Dead Zone Compensation Method for Permanent Magnet Synchronous Motors

Abstract

This invention belongs to the field of motor control technology, and particularly relates to a dead-zone compensation method for permanent magnet synchronous motors. It includes: S1: Constructing the open-loop transfer function of the current loop system of the permanent magnet synchronous motor in the shaft complex plane; S2: Based on the open-loop transfer function of the current loop system, constructing a distortion voltage compensation loop that includes the closed-loop tracking transfer function and the closed-loop disturbance transfer function of the current loop system; S3: Configuring additional terms of the closed-loop disturbance transfer function based on the notch filter principle, and solving the open-loop transfer function of the enhanced resonant controller based on the configuration results of the additional terms; S4: Solving the open-loop transfer functions of the 6th harmonic enhanced resonant controller and the 12th harmonic enhanced resonant controller based on the open-loop transfer function of the enhanced resonant controller, thereby realizing the configuration of the distortion voltage compensation loop. This invention is not limited by the current polarity determination accuracy of the sensor and has better compensation accuracy and harmonic suppression effect.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of motor control, and particularly relates to a dead-time compensation method for a permanent magnet synchronous motor. BACKGROUND

[0002] The permanent magnet synchronous motor is widely applied in the fields of electric vehicles, aerospace, railway traction, household equipment and the like due to the advantages of high power density and high efficiency. In the actual control of the permanent magnet synchronous motor, in order to avoid the shoot-through phenomenon of the upper and lower switching elements of the inverter, a dead-time must be set in the switching process. The dead-time directly introduces the distorted voltage dominated by 6th and 12th harmonics, so that the actual output voltage and the ideal output voltage exist deviation, and further cause the distortion of phase current and torque ripple. The traditional offline compensation method is limited by the current polarity judgment accuracy of the sensor, and needs to know the parameters of the switching element. However, the 6th and 12th harmonics will interfere with the current polarity judgment, and the parameters of the switching element are difficult to measure and change with the working state of the system, which makes the offline compensation method inaccurate and even causes miscompensation. SUMMARY

[0003] Therefore, the application aims to provide a dead-time compensation method for a permanent magnet synchronous motor, so as to solve the problem that the existing offline compensation method is limited by the current polarity judgment accuracy of the sensor and needs to know the parameters of the switching element. The application realizes effective compensation of the distorted voltage dominated by 6th and 12th harmonics. Compared with the traditional offline compensation method, the application does not need to know the parameters of the switching element, is not limited by the current polarity judgment accuracy of the sensor, has better compensation accuracy and harmonic suppression effect. The application helps to provide a new idea for realizing an accurate dead-time compensation method for a permanent magnet synchronous motor.

[0004] To achieve the above-mentioned purpose, the technical scheme of the application is as follows:

[0005] A dead-time compensation method for a permanent magnet synchronous motor, specifically comprising the following steps:

[0006] S1: constructing an open-loop transfer function of a current loop system of the permanent magnet synchronous motor in a d-q plane;

[0007] S2: based on the open-loop transfer function of the current loop system, constructing a distorted voltage compensation loop including a closed-loop tracking transfer function and a closed-loop disturbance transfer function of the current loop system;

[0008] S3: configuring an additional term of the closed-loop disturbance transfer function based on the notch principle, and solving an open-loop transfer function of an enhanced resonant controller based on the configuration result of the additional term;

[0009] ​The enhanced resonance controller is composed of a 6th harmonic enhanced resonance controller and a 12th harmonic enhanced resonance controller in parallel;

[0010] S4: based on the open loop transfer function of the enhanced resonance controller, the open loop transfer functions of the 6th harmonic enhanced resonance controller and the 12th harmonic enhanced resonance controller are solved respectively, and the configuration of the distortion voltage compensation loop is realized.

