Method for flux linkage observation of permanent magnet synchronous motor based on limit cycle oscillator

Abstract

The application discloses a kind of permanent magnet synchronous motor flux linkage observation methods based on limit cycle oscillator, belongs to motor control technical field.The present application is aimed at the problem that the existing flux linkage observation methods based on second-order generalized integrator have poor suppression ability to direct current bias and harmonic disturbance of each frequency.Utilize the voltage model and current model of permanent magnet synchronous motor to estimate motor stator flux linkage respectively, the stator flux linkage obtained by two kinds of algorithms is different, and the stator flux linkage estimation error is obtained;Using proportional-integral controller, the stator electromotive force correction value is calculated based on the stator flux linkage estimation error;The stator electromotive force correction value is compensated to the stator electromotive force estimated by voltage model, and the modified stator electromotive force is obtained;Again, the second-order generalized integrator with limit cycle oscillator is used to process the modified voltage model to estimate the stator flux linkage, and then the stator flux linkage estimated by the voltage model is used for the calculation of the next period.The application is used for motor flux linkage observation.

Description

Technical Field

[0001] This invention relates to a method for observing flux linkage in a permanent magnet synchronous motor based on a limit cycle oscillator, belonging to the field of motor control technology. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) have been widely used in industrial production and other fields due to their high efficiency and high power density. In many applications, the installation of position sensors not only increases system costs but also reduces the reliability of the drive system. Therefore, sensorless algorithms that use signals such as voltage and current to estimate the rotor position of the motor online have been extensively studied.

[0003] Due to the influence of sampling bias, inverter nonlinearity, dead-zone setting, and harmonics introduced by the motor's structural design, traditional sensorless algorithms for permanent magnet synchronous motors based on the flux linkage model are significantly affected by DC bias and harmonics. To address this issue, researchers have introduced a second-order generalized integrator with filtering capabilities at its integral output into the flux linkage observer, replacing the function of the first-order integrator and improving the algorithm's ability to filter out DC bias and harmonics.

[0004] However, theoretical analysis and experimental verification revealed that under conditions of significant harmonic disturbances, the existing second-order generalized integrator algorithm's ability to filter DC bias and harmonics is limited. Increasing the algorithm gain to enhance suppression capability severely impacts the system's dynamic performance. Furthermore, due to the influence of the linear integrator in the second-order generalized integrator structure, it fails to suppress disturbances in the fundamental flux amplitude introduced by parameter changes caused by magnetic field saturation. These disturbances are introduced into flux position estimation, affecting the disturbance rejection performance of the sensorless algorithm. Therefore, improving the disturbance rejection capability of the sensorless algorithm for permanent magnet synchronous motors based on the flux model is of significant theoretical and practical importance. Summary of the Invention

[0005] To address the problem that existing flux linkage observation methods based on second-order generalized integrators have poor suppression capabilities for DC bias and harmonic disturbances at various frequencies, this invention provides a flux linkage observation method for permanent magnet synchronous motors based on a limit loop oscillator.

[0006] The present invention provides a method for observing the flux linkage of a permanent magnet synchronous motor based on a limit cycle oscillator, comprising:

[0007] Step 1: Estimate the stator flux linkage of the permanent magnet synchronous motor using the voltage model and current model respectively, and subtract the stator flux linkage obtained by the two algorithms to obtain the stator flux linkage estimation error;

[0008] Step 2: The stator electromotive force correction value is calculated based on the stator flux estimation error using a proportional-integral controller; the stator electromotive force correction value is then compensated into the stator electromotive force estimated by the voltage model to obtain the corrected stator electromotive force.

[0009] Step 3: The corrected stator electromotive force is processed by a second-order generalized integrator with a limit loop oscillator to obtain the corrected voltage model estimate of the stator flux linkage;

[0010] Step 4: Use the stator flux estimated by the corrected voltage model as the stator flux estimated by the voltage model, return to Step 1 to continue the calculation of the stator flux estimated by the corrected voltage model for the next cycle, until the end.

[0011] According to the permanent magnet synchronous motor flux linkage observation method based on limit cycle oscillator of the present invention, in step one, the voltage model of the two-phase stationary shaft system of the permanent magnet synchronous motor is as follows:

[0012]

[0013] In the formula ψ sα_VM For the α-axis stator flux linkage based on the voltage model, ψ sβ_VM For the β-axis stator flux linkage based on the voltage model, u sα For the α-axis stator voltage, u sβ For the β-axis stator voltage, i sα Let i be the α-axis stator current. sβ R is the β-axis stator current. s This is the stator resistance.

