[0061] (5)

[0062] Where: , ( MT s ) 2 + ( ML s ) 2 =1.

[0063] The equations in formula (5) are written as a ( xx 0)+ b ( yy 0)=0, where a , b , x , y , x 0 and y The definition of 0 is shown in formula (5), where a =- MT s , b = ML s This embodiment uses a linear fitting method based on orthogonal regression, by adjusting the coefficients of the fitting line in equation (5) a and b Calculations are performed to estimate the stator inductance L s Correspondingly, the N The horizontal coordinate of the sampling point is The vertical axis is , n =1, 2, …, N ,like Figure 2 As shown, Figure 2 The solid points in the figure are used to calculate the fitted straight line. N sampling points.

[0064] Based on formula (5), the stator inductance calculation matrix is ​​constructed as follows:

[0065] (6)

[0066] Where: S represents the stator inductance calculation matrix, n =1,2,…, N , , , =AVERAGE( x 1, x 2,…, x n ), =AVERAGE( y 1, y 2,…, y n ), AVERAGE( ) means to find the average, k Indicates the sequence number of the current control moment.

[0067] In obtaining the stator inductance calculation matrix S After that, we calculate S The eigenvector corresponding to the minimum eigenvalue of v =[ a , b ] T .

[0068] Step 3: Calculate the estimated value of stator inductance based on the eigenvector obtained in step 2.

[0069] From formula (5), we can see that a = MTs , b = ML s , so the calculation expression of the estimated inductance can be obtained as follows:

[0070] (7)

[0071] Where: represents the estimated value of the motor stator inductance, [ a , b ] T represents the eigenvector corresponding to the minimum eigenvalue of the stator inductance calculation matrix, T s Indicates the control period.

[0072] Step 4: Substitute the estimated value of stator inductance obtained in step 3 into the motor current increment prediction model established in step 1, and use the estimated value of stator inductance to replace the nominal value of stator inductance in the model to obtain a motor current increment prediction model based on the estimated value of stator inductance.

[0073] Estimated stator inductance Substituting into the current increment prediction model, the motor current increment prediction model based on the estimated value of stator inductance is as follows:

[0074] (8)

[0075] Step 5: A cost function is constructed by the motor current increment prediction model based on the estimated value of the stator inductance. The cost function is used to calculate the optimal stator voltage increment. Finally, the optimal stator voltage increment is added to the stator voltage applied at the current control moment to obtain the optimal stator voltage at the next control moment.

[0076] The cost function is constructed according to formula (8): J And minimize it:

[0077] (9)

[0078] Where: J represents the cost function, D i d * and D i q * They are the d-axis current increment reference value and the q-axis current increment reference value, , Indicates k +2 The predicted value of the d-axis current at the control time, Indicates k +1 d-axis current at the control moment; , Indicates k +2 The predicted value of the q-axis current at the control time, Indicates k +1 q-axis current at the control moment; , , Indicates k +1 The d-axis stator voltage applied at the control moment, Indicates k The d-axis stator voltage applied at the control moment, , Indicates k +1 The q-axis stator voltage applied at the control time, Indicates k Controls the q-axis stator voltage applied at the instant.

[0079] For formula (9), find The derivative of can be used to obtain the cost function J The extreme value conditions of are:

[0080] (10)

[0081] By solving equation (10), we can get the optimal voltage increment: .

[0082] The optimal voltage increment and the stator voltage applied at the current control moment Add together and get the optimal stator voltage to be applied at the next control moment:

[0083] (11)

[0084] The overall framework of the motor robust model predictive control method based on linear fitting in this embodiment is as follows: Figure 1 As shown, it estimates the stator inductance by using a linear fitting method based on orthogonal regression, which improves the robustness of the model predictive control while avoiding excessive calculation and complex parameter setting work.

[0085] In order to better illustrate the technical effect of the method of the present invention, we will verify the feasibility through simulation data below.

[0086] A 3.1kW permanent magnet synchronous motor system is used in this verification example. The motor parameters are shown in Table 1. The sampling frequency and control frequency in the simulation are both 10kHz.

[0087] Table 1

[0088]

[0089] In order to verify the feasibility and effectiveness of the method of the present invention, we used Matlab / Simulink to monitor the state changes of the motor when the speed ramped up and entered the high-speed operating condition under different model predictive control methods.

[0090] (1) Comparison of steady-state control performance.

[0091] In order to verify the steady-state performance of the robust model predictive control method of the present invention, we will compare the steady-state current quality of the robust model predictive control of the present invention and the traditional model predictive control method based on the current increment prediction model. In the simulation, the model predictive control method based on the current increment prediction model used for comparison uses the nominal inductance parameter, and the robust model predictive control method of the present invention uses the inductance estimated based on the linear fitting method. The two methods have different values ​​for the motor d-axis current. i d , q-axis current i q , A phase current i A The simulation waveform of the A phase current THD (total harmonic distortion) is as follows: Figure 3~Figure 6 shown.

[0092] By comparing the two model predictive control methods, it can be seen that the steady-state current quality of the robust model predictive control method of the present invention is consistent with the model predictive control method based on the current increment prediction model. Therefore, although the robust model predictive control method of the present invention adopts estimation, it does not affect the steady-state control performance of the motor, and can obtain a steady-state current quality that is consistent with the traditional model predictive control based on the current increment prediction model using nominal inductance parameters.

