A model predictive control method and system for effectively suppressing the second harmonic of a permanent magnet synchronous motor

Abstract

This invention belongs to the technical field of motor control and discloses a model predictive control method and system for effectively suppressing the second harmonic of a permanent magnet synchronous motor. The method includes the following steps: obtaining the three-phase input current of the permanent magnet synchronous motor at the current moment, converting the three-phase input current into a sum-i current in a coordinate system; extracting the two orthogonal components of the second harmonic at the current moment from the transfer function of the current input to a second-order generalized integrator; calculating the second harmonic component at the next moment using the two orthogonal components of the second harmonic at the current moment; compensating the fundamental current reference command at the next moment using the second harmonic component at the next moment, obtaining the compensated fundamental current reference command at the next moment, thus achieving the suppression of the second harmonic current at the next moment. This invention solves the problem of not suppressing the second harmonic in the control of permanent magnet synchronous motors.

Description

Technical Field

[0001] This invention belongs to the field of motor control technology, and more specifically, relates to a model predictive control method and system for effectively suppressing the second harmonics of a permanent magnet synchronous motor. Background Technology

[0002] In recent years, Model Predictive Control (MPC) has been considered a powerful alternative to Default Voltage Control (FOC) due to its intuitive principles, ease of handling multiple constraints, and fast dynamic response. Among these, Finite Control Set Model Predictive Control (FCS-MPC) can directly calculate the optimal voltage vector and apply it to the inverter by minimizing the value function. It boasts a simple structure and is easy to add constraints. However, traditional single-vector FCS-MPC outputs only a single voltage vector within a single control cycle, resulting in a significant error between the expected and actual output voltages and poor steady-state performance. Specifically, this manifests as high harmonic content in the phase current and large torque ripple.

[0003] For harmonic suppression control of FCS-MPC, it is mainly divided into three categories: multi-vector modulation strategy, harmonic extraction and compensation method, and observer-based parameter identification and disturbance compensation.

[0004] The multi-vector modulation strategy mainly involves selecting... Multiple adjacent large vectors in a subspace are synthesized into a single output multi-voltage composite vector according to a specific duty cycle to reduce low-order harmonic currents. For example, a virtual vector model predictive control method for a six-phase permanent magnet synchronous motor in a ship [CN202510250417.1], based on the multi-degree-of-freedom structural characteristics of the six-phase permanent magnet synchronous motor, divides the control space into two controllable subspaces, α-β and xy, through vector space decoupling transformation. It fully utilizes the reverse distribution and mutual superposition and cancellation characteristics of the voltage vectors in the xy subspace, and designs a virtual voltage vector synthesis strategy based on the volt-second balance principle to optimize the voltage vector distribution and eliminate harmonic currents in the xy space. Current delay compensation technology is also introduced.

[0005] The most mainstream harmonic extraction and compensation method currently is the cost function optimization method. This method mainly achieves multi-objective optimization by explicitly adding harmonic suppression terms to the cost function of MPC and designing corresponding weight coefficients. For example, the published patent: A method for current harmonic suppression of permanent magnet synchronous motor based on model predictive control [CN202511195475.5], designs and constructs a cost function in the prediction model that includes a fundamental current tracking term and a higher-order current harmonic suppression term, calculates the current harmonic term factor, traverses the voltage vectors corresponding to all switching states of the inverter, calculates the predicted current and cost function under the action of the voltage vector, selects the optimal voltage vector that minimizes the cost function, and generates a switching signal to drive the permanent magnet synchronous motor. However, its construction establishes a prediction model that includes fundamental tracking and higher-order harmonic suppression.

[0006] Despite the significant progress made by the aforementioned methods in harmonic suppression, the following shortcomings remain: 1) Insufficient targeted research on second harmonics; 2) Lack of dynamic prediction models for second harmonics. Since odd-order harmonics such as the 5th and 7th harmonics in a three-phase system are the main products of nonlinear factors such as dead zones, and can cause more severe 6th harmonic torque ripple, their control priority is far higher than that of second harmonics, which only appear under asymmetrical operating conditions. However, this does not mean that second harmonic suppression is unimportant. When a three-phase system is unbalanced, second harmonics are the main factor causing fluctuations. Therefore, this patent designs a second-order harmonic suppression method based on model predictive control of a permanent magnet synchronous motor. Summary of the Invention

[0007] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a model predictive control method and system for effectively suppressing the second harmonic of permanent magnet synchronous motor, and solves the problem of not suppressing the second harmonic in the control of permanent magnet synchronous motor.