[0014] According to the permanent magnet synchronous motor flux linkage observation method based on a limiting ring oscillator of the present invention, in step one, the method for estimating the stator flux linkage of the motor using the current model of the permanent magnet synchronous motor is as follows:

[0015] Calculate the stator flux linkage in a two-phase rotating coordinate system:

[0016]

[0017] In the formula ψ sd For the d-axis stator flux linkage, ψ sq For the q-axis stator flux linkage, ψ m For permanent magnet flux linkage, L d For the d-axis inductance, L q For q-axis inductance, i sd For the d-axis stator current, i sq This refers to the q-axis stator current.

[0018] d-axis stator flux linkage ψ sd and q-axis stator flux linkage ψ sq Performing the iPark transformation yields the α-axis stator flux linkage ψ based on the current model.sα_CM and β-axis stator flux linkage ψ based on current model sβ_CM :

[0019]

[0020] In the formula θ e The electric angle is the motor angle.

[0021] According to the permanent magnet synchronous motor flux linkage observation method based on limit cycle oscillator of the present invention, the stator flux linkage estimation error in step one is:

[0022]

[0023] In the formula ψ sα_err For the α-axis stator flux linkage estimation error, ψ sβ_err This represents the estimation error of the stator flux linkage along the β-axis.

[0024] According to the permanent magnet synchronous motor flux linkage observation method based on a limit loop oscillator of the present invention, the method for calculating the stator electromotive force correction value based on the stator flux linkage estimation error using a proportional-integral controller in step two is as follows:

[0025]

[0026] In the formula e sα_err k is the correction value for the stator electromotive force along the α-axis. p1 k is the proportional gain of the α-axis proportional-integral controller. i1 e is the integral gain of the α-axis proportional-integral controller; sβ_err k is the correction value for the β-axis stator electromotive force. p2 k is the proportional gain of the β-axis proportional-integral controller. i2 This is the integral gain of the β-axis proportional-integral controller.

[0027] According to the permanent magnet synchronous motor flux linkage observation method based on limit cycle oscillator of the present invention, the method for estimating the stator electromotive force in step two by voltage model is as follows:

[0028]

[0029] In the formula e sα_VM For the α-axis stator electromotive force based on the voltage model, e sβ_VM This is the β-axis stator electromotive force based on the voltage model.

[0030] According to the permanent magnet synchronous motor flux linkage observation method based on limit cycle oscillator of the present invention, the method for obtaining the corrected stator electromotive force in step two is as follows:

[0031]

[0032] In the formula esα For the corrected α-axis stator electromotive force, e sβ This is the corrected β-axis stator electromotive force.

[0033] According to the permanent magnet synchronous motor flux observation method based on a limit cycle oscillator of the present invention, in step three, the α-axis and β-axis control laws of the second-order generalized integrator with the limit cycle oscillator are the same, and the α-axis control law is:

[0034]

[0035] In the formula To estimate the center frequency, ε α For e sα With e′ sα The difference, k is the algorithm gain coefficient, e′ sα α is the stator electromotive force of the second-order generalized integrator filter output, q is the orthogonal component, A0 is the convergence radius of the limit loop, s is the complex variable, and Γ is the gain coefficient of the frequency-locked loop.

[0036] According to the permanent magnet synchronous motor flux observation method based on limit cycle oscillator of the present invention, the calculation method for estimating stator flux through the corrected α-axis voltage model in step three is as follows:

[0037]

[0038] In the formula ψ sα Estimate stator flux linkage for the corrected α-axis voltage model.

[0039] According to the permanent magnet synchronous motor flux observation method based on the limiting ring oscillator of the present invention, the calculation method for estimating the stator flux through the corrected β-axis voltage model in step three is as follows:

[0040] The β-axis control law of a second-order generalized integrator with a limit cycle oscillator is:

[0041]

[0042] ε β For e sβ With e′ sβ The difference, e′ sβ The β-axis stator electromotive force is the filtered output of the second-order generalized integrator.

