A low-frequency sinusoidal signal injection based adaptive rotor position error compensation method

Abstract

The application discloses a kind of self-adapting rotor position error compensation methods based on low-frequency sinusoidal signal injection, specifically: a small amplitude low-frequency sinusoidal signal is injected into rotor position signal;Based on the small amplitude low-frequency sinusoidal signal injection, the mathematical model of permanent magnet synchronous motor under γδ coordinate system is constructed;The component and of voltage on γ axis and δ axis are obtained;Two parameters consistent generalized integrator voltage signals are processed;The amplitude of two sets of orthogonal signals is calculated;And based on amplitude, construct objective function;Solve the screen objective function, obtain the rotor optimal position error compensation value.It has excellent robustness, without accurate modeling, the difference between estimated rotor position signal and actual rotor position signal can be extracted, and the estimated rotor position signal is compensated according to rotor position error.

Description

Technical Field

[0001] This invention belongs to the field of permanent magnet synchronous motor control, and particularly relates to an adaptive rotor position error compensation method by low-frequency sinusoidal signal injection. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in applications such as industrial drives, home appliances, electric vehicles, and the aerospace industry. Accurate rotor position information is crucial for high-performance PMSM drive systems. Typically, rotor position information is obtained using mechanical position sensors. However, mechanical position sensors increase the cost and size of PMSM drive systems, and their reliability decreases under vibration and high temperatures in extreme environments. To overcome these limitations, sensorless control methods are emerging as a promising alternative.

[0003] Sensorless control strategies for permanent magnet synchronous motors (PMSMs) are mainly divided into two categories: salient polarity-based methods and model-based methods. Salient polarity-based methods are primarily used in the zero-speed domain, where the back EMF signal of the motor is weak, making it difficult to directly extract position information. Therefore, additional voltage or current signals are injected into the PMSM to utilize anisotropy to identify the rotor's spatial position. However, this method relies on salient polarity and leads to noise and additional energy losses. Model-based methods estimate the back EMF or flux linkage from the motor model using state observers, thus reducing the dependence on motor salient polarity. Important observers include extended Kalman filters, model reference adaptive rotors, and sliding mode observers. However, model-based methods rely on accurate mathematical models of the PMSM. In practical applications, the digital application of algorithms and complex operating environments can introduce many non-ideal factors, such as inverter nonlinearity, parameter mismatch, and digital delay. These unmodeled nonlinear factors will undoubtedly cause significant position errors, thus increasing system losses, reducing sensorless control performance, and even causing motor drive instability.

[0004] In conclusion, achieving high-precision sensorless control of permanent magnet synchronous motors is of significant research importance. Summary of the Invention

[0005] Purpose of the invention: In order to solve the problems existing in the prior art, the present invention provides an adaptive rotor position error compensation method by low-frequency sinusoidal signal injection.

[0006] Technical solution: This invention provides an adaptive rotor position error compensation method based on low-frequency sinusoidal signal injection, specifically as follows:

[0007] A low-amplitude, low-frequency sinusoidal signal is injected into the rotor position signal;

[0008] Based on the injected small-amplitude low-frequency sinusoidal signal, a mathematical model of the permanent magnet synchronous motor in the γδ coordinate system is constructed; the voltage components on the γ and δ axes are obtained. and ;

[0009] Using two generalized integrator voltage signals with consistent parameters and Processing is performed to obtain the same as The corresponding γ-axis fundamental voltage and its orthogonal components and with The corresponding delta-axis fundamental voltage and its orthogonal components ;

[0010] Calculate the amplitudes of two sets of orthogonal signals; and construct an objective function based on the amplitudes.

[0011] Solve the objective function to obtain the optimal rotor position error compensation value.

[0012] Furthermore, the expression for a small-amplitude, low-frequency sinusoidal signal is:

[0013] ;

[0014] Among them, A s It is the amplitude of the injected signal, ω s It is the angular frequency of the injected signal. A small-amplitude, low-frequency sinusoidal signal satisfies the following condition:

[0015] .