[0008] To achieve the above objectives, according to one aspect of the present invention, a model predictive control method for effectively suppressing the second harmonic of a permanent magnet synchronous motor is provided, the method comprising the following steps: Obtain the three-phase input current of the permanent magnet synchronous motor at the current moment, and convert the three-phase input current into... In the coordinate system and i Current; the current Extract the two orthogonal components of the second harmonic at the current time from the transfer function of the input second-order generalized integrator; The second harmonic component at the next moment is calculated using the two orthogonal components of the second harmonic at the current moment; the fundamental current reference command at the next moment is compensated using the second harmonic component at the next moment to obtain the compensated fundamental current reference command at the next moment; the permanent magnet synchronous motor is controlled according to the compensated fundamental current reference command to achieve the suppression of the second harmonic current at the next moment.

[0009] More preferably, the formula for calculating the second-order harmonic orthogonal components at the next time step using the two orthogonal components of the second-order harmonic at the current time step is as follows:

[0010] in, It is the electric angular velocity of the motor. To control the cycle, and yes The second harmonic orthogonal components at time t, and Through Predicted in real time The second-order harmonic orthogonal components at time t.

[0011] More preferably, the second harmonic component at the next moment needs to be converted into... The transformation formula for the second harmonic component in a rotating coordinate system is as follows:

[0012] in, and yes Second harmonic component in coordinate system This is the Park transformation matrix. yes The electrical angle of the motor at any given time.

[0013] More preferably, the formula for compensating the fundamental current reference command at the next moment using the second harmonic component at the next moment is as follows:

[0014] in, and The new current reference command at time k+1 after compensating for the second harmonic component. and for Current reference command at any time, and yes Second harmonic component in coordinate system.

[0015] More preferably, the transfer function of the second-order generalized integrator is as follows:

[0016] in, The damping coefficient determines the filter's bandwidth and dynamic response speed. These are complex variables in the transfer function. It is the electric angular velocity of the motor.

[0017] According to one aspect of the present invention, a system is provided that utilizes the model predictive control method for effectively suppressing the second harmonic of a permanent magnet synchronous motor as described above. The system includes an inverter, a permanent magnet synchronous motor, a second harmonic suppression module, and a finite set model predictive control module, wherein: The second harmonic suppression module is connected to the permanent magnet synchronous motor and uses the control method described in any one of claims 1-4 to convert the three-phase input current of the permanent magnet synchronous motor at the current moment into a compensated fundamental current reference command at the next moment. The finite set model predictive control module is connected to the second harmonic suppression module and is used to convert the compensated fundamental current reference command at the next time moment into the duty cycle and effective vector at the next time moment and transmit it to the inverter. The inverter is connected to the permanent magnet synchronous motor. After receiving the duty cycle and effective vector of the next moment, the inverter converts them into the control current for controlling the permanent magnet synchronous motor at the next moment, and controls the permanent magnet synchronous motor according to the control current of the next moment.

[0018] According to another aspect of the present invention, a control method for controlling a permanent magnet synchronous motor using the above-described system is provided, the method comprising the following steps: Calculate the reference command for the compensated fundamental current at the next moment based on the current three-phase input current of the permanent magnet synchronous motor; The fundamental current reference command after compensation at the next time moment is converted into duty cycle and effective vector; The inverter input is calculated using the duty cycle and effective vector. The inverter outputs the control current for the permanent magnet synchronous motor at the next moment, and controls the permanent magnet synchronous motor according to the control current.

[0019] More preferably, the formula for calculating the duty cycle is as follows:

[0020] in, and These are the d-axis and q-axis current command values. and Current value after interaction with zero vector and The error value, with the superscript 0 indicating zero vector action, and These are the d-axis and q-axis current reference command values. and d-axis and q-axis current values ​​after interaction with the effective vector and Error value, superscript It is an effective vector action.

