Permanent magnet synchronous motor multiple coefficient back emf observation method

Abstract

The application belongs to the technical field of motor control, and particularly relates to a permanent magnet synchronous motor complex coefficient back electromotive force observation method. The method comprises the following steps: S1: constructing a three-order complex coefficient transfer function of a back electromotive force observer, converging design variables of the three-order complex coefficient transfer function into three-degree-of-freedom tuning parameters by explicitly configuring zero points and pole points of the three-order complex coefficient transfer function; S2: restricting the three-degree-of-freedom tuning parameters into a single group delay parameter through a Bezier type pole mapping, and realizing global optimization of dynamic tracking and steady-state observation by adjusting an adaptive parameter of the group delay parameter; and S3: constructing a closed-loop observation control loop, and realizing complex coefficient back electromotive force observation of the permanent magnet synchronous motor under the condition of no position sensor by configuring an angular frequency adaptive controller in the closed-loop observation control loop. The application significantly improves the convergence quality of the back electromotive force observation under the premise of guaranteeing the fast dynamic convergence characteristics.

Description

Technical Field

[0001] This invention belongs to the field of motor control technology, and in particular relates to a method for observing the complex coefficient back EMF of a permanent magnet synchronous motor. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in electric transportation and industrial drives due to their excellent power density, high efficiency, and fast dynamic response. Traditional PMSM control relies on position sensors to obtain rotor angular frequency and position information. However, position sensors suffer from drawbacks such as high hardware cost, complex system structure, and poor reliability under extreme conditions, becoming a bottleneck restricting the stability and practicality of the control system. Therefore, sensorless back-EMF observation technology has become a research frontier for high-performance motor drives. However, traditional real-coefficient back-EMF observation methods have three inherent limitations: first, they lack targeted integer harmonic suppression performance, making it difficult to effectively suppress harmonic disturbances under complex operating conditions; second, parameter engineering optimization is difficult; and third, to pursue higher dynamic tracking performance, the observer bandwidth needs to be increased, which significantly amplifies measurement noise, leading to a decrease in the system's steady-state observation accuracy, making it impossible to simultaneously achieve both steady-state observation accuracy and dynamic tracking performance. These factors collectively limit the control accuracy of traditional real-coefficient back-EMF observation methods under sensorless conditions. Summary of the Invention

[0003] In view of this, the present invention aims to provide a complex-coefficient back EMF observation method for permanent magnet synchronous motors (PMSMs) to address the problems of insufficient integer harmonic suppression performance, difficulty in parameter engineering optimization, and the inability to simultaneously achieve steady-state observation accuracy and dynamic tracking performance, thus limiting the control accuracy of sensorless systems. This invention can achieve targeted integer harmonic suppression while constraining multi-degree-of-freedom tuning parameters to a single group delay parameter, and balances dynamic tracking performance with steady-state observation accuracy. While ensuring rapid dynamic convergence, it significantly improves the convergence quality of back EMF observation, contributing a new approach to high-precision, high-dynamic-performance sensorless control of PMSMs.

[0004] To achieve the above objectives, the technical solution created by this invention is implemented as follows: A method for observing the complex coefficient back electromotive force of a permanent magnet synchronous motor specifically includes the following steps: S1: Based on the complex coefficient voltage equation of permanent magnet synchronous motor, construct the third-order complex coefficient transfer function of back EMF observer. By explicitly configuring the zeros and poles of the third-order complex coefficient transfer function, the design variables of the third-order complex coefficient transfer function are converged into three-degree-of-freedom tuning parameters. S2: By constraining the three-degree-of-freedom tuning parameters to a single group delay parameter through Bessel-type pole mapping, the complex coefficient transfer function after Bessel configuration is obtained, and global optimization of dynamic tracking and steady-state observation is achieved by adjusting the adaptive parameters of the group delay parameter. S3: A closed-loop observation control loop is constructed using the stator voltage vector and stator current vector as inputs. By configuring the angular frequency adaptive controller in the closed-loop observation control loop, the frequency domain characteristics of the closed-loop transfer function of the closed-loop observation control loop are matched with the complex coefficient transfer function, thereby realizing the observation of the complex coefficient back EMF of the permanent magnet synchronous motor without position sensors.

