CN114039519A - Permanent magnet synchronous motor torque ripple suppression method, servo system and storage medium - Google Patents

Abstract

The invention discloses a method for inhibiting torque ripple of a permanent magnet synchronous motor based on robust fractional order vector resonance, which comprises the following steps: collecting parameters of a permanent magnet synchronous motor in real time, and establishing a mathematical model of the permanent magnet synchronous motor; designing a robust internal model controller and a fractional order vector resonance controller for designing the robust fractional order vector resonance controller; and based on the robust fractional order vector resonance controller, driving the permanent magnet synchronous motor to operate by adopting an SVPWM control strategy. The invention also discloses a permanent magnet synchronous motor rotating speed servo system based on robust fractional order vector resonance and a computer readable storage medium. According to the invention, through the combination of robust internal model control and fractional order vector resonance control, the robustness of a current loop of the permanent magnet synchronous motor is improved, and the torque pulsation of the permanent magnet synchronous motor can be effectively inhibited.

Description

Permanent magnet synchronous motor torque ripple suppression method, servo system and storage medium

technical field

The present invention relates to the technical field of rotational speed control of permanent magnet synchronous motors, in particular to a method for suppressing torque ripple of permanent magnet synchronous motors, a servo system and a storage medium.

Background technique

Permanent magnet synchronous motors have been widely used in electric vehicles, CNC machine tools and robot servo control and other technical fields due to their simple structure, small size, reliable operation, low power loss, high efficiency and good speed regulation performance. However, due to parameter mismatch, the nonlinear and uncertain disturbance of the controlled model inevitably exists in the motor servo system, resulting in torque ripple, which reduces the tracking performance and stability. Therefore, for the permanent magnet synchronous motor, the design of the motor body and the choice of its control strategy have a great influence on the motor torque ripple.

At present, the methods to solve the torque ripple of permanent magnet synchronous motors can be divided into two categories. One is to reduce the torque ripple by optimizing the key dimensions of the motor; Torque ripple is suppressed. The resonant controller is a common control strategy for suppressing torque ripple. Usually, multiple resonance controllers are connected in parallel in the current loop or speed loop to reduce the torque ripple. In practical applications, the commonly used resonance control methods such as the resonance controller have large gain and robustness to the change of resonance frequency, so there will be steady-state errors and incomplete suppression during use. Robust internal model control is a common control method in servo control systems. By designing two low-pass filters, a preset dynamic response can be achieved, and it has good robustness to the parameter changes of the controlled object. In fact, the establishment of any control strategy will increase the complexity of the system. Therefore, there is an urgent need in the art for a control strategy that can effectively suppress the torque ripple of the permanent magnet synchronous motor and improve the robustness control of the parameters of the permanent magnet synchronous motor without putting a lot of pressure on the system.

SUMMARY OF THE INVENTION

The main purpose of the present invention is to provide a torque ripple suppression method, a servo system and a storage medium for a permanent magnet synchronous motor, which aims to solve how to effectively suppress the torque ripple of the permanent magnet synchronous motor and improve the parameter stability of the permanent magnet synchronous motor. At the same time of sticky control, there is no technical problem of the control strategy that brings great pressure to the system.

In order to achieve the above object, a kind of permanent magnet synchronous motor torque ripple suppression method based on robust fractional vector resonance provided by the present invention, described permanent magnet synchronous motor torque ripple suppression method comprises the following steps:

Collect the parameters of the permanent magnet synchronous motor in real time, and establish the mathematical model of the permanent magnet synchronous motor;

Design a robust internal mode controller and a fractional-order vector resonance controller to design a robust fractional-order vector resonance controller;

Based on the robust fractional-order vector resonance controller, the SVPWM control strategy is used to drive the permanent magnet synchronous motor to run.

Optionally, the establishment of a permanent magnet synchronous motor mathematical model specifically adopts the following form:

Formula one:

where U _d and U _q are the d-axis and q-axis voltages in the rotating coordinate system, respectively; id and i _q are the _d -axis and q-axis currents, respectively; R _d and R _q are the d-axis and q-axis inductances, respectively; L _d and L _q are the d-axis and q-axis resistances, respectively; ω _h is the electrical angular frequency of the motor; Ψ _f is the motor flux linkage; t is the time;

The discretization of the above model completes the establishment of the model.