[0016] Furthermore, the mathematical model of the permanent magnet synchronous motor in the γδ coordinate system is constructed as follows: considering the influence of rotor position estimation error and inverter nonlinearity, the voltage signal of the permanent magnet synchronous motor in the three-phase stationary coordinate system is collected, and the estimated rotor position is used as the transformation angle for Park coordinate transformation, thereby obtaining the two-axis voltage components u in the γδ rotating coordinate system. γ and u δ :

[0017] ;

[0018] Among them, R s Let p be the stator resistance, p be the differential operator, and L be the stator resistance. d With L q These are the inductance components on the two coordinate axes in the dq coordinate system; i γ with i δ These are the current components on the two coordinate axes in the γδ coordinate system, ω e Let D be the electric angular velocity. d With D qAll are distortion coefficients, D λ With D δ These are the DC voltage components on the two coordinate axes in the γδ coordinate system, V dt The inverter's nonlinear distortion voltage error, Δθ, is caused by the dead time of switching devices, the turn-on / turn-off delay of switching devices, and the voltage drop of switching devices / diodes. e The rotor position error is the error between the estimated rotor position and the actual rotor position. Back electromotive force;

[0019] Furthermore, a third-order generalized integrator is used to analyze the voltage signal u. γ and u δ After processing, the closed-loop transfer function expression of the third-order generalized integrator is as follows:

[0020] ;

[0021] in, include and , include and , include and , and This represents the adjustable parameters of the third-order generalized integrator. It is a differential operator;

[0022] Based on the above transfer function, we obtain , , and The expression is:

[0023] .

[0024] Furthermore, the amplitudes of the two sets of orthogonal signals are calculated using the following formula:

[0025] ;

[0026] Where LPF(.) represents low-pass filtering, for and amplitude, for and amplitude, , Δθ e This represents the rotor position error.

[0027] Furthermore, the expression for the objective function based on the magnitude is shown below:

[0028] ;

[0029] Among them, is and the amplitude of is and the amplitude of

[0030] Furthermore, when the symbol-based update strategy approximates gradient descent, the optimal rotor position error compensation value is obtained:

[0031] ;

[0032] ;

[0033] Among them, F represents the objective function, k represents the discrete time index, represents the rotor position error compensation value at time k, η is the learning rate, sign() is the sign function, represents the gradient, and the rotor position error compensation value is adjusted according to to make the objective function tend to the minimum value; when the objective function is the minimum, the following conditions are satisfied:

[0034] .

[0035] Furthermore, when a low-amplitude low-frequency sine signal is injected for a certain time and then the optimal position error compensation value is searched, when 0 < ηF < a; the injection of the low-amplitude low-frequency sine signal is immediately stopped, and a represents the preset search step.

[0036] A sensorless closed-loop control method for a permanent magnet synchronous motor, specifically: collecting the αβ-axis voltage and current signals of the permanent magnet synchronous motor, obtaining the back electromotive force vector of the permanent magnet synchronous motor, and using a phase-locked loop to estimate the motor speed and rotor position signal according to the back electromotive force vector of the motor; compensating the optimal rotor position error compensation value implemented by claims 1-8 to the rotor position signal, and the phase-locked loop extracts the motor speed and rotor position signal again and inputs them into the closed-loop control system of the permanent magnet synchronous motor to achieve sensorless closed-loop control of the permanent magnet synchronous motor.

[0037] Beneficial effects:

[0038] (1) The adaptive rotor position error compensation method designed in this invention is based on low-frequency sine signal injection, has excellent robustness, can extract the difference between the estimated rotor position signal and the actual rotor position signal without precise modeling, and compensates the estimated rotor position signal according to the rotor position error.