[0005] Furthermore, in step S1, the expression for the complex coefficient voltage equation of the permanent magnet synchronous motor is: ; in, For differential operators, for The complex vector of stator current on the shaft. For stator inductance scalar, for The stator voltage complex vector of the axis, For stator resistance scalar, for The complex vector of the back electromotive force of the axis.

[0006] Furthermore, in step S1, the third-order complex coefficient transfer function of the back EMF observer is: ; in, It is a third-order complex coefficient transfer function. For the Laplace operator, and For the zero point of the complex coefficient, , and For complex coefficient poles, This represents the total gain.

[0007] Furthermore, in step S1, the zeros and poles of the third-order complex coefficient transfer function are explicitly configured using the following formula, thereby converging the design variables of the third-order complex coefficient transfer function into three-degree-of-freedom tuning parameters: ; ; ; in, and For the zero point of the complex coefficient, , and For complex coefficient poles, For total gain, The rotor angular frequency, Central pole The real part of the attenuation coefficient, For conjugate pole pairs and The real part of the attenuation coefficient, For conjugate pole pairs and The imaginary part of the parameter is separated. It is the imaginary unit.

[0008] Furthermore, in step S2, the specific operation of constraining the three-degree-of-freedom tuning parameters into a single group delay parameter through Bessel-type pole mapping is as follows: ; in, Central pole The real part of the attenuation coefficient, For conjugate pole pairs and The real part of the attenuation coefficient, For conjugate pole pairs and The imaginary part of the parameter is separated. This is the group delay parameter.

[0009] Furthermore, in step S2, the complex coefficient transfer function after Bessel configuration... The expression is: ; in, The rotor angular frequency, For group delay parameters, The rotor angular frequency point, It is the imaginary unit.

[0010] Furthermore, in step S2, the expression for the group delay parameter is: ; in, For group delay parameters, For adaptive parameters, It is the estimated rotor angular frequency.

[0011] Furthermore, in step S3, the expression for the closed-loop observation control loop is: ; in, for The estimated back electromotive force vector of the axis, for The estimated stator current vector of the shaft. and It is an angular frequency adaptive controller. for The stator voltage complex vector of the axis, for The complex vector of stator current on the shaft. for The estimated back electromotive force vector of the axis, for The estimated stator current vector of the shaft. For stator inductance scalar, The rotor angular frequency point, This is a scalar value for the stator resistance.

[0012] Furthermore, in step S4, the closed-loop transfer function of the closed-loop observation control loop is: ; in, This is the closed-loop transfer function of the closed-loop observation control loop.

[0013] Furthermore, in step S4, the angular frequency adaptive controller and Specifically: ; ; in, and All are angular frequency adaptive controllers. For molecular dynamics with notched wave characteristics, It is the estimated rotor angular frequency. For adaptive parameters, The imaginary unit, The rotor angular frequency point, For stator inductance scalar, This is a scalar value for the stator resistance.

[0014] Compared with the prior art, the present invention can achieve the following beneficial effects: This invention presents a method for observing the complex coefficient back EMF of a permanent magnet synchronous motor. By configuring the third-order complex coefficient transfer function of the back EMF observer in a Bessel configuration, it rigorously satisfies the requirements of zero phase lag and zero amplitude attenuation in sensorless back EMF observation. Simultaneously, it achieves the design of constraining multi-degree-of-freedom tuning parameters to a single group delay parameter, greatly simplifying the engineering tuning difficulty. Through the single group delay parameter... The adaptive design balances high-bandwidth dynamic tracking performance of back EMF under dynamic conditions with steady-state observation accuracy of integer harmonics and high-frequency noise under steady-state conditions, achieving global optimization of dynamic tracking performance and steady-state observation accuracy. Furthermore, it maintains constant suppression performance of DC bias components at different rotor angular frequencies. Finally, this invention introduces a physically defined angular frequency adaptive controller. and This invention establishes a closed-loop observation and control system. In summary, this invention provides a reliable new approach for sensorless control of high-precision, high-dynamic-performance permanent magnet synchronous motors. Attached Figure Description