Optionally, the design of a robust internal model controller and a fractional-order vector resonance controller to design a robust fractional-order vector resonance controller includes:

Design a robust internal model controller, and control the stability of the robust internal model controller, specifically in the following form:

Defining the preset dynamic response transfer function of the robust internal model controller is expressed by formula 2:

The disturbance rejection filter is expressed by Equation 3:

where τ represents the time constant; λ is a constant related to the bandwidth of the disturbance suppression filter, wherein the parameter selection is 1/τ<<1/λ;

The robust internal model controller designed according to Equation 2 and Equation 3 is expressed by Equation 4:

Through the inverse Laplace transform, the following time domain control law can be expressed by Equation 5:

in the formula

To avoid integration iteration errors, define the following state variables:

x ₁ =e(t)

The parameters in the formula satisfy

Based on the definition of integral iterative error, the time domain control law is converted from Equation 5 and expressed in Equation 6:

u _IMO =(k _pe +k _py )x ₁ +(k _ie1 +k _iy1 )x ₂ +(k _ie2 +k _iy2 )x ₈ +k _ie8 x ₄

The differential form of the current loop transfer function is expressed by Equation 7:

According to formula 6 and formula 7, the state equation of the current loop is obtained as

为状态变量，A为赫尔维茨矩阵时，所述鲁棒内模控制 器稳定；when

is a state variable, when A is a Hurwitz matrix, the robust internal model controller is stable;

According to the designed robust internal mode controller and the fractional-order vector resonance controller, a robust fractional-order vector resonance controller is designed.

Optionally, the design of a robust internal model controller and a fractional-order vector resonance controller to design a robust fractional-order vector resonance controller includes:

Design a fractional-order vector resonance controller, and control the stability of the fractional-order vector resonance controller, specifically in the following form:

The fractional-order calculus is introduced into the resonant controller to obtain the following control law of the fractional-order vector resonant controller, which is expressed by Equation 8:

where k _r , ω _e , and α represent the controller gain coefficient, damping frequency, and fractional order, respectively;

Rewrite Equation 8 as Equation 9:

where Y(s) _k and R(s) _k respectively represent the input and output of the fractional-order vector resonance controller at time k ^th ;

According to the designed robust internal mode controller and the fractional-order vector resonance controller, a robust fractional-order vector resonance controller is designed.

Optionally, the design of a robust internal model controller and a fractional-order vector resonance controller to design a robust fractional-order vector resonance controller includes:

According to the designed robust internal model controller and the fractional-order vector resonance controller, a robust fractional-order vector resonance controller is designed, specifically in the following form:

F(s), C _A (s) and C _B (s) are the components of the internal model controller, and the closed-loop transfer function of the robust fractional-order vector resonance controller is obtained as follows:

where i(s) and _iref (s) represent the transfer functions of i(t) and _iref (t) in the s domain;

The fractional-order zero-pole in G _FOVR (s) is obtained by the Outstaloup method to obtain the integer-order zero-pole transfer function as Equation 11:

The design of the robust fractional-order vector resonance controller is completed by importing the above formula.

Optionally, after the design of the robust fractional-order vector resonance controller, the method for suppressing torque ripple of the permanent magnet synchronous motor further includes:

The stability analysis of the robust fractional-order vector resonance controller is carried out in the following form:

The stability of the robust fractional-order vector resonance controller should satisfy the following conditions, using formula 12:

式中||·||_∞表无穷范数；

where ||·|| _∞ represents the infinity norm;

According to formula 10 and formula 11, the closed-loop transfer function formula 13 of the current loop is obtained:

When A is a Hurwitz matrix, and all eigenvalues of 1+G _p (s)(C _A (s)+C _B (s)) fall on the left half-plane of the s domain, the stability is given by the following transfer function formula Fourteen determine:

It can be obtained from the small gain theorem that the closed loop meets the following conditions, which is expressed by Equation 15:

If Equation 15 can prove Equation 12, the robust fractional-order vector resonance controller is stable.

Optionally, after the design of the robust fractional-order vector resonance controller, the method for suppressing torque ripple of the permanent magnet synchronous motor further includes:

The robust stability analysis of the robust fractional-order vector resonant controller is carried out in the following form:

When the mathematical model of the permanent magnet synchronous motor is mismatched, the controlled object can be represented by formula 16:

where ΔG _p (s) represents the model error;

The robust stability of the robust fractional-order vector resonant controller is when and satisfying the following conditions, expressed by formula 17:

When the mathematical model of the permanent magnet synchronous motor is mismatched, the current loop characteristic polynomial can be expressed by formula 18:

in the formula

It can be obtained from the small gain theorem that the robust stability of the current loop satisfies the following conditions, expressed by Equation 19:

||Q(s)ΔG _p (s)|| _∞ ≤||Q(s)|| _∞ ||ΔG _p (s)|| _∞ ＜1

From this, formula 20 can be obtained:

If Formula 20 can prove Formula 17, then the robust fractional-order vector resonance controller is robust and stable.