[0021] More preferably, the formula for calculating the effective vector is as follows:

[0022] Where A, B, and C are three transformation matrices, and C is the identity matrix, as detailed below: , , , , , , For the present k Moment dq shaft current, For prediction k+1 time dq shaft current, For output current, To control the cycle, and These are the transformation matrices for the Park and Clark transformations, respectively. It is the electric angular velocity of the motor. It is the electrical angle of the motor at time k. This is the DC bus voltage. for Shaft inductor, for Shaft inductor, For the size of the magnetic flux, and for shaft and The magnitude of the shaft current, The resistance of the motor. and for shaft and axis The magnitude of the current at any given moment. for Three-phase switch status.

[0023] According to another aspect of the present invention, a system is provided that utilizes the model predictive control method for effectively suppressing the second harmonic of a permanent magnet synchronous motor as described above. The system includes an actuator for executing the model predictive control method for effectively suppressing the second harmonic of a permanent magnet synchronous motor as described above.

[0024] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art: 1. This invention calculates the second harmonic component of the next time step by utilizing the two orthogonal components of the second harmonic at the current time step, thereby predicting the second harmonic component of the next time step. Then, the prediction result is used to compensate the fundamental current reference command at the next time step. By integrating harmonic compensation into the reference command, the model predictive control actively selects the voltage vector that is conducive to reducing harmonics during the tracking process, thereby effectively suppressing the second harmonic current at the next time step, reducing the second harmonic content in the current, reducing torque ripple, and improving the motor's operating efficiency and steady-state accuracy.

[0025] 2. This invention accurately describes the dynamic behavior of the second harmonic in the stationary coordinate system by using a rotating vector model, and extrapolates the current information extracted by the second-order filter system to future times through a prediction model, providing accurate compensation for reference correction and avoiding the phase lag problem caused by simple filtering.

[0026] 3. This invention uses a second-order generalized integrator to extract second-order harmonic current. Compared with traditional methods, which struggle to balance extraction accuracy, dynamic response speed, and system bandwidth, this invention is also more flexible and easier to implement. It can deliver more accurate results and ensure the effectiveness of the method in the steady-state domain.

[0027] 4. This invention converts the fundamental current reference command after compensation at the next time step into the duty cycle and effective vector at the next time step and transmits it to the inverter. It does not require changing the core structure and value function of the original finite set model predictive control module (FCS-MPC). Only the reference value needs to be preprocessed at the input end. It is easy to integrate into existing control systems and has a small computational burden. Attached Figure Description

[0028] Figure 1 This is a flowchart illustrating a model predictive control method for effectively suppressing the second harmonic of a permanent magnet synchronous motor, constructed according to a preferred embodiment of the present invention.

[0029] Figure 2 This is a schematic diagram of the system controlled by the model predictive control method for effectively suppressing the second harmonic of a permanent magnet synchronous motor, constructed according to a preferred embodiment of the present invention.

[0030] Figure 3This is a comparison diagram of steady-state velocity frequency domain before and after second harmonic suppression, constructed according to a preferred embodiment of the present invention.

[0031] Figure 4 This is a time-domain comparison diagram of steady-state velocity before and after second harmonic suppression, constructed according to a preferred embodiment of the present invention. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0033] A model predictive control method for effectively suppressing second harmonics in permanent magnet synchronous motors is presented. This method effectively suppresses second harmonics, thereby enabling more precise achievement of the control objective. The method mainly includes the following key technologies: Obtain the three-phase currents (a, b, c) input to the permanent magnet synchronous motor and convert them into... , In the coordinate system and current, The input is fed into the SOGI of the second-order generalized integrator to extract the two orthogonal components of the second-order harmonic, which are respectively and ,Will and Input the harmonic model predictor to obtain the second-order harmonic quadrature components at the next time step.

[0034] (1) Construct a second-order filter system that can extract the second harmonic component in real time.

[0035] The second-order generalized integrator is a core signal processing tool used to extract instantaneous information of a specific frequency from a current signal containing noise and a fundamental frequency in real time and accurately, and to generate its orthogonal components. In the overall method, it plays a role in harmonic information extraction. Since the second harmonic is a rotating vector in the αβ stationary coordinate system, the instantaneous amplitude of the second harmonic alone is not enough. Therefore, a pair of orthogonal components is needed to fully describe its instantaneous magnitude and phase.

[0036] The second-order generalized integrator (SOGI) extracts second-order harmonics and further suppresses them.