[0015] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 A flowchart illustrating the method for observing the complex coefficient back EMF of a permanent magnet synchronous motor as described in an embodiment of the present invention; Figure 2 A flowchart illustrating the observation of the complex coefficient back EMF of a permanent magnet synchronous motor as described in an embodiment of the present invention; Figure 3 Bode plots of complex coefficient transfer functions under the Bessel configuration described in the embodiments of the present invention, (a) Bode plots under different group delays, (b) Bode plots under different rotational speeds; Figure 4 The following diagrams compare the characteristics of the complex coefficient back EMF observation method described in the present invention and the traditional full-order real coefficient back EMF observation method: (a) is a comparison of the amplitude-frequency characteristics of the two methods, and (b) is a comparison of the amplitude-group delay of the two methods. Figure 5 The experimental results of the complex coefficient back EMF observation method and the traditional full-order real coefficient back EMF observation method under dynamic operating conditions are compared in the following figure: (a) is the experimental result of the traditional full-order real coefficient back EMF observation method, and (b) is the experimental result of the complex coefficient back EMF observation method. Detailed Implementation

[0016] 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 specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0017] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0018] 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.

[0019] 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.

[0020] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0021] like Figure 1 As shown, this invention provides a method for observing the complex coefficient back electromotive force of a permanent magnet synchronous motor, specifically including the following steps: S1: Based on the complex coefficient voltage equation of permanent magnet synchronous motor, construct the third-order complex coefficient transfer function of back EMF observer. By explicitly configuring the zeros and poles of the third-order complex coefficient transfer function, the design variables of the third-order complex coefficient transfer function are converged into three-degree-of-freedom tuning parameters. S2: By constraining the three-degree-of-freedom tuning parameters to a single group delay parameter through Bessel-type pole mapping, the complex coefficient transfer function after Bessel configuration is obtained, and global optimization of dynamic tracking and steady-state observation is achieved by adjusting the adaptive parameters of the group delay parameter. S3: A closed-loop observation control loop is constructed using the stator voltage vector and stator current vector as inputs. By configuring the angular frequency adaptive controller in the closed-loop observation control loop, the frequency domain characteristics of the closed-loop transfer function of the closed-loop observation control loop are matched with the complex coefficient transfer function, thereby realizing the observation of the complex coefficient back EMF of the permanent magnet synchronous motor without position sensors.

[0022] It should be noted that, firstly, based on the complex coefficient voltage model of the permanent magnet synchronous motor, a third-order complex coefficient transfer function for observing the back EMF is constructed. By explicitly configuring the zeros and poles, and considering the zero phase lag and zero amplitude attenuation requirements for back EMF observation without position sensors, multiple design variables are converged into three-degree-of-freedom tuning parameters. Then, through Bessel-type pole mapping, the three-degree-of-freedom tuning parameters are further constrained to a single group delay parameter, achieving a Bessel-type configuration of the third-order complex coefficient transfer function. An adaptive group delay mechanism is used to balance dynamic tracking performance and integer harmonic suppression performance, achieving global optimization of dynamic tracking and steady-state observation. Finally, a closed-loop observation control loop framework is built, and an angular frequency adaptive controller is introduced to configure the control loop, realizing complex coefficient back EMF observation under sensorless control.