[0011] Further, in step S1, the open loop transfer function of the current loop system of the permanent magnet synchronous motor :

[0012] ;

[0013] wherein, , and are the stator resistance and the stator inductance respectively, is the sampling period of the current loop, is the electrical angular velocity, is a complex variable in the discrete domain, is the imaginary unit.

[0014] Further, in step S2, the closed loop tracking transfer function and the closed loop disturbance transfer function of the current loop system are:

[0015] ;

[0016] wherein, is the closed loop tracking transfer function, is the closed loop disturbance transfer function, is the internal model control link, is the open loop transfer function of the current loop system, is a complex variable in the discrete domain, is the open loop transfer function of the enhanced resonance controller before correction, is the equivalent link of .

[0017] Further, in step S2, the distortion voltage compensation loop further includes estimating the open loop transfer function of the current loop system :

[0018] ;

[0019] wherein, , and represent the estimated stator resistance and the estimated stator inductance respectively, is the sampling period of the current loop, is the electrical angular velocity.

[0020] Further, in step S3, the additional term of the closed-loop disturbance transfer function is configured as a standard second-order notch filter, the continuous transfer function of the standard second-order notch filter is:

[0021] ;

[0022] wherein, is the Laplace operator, is the center frequency to be suppressed by the filter, is the filter bandwidth, is the open-loop transfer function of the enhanced resonant controller before modification, is the open-loop transfer function of the current loop system.

[0023] Further, in step S4, the open-loop transfer function of the enhanced resonant controller is:

[0024] ;

[0025] wherein, and are the stator resistance and the stator inductance, respectively, is the sampling period of the current loop, is the center frequency to be suppressed by the filter, is the filter bandwidth, is a complex variable in the discrete domain, is the open-loop transfer function of the enhanced resonant controller before modification, , is the attenuation factor.

[0026] Further, the open-loop transfer function of the enhanced resonant controller before modification is:

[0027] ;

[0028] wherein, is the stator resistance, is the sampling period of the current loop, is the center frequency to be suppressed by the filter, is the filter bandwidth, , is the attenuation factor, is a complex variable in the discrete domain.

[0029] Further, the open loop transfer function of the modified enhanced resonant controller is obtained by solving the discrete transfer function and the open loop transfer function of the current loop system, wherein the discrete transfer function is obtained by discretizing the continuous transfer function of the standard second-order notch filter using the pre-distortion bilinear transformation method, and the discrete transfer function is:

[0030] ;

[0031] wherein, is the sampling period of the current loop, is the center frequency to be suppressed by the filter, is the filter bandwidth, is a complex variable in the discrete domain.

[0032] Further, in step S4, the open loop transfer function of the 6th harmonic enhanced resonant controller and the open loop transfer function of the 12th harmonic enhanced resonant controller are:

[0033] ;

[0034] wherein, and are the filter bandwidths of and respectively, is the open loop transfer function of the 6th harmonic enhanced resonant controller, is the open loop transfer function of the 12th harmonic enhanced resonant controller, is the resonant frequency corresponding to the 6th harmonic enhanced resonant controller, is the resonant frequency corresponding to the 12th harmonic enhanced resonant controller, is the sampling period of the current loop, is the center frequency to be suppressed by the filter, is a complex variable in the discrete domain, is the stator resistance, , is the attenuation factor, is the rotor electrical angular velocity of the permanent magnet synchronous motor.

[0035] Compared with the prior art, the application can achieve the following beneficial effects:

[0036] The dead-time compensation method of the permanent magnet synchronous motor provided by the application can compensate the distortion voltage dominated by 6th harmonic and 12th harmonic in real time, and does not need to know the parameters of the inverter switching device and is not limited by the current polarity judgment accuracy of the sensor. From the form of the closed-loop tracking transfer function and the closed-loop disturbance transfer function, the structure of the application can effectively suppress the 6th harmonic disturbance and 12th harmonic disturbance caused by the dead-time effect, but does not affect the closed-loop frequency response characteristics of the original system and the disturbance frequency response characteristics of other frequency bands, thereby realizing effective compensation of the distortion voltage. BRIEF DESCRIPTION OF DRAWINGS