[0037] The continuous-domain transfer function of SOGI is as follows:

[0038] in, represent or axis, and Indicates by Similarly, by inputting the extracted second harmonic quadrature components, we can obtain... and ; The damping coefficient determines the filter's bandwidth and dynamic response speed; it is typically set here. .

[0039] SOGI exhibits bandpass characteristics at its resonant frequency, enabling it to accurately extract the second harmonic component from complex current signals containing the fundamental frequency and other harmonics, while simultaneously outputting its quadrature components. and These two orthogonal components completely describe the second harmonic vector at the current moment. The instantaneous magnitude and phase in the stationary coordinate system provide an accurate initial state for subsequent predictions.

[0040] (2) Establish a prediction model describing the dynamic behavior of second harmonics.

[0041] The premise of establishing a model for predicting second harmonics is that within an extremely short control period, the harmonic amplitude can be assumed to remain constant, with only the phase changing. Furthermore, the second harmonic can be regarded as a uniformly rotating spatial vector, and the position at the next moment can be calculated using the position value at the current moment, thereby obtaining the predicted harmonic value at the next moment.

[0042] After obtaining the second harmonic vector from SOGI, a dynamic prediction model for the second harmonic is established, taking into account a control cycle. In a very short period, the control background for harmonic suppression is during the steady-state period. The amplitude of the second harmonic can be approximated as constant, with only the phase changing at an angular velocity. Since the second harmonic rotates at a constant speed, it can be considered as a uniformly rotating spatial vector. The evolution of the second harmonic from the current moment to the next moment can be described using a rotation matrix. The harmonic model predictor is as follows:

[0043] The model utilizes the currently extracted and Calculate the next moment and The harmonic state provides a basis for prediction and compensation.

[0044] After obtaining the harmonic state at the next moment, the Park transform is applied (rotation angle is...). After transforming to a rotating coordinate system, we get Second harmonic component under axis and The details are as follows:

[0045] (3) Convert the predicted future harmonics into reference command correction values, subtract the predicted second harmonic component from the original reference current, and obtain the current fundamental reference command.

[0046] The result The second harmonic component below the axis is used as a harmonic compensation amount and is subtracted from the original fundamental current reference command to form a new current reference command:

[0047] The new reference command is essentially a superposition of the fundamental reference command and harmonic compensation, which enables the subsequent model predictive controller to indirectly suppress the second harmonic current when tracking the corrected reference value.

[0048] The reference current command value can actually be transformed into a combination of the fundamental reference command value and the harmonic compensation command value. In this way, the model will track the reference value that includes harmonic compensation, thereby indirectly suppressing harmonics. This method only requires modifying the command value and does not affect the overall model predictive control logic.

[0049] like Figure 2 As shown, this invention also discloses a system controlled by the above-mentioned model predictive control method for effectively suppressing the second harmonic of a permanent magnet synchronous motor. The system includes an inverter, a permanent magnet synchronous motor, a second harmonic suppression module, and a finite set model predictive control module, wherein: The second harmonic suppression module is connected to the permanent magnet synchronous motor, and the above control method converts the three-phase input current of the permanent magnet synchronous motor at the current moment into a compensated fundamental current reference command for the next moment.

[0050] The finite set model predictive control module is connected to the second harmonic suppression module and is used to convert the compensated fundamental current reference command for the next time step into the duty cycle and effective vector for the next time step and transmit it to the inverter.

[0051] The inverter is connected to the permanent magnet synchronous motor. After receiving the duty cycle and effective vector of the next moment, the inverter converts them into the control current for controlling the permanent magnet synchronous motor at the next moment, and controls the permanent magnet synchronous motor according to the control current of the next moment.

[0052] (1) Calculate the effective vectors for controlling the on and off states of the inverter.

[0053] The voltage equation of the motor is rewritten in discrete state-space form to control the motion of the permanent magnet synchronous motor.

[0054] in, , , , , , , To control the cycle, and These are the transformation matrices for the Park and Clark transformations, respectively.

[0055] Feedback current and Substituting into the above formula, since the zero vector is acting, for Therefore, the inverter does not output voltage at this time. and If the value is 0, then the current value after the zero vector action can be calculated. and Then the current command value and and and The difference and It should be the current value after the effective vector action, and then it should be converted into... In the coordinate system, the difference vector is obtained in The components in the coordinate system, whose directions can be approximated by the direction of the desired voltage vector, are used to select the effective vector by their angles.