[0023] S1: First, establish the permanent magnet synchronous motor in Complex coefficient voltage equation of the shaft: (1.1); In the formula: It is a differential operator. for The stator voltage complex vector of the axis, for The complex vector of stator current on the shaft. for The complex vector of the back electromotive force of the axis, For stator resistance scalar, For stator inductance scalar. For back electromotive force complex vector. Satisfying mathematical relations ,in The imaginary unit, for Back-axis electromotive force component, for Back-axis electromotive force component. and It is the electromotive force induced in the stator windings when the rotor permanent magnet rotates, and its relationship with the rotor position and rotor angular frequency is as follows: (1.2); In the formula: The rotor angular frequency, For rotor position, For permanent magnet flux linkage. From equation (1.2), it can be seen that the phase of the back EMF vector is related to the rotor position. Strictly bound, amplitude and rotor angular frequency It is directly proportional to the back electromotive force, and complete information about the rotor motion state can be obtained by observing the back electromotive force.

[0024] Furthermore, the third-order complex coefficient transfer function of the back-potential observer is designed. for: (1.3); In the formula: It is a third-order complex coefficient transfer function; For the Laplace operator; and It is the zero point of the complex coefficient; , and These are poles with complex coefficients; This represents the total gain. To suppress integer harmonic disturbances, dominated by the -5th and +7th harmonics, caused by the non-ideal characteristics of the inverter, this invention explicitly places two zeros at the corresponding harmonic frequencies on the imaginary axis, namely: (1.4); In the formula: and These correspond to the angular frequencies of the -5th and +7th harmonics, respectively. When the input signal frequency coincides with the zero point, the amplitude of the numerator term of the third-order complex coefficient transfer function is 0. Therefore, this configuration can achieve infinite-depth attenuation of the -5th and +7th harmonics in the frequency domain, eliminating the interference of these integer harmonics on the back potential observation. Since the phase contributions of the two zero points are respectively... and The total phase contribution is 0, therefore no phase lag is introduced at the zero point. This is to ensure the rotor angular frequency point... The total phase contribution at that point is The three complex coefficient poles are distributed geometrically symmetrically around the rotor angular frequency: (1.5); In the formula: Central pole The real part of the attenuation coefficient, For conjugate pole pairs and The real part of the attenuation coefficient, For conjugate pole pairs and The imaginary part of the parameter. At the rotor angular frequency point. At that point, the phase corresponding to the central pole is The conjugate pole pairs have equal phase magnitudes but opposite signs; therefore, the total phase contribution of the three complex coefficient poles in this geometrically symmetric distribution is... It naturally meets the zero-phase lag requirement for back EMF observation without position sensors.

[0025] Furthermore, substituting equations (1.5) and (1.4) into (1.3), at the rotor angular frequency point... At that point, the total magnitude of the contribution of the zero point of the complex coefficients is The total magnitude of the pole contribution of the complex coefficients is To meet the zero amplitude attenuation requirement for back EMF observation without position sensors, a total gain is required. Configured as: (1.6); Equation (1.6) shows that: four design variables Convergence to three-degree-of-freedom parameter tuning .