In addition, in order to achieve the above purpose, the present invention also provides a permanent magnet synchronous motor speed servo system based on robust fractional-order vector resonance, including: a processor, a permanent magnet synchronous motor, a three-phase inverter, a speed PI controller, Space voltage vector pulse width modulation (SVPWM), robust fractional order vector resonance controller;

the robust fractional-order vector resonance controller for generating a control voltage;

the speed PI controller for generating a control current;

The processor is used to control the on-off of the three-phase inverter power device using the SVPWM control strategy to drive the operation of the permanent magnet synchronous motor;

The processor is further configured to execute the steps of the method for suppressing torque ripple of a permanent magnet synchronous motor based on robust fractional-order vector resonance as described in any one of the above.

In addition, in order to achieve the above object, the present invention also provides a computer-readable storage medium, where a torque ripple suppression program is stored on the computer-readable storage medium, and the torque ripple suppression program is executed by a processor to achieve the above-mentioned The steps of any one of the method for suppressing torque ripple of permanent magnet synchronous motor based on robust fractional-order vector resonance.

The present invention first collects the parameters of the permanent magnet synchronous motor in real time, establishes a mathematical model of the permanent magnet synchronous motor, and then designs a robust internal model controller and a fractional-order vector resonance controller, so as to design a robust fractional-order vector resonance controller, Finally, based on the robust fractional-order vector resonance controller, the SVPWM control strategy is used to drive the permanent magnet synchronous motor to run. By combining robust internal model control and fractional-order vector resonance control, the present invention not only improves the robustness of the current loop of the permanent magnet synchronous motor, but also can effectively suppress the torque ripple of the permanent magnet synchronous motor.

Description of drawings

In order to illustrate the technical solutions of the embodiments of the present invention more clearly, the following briefly introduces the accompanying drawings that are used in the description of the embodiments of the present invention or the prior art. Obviously, the drawings described below are only for the present invention. In some embodiments, for those of ordinary skill in the art, other drawings can also be obtained according to these drawings without any creative effort.

Fig. 1 is the structural representation of the operating environment of the permanent magnet synchronous motor rotational speed servo system based on robust fractional-order vector resonance that the embodiment scheme of the present invention relates to;

Fig. 2 is a schematic flowchart of an embodiment of a method for suppressing torque ripple of a permanent magnet synchronous motor based on robust fractional-order vector resonance of the present invention;

Fig. 3 is the block diagram of fractional order vector resonance controller;

Fig. 4 is the frequency response diagram of fractional order vector resonance controller;

Figure 5 is a block diagram of a robust fractional-order vector resonance controller;

Fig. 6 is a system structural block diagram of an embodiment of a permanent magnet synchronous motor rotational speed servo system based on robust fractional vector resonance of the present invention.

The realization, functional characteristics and advantages of the object of the present invention will be further described with reference to the accompanying drawings in conjunction with the embodiments.

Detailed ways

It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

Referring to Fig. 1, Fig. 1 is a schematic structural diagram of the operating environment of the permanent magnet synchronous motor speed servo system based on the robust fractional-order vector resonance according to the embodiment of the present invention.

As shown in Figure 1, the permanent magnet synchronous motor speed servo system based on robust fractional vector resonance may include: a processor 1001, such as a CPU, a communication bus 1002, a user interface 1003, a network interface 1004, and a memory 1005. Among them, the communication bus 1002 is used to realize the connection and communication between these components. The user interface 1003 may include a display screen (Display), an input unit such as a keyboard (Keyboard), and the network interface 1004 may optionally include a standard wired interface and a wireless interface (such as a WI-FI interface). The memory 1005 may be high-speed RAM memory, or may be non-volatile memory, such as disk memory. Optionally, the memory 1005 may also be a storage device independent of the aforementioned processor 1001.

Those skilled in the art can understand that the hardware structure of the permanent magnet synchronous motor speed servo system based on the robust fractional-order vector resonance shown in FIG. 1 does not constitute a limitation on the permanent magnet synchronous motor speed servo system. More or fewer components, or a combination of certain components, or a different arrangement of components.

As shown in FIG. 1, the memory 1005 as a computer-readable storage medium may include an operating system, a network communication module, a user interface module and a computer program. Among them, the operating system is a program that manages and controls the permanent magnet synchronous motor speed servo system and software resources, and supports the operation of the torque ripple suppression program and other software and/or programs.

In the hardware structure of the permanent magnet synchronous motor speed servo system shown in FIG. 1 , the network interface 1004 is mainly used to access the network; the user interface 1003 is mainly used to detect confirmation commands and edit commands. And the processor 1001 can be used to call the torque ripple suppression program stored in the memory 1005, and execute the torque ripple suppression program.