[0093] (2) Robustness analysis

[0094] In order to verify the robustness of the method under parameter disturbance, Figure 7 and Figure 8 The experimental waveforms of d and q axis currents of the robust model predictive control method of the present invention and the traditional model predictive control method based on the current increment prediction model before and after the stator inductance step change are given. L d and L q is the nominal value in Table 1, and then the inductance in the algorithm increases by 100%. In the experiment, the motor operating conditions are ① n =200r / min, T L =15N·m;② n =2000r / min, T L =15N·m.

[0095] contrast Figure 7 and Figure 8 It can be seen that when the motor parameters suddenly change, the traditional model predictive control method based on the current increment prediction model i d and i q Obvious fluctuations occur, and the q-axis current deviates significantly from its reference value, while the inductance mutation does not affect the d- and q-axis current control performance of the robust model predictive control method of the present invention. It can be seen that the robust model predictive control method of the present invention has excellent robustness.

[0096] The above description of the embodiments is to facilitate the understanding and application of the present invention by those skilled in the art. It is obvious that those skilled in the art can easily make various modifications to the above embodiments and apply the general principles described herein to other embodiments without creative work. Therefore, the present invention is not limited to the above embodiments. Improvements and modifications made by those skilled in the art to the present invention based on the disclosure of the present invention should be within the protection scope of the present invention.

Claims

1. A motor robust model predictive control method based on linear fitting, comprising the following steps: (1) Taking the current increment of the motor stator current in two adjacent control cycles as the prediction quantity and the voltage increment of the motor stator voltage in two adjacent control cycles as the control quantity, a motor current increment prediction model is established; (2) A stator inductance estimation model is established based on the q-axis stator current increment in the motor current increment prediction model, thereby obtaining a stator inductance calculation matrix and calculating the eigenvector corresponding to its minimum eigenvalue; (3) calculating an estimated value of stator inductance according to the eigenvector; (4) Substituting the estimated value of stator inductance into the motor current increment prediction model established in step (1) to obtain a motor current increment prediction model based on the estimated value of stator inductance; (5) A cost function is constructed based on the motor current increment prediction model obtained in step (4), and the optimal stator voltage increment is obtained by minimizing the cost function. The optimal stator voltage increment is then added to the stator voltage at the current control moment to obtain the stator voltage at the next control moment.

2. The motor robust model predictive control method based on linear fitting according to claim 1, characterized in that: The expression of the motor current increment prediction model in step (1) is as follows: in: and They represent the d-axis stator current increment of the motor in the k+1th control cycle and the kth control cycle respectively, and They represent the q-axis stator current increment of the motor in the k+1th control cycle and the kth control cycle respectively, and They represent the d-axis stator voltage increment and q-axis stator voltage increment of the motor in the kth control cycle, respectively. s Indicates the duration of the control cycle, L s represents the stator inductance, represents the rotational angular velocity of the motor rotor at the kth control moment, where k is an integer greater than or equal to 0.

3. The motor robust model predictive control method based on linear fitting according to claim 1, characterized in that: The stator inductance estimation model is expressed as follows: Where: M is a variable coefficient greater than 0 so that (MT s ) 2 +(ML s ) 2 =1, and They represent the d-axis stator current increment and q-axis stator current increment of the motor in the k-1th control cycle, respectively. represents the d-axis stator voltage increment of the motor in the k-1th control cycle, represents the lumped dependent variable of the q-axis stator current increment in the k-th control cycle, T s Indicates the duration of the control cycle, L s represents the stator inductance, Represents the rotational angular velocity of the motor rotor at the k-1th control moment.

4. The motor robust model predictive control method based on linear fitting according to claim 1, characterized in that: In the step (2), the stator inductance calculation matrix is ​​calculated based on the stator inductance estimation model by the following expression: Where: S is the stator inductance calculation matrix, represents the q-axis stator voltage increment of the motor in the knth control cycle, represents the lumped dependent variable of the q-axis stator current increment in the k-n+1th control period, AVERAGE() means averaging, and N is the number of set sampling control points.

5. The motor robust model predictive control method based on linear fitting according to claim 1, characterized in that: In step (3), the estimated value of the stator inductance is calculated by the following formula: in: is the estimated value of stator inductance, [a,b] T is the eigenvector corresponding to the minimum eigenvalue of the stator inductance calculation matrix, T s Indicates the duration of the control cycle.

6. The motor robust model predictive control method based on linear fitting according to claim 1, characterized in that: In step (5), the cost function is minimized by the following formula: Where: J is the cost function, and They represent the d-axis stator current increment and q-axis stator current increment of the motor in the k+2th control cycle, respectively. and They represent the d-axis stator current increment reference value and the q-axis stator current increment reference value respectively, It represents the stator voltage increment of the motor in the k+1th control cycle, that is, the optimal stator voltage increment.

7. The motor robust model predictive control method based on linear fitting according to claim 6 is characterized in that: In step (5), the optimal stator voltage increment is added to the stator voltage applied at the current control moment to obtain the stator voltage at the next control moment, that is, in and They represent the stator voltage of the motor at the kth control moment and the k+1th control moment respectively.

8. A computer device comprising a memory and a processor, characterized in that: The memory stores a computer program, and the processor is used to execute the computer program to implement a motor robust model predictive control method based on linear fitting as claimed in any one of claims 1 to 7.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the computer program implements a motor robust model predictive control method based on linear fitting as claimed in any one of claims 1 to 7.

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