[0026] S2: This invention utilizes the standard normalized poles of a third-order Bessel low-pass filter for optimized configuration, leveraging the maximum flat group delay characteristic of the Bessel polynomial to ensure the integrity of the back potential waveform observation. The standard normalized pole values ​​are... and After dividing the normalized poles by the target group delay, the entire system is translated along the imaginary axis. The Bessel-type target pole centered on the rotor angular frequency is obtained. This Bessel-type target pole is then matched one-to-one with the geometrically symmetric poles in equation (1.5) to obtain: (1.7); In the formula: This is the target group delay. At this point, the multi-degree-of-freedom optimization parameters have been completed. Constrained to a single group of delay parameters This achieves the Bessel configuration for the third-order complex coefficient transfer function. Combining equations (1.7), (1.3), (1.4), (1.5), and (1.6), the complete complex coefficient transfer function under the Bessel configuration is obtained: (1.8); In equation (1.8), the complete complex coefficient transfer function designed in this invention has the following key characteristics: regardless of How to choose the value, at the rotor angular frequency point Zero amplitude attenuation and zero phase hysteresis are maintained at all frequencies; deep attenuation is achieved at the -5th and +7th harmonic frequencies; only a single group delay parameter is used. A complete complex coefficient transfer function has been expressed. It should be noted that the group delay parameter... There is a key trade-off in this setup: greater group latency. It will compress bandwidth, thereby enhancing steady-state suppression performance of integer harmonics and high-frequency noise, but at the expense of dynamic tracking performance; smaller group delay. This expands the bandwidth, thereby enhancing dynamic back-potential tracking performance, but at the expense of steady-state suppression performance. To resolve this contradiction, this invention defines the adaptive group delay as: (1.9); In the formula: For adaptive parameters, To estimate the rotor angular frequency. The physical meaning of this adaptive mechanism is that when the rotor's estimated angular frequency... When adding, automatically reduce group latency. This broadens the bandwidth of the back EMF observer and accelerates the dynamic tracking performance of rapidly changing back EMF; conversely, when the rotor estimates the angular frequency... When the group delay is reduced, the group latency is automatically increased. This mechanism enhances the suppression of integer harmonics and high-frequency noise, improving the accuracy of steady-state observations. It maintains a constant suppression depth of the DC bias component at different rotor angular frequencies.

[0027] In practical applications, only the adaptive parameters need to be adjusted. To balance dynamic and steady-state performance. Specifically, to reduce under dynamic conditions. To achieve stronger dynamic tracking performance and increase performance under steady-state conditions. To achieve higher steady-state observation accuracy and realize global optimization of dynamic tracking and steady-state observation.

[0028] S3: The complete complex coefficient transfer function under the Bessel configuration describes the frequency domain characteristics required by this invention. The adaptive group delay parameter takes into account the global optimization of dynamic tracking and steady-state observation required by this invention. However, to realize this characteristic in the actual control system of permanent magnet synchronous motor, a closed-loop observation control loop must be constructed to complete the final construction of the complex coefficient back EMF observation method provided by this invention.

[0029] Stator voltage vector and stator current vector As the input, design the closed-loop observation control loop framework as follows: Figure 2 As shown in the figure and It is the angular frequency adaptive controller to be designed, by Figure 2 The closed-loop observer equation for the control loop (i.e., the closed-loop observer control loop) is: (1.10); In the formula: for The estimated back electromotive force vector of the axis, for By simplifying equation (1.10) to obtain the estimated stator current vector of the shaft, we can obtain the closed-loop transfer function from the actual back EMF to the estimated back EMF. : (1.11); Equation (1.11) shows that the closed-loop transfer function Its frequency domain characteristics are entirely determined by two angular frequency adaptive controllers. and This is jointly determined. To ensure that the frequency domain characteristics of this closed-loop structure perfectly match the aforementioned complete complex coefficient transfer function (1.8), an ideal dual integrator is selected. As the denominator of the basic filter, two angular frequency adaptive controllers are derived. and Specific design results: (1.12); In the formula: The molecular dynamics representing the wave characteristics are specifically expressed as follows: (1.13); The angular frequency adaptive controller described in equations (1.12) and (1.13) and The physical meanings are as follows: Used to offset stator resistance and stator inductance. The pole effect enables the closed-loop transfer function to accurately match the target frequency domain characteristics; Used to directly achieve the required complex coefficient zero-point configuration and amplitude compensation for specific frequency bands.

[0030] like Figure 2 As shown, It is the reference angular frequency. yes Shaft reference current, PI represents proportional-integral controller. The sensorless back EMF observation method for permanent magnet synchronous motors provided by this invention uses a phase-locked loop to estimate the back EMF vector. The estimated angular frequency of the rotor is obtained from this. and estimated location It then feeds back the data to the rest of the system's control loops in real time.