Based on the above-mentioned hardware structure of the permanent magnet synchronous motor speed servo system based on the robust fractional-order vector resonance, a permanent magnet synchronous motor torque ripple suppression based on the robust fractional-order vector resonance based on the operation state of the permanent magnet synchronous motor speed servo system of the present invention is proposed. Various embodiments of the method.

Referring to FIG. 2, FIG. 2 is a schematic flowchart of an embodiment of a method for suppressing torque ripple of a permanent magnet synchronous motor based on robust fractional-order vector resonance according to the present invention.

In the present embodiment, a method for suppressing torque ripple of permanent magnet synchronous motor based on robust fractional-order vector resonance, comprising the following steps:

Step S10, collect the parameters of the permanent magnet synchronous motor in real time, and establish a mathematical model of the permanent magnet synchronous motor;

Step S20, design a robust internal model controller and a fractional-order vector resonance controller, to design a robust fractional-order vector resonance controller;

In this embodiment, the resonance controller is a common control strategy for suppressing torque ripple. Usually, multiple resonance controllers are connected in parallel in the current loop or speed loop to achieve the purpose of reducing torque ripple. In practical applications, the resonant controller is a commonly used resonant control method due to its large gain and robustness to resonant frequency changes. However, this type of controller will have steady-state errors during use. Therefore, this paper introduces the fractional calculus into the design of the resonant controller to further suppress the current loop harmonics.

In this embodiment, the robust internal model control is a control method that is commonly used in servo control systems. It can achieve a preset dynamic response by designing two low-pass filters, and has good robustness to the parameter changes of the controlled object. Therefore, this paper applies the control strategy to the design of the current loop controller, so as to achieve a good dynamic response of the current loop and suppress the unmodeled disturbance of the current loop.

Step S30, based on the robust fractional-order vector resonance controller, the SVPWM control strategy is used to drive the permanent magnet synchronous motor to run.

In this embodiment, the fractional-order vector resonance control technology can effectively suppress the periodic harmonics existing in the current loop and suppress the torque ripple generated by them. periodic perturbations and improve the dynamic response of the current loop. Aiming at the lack of gain and phase margin of traditional resonance control, fractional calculus is introduced into the design of resonance controller to improve the harmonic suppression ability. The invention combines the advantages of robust internal model control and fractional resonance control, not only improves the robustness of the current loop of the permanent magnet synchronous motor, but also can effectively suppress the torque ripple of the permanent magnet synchronous motor. The present invention can ensure good robustness and dynamic response performance of the control system while effectively suppressing the harmonics of the current loop.

Based on the above embodiment, in this embodiment, the mathematical model of the permanent magnet synchronous motor is established in step S10, and the specific form is as follows:

Formula one:

where U _d and U _q are the d-axis and q-axis voltages in the rotating coordinate system, respectively; id and i _q are the _d -axis and q-axis currents, respectively; R _d and R _q are the d-axis and q-axis inductances, respectively; L _d and L _q are the d-axis and q-axis resistances, respectively; ω _h is the electrical angular frequency of the motor; Ψ _f is the motor flux linkage; t is the time;

The discretization of the above model completes the establishment of the model.

In this embodiment, when the motor is a surface mount motor (R _d =R _q =R, L _d =L _q =L), the current loop model can be expressed as

Then, its nominal model is

In the formula, L _n and R _n respectively represent the nominal electric group and inductance of the current loop, which can be obtained in real time through the motor test.

Based on the above embodiment, in this embodiment, in step S20, a robust internal model controller and a fractional-order vector resonance controller are designed to design a robust fractional-order vector resonance controller, including:

The robust internal model controller is designed and the stability of the robust internal model controller is controlled in the following form:

Defining the preset dynamic response transfer function of the robust internal model controller is expressed by formula 2:

The disturbance rejection filter is expressed by Equation 3:

where τ represents the time constant, the smaller the value, the faster the dynamic response; λ is a constant related to the bandwidth of the disturbance suppression filter, the smaller the value, the stronger the disturbance suppression ability, but the more sensitive the system is to noise, therefore, in When selecting parameters, 1/τ<<1/λ is preferred, so that the controller has good robustness to current loop disturbance;

The robust internal model controller designed according to Equation 2 and Equation 3 is expressed by Equation 4:

Through the inverse Laplace transform, the following time domain control law can be expressed by Equation 5:

in the formula

To avoid integration iteration errors, define the following state variables:

x ₁ =e(t)