[0056] After selecting the effective vector, perform current prediction y again. and No longer 0, value is That is, the current value after the effective vector action can be calculated. and and current command value and and and error value and .

[0057] (2) Solve for the duty cycle Construct a cost function, solve for the duty cycle when the cost function is minimized, and solve for the product of the duty cycle and the effective vector. Based on the idea of ​​predictive control using a duty cycle optimization model, the predicted current for the next cycle can be expressed as:

[0058] In the formula The predicted current under zero vector action, For the predicted current under effective vector action, The duty cycle represents the proportion of time during which the effective vector acts. It is the direct axis and the quadrature axis.

[0059] Therefore, the corresponding current error is shown below:

[0060] Based on the above formula, we can derive the information about the duty cycle. The cost function, i.e.:

[0061] From the above formula Taking the partial derivative and setting it to zero, we get:

[0062] Finally Multiplying the calculated effective vector yields the output for the inverter, which controls the opening and closing of the inverter's switches. The inverter is used to power a permanent magnet synchronous motor.

[0063] The present invention will be further described below with reference to specific embodiments.

[0064] To verify the feasibility of this method, the invention was deployed in a matching integrated drive and control CNC system. The specific implementation steps of this invention are as follows: (1) Obtain the relevant parameters of the permanent magnet synchronous motor. The parameters required for calculation by this method are as follows:

[0065] (2) The CU100 controller continuously checks whether the current feedback module is working properly and whether the motor is enabled. If the current feedback module is working properly and the motor is enabled, then proceed to (3).

[0066] (3) After receiving the speed command, the CU100 controller performs a speed loop PI control and outputs a current command. , .

[0067] (4) Transfer current command , , , The input is a single-step dual-vector FCS-MPC controller, which runs the algorithm and outputs the effective vector and duty cycle. After multiplying the two, it is converted into the corresponding pulse width modulation (PWM) signal. After being amplified and isolated by the drive circuit, it is input to the insulated-gate bipolar transistor (IGBT) to output the three-phase current to the motor.

[0068] (5) Read the three-phase current of the motor , , After feedback, a Clark transformation is performed to obtain the coordinates in the stationary coordinate system. Current, to The input to SOGI yields two components of the second harmonic in the stationary coordinate system. and .

[0069] (6) and The input is fed into the harmonic model predictive controller to obtain the predicted next time step. and .

[0070] (7) , , , Obtained by performing park transformation Rotating coordinate system , , , .

[0071] (8) Current command output by the speed loop PI , minus , Received and As a new instruction, and with , The inputs are fed into the single-step dual-vector FCS-MPC controller, and then (4) is performed, repeating this process.

[0072] Given a speed command of 75 rpm, the second harmonic frequency can be calculated to be 12.5 Hz. The steady-state speed frequency domain diagrams for using the dual-vector FCS-MPC alone and using the dual-vector FCS-MPC combined with the MPC harmonic suppression method are shown below. Figure 3 As shown, the time-domain plot is as follows Figure 4As shown, the second harmonic component decreased from 1.04772 to 0.4341. The speed fluctuation decreased from 1.62 rpm to 1.13 rpm.

[0073] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A model predictive control method for effectively suppressing the second harmonic of a permanent magnet synchronous motor, characterized in that, The method includes the following steps: Obtain the three-phase input current of the permanent magnet synchronous motor at the current moment, and convert the three-phase input current into... In the coordinate system and i Current; the current Extract the two orthogonal components of the second harmonic at the current time from the transfer function of the input second-order generalized integrator; The second harmonic component at the next time step is calculated using the two orthogonal components of the second harmonic at the current time step. The second harmonic component of the next moment is used to compensate the fundamental current reference command of the next moment, so as to obtain the compensated fundamental current reference command of the next moment. The permanent magnet synchronous motor is controlled according to the compensated fundamental current reference command, thus realizing the suppression of the second harmonic current of the next moment.