[0037] The accompanying drawings, which form a part of the present application, are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification. The illustrations are shown to explain the application and are not intended to limit the application in any way. In the drawings:

[0038] Figure 1 The flowchart of the dead-time compensation method of the permanent magnet synchronous motor provided by the embodiment of the application;

[0039] Figure 2 The principle diagram of the dead-time compensation method of the permanent magnet synchronous motor provided by the embodiment of the application;

[0040] Figure 3 The Bode diagram of the closed-loop tracking transfer function provided by the embodiment of the application;

[0041] Figure 4 The Bode diagram of the closed-loop disturbance transfer function provided by the embodiment of the application;

[0042] Figure 5 The compensation voltage waveform and total harmonic distortion analysis diagram output by the distortion voltage compensation loop provided by the embodiment of the application;

[0043] Figure 6 The three-phase current waveform diagram provided by the embodiment of the application. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical scheme and advantages of the application clearer, the application is further described in detail below with reference to the drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the application, and do not constitute a limitation on the application.

[0045] It should be noted that the embodiments in the application and the features in the embodiments can be combined with each other without conflict.

[0046] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0047] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0048] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0049] like Figure 1 As shown, this invention proposes a method for dead-time compensation of a permanent magnet synchronous motor, specifically including the following steps: S1: In S1: Construct the open-loop transfer function of the current loop system of the permanent magnet synchronous motor using a complex plane; S2: Based on the open-loop transfer function of the current loop system, construct a distortion voltage compensation loop that includes the closed-loop tracking transfer function and the closed-loop disturbance transfer function of the current loop system; S3: Configure additional terms of the closed-loop disturbance transfer function based on the notch filter principle, and solve the open-loop transfer function of the enhanced resonant controller based on the configuration results of the additional terms; The enhanced resonant controller consists of a 6th harmonic enhanced resonant controller and a 12th harmonic enhanced resonant controller connected in parallel; S4: Solve the open-loop transfer functions of the 6th harmonic enhanced resonant controller and the 12th harmonic enhanced resonant controller based on the open-loop transfer function of the enhanced resonant controller, and realize the configuration of the distortion voltage compensation loop.

[0050] It should be noted that the application is based on the discrete domain complex plane model of permanent magnet synchronous motor, a closed-loop tracking performance and disturbance suppression performance decoupling distortion voltage compensation loop is designed; Then based on the principle of notch wave, the additional term of closed-loop disturbance transfer function is configured, the discrete transfer function of the control link in the distortion voltage compensation loop is obtained, and the configuration of the distortion voltage compensation loop is realized.

[0051] System open-loop transfer function link , one beat delay link , internal model control link The position in the main loop is shown in Figure 2 , in addition, Figure 2 It also shows the estimated system open-loop transfer function link , 6th harmonic enhanced resonance controller And 12th harmonic enhanced resonance controller In the position of the distortion voltage compensation loop. Together with the estimated open-loop transfer function link In series Simulate the effect of one beat delay.

[0052] First, the mathematical model is established in the Axis complex plane, the system open-loop transfer function of the permanent magnet synchronous motor system from the voltage input to the stator current output Can be expressed as:

[0053] (1);

[0054] In the formula: , And Respectively represent the stator resistance and the stator inductance, Is the sampling period of the current loop, Is the electrical angular velocity, Is the sampling period of the current loop, Is a complex variable in the discrete domain, Is the imaginary unit.