[0031] Figure 3 Figure (a) shows the Bode plots of the complete complex coefficient transfer function under the Bessel configuration proposed in this invention under different group delays, where the permanent magnet synchronous motor speed is 750 r / min. It can be seen that under different group delays, the complex coefficient transfer function proposed in this invention can always ensure the rotor angular frequency point. The zero amplitude attenuation and zero phase lag at the point of origin, and the compression of system bandwidth as the group delay increases, indicate a decrease in dynamic tracking performance; the notch depths of the -5th and +7th harmonics become deeper, indicating enhanced steady-state suppression performance against integer harmonics and high-frequency noise. Figure 3Figure (b) shows the Bode plots of the complete complex coefficient transfer function under the Bessel configuration proposed in this invention at different rotational speeds, where the rotational speeds are 500 r / min, 750 r / min, and 1000 r / min, and the adaptive parameters are... When the value is 5, it can be seen that at different rotational speeds, the amplitude of the proposed method in this invention remains at -20dB at the DC component, indicating constant suppression of the bias at the DC component. At different rotational speeds, the proposed method in this invention consistently maintains deep notch suppression at the -5th and +7th harmonics, and the amplitude in the high-frequency band is much less than 0dB, representing that it can maintain deep suppression of integer harmonics and high-frequency noise at different rotational speeds.

[0032] Figure 4 Figure (a) shows a comparison of the amplitude-frequency characteristics of the complex coefficient back EMF observation method proposed in this invention and the traditional full-order real coefficient back EMF observation method. It can be seen that the traditional full-order real coefficient back EMF observation method lacks the ability to suppress the -5th and +7th integer harmonics, while the complex coefficient back EMF observation method proposed in this invention effectively maintains the selective suppression performance of integer harmonics. Figure 4 (b) in the paper presents a comparison of the amplitude-group delay between the complex coefficient back EMF observation method proposed in this invention and the traditional full-order real coefficient back EMF observation method. It can be seen that the method proposed in this invention effectively maintains the maximum flat group delay and ensures the integrity of the back EMF waveform observation.

[0033] Figure 5 The experimental results of the complex coefficient back EMF observation method proposed in this invention and the traditional full-order real coefficient back EMF observation method under dynamic conditions were compared. The initial speed of the permanent magnet synchronous motor was 600 r / min, which increased to 1000 r / min at 2 s and further increased to 1400 r / min at 4 s. From top to bottom, the estimated back EMF waveform at 600 r / min steady state, the total harmonic distortion (THD) analysis of the estimated back EMF, the rotor estimated speed and actual speed waveforms, the estimated speed error waveform, and the estimated position error waveform are shown. It can be seen that compared with the traditional full-order real coefficient back EMF observation method, the total THD of the method proposed in this invention is reduced from 9.02% to 0.65%, and the maximum speed error and maximum position error are significantly smaller in both acceleration phases. At the same time, the position observation accuracy is improved in both dynamic and steady-state conditions. The experimental results show that this invention significantly improves the position observation accuracy of the system in both dynamic and steady-state conditions, perfectly balancing the global optimization of dynamic tracking and steady-state observation.

[0034] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0035] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. 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 substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for observing the complex coefficient back electromotive force of a permanent magnet synchronous motor, characterized in that: Specifically, the steps include the following: S1: Based on the complex coefficient voltage equation of permanent magnet synchronous motor, construct the third-order complex coefficient transfer function of back EMF observer. By explicitly configuring the zeros and poles of the third-order complex coefficient transfer function, the design variables of the third-order complex coefficient transfer function are converged into three-degree-of-freedom tuning parameters. S2: By constraining the three-degree-of-freedom tuning parameters to a single group delay parameter through Bessel-type pole mapping, the complex coefficient transfer function after Bessel configuration is obtained, and global optimization of dynamic tracking and steady-state observation is achieved by adjusting the adaptive parameters of the group delay parameter. S3: A closed-loop observation control loop is constructed using the stator voltage vector and stator current vector as inputs. By configuring the angular frequency adaptive controller in the closed-loop observation control loop, the frequency domain characteristics of the closed-loop transfer function of the closed-loop observation control loop are matched with the complex coefficient transfer function, thereby realizing the observation of the complex coefficient back EMF of the permanent magnet synchronous motor without position sensors.