[0039] (2) The adaptive rotor position error compensation method designed in this invention uses the gradient descent method to search for the optimal rotor position signal compensation value. The algorithm logic is simple, does not require complex matrix operations or iterative solution process, has low computational complexity, is easy to implement in engineering, and can effectively improve the real-time control performance of the system. Attached Figure Description

[0040] Figure 1 This is a control block diagram of the sensorless adaptive rotor position error compensation method for permanent magnet synchronous motors based on low-frequency sinusoidal signal injection, according to the present invention.

[0041] Figure 2 The following diagrams illustrate the verification of the signal demodulation procedure of the present invention under different rotor position errors: (a) shows the waveform of the injected signal and the waveform of the voltage signal before demodulation as a function of the injected bias; (b) shows the waveform of the voltage signal after demodulation as a function of the injected bias; and (c) shows the waveforms of the two sets of orthogonal signals, the cost function F, and the rotor position error.

[0042] Figure 3 The diagrams are for verifying the effectiveness of the rotor position error compensation method of the present invention. (a) shows the motor speed, cost function F and voltage waveform before and after the method of the present invention is enabled, and (b) shows the rotor position error compensation value and rotor position error waveform before and after the method of the present invention is enabled.

[0043] Figure 4 The diagrams show the effectiveness of the method of the present invention under low speed and small rotor position error conditions. (a) shows the motor speed, cost function F and voltage waveform before demodulation before and after signal injection is enabled and stopped. (b) shows the rotor position error compensation value and rotor position error waveform before and after signal injection is enabled and stopped.

[0044] Figure 5 This diagram shows the effectiveness of the method of the present invention under a reference speed of 1500 rpm and light load conditions.

[0045] Figure 6 This is a diagram verifying the effectiveness of the method of the present invention under a reference speed of 1500 rpm and rated load conditions.

[0046] Figure 7 This is a graph showing the relationship between different initial rotor position errors and rotor position errors after compensation using the proposed method. Detailed Implementation

[0047] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0048] like Figure 1 The present invention provides the following technical method:

[0049] In a first aspect, the present invention provides an adaptive rotor position error compensation method based on low-frequency sinusoidal signal injection. The rotor position error compensation method first uses a back EMF observer and a phase-locked loop to acquire rotational speed and rotor position signals, and then injects a small-amplitude low-frequency sinusoidal signal into the rotor position signal. The mathematical expression of this injected signal is:

[0050] ;

[0051] Where, ω s It is the angular frequency of the injected signal, A s This is the amplitude of the injected signal. Since the amplitude of the injected signal is relatively small, it satisfies the following approximate condition:

[0052] ;

[0053] After injecting a low-frequency sinusoidal signal, considering the effects of rotor position estimation error and inverter nonlinearity, the mathematical model of the permanent magnet synchronous motor in the γδ coordinate system can be expressed as:

[0054]

[0055] In the formula, u γ with u δ These are the voltage components on the two coordinate axes in the γδ coordinate system; R s p is the stator resistance; p is the differential operator; L d With L q These represent the inductance components on the two coordinate axes in the dq coordinate system; ω e i is the electric angular velocity; γ with i δ These are the current components on the two coordinate axes in the γδ coordinate system; V dt The inverter's nonlinear distortion voltage error is caused by the dead time of switching devices, the turn-on / turn-off delay of switching devices, and the voltage drop of switching devices / diodes; D d With D q The distortion coefficient is Δθ. e D represents the rotor position error (the error between the estimated rotor position and the actual rotor position). λ With D δ These represent the DC voltage components on the two coordinate axes in the γδ coordinate system. It is the back electromotive force.

[0056] Under steady-state conditions, the current in the γδ coordinate system is constrained to a constant, where D... λ D δ Eex cosΔθ e With E ex sinΔθ e The main components include DC bias, sixth harmonic, and other high-frequency harmonic components. The remaining items are E. ex A s sinω s tcosΔθ e and E ex A s sinω s tsinΔθ e This represents the low-frequency component, which contains the rotor position error signal, and can be used to design adaptive rotor error compensation methods.