The parameters in the formula satisfy

Based on the definition of integral iterative error, the time domain control law is converted from Equation 5 and expressed in Equation 6:

u _IMO =(k _pe +k _py )x ₁ +(k _ie1 +k _iy1 )x ₂ +(k _ie2 +k _iy2 )x ₈ +k _ie8 x ₄

The differential form of the current loop transfer function is expressed by Equation 7:

According to formula 6 and formula 7, and assuming that the reference current changes slowly, the state equation of the current loop can be obtained as

为状态变量，

为常值矩阵，其元素in,

is the state variable,

is a constant-valued matrix whose elements

A(4,1)=-k _ie8 /L, A(4,2)=-(k _ie2 +k _iy2 )/L, A(4,2)=-(k _ie2 +k _iy2 )/L

A(4,3)=-(k _pe +k _py +R)/L, A(1,2)=A(2,3)=A(3,4)=1

The rest are all 0, then as long as A is the Hurwitz matrix, the current loop closed-loop system is stable, and the current error will tend to 0 in a limited time, that is, the robust internal model controller is stable;

Finally, according to the designed robust internal model controller and fractional-order vector resonance controller, a robust fractional-order vector resonance controller is designed.

Referring to FIG. 3, FIG. 3 is a block diagram of a fractional-order vector resonance controller.

As shown in the figure, based on the above embodiment, in order to solve the decrease of harmonic suppression capability caused by insufficient gain of the traditional resonance controller, fractional calculus is introduced into the resonance controller. Specifically, in this embodiment,

Step S20, designing a robust internal model controller and a fractional-order vector resonance controller to design a robust fractional-order vector resonance controller, including:

The fractional-order vector resonance controller is designed, and the stability of the fractional-order vector resonance controller is controlled, and the specific form is as follows:

The fractional-order calculus is introduced into the resonant controller to obtain the following control law of the fractional-order vector resonant controller, which is expressed by Equation 8:

分别表示控制器增益系数， 阻尼频率，以及分数阶阶次；where k _r , ω _e , α

respectively represent the controller gain coefficient, damping frequency, and fractional order;

Rewrite Equation 8 as Equation 9:

where Y(s) _k and R(s) _k represent the input and output of the fractional-order vector resonance controller at time k ^th respectively;

According to the designed robust internal mode controller and fractional-order vector resonance controller, a robust fractional-order vector resonance controller is designed.

Further, in order to illustrate the influence of parameters k _r w _c and a on the frequency of the resonant controller, this paper analyzes its frequency characteristics with the resonant frequency w=400πrad/s.

Referring to FIG. 4, FIG. 4 is a frequency response diagram of the fractional order vector resonance controller.

In this embodiment, (a) when the damping frequency and order are fixed values of 10 rad/s and 1, the frequency response of the resonance controller varies with the gain coefficient k _r . ( _b ) When the gain coefficient and order are fixed values of 10 and 1, the frequency response of the resonant controller varies with the damping frequency parameter wc. (c) When the gain coefficient and damping frequency are fixed values of 10 and 10 rad/s, the frequency response of the resonant controller varies with the order a.

Panel (a) shows the Bode plot for different k _r and a fixed w _c =10 rad/s and a=1. It can be observed that the peak gain of the FOVR controller is proportional to the gain factor. Increasing its value increases the gain at the resonance point, thereby improving harmonic rejection, but the bandwidth is almost unchanged. Graph (b) shows the amplitude-frequency characteristics of the FOVR controller, varying when k _r =10 and a=1. It shows that reducing the damping frequency coefficient can increase the gain, but reduce the bandwidth, which will result in poor robustness to frequency changes. In the actual controller design, 5 ~ 15rad/s is a reference design range. Figure (c) illustrates the effect of order on the FOVR controller when k _r =10 rad/s, w _c =10. It can be observed that a larger order increases the gain, however, the bandwidth remains the same while the frequency response curve shifts above 0°, indicating that the phase delay will decrease in open loop. Therefore, this parameter can be regarded as a parameter that can adjust the gain and phase difference of the FOVR controller.

The analysis of the above parameters shows that the peak gain, bandwidth and phase delay can be adjusted more smoothly in the resonant controller compared with the traditional resonant controller. In addition, increasing the order increases the degree of freedom of the VR controller, thereby improving the harmonic suppression performance.

Referring to FIG. 5, FIG. 5 is a block diagram of a robust fractional-order vector resonance controller.