[0055] Considering the actual control process needs to calculate the time, there is also a one beat delay Between the inverter voltage input and the disturbance input, which is specifically expressed as:

[0056] (2);

[0057] According to the internal model design rule, the controller is composed of an inverse system model and an integrator with a gain that determines the closed-loop bandwidth. Since the inverse model of the open-loop transfer function Cannot be directly physically realized, an additional Link is added in digital applications, and the internal model control link Is designed as:

[0058] (3);

[0059] In the formula: k is the closed-loop bandwidth gain. Let k be 0.25 to achieve optimal closed-loop tracking performance. The design is as follows: Figure 2 The distortion voltage compensation circuit shown, the distortion voltage compensation circuit in This is to estimate the open-loop transfer function of the current loop system:

[0060] (4);

[0061] In the formula: , and These represent the estimated stator resistance and the estimated stator inductance, respectively. If the estimated parameters are accurate, then... and system open-loop transfer function Completely equivalent.

[0062] like Figure 2 As shown, in the distortion voltage compensation circuit, and These are enhanced resonant controllers (ERCs) targeting the 6th and 12th harmonics, respectively, connected in parallel. and Merged into an enhanced resonant controller Find the closed-loop tracking transfer function of the current loop system. and closed-loop disturbance transfer function for:

[0063] (5);

[0064] In the formula: yes The equivalent link. Equation (5) shows that the distortion voltage compensation circuit will not affect the closed-loop tracking transfer function. The effect only applies to the closed-loop disturbance transfer function. The impact is manifested in the introduction of additional items. .

[0065] The above, by introducing, such as Figure 2 The distortion voltage compensation circuit shown effectively configures the system's disturbance suppression characteristics without changing the system's closed-loop tracking characteristics. Therefore, the distortion voltage compensation circuit of the present invention achieves decoupling of closed-loop tracking performance and disturbance suppression performance, and can maintain the original closed-loop tracking capability while effectively suppressing distortion voltage disturbances.

[0066] Next, the present invention configures additional terms in the closed-loop disturbance transfer function. This effectively compensates for voltage distortion dominated by the 6th and 12th harmonics, reducing the impact of dead time on phase current distortion. Specifically, additional items... Configured as a standard second-order notch filter, the continuous transfer function of the standard second-order notch filter. for:

[0067] (6);

[0068] In the formula: It is the Laplace operator. It is the center frequency that the filter wants to suppress. This is the filter bandwidth. Equation (6) is discretized using the pre-distortion bilinear transform method to obtain the discrete transfer function. :

[0069] (7);

[0070] In the formula: sin represents the sine operation, and cos represents the cosine operation. Combining equations (1) and (7), the open-loop transfer function of the enhanced resonant controller before modification can be obtained. The expression:

[0071] (8);

[0072] Due to the process The highest order of the molecule is 2 higher than the highest order of the denominator, which cannot be physically realized, therefore multiplying by... This is used to correct the open-loop transfer function. The purpose of this is to reduce the order of the numerator by 2 to match the order of the denominator, thereby satisfying the causal requirement; Its function is at the center frequency Compensation will be provided for the delay. The resulting phase shift ensures the optimal frequency response at the center frequency point.

[0073] Multiply The open-loop transfer function of the enhanced resonant controller for:

[0074] (9);

[0075] When the enhanced resonant controller is implemented using equation (9), the closed-loop disturbance transfer function is... At the center frequency A notch filter effect occurs. To effectively compensate for voltage distortion dominated by the 6th and 12th harmonics, a configuration is needed. Parallel links and The center frequencies are respectively and , the effective compensation of distortion voltage is realized. and is expressed as:

[0076] (10);

[0077] In the formula: and are respectively and The filter bandwidths are selected as the fixed gain times of the respective corresponding resonance frequencies and resonance frequencies to realize consistent harmonic attenuation effects at the 6th harmonic frequency and the 12th harmonic frequency.

[0078] As shown in Figure 3 , the permanent magnet synchronous motor speed is 500 r / min, the filter bandwidth and the filter bandwidth are respectively 0.05 times of the resonance frequencies and , the Bode diagram of the corresponding closed-loop tracking transfer function before and after the introduction of the distortion voltage compensation loop, since the mathematical model is established based on the axis complex plane, so each case will correspond to two curves of positive sequence and negative sequence. As Figure 3 can be seen, the closed-loop frequency characteristic response curves completely coincide, indicating that the introduction of the distortion voltage compensation loop of the application will not change the closed-loop tracking characteristics of the original system, effectively ensuring the stability of the current loop when tracking the reference.