[0057] To obtain the rotor position estimation error, the three-phase stationary coordinate system voltage signal is first acquired from the sensor. The estimated rotor position is then used as the transformation angle for Park coordinate transformation, thereby obtaining the two-axis voltage components u in the γδ rotating coordinate system. γ and u δ Then, two third-order generalized integrators (TOGIs) with completely identical parameters are used to analyze the voltage signal u. γ and u δ Process u γ and u δ What are these voltage signals? TOGI's output has d... γ,δ and its orthogonal components q γ,δ The closed-loop transfer function expression for TOGI is as follows:

[0058]

[0059] In the formula, s is the differential operator; u γ , δ Represents voltage signal u γ and u δ ;d γ,δ Represents d γ and d δ ;q γ,δ Represents q γ and q δ .

[0060] Where D(s) is u γ , δ With d γ , δ The transfer function u between γ , δ Yes, Q(s) is u γ , δ With q γ , δThe transfer function between them, k and k0 are two adjustable parameters of TOGI. Since TOGI can be derived from the voltage signal u... γ and u δ After removing DC bias, the sixth harmonic, and other higher harmonics, the resonant frequency is ω. s The ideal d γ , δ With q γ , δ The output is as follows:

[0061] ;

[0062] in, .

[0063] The amplitudes of the two sets of orthogonal signals can be calculated using the following formula:

[0064] ;

[0065] Where LPF(.) represents the signal after low-pass filtering, A γ and A δ These correspond to two sets of orthogonal signals (d) γ With d δ , q γ With q δ The amplitude of ).

[0066] Based on the above formula, a novel cost function is designed, and its mathematical expression is as follows:

[0067] ;

[0068] The non-zero value Δθ cannot be directly determined from the above formula. e The sign of the cost function F is always non-negative and varies with |Δθ. e As | increases, F increases. Therefore, F is a typical convex function, and its minimum value is at Δθ. e At point =0, the theoretical value of F is zero.

[0069] Then, the gradient descent method is used to minimize the cost function F, and a rotor position error compensation value θ. com This compensation value is added to the estimated rotor position signal to achieve closed-loop control. It is adaptively adjusted using an extreme value search algorithm to make the cost function F approach its minimum value. F reaches its minimum value when the following condition is met:

[0070] ;

[0071] In practical engineering applications, F with respect to θ comThe derivative of is often difficult to obtain directly. Therefore, a sign-based update strategy is used to approximate gradient descent, which does not rely on the explicit derivative. The mathematical expression of this gradient descent method is as follows:

[0072]

[0073]

[0074] Where η is the learning rate, sign(.) is the sign function, and k represents the discrete-time index. This represents the gradient.

[0075] Considering the settling time of the cost function F, the GDO method is activated to minimize F after the signal injection lasts for one second, thereby finding the optimal position error compensation value. To avoid the injected signal affecting the sensorless control system, signal injection needs to be terminated immediately after the optimal compensation value is found, putting the system into a "stop injection" state. To achieve system state switching, the search step size threshold is set to 0.5°. When the constraint 0 < ηF < 0.5° is met, it indicates that the optimal position compensation value has been found.

[0076] Secondly, the present invention provides a sensorless control method for a permanent magnet synchronous motor based on adaptive rotor position signal error compensation using low-frequency sinusoidal signal injection, the method comprising:

[0077] First, the motor's αβ axis voltage and current signals are input to the back EMF observer to estimate the extended back EMF vector. The motor's back EMF vector is then input to an orthogonal phase-locked loop to estimate the motor's speed and rotor position signals. Next, a low-frequency sinusoidal signal is injected into the estimated rotor position signal. Then, the estimated rotor position signal is used to perform coordinate transformation on the motor's voltage signal in the three-phase stationary coordinate system to obtain the voltage in the γδ coordinate system. This voltage signal is used as input, and the optimal compensation value for the estimated rotor position signal error is obtained through the aforementioned method.