Based on the above embodiment, in this embodiment, in step S20, a robust internal model controller and a fractional-order vector resonance controller are designed to design a robust fractional-order vector resonance controller, including:

According to the designed robust internal mode controller and fractional-order vector resonance controller, a robust fractional-order vector resonance controller is designed, and the specific form is as follows:

F(s), C _A (s) and C _B (s) are the components of the internal model controller, and the closed-loop transfer function of the robust fractional-order vector resonance controller is obtained as follows:

where i(s) and _iref (s) represent the transfer functions of i(t) and _iref (t) in the s domain;

外，G_FOVR(s)中的分 数阶零极点通过Outstaloup方法得到整数阶零极点的传递函数为公式十一：The fractional operator s ^a in G _FOVR (s) will generate multiple fractional zeros and poles; dividing the zeros of the resonant controller itself z ₁ = -R/L and the poles

In addition, the fractional-order zero-pole in G _FOVR (s) obtains the integer-order zero-pole transfer function by the Outstaloup method as formula 11:

The design of the robust fractional-order vector resonance controller is completed by importing the above formula.

Further, after step S20, the method for suppressing torque ripple of the permanent magnet synchronous motor further includes:

The stability analysis of the robust fractional-order vector resonance controller is carried out in the following form:

The stability of the robust fractional-order vector resonant controller satisfies the following conditions, using Equation 12:

式中||·||_∞表无穷范数；

where ||·|| _∞ represents the infinity norm;

According to formula 10 and formula 11, the closed-loop transfer function formula 13 of the current loop is obtained:

When A is a Hurwitz matrix, the controllers C _A (s) and C _B (s) can make 1+G _p (s)(C _A (s)+C _B (s)) stable, that is, 1+G All the eigenvalues of _p (s)(C _A (s)+C _B (s)) fall on the left half-plane of the s domain, then the stability is determined by the following transfer function formula 14:

It can be obtained from the small gain theorem that the closed loop meets the following conditions, which is expressed by Equation 15:

If Equation 15 can prove Equation 12, then the robust fractional-order vector resonance controller is stable.

Further, after step S20, the method for suppressing torque ripple of the permanent magnet synchronous motor further includes:

The robust stability analysis of the robust fractional-order vector resonant controller is carried out in the following form:

When the mathematical model of the permanent magnet synchronous motor is mismatched, the controlled object can be represented by formula 16:

where ΔG _p (s) represents the model error;

The robust stability of the robust fractional-order vector resonant controller is when and satisfying the following conditions, expressed by Equation 17:

When the mathematical model of the permanent magnet synchronous motor is mismatched, the current loop characteristic polynomial can be expressed by Equation 18:

in the formula

It can be obtained from the small gain theorem that the robust stability of the current loop satisfies the following conditions, expressed by Equation 19:

||Q(s)ΔG _p (s)|| _∞ ≤||Q(s)|| _∞ ||ΔG _p (s)|| _∞ ＜1

From this, formula 20 can be obtained:

If Equation 20 can prove Equation 17, then the robust fractional-order vector resonance controller is robust and stable.

In this embodiment, the advantages of robust internal model control and fractional-order resonance control are combined, which not only improves the robustness of the current loop of the permanent magnet synchronous motor, but also can effectively suppress the torque ripple of the permanent magnet synchronous motor. The present invention can ensure good robustness and dynamic response performance of the control system while effectively suppressing the harmonics of the current loop.

Referring to Fig. 6, Fig. 6 is a system structural block diagram of an embodiment of a permanent magnet synchronous motor speed servo system based on robust fractional vector resonance of the present invention.

Permanent magnet synchronous motor speed servo system based on robust fractional-order vector resonance, including: processor, permanent magnet synchronous motor, three-phase inverter, speed PI controller, space voltage vector pulse width modulation (SVPWM), robust fractional Order vector resonance controller (current controller); it also includes a position sensor and a coordinate transformation module.

Robust fractional-order vector resonance controller for generating control voltages;

Speed PI controller for generating control current;

The processor is used to control the on-off of the three-phase inverter power unit by using the SVPWM control strategy to drive the permanent magnet synchronous motor to run;

The processor is further configured to execute the steps of the method for suppressing torque ripple of a permanent magnet synchronous motor based on robust fractional-order vector resonance as described above.

Specifically, the speed loop adopts the PI controller to generate the q-axis current given value, and the current loop adopts the robust fractional-order vector resonance controller to generate the control voltage. The SVPWM control strategy is used to control the on-off of the three-phase inverter power device, and finally drive the permanent magnet synchronous motor to run.

In addition, a computer-readable storage medium storing a torque ripple suppression program on the computer-readable storage medium, when the torque ripple suppression program is executed by a processor, implements the robustness-based method according to any one of the above. Steps of torque ripple suppression method for permanent magnet synchronous motor based on rod fractional vector resonance.