2. The method for observing the complex coefficient back EMF of a permanent magnet synchronous motor according to claim 1, characterized in that: In step S1, the expression for the complex coefficient voltage equation of the permanent magnet synchronous motor is: ； in, For differential operators, for The complex vector of stator current on the shaft. For stator inductance scalar, for The stator voltage complex vector of the axis, For stator resistance scalar, for The complex vector of the back electromotive force of the axis.

3. The method for observing the complex coefficient back EMF of a permanent magnet synchronous motor according to claim 1, characterized in that: In step S1, the third-order complex coefficient transfer function of the back EMF observer is: ； in, It is a third-order complex coefficient transfer function. For the Laplace operator, and For the zero point of the complex coefficient, , and For complex coefficient poles, This represents the total gain.

4. The method for observing the complex coefficient back EMF of a permanent magnet synchronous motor according to claim 3, characterized in that: In step S1, the zeros and poles of the third-order complex coefficient transfer function are explicitly configured using the following formula, thereby converging the design variables of the third-order complex coefficient transfer function into three-degree-of-freedom tuning parameters: ； ； ； in, and For the zero point of the complex coefficient, , and For complex coefficient poles, For total gain, The rotor angular frequency, Central pole The real part of the attenuation coefficient, For conjugate pole pairs and The real part of the attenuation coefficient, For conjugate pole pairs and The imaginary part of the parameter is separated. It is the imaginary unit.

5. The method for observing the complex coefficient back EMF of a permanent magnet synchronous motor according to claim 3, characterized in that: In step S2, the specific operation of constraining the three-degree-of-freedom tuning parameters to a single group delay parameter through Bessel-type pole mapping is as follows: ； in, Central pole The real part of the attenuation coefficient, For conjugate pole pairs and The real part of the attenuation coefficient, For conjugate pole pairs and The imaginary part of the parameter is separated. This is the group delay parameter.

6. The method for observing the complex coefficient back EMF of a permanent magnet synchronous motor according to claim 1, characterized in that: In step S2, the complex coefficient transfer function after Bessel configuration The expression is: ； in, The rotor angular frequency, For group delay parameters, The rotor angular frequency point, It is the imaginary unit.

7. The method for observing the complex coefficient back EMF of a permanent magnet synchronous motor according to claim 1, characterized in that: In step S2, the expression for the group delay parameter is: ； in, For group delay parameters, For adaptive parameters, It is the estimated rotor angular frequency.

8. The method for observing the complex coefficient back EMF of a permanent magnet synchronous motor according to claim 1, characterized in that: In step S3, the expression for the closed-loop observation control loop is: ； in, for The estimated back electromotive force vector of the axis, for The estimated stator current vector of the shaft. and It is an angular frequency adaptive controller. for The stator voltage complex vector of the axis, for The complex vector of stator current on the shaft. for The estimated back electromotive force vector of the axis, for The estimated stator current vector of the shaft. For stator inductance scalar, The rotor angular frequency point, This is a scalar value for the stator resistance.

9. The method for observing the complex coefficient back EMF of a permanent magnet synchronous motor according to claim 8, characterized in that: In step S4, the closed-loop transfer function of the closed-loop observation control loop is: ； in, This is the closed-loop transfer function of the closed-loop observation control loop.

10. The method for observing the complex coefficient back EMF of a permanent magnet synchronous motor according to claim 9, characterized in that: In step S4, the angular frequency adaptive controller and Specifically: ； ； in, and All are angular frequency adaptive controllers. For molecular dynamics with notched wave characteristics, It is the estimated rotor angular frequency. For adaptive parameters, The imaginary unit, The rotor angular frequency point, For stator inductance scalar, This is a scalar value for the stator resistance.

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