[0079] As shown in Figure 4 , the permanent magnet synchronous motor speed is 500 r / min, the filter bandwidth and the filter bandwidth are respectively 0.05 times of the resonance frequencies and , the Bode diagram of the corresponding closed-loop disturbance transfer function. As Figure 4 can be seen, after the introduction of the distortion voltage compensation loop, the disturbance frequency characteristic response curve has a significant resonance amplitude attenuation at the resonance frequency and the resonance frequency, and coincides with the original system at other frequency bands, indicating that the application can effectively suppress the 6th harmonic and 12th harmonic dominant distortion voltage disturbance, realize effective dead zone compensation without affecting the performance of other frequency bands of the system.

[0080] As shown in Figure 5 , the permanent magnet synchronous motor speed is 500 r / min, the filter bandwidth and the filter bandwidth respectively, 0.05 times of the resonance frequency and The compensation voltage waveform output by the distortion voltage compensation circuit and the total harmonic distortion are analyzed when the filter bandwidth Figure 5 The THD in the formula represents the total harmonic distortion (THD), and the DC represents the direct current (DC). It can be seen from the formula that Figure 5 The compensated distortion voltage is mainly the alternating component of the 6th harmonic and the 12th harmonic, which is consistent with the harmonic characteristics of the distortion voltage caused by the dead time, so the compensation effect of the distortion voltage compensation circuit proposed in the application is verified.

[0081] As shown in Figure 6 , the permanent magnet synchronous motor speed is 500r / min, the filter bandwidth and the filter bandwidth respectively, 0.05 times of the resonance frequency and The three-phase current waveform when the filter bandwidth is 0.05 times of the resonance frequency, wherein no compensation measure is used within 0.3-0.4s, the traditional offline compensation method is used within 0.5-0.6s, the 6th distortion voltage compensation is introduced within 0.7-0.8s, and the 6th and 12th distortion voltage compensations are introduced simultaneously within 0.9-1s. It can be seen from the formula that Figure 6 The three-phase waveform after the 6th and 12th distortion voltage compensations is the best sine, and compared with the traditional offline compensation method, the THD is further reduced by 8.65%, which has better compensation accuracy and harmonic suppression effect.

[0082] Therefore, compared with the traditional offline compensation method, the compensation method of the application realizes better compensation accuracy and harmonic suppression effect without knowing the parameters of the inverter switching device and being limited by the current polarity judgment accuracy of the sensor, which helps to provide a new idea for realizing the precise dead-time compensation method of the permanent magnet synchronous motor.

[0083] It should be understood that the various forms of the flow shown above can be used to reorder, add or delete steps. For example, the steps described in the present disclosure can be executed in parallel, sequentially or in different orders, as long as the desired results of the technical solutions of the present disclosure can be achieved, which is not limited herein.

[0084] The above specific embodiments do not constitute a limitation on the scope of protection of the present application. Those skilled in the art should understand that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modifications, equivalent replacements and improvements made within the spirit and principles of the present application shall be included in the scope of protection of the present application.