[0078] The motor speed and rotor position signals are input to the motor closed-loop control system to achieve sensorless closed-loop control of the permanent magnet synchronous motor.

[0079] Thirdly, this invention provides a sensorless adaptive rotor position error compensation method for permanent magnet synchronous motors based on low-frequency sinusoidal signal injection, the method comprising:

[0080] The optimal compensation value solution module is used to take the collected voltage signal in the motor γδ coordinate system as input and obtain the optimal compensation value for estimating the rotor position signal error.

[0081] Back EMF observation module: It is used to take the collected motor αβ axis voltage and current signals as input, obtain the motor back EMF vector, and use the phase-locked loop to estimate the motor speed and rotor position signals based on the motor back EMF vector.

[0082] Rotor position signal compensation module: The optimal compensation value for the estimated rotor position signal error is applied to the preceding rotor position signal.

[0083] Motor speed and rotor position extraction module: Based on the estimated back EMF vector of the motor, a phase-locked loop is used to extract the motor speed and rotor position signals.

[0084] Motor speed and rotor position signal transmission module: used to input the motor speed and rotor position signals extracted by the phase-locked loop to the motor closed-loop control system to realize sensorless closed-loop control of the permanent magnet synchronous motor.

[0085] In one embodiment of the present invention, the estimated rotor electrical angular velocity is subtracted from the given rotor electrical angular velocity to obtain a speed difference value; the speed difference value is input to a speed PI controller to obtain a given current for the dq axis; the three-phase current of the permanent magnet synchronous motor is obtained through current sampling, and the three-phase current is sequentially transformed by Clark and Park transformations to obtain a current feedback value; the given current for the dq axis and the current feedback value are subtracted to obtain a current difference value; the current difference value is input to a current PI controller to obtain a reference voltage for the dq axis; the reference voltage for the dq axis is transformed by coordinate transformation to obtain an αβ axis voltage; the αβ axis voltage is input to an SVPWM modulation module to output a duty cycle signal; the duty cycle signal is input to an inverter to control the inverter's on / off state, and this constitutes the aforementioned permanent magnet synchronous motor control device. For a description of a sensorless control device for a permanent magnet synchronous motor based on adaptive rotor position error compensation using low-frequency sinusoidal signal injection, please refer to the description of the same or similar parts above, and will not be repeated here.

[0086] The beneficial effects of this invention were verified through an experimental platform. The parameters of the permanent magnet synchronous motor used were: rated power 750W, rated frequency 250Hz, rated speed 3000rpm, number of pole pairs 5, d-axis inductance 4.7mH, q-axis inductance 6.7mH, stator resistance 0.9Ω, permanent magnet flux linkage 0.053Wb, rated current 4.2A, and rated load 1.6N∙m. The sampling frequency and switching frequency were both 10kHz.

[0087] Figure 2This paper describes the signal demodulation process of the proposed rotor position compensation method under different rotor position signal errors. In the experiment, a rotor position bias varying from 30° to -30° is injected into the estimated rotor position signal. The frequency and amplitude of the injected low-frequency sinusoidal signal are 30Hz and 0.07rad, respectively. Because the amplitude of the injected signal is very small, its influence on the voltage in the γδ coordinate system can be ignored. Two TOGIs can effectively remove the DC bias and higher harmonic components to obtain the low-frequency voltage signal (d). γ , d δ , q γ and q δ Within the aforementioned rotor position error offset range, the amplitudes of both sets of orthogonal signals can be accurately extracted. The calculated cost function F decreases as the rotor position error offset decreases, indicating that the optimal error compensation value can be found by minimizing F.