2. The model predictive control method for effectively suppressing the second harmonic of a permanent magnet synchronous motor as described in claim 1, characterized in that, The formula for calculating the second-order harmonic orthogonal components at the next time step using the two orthogonal components of the second-order harmonic at the current time step is as follows: in, It is the electric angular velocity of the motor. To control the cycle, and yes The second harmonic orthogonal components at time t, and Through Predicted in real time The second-order harmonic orthogonal components at time t.

3. The model predictive control method for effectively suppressing the second harmonic of a permanent magnet synchronous motor as described in claim 2, characterized in that, The second harmonic component at the next moment needs to be converted to... The transformation formula for the second harmonic component in a rotating coordinate system is as follows: in, and yes Second harmonic component in coordinate system This is the Park transformation matrix. yes The electrical angle of the motor at any given time.

4. The model predictive control method for effectively suppressing the second harmonic of a permanent magnet synchronous motor as described in claim 3, characterized in that, The formula for compensating the fundamental current reference command at the next moment using the second harmonic component at the next moment is as follows: in, and The new current reference command at time k+1 after compensating for the second harmonic component. and for Current reference command at any time, and yes Second harmonic component in coordinate system.

5. A model predictive control method for effectively suppressing the second harmonic of a permanent magnet synchronous motor as described in claim 1 or 4, characterized in that, The transfer function of the second-order generalized integrator is as follows: in, The damping coefficient determines the filter's bandwidth and dynamic response speed. These are complex variables in the transfer function. It is the electric angular velocity of the motor.

6. A system controlled using the model predictive control method for effectively suppressing the second harmonic of a permanent magnet synchronous motor as described in any one of claims 1-5, characterized in that, The system includes an inverter, a permanent magnet synchronous motor, a second harmonic suppression module, and a finite set model predictive control module, wherein: The second harmonic suppression module is connected to the permanent magnet synchronous motor and uses the control method described in any one of claims 1-4 to convert the three-phase input current of the permanent magnet synchronous motor at the current moment into a compensated fundamental current reference command at the next moment. The finite set model predictive control module is connected to the second harmonic suppression module and is used to convert the compensated fundamental current reference command at the next time moment into the duty cycle and effective vector at the next time moment and transmit it to the inverter. The inverter is connected to the permanent magnet synchronous motor. After receiving the duty cycle and effective vector of the next moment, the inverter converts them into the control current for controlling the permanent magnet synchronous motor at the next moment, and controls the permanent magnet synchronous motor according to the control current of the next moment.

7. The control method for a permanent magnet synchronous motor by the system as described in claim 6, characterized in that, The method includes the following steps: Calculate the reference command for the compensated fundamental current at the next moment based on the current three-phase input current of the permanent magnet synchronous motor; The fundamental current reference command after compensation at the next time moment is converted into duty cycle and effective vector; The inverter input is calculated using the duty cycle and effective vector. The inverter outputs the control current for the permanent magnet synchronous motor at the next moment, and controls the permanent magnet synchronous motor according to the control current.

8. The control method for a permanent magnet synchronous motor as described in claim 7, characterized in that, The formula for calculating the duty cycle is as follows: in, and These are the d-axis and q-axis current command values. and Current value after interaction with zero vector and The error value, with the superscript 0 indicating zero vector action, and These are the d-axis and q-axis current reference command values. and d-axis and q-axis current values ​​after interaction with the effective vector and Error value, superscript It is an effective vector action.

9. The control method for a permanent magnet synchronous motor as described in claim 7 or 8, characterized in that, The formula for calculating the effective vector is as follows: Where A, B, and C are three transformation matrices, and C is the identity matrix, as detailed below: , , , , , , For the present k Moment dq shaft current, For prediction k+1 time dq shaft current, For output current, To control the cycle, and These are the transformation matrices for the Park and Clark transformations, respectively. It is the electric angular velocity of the motor. It is the electrical angle of the motor at time k. This is the DC bus voltage. for Shaft inductor, for Shaft inductor, For the size of the magnetic flux, and for shaft and The magnitude of the shaft current, The resistance of the motor. and for shaft and axis The magnitude of the current at any given moment. for Three-phase switch status.

10. A system utilizing the model predictive control method for effectively suppressing the second harmonic of a permanent magnet synchronous motor as described in any one of claims 1-5, characterized in that, The system includes an actuator for performing a model predictive control method for effectively suppressing the second harmonics of a permanent magnet synchronous motor as described in any one of claims 1-5.

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