The specific embodiments of the computer-readable storage medium of the present invention are basically the same as the above-mentioned embodiments of the method for suppressing torque ripple of a permanent magnet synchronous motor based on robust fractional-order vector resonance, and will not be described in detail here.

It should be noted that, herein, the terms "comprising", "comprising" or any other variation thereof are intended to encompass non-exclusive inclusion, such that a process, method, article or device comprising a series of elements includes not only those elements, It also includes other elements not expressly listed or inherent to such a process, method, article or apparatus. Without further limitation, an element qualified by the phrase "comprising a..." does not preclude the presence of additional identical elements in a process, method, article or apparatus that includes the element.

The above-mentioned serial numbers of the embodiments of the present invention are only for description, and do not represent the advantages or disadvantages of the embodiments.

From the description of the above embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus a necessary general hardware platform, and of course hardware can also be used, but in many cases the former is better implementation. Based on such understanding, the technical solutions of the present invention essentially or the parts that contribute to the prior art can be embodied in the form of software products, and the computer software products are stored in a readable storage medium (such as ROM/RAM, magnetic disk, optical disc), including several instructions to make a terminal (which may be a computer, a server, or a network device, etc.) execute the methods of the various embodiments of the present invention.

The embodiments of the present invention have been described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific embodiments, which are merely illustrative rather than restrictive. Under the inspiration of the present invention, without departing from the scope of protection of the purpose of the present invention and the claims, many forms can be made. Directly or indirectly used in other related technical fields, these all belong to the protection of the present invention.

The above are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Any equivalent structure or equivalent process transformation made by using the contents of the description and drawings of the present invention, or directly or indirectly applied in other related technical fields , are similarly included in the scope of patent protection of the present invention.

Claims (9)

1. a permanent magnet synchronous motor torque ripple suppression method based on robust fractional-order vector resonance, is characterized in that, described permanent magnet synchronous motor torque ripple suppression method comprises the following steps: Collect the parameters of the permanent magnet synchronous motor in real time, and establish the mathematical model of the permanent magnet synchronous motor; Design a robust internal model controller and a fractional-order vector resonance controller to design a robust fractional-order vector resonance controller; Based on the robust fractional-order vector resonance controller, the SVPWM control strategy is used to drive the permanent magnet synchronous motor to run. 2. The method for suppressing torque ripple of a permanent magnet synchronous motor as claimed in claim 1, wherein the described establishment of a permanent magnet synchronous motor mathematical model specifically adopts the following form: Formula one:

where U _d and U _q are the d-axis and q-axis voltages in the rotating coordinate system, respectively; id and i _q are the _d -axis and q-axis currents, respectively; R _d and R _q are the d-axis and q-axis inductances, respectively; L _d and L _q are the d-axis and q-axis resistances, respectively; ω _h is the electrical angular frequency of the motor; Ψ _f is the motor flux linkage; t is the time; The discretization of the above model completes the establishment of the model. 3. The method for suppressing torque ripple of permanent magnet synchronous motor as claimed in claim 1, wherein the described design robust internal model controller and fractional-order vector resonance controller are used to design robust fractional-order vector resonance control The device includes: Design a robust internal model controller, and control the stability of the robust internal model controller, specifically in the following form: Defining the preset dynamic response transfer function of the robust internal model controller is expressed by formula 2:

The disturbance rejection filter is expressed by Equation 3:

where τ represents the time constant; λ is a constant related to the bandwidth of the disturbance suppression filter, wherein the parameter selection is 1/τ<<1/λ; The robust internal model controller designed according to Equation 2 and Equation 3 is expressed by Equation 4:

Through the inverse Laplace transform, the following time-domain control law can be expressed by Equation 5:

where e(t)= _iref F(s)-i(t),

To avoid integration iteration errors, define the following state variables: x ₁ =e(t)

The parameters in the formula satisfy

Based on the definition of integral iterative error, the time domain control law is converted from Equation 5 and expressed in Equation 6: u _IMO =(k _pc +k _py )x ₁ +(k _ic1 +k _iy1 )x ₂ +(k _ic2 +k _iy2 )x ₃ +k _ic3 x ₄ The differential form of the current loop transfer function is expressed by Equation 7:

According to formula 6 and formula 7, the state equation of the current loop is obtained as

when

is a state variable, when A is a Hurwitz matrix, the robust internal model controller is stable; According to the designed robust internal model controller and the fractional-order vector resonance controller, a robust fractional-order vector resonance controller is designed. 4. The method for suppressing torque ripple of a permanent magnet synchronous motor as claimed in claim 1, wherein the described design robust internal model controller and fractional-order vector resonance controller are used to design robust fractional-order vector resonance control The device includes: Design a fractional-order vector resonance controller, and control the stability of the fractional-order vector resonance controller, specifically in the following form: The fractional-order calculus is introduced into the resonant controller to obtain the following control law of the fractional-order vector resonant controller, which is expressed by Equation 8:

where k _r , ω _o , and α represent the controller gain coefficient, damping frequency, and fractional order, respectively; Rewrite Equation 8 as Equation 9:

where Y(s) _h , R(s) _k , respectively represent the input and output of the fractional-order vector resonance controller at time k ^th ; According to the designed robust internal model controller and the fractional-order vector resonance controller, a robust fractional-order vector resonance controller is designed. 5. The method for suppressing torque ripple of permanent magnet synchronous motor as claimed in claim 3 and 4, wherein the described design robust internal model controller and fractional-order vector resonance controller are used to design robust fractional-order vector Resonant controllers include: According to the designed robust internal model controller and the fractional-order vector resonance controller, a robust fractional-order vector resonance controller is designed, and the specific form is as follows: F(s), C _A (s) and C _B (s) are the components of the internal model controller, and the closed-loop transfer function of the robust fractional-order vector resonance controller is obtained as follows:

where i(s) and _iref (s) represent the transfer functions of i(t) and _iref (t) in the s domain; The fractional-order zero-pole in G _FOVR (s) is obtained by the Outstaloup method to obtain the integer-order zero-pole transfer function as Equation 11:

The design of the robust fractional-order vector resonance controller is completed by importing the above formula. 6 . The method for suppressing torque ripple of a permanent magnet synchronous motor according to claim 5 , wherein after the robust fractional-order vector resonance controller is designed, the method for suppressing torque ripple of a permanent magnet synchronous motor further comprises: 7 . : The stability analysis of the robust fractional-order vector resonance controller is carried out in the following form: The stability of the robust fractional-order vector resonance controller should satisfy the following conditions, using formula 12:

where ||·|| _∞ represents the infinity norm; According to formula 10 and formula 11, the closed-loop transfer function formula 13 of the current loop is obtained:

When A is a Hurwitz matrix, and all eigenvalues of 1+G _p (s)(C _A (s)+C _B (s)) fall on the left half-plane of the s domain, the stability is given by the following transfer function formula Fourteen determine:

It can be obtained from the small gain theorem that the closed loop meets the following conditions, which is expressed by Equation 15:

If Equation 15 can prove Equation 12, the robust fractional-order vector resonance controller is stable. 7 . The method for suppressing torque ripple of a permanent magnet synchronous motor according to claim 6 , wherein after the design of the robust fractional-order vector resonance controller, the method for suppressing torque ripple of the permanent magnet synchronous motor further comprises: 8 . : The robust stability analysis of the robust fractional-order vector resonance controller is performed in the following form: When the mathematical model of the permanent magnet synchronous motor is mismatched, the controlled object can be represented by formula 16:

where ΔG _p (s) represents the model error; The robust stability of the robust fractional-order vector resonant controller is when and satisfying the following conditions, expressed by formula 17:

When the mathematical model of the permanent magnet synchronous motor is mismatched, the current loop characteristic polynomial can be expressed by formula 18:

in the formula

It can be obtained from the small gain theorem that the robust stability of the current loop satisfies the following conditions, expressed by Equation 19: ||Q(s)ΔG _p (s)|| _∞ ≤||Q(s)|| _∞ ||ΔG _p (s)|| _∞ ＜1 From this, formula 20 can be obtained:

If Formula 20 can prove Formula 17, the robust fractional-order vector resonance controller is robust and stable. 8. A permanent magnet synchronous motor speed servo system based on robust fractional vector resonance, wherein the permanent magnet synchronous motor speed servo system comprises: a processor, a permanent magnet synchronous motor, a three-phase inverter, a speed PI controller, space voltage vector pulse width modulation (SVPWM), robust fractional order vector resonance controller; the robust fractional-order vector resonance controller for generating a control voltage; the speed PI controller for generating a control current; The processor is configured to use the SVPWM control strategy to control the on-off of the three-phase inverter power device, so as to drive the permanent magnet synchronous motor to run; The processor is further configured to execute the steps of the method for suppressing torque ripple of permanent magnet synchronous motor based on robust fractional-order vector resonance according to any one of claims 1 to 7. 9 . A computer-readable storage medium, characterized in that a torque ripple suppression program is stored on the computer-readable storage medium, and the torque ripple suppression program is executed by a processor to achieve the performance as claimed in claims 1 to 7 The steps of any one of the method for suppressing torque ripple of permanent magnet synchronous motor based on robust fractional-order vector resonance.

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