[0088] Figure 3 To verify the effectiveness of the GDO method in the proposed rotor position error compensation method, a rotor position offset error of -30° was artificially injected into the estimated rotor position. The reference value of the rotational speed in the figure is 1000 rpm. As shown in the figure, the estimated rotational speed can accurately track the reference value during the search process, indicating that the injected signal has little impact on the speed tracking performance. After the GDO algorithm is enabled, the rotor position error signal compensation value θ can be dynamically adjusted. com This gradually reduces the cost function F, and the optimal compensation value is obtained after 2.8 seconds. When the compensation of the GDO method is less than 0.5°, signal injection is terminated to avoid the negative impact caused by the injected signal. Finally, the rotor position error stabilizes and fluctuates around 0°.

[0089] Figure 4 This experiment aimed to verify the effectiveness of the proposed GDO method for rotor position error compensation under low-speed and small rotor position error conditions. In the experiment, a DC bias of -10° was artificially injected into the estimated position signal. The reference speed in the figure is 300 rpm. After the GDO method was activated, the optimal compensation value was found within 1.3 seconds, successfully compensating the rotor position signal bias to zero. Experimental results show that the proposed GDO method is effective under different rotor position bias errors.

[0090] Figure 5This experiment aimed to verify the effectiveness of the proposed rotor position error compensation method under a reference speed of 1500 rpm and light load conditions. In the experiment, a 30° rotor position offset was artificially injected into the rotor position signal. The load during the test was 30% of the rated load. After activating the proposed method, a low-frequency sinusoidal signal was injected into the estimated position for one second to excite the response signal. After the cost function F stabilized, the proposed GDO method was activated to find the optimal rotor position error compensation value. During the process of the rotor position error approaching zero, the phase current of phase A decreased from 2.2A to 1.6A. Subsequently, the signal injection was terminated, and the rotor position signal compensation program was stopped. Experimental results show that the proposed method is feasible under light load conditions.

[0091] Figure 6 The purpose of this study was to verify the effectiveness of the proposed rotor position error compensation method under a reference speed of 1500 rpm and rated load conditions. Under rated load, the rotor position error caused by magnetic saturation is approximately 14°. After applying the proposed method, the rotor position error was reduced to near zero, and the phase current of phase A decreased from 6.7A to 6.0A. Experimental results demonstrate the feasibility of the proposed method under rated load conditions.

[0092] Figure 7 The purpose of this study was to verify the effectiveness of the proposed rotor position error compensation method under different initial position error conditions. In the experiment, the initial position error ranged from -30° to 30°, and after compensation, it could be maintained within ±2°. The experimental results demonstrate the effectiveness of the proposed GDO method under different initial position error conditions.

[0093] The experimental results above show that the permanent magnet synchronous motor control method of the present invention can obtain the optimal rotor position error compensation value according to the proposed method and compensate it to the rotor position signal, thereby reducing the rotor position estimation error and effectively improving the accuracy of sensorless control.

[0094] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0095] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of this patent should be determined by the appended claims.

[0096] It should also be noted that the various specific technical features described in the above embodiments can be combined in any suitable manner without contradiction. To avoid unnecessary repetition, the present invention will not describe the various possible combinations separately.

Claims

1. An adaptive rotor position error compensation method based on low-frequency sinusoidal signal injection, characterized in that, Specifically: Inject a small - amplitude and low - frequency sinusoidal signal into the rotor position signal; Based on the injected small-amplitude low-frequency sinusoidal signal, a mathematical model of the permanent magnet synchronous motor in the γδ coordinate system is constructed; the voltage components on the γ and δ axes are obtained. and ; Using two generalized integrator voltage signals with consistent parameters and Processing is performed to obtain the same as The corresponding γ-axis fundamental voltage and its orthogonal components and with The corresponding delta-axis fundamental voltage and its orthogonal components ; Calculate the amplitudes of two groups of orthogonal signals; and construct an objective function based on the amplitudes; Solve the objective function to obtain the optimal rotor position error compensation value.