Claims

1. A dead-time compensation method for permanent magnet synchronous motor, characterized in that: Specifically comprising the following steps: S1: In The axis complex plane constructs the open-loop transfer function of the current loop system of the permanent magnet synchronous motor. S2: based on the open loop transfer function of the current loop system, constructing a distorted voltage compensation loop comprising the closed loop tracking transfer function and the closed loop disturbance transfer function of the current loop system; In step S2, the closed loop tracking transfer function and the closed loop disturbance transfer function of the current loop system are: ； wherein is a closed loop tracking transfer function, is a closed loop disturbance transfer function, is an inner model control element, is a current loop system open loop transfer function, is a complex variable in the discrete domain, is an open loop transfer function of the enhanced resonant controller before modification, is an equivalent element of is an equivalent element of S3: configuring an additional term of the closed loop disturbance transfer function based on the trap wave principle, and solving the open loop transfer function of the enhanced resonance controller based on the configuration result of the additional term; The enhanced resonance controller is composed of a 6th harmonic enhanced resonance controller and a 12th harmonic enhanced resonance controller in parallel; S4: solving the open loop transfer function of the 6th harmonic enhanced resonance controller and the 12th harmonic enhanced resonance controller respectively based on the open loop transfer function of the enhanced resonance controller, and realizing the configuration of the distorted voltage compensation loop; In step S4, the open loop transfer function of the enhanced resonant controller is determined as: f = 1 / (2 * pi * f0) ； wherein, and Rsand Lsare the stator resistance and stator inductance, respectively, Ts is the sampling period of the current loop, ωc is the center frequency to be suppressed by the filter, B is the filter bandwidth, z is the complex variable in the discrete domain, G0(s) is the open-loop transfer function of the enhanced resonant controller before modification, , k is the attenuation factor; In step S4, the open loop transfer function of the 6th harmonic enhanced resonance controller and the open loop transfer function of the 12th harmonic enhanced resonance controller are: ； wherein, and are respectively and the filter bandwidth, is the open-loop transfer function of the 6th harmonic enhanced resonant controller, is the open-loop transfer function of the 12th harmonic enhanced resonant controller, is the resonant frequency corresponding to the 6th harmonic enhanced resonant controller, is the resonant frequency corresponding to the 12th harmonic enhanced resonant controller, is the sampling period of the current loop, is the center frequency to be suppressed by the filter, is a complex variable in the discrete domain, is the stator resistance, , is the damping factor, is the rotor electrical angular speed of the permanent magnet synchronous motor.

2. The dead-time compensation method of a permanent magnet synchronous motor according to claim 1, characterized in that: In step S1, the open-loop transfer function of the current loop system of the permanent magnet synchronous motor : ； wherein, , and are the stator resistance and stator inductance, respectively, is the sampling period of the current loop, is the electrical angular velocity, is the complex variable of the discrete domain, is the imaginary unit.

3. The dead-time compensation method of a permanent magnet synchronous motor according to claim 1, characterized by: In step S2, the distortion voltage compensation loop further comprises estimating an open loop transfer function of the current loop system : ； wherein, , and respectively represent the estimated stator resistance and the estimated stator inductance, is the sampling period of the current loop, is the electrical angular speed.

4. The dead-time compensation method of a permanent magnet synchronous motor according to claim 1, characterized by: In step S3, the additional term of the closed loop disturbance transfer function is The additional term is configured as a standard second order notch filter with a continuous transfer function of: ； wherein is the Laplace operator, is the center frequency to be suppressed by the filter, is the filter bandwidth, is the open loop transfer function of the enhanced resonant controller before modification, is the open loop transfer function of the current loop system.

5. The dead-time compensation method of a permanent magnet synchronous motor according to claim 4, characterized in that: Open loop transfer function of the enhanced resonant controller before modification is: ； wherein is the stator resistance, is the sampling period of the current loop, is the center frequency to be suppressed by the filter, is the filter bandwidth, , is the attenuation factor, is the complex variable of the discrete domain.

6. The dead-time compensation method of a permanent magnet synchronous motor according to claim 5, characterized in that: The open loop transfer function of the modified enhanced resonant controller is derived by combining the discrete transfer function and the open loop transfer function of the current loop system, wherein the discrete transfer function is derived by discretizing the continuous transfer function of a standard second-order notch filter using a pre-distorted bilinear transformation method, and the discrete transfer function is : ； wherein is the sampling period of the current loop, is the center frequency to be suppressed by the filter, is the filter bandwidth, is a complex variable of the discrete domain.

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