2. The adaptive rotor position error compensation method based on low-frequency sinusoidal signal injection according to claim 1, characterized in that, The expression of the small - amplitude and low - frequency sinusoidal signal is: ； Among them, A s It is the amplitude of the injected signal, ω s It is the angular frequency of the injected signal. A small-amplitude, low-frequency sinusoidal signal satisfies the following condition: 。 3. The adaptive rotor position error compensation method based on low-frequency sinusoidal signal injection according to claim 2, characterized in that, The mathematical model of the permanent magnet synchronous motor in the γδ coordinate system is constructed as follows: Considering the influence of rotor position estimation error and inverter nonlinearity, the voltage signal of the permanent magnet synchronous motor in the three-phase stationary coordinate system is collected. The estimated rotor position is used as the transformation angle for Park coordinate transformation, thereby obtaining the two-axis voltage components u in the γδ rotating coordinate system. γ and u δ : ； Among them, R s Let p be the stator resistance, p be the differential operator, and L be the stator resistance. d With L q These are the inductance components on the two coordinate axes in the dq coordinate system; i γ with i δ These are the current components on the two coordinate axes in the γδ coordinate system, ω e Let D be the electric angular velocity. d With D q All are distortion coefficients, D λ With D δ These are the DC voltage components on the two coordinate axes in the γδ coordinate system, V dt The inverter's nonlinear distortion voltage error, Δθ, is caused by the dead time of switching devices, the turn-on / turn-off delay of switching devices, and the voltage drop of switching devices / diodes. e The rotor position error is the error between the estimated rotor position and the actual rotor position. It is the back electromotive force.

4. The adaptive rotor position error compensation method based on low-frequency sinusoidal signal injection according to claim 3, characterized in that, A third-order generalized integrator is used to analyze the voltage signal u. γ and u δ After processing, the closed-loop transfer function expression of the third-order generalized integrator is as follows: ； in, include and , include and , include and , and This represents the adjustable parameters of the third-order generalized integrator. It is a differential operator; Based on the above transfer function, we obtain , , and The expression is: 。 5. The adaptive rotor position error compensation method based on low-frequency sinusoidal signal injection according to claim 4, characterized in that, Use the following formula to calculate the amplitudes of two groups of orthogonal signals: ； Where LPF(.) represents low-pass filtering, for and amplitude, for and amplitude, , Δθ e This represents the rotor position error.

6. The adaptive rotor position error compensation method based on low-frequency sinusoidal signal injection according to claim 1, characterized in that, The expression of the objective function constructed based on the amplitudes is as follows: ； in, for and amplitude, for and The amplitude.

7. The adaptive rotor position error compensation method based on low-frequency sinusoidal signal injection according to claim 1, characterized in that, When the sign - based update strategy approximates gradient descent, obtain the optimal rotor position error compensation value: ； ； Where F represents the objective function, and k represents the discrete-time index. This represents the rotor position error compensation value at time k, where η is the learning rate and sign() is the sign function. Representing the gradient, according to The rotor position error compensation value is adjusted so that the objective function tends to its minimum value; the following condition is satisfied when the objective function is minimized: 。 8. The adaptive rotor position error compensation method based on low-frequency sinusoidal signal injection according to claim 7, characterized in that, When the small - amplitude and low - frequency sinusoidal signal is injected for a certain time and then search for the optimal position error compensation value, immediately stop injecting the small - amplitude and low - frequency sinusoidal signal when \(0\lt\eta F\lt a\); \(a\) represents the preset search step size.

9. A sensorless closed-loop control method based on a permanent magnet synchronous motor, characterized in that, Collect the voltage and current signals of the \(\alpha\beta\) axes of the permanent - magnet synchronous motor, obtain the back - electromotive - force vector of the permanent - magnet synchronous motor, and use a phase - locked loop to estimate the motor speed and rotor position signal according to the back - electromotive - force vector of the motor; Compensate the optimal rotor position error compensation value achieved by claims 1 - 8 to the rotor position signal, the phase - locked loop extracts the motor speed and rotor position signal again, and inputs them into the closed - loop control system of the permanent - magnet synchronous motor to achieve sensorless closed - loop control of the permanent - magnet synchronous motor.

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