[0043] The corrected β-axis voltage model estimates the stator flux linkage ψ. sβ for:

[0044]

[0045] The beneficial effects of this invention are as follows: The method of this invention is used to replace the position sensor. The final corrected voltage model estimate of the stator flux can filter out the DC bias and harmonic disturbances in the voltage and current signals, improve the anti-interference capability of the permanent magnet synchronous motor flux observer against various types of disturbances, and broaden the operating range of the permanent magnet synchronous motor based on the model-based sensorless algorithm. Attached Figure Description

[0046] Figure 1 This is a block diagram of a sensorless control method for a permanent magnet synchronous motor based on flux linkage observation using a limit cycle oscillator; the diagram shows... For a given rotational speed value, ω e This is the motor speed value. The given value for the d-axis current. The q-axis current is given a value. The given value for the d-axis voltage. U is the q-axis voltage setpoint. dc i is the DC bus voltage. a i b i c These represent the currents of phases a, b, and c, respectively, and ε represents the input current e. sα With e′ sα The difference between or e sβ With e′ sβ The difference, PI is a proportional-integral controller, MTPA is a maximum torque-current ratio controller;

[0047] Figure 2 This is a control block diagram of the permanent magnet synchronous motor flux linkage observation method based on a limit cycle oscillator described in this invention. Figure 2 Lieutenant General Figure 1 The voltage and current models are expanded in the figure; Park is the Park transform module, iPark is the inverse Park transform module, and SOGI-LCO is a second-order generalized integrator algorithm with a limit cycle oscillator.

[0048] Figure 3 for Figure 2 The SOGI-LCO module in the α-axis expansion form, whose input is the corrected α-axis stator electromotive force e. sα The output is the corrected α-axis voltage model estimate of the stator flux linkage ψ from the flux linkage observer. sα The internal structure of the SOGI-LCO module used for the β-axis is the same as that for the α-axis, and the input is the corrected β-axis stator electromotive force e. sβ The output is the stator flux ψ estimated by the corrected β-axis voltage model of the designed flux observer. sβ ;

[0049] Figure 4 The parameter design range for the algorithm of this invention is given by ζ, where ζ is the damping coefficient and ω is the damping coefficient.n The center frequency;

[0050] Figure 5 The figure shows the experimental waveform of rotor position estimation error when the flux linkage observation method of the permanent magnet synchronous motor based on the limit cycle oscillator proposed in this invention is not used in a specific embodiment; To estimate the rotational speed, Δθ e This represents the position estimation error;

[0051] Figure 6 The Fourier analysis diagram of the α-axis stator electromotive force in a specific embodiment when the method of the present invention is not used for suppression;

[0052] Figure 7 The experimental waveform diagram shows the rotor position estimation error when using the method of the present invention.

[0053] Figure 8 The image shows the Fourier analysis diagram of the α-axis stator electromotive force when using the method of this invention. Detailed Implementation

[0054] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0055] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0056] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the invention.

[0057] Specific Implementation Method 1: Combination Figure 1 As shown, this invention provides a method for observing the flux linkage of a permanent magnet synchronous motor based on a limiting cycle oscillator, using a permanent magnet synchronous motor flux linkage observer for observation, including:

[0058] Step 1: Due to the influence of sampling bias, inverter nonlinearity, dead-time setting, and DC bias and harmonics introduced by the motor body structure design, the traditional sensorless algorithm for permanent magnet synchronous motors based on the flux linkage model method is significantly affected, resulting in a large number of harmonics in the output flux linkage estimate and position estimate. To improve the disturbance rejection capability of the flux linkage observer, this implementation adopts a flux linkage estimation method based on a voltage-current hybrid model, and designs a second-order generalized integrator with a limit loop oscillator to improve the algorithm's disturbance rejection capability and dynamic performance. First, the stator flux linkage of the permanent magnet synchronous motor is estimated using the voltage model and current model respectively. The stator flux linkage obtained by the two algorithms is subtracted to obtain the stator flux linkage estimation error.

[0059] Step 2: The stator electromotive force (EMF) correction value is calculated based on the stator flux estimation error using a proportional-integral controller; the stator EMF correction value is then compensated into the stator EMF estimated by the voltage model using a closed-loop feedback approach to obtain the corrected stator EMF; thereby gradually reducing the error between the voltage model stator EMF estimation value and the actual value.

[0060] Step 3: A second-order generalized integrator with a limiting loop oscillator is used to filter and integrate the corrected stator electromotive force (EMF). This filters out the DC bias and harmonic disturbances of each frequency in the corrected stator EMF. Simultaneously, the integrator's built-in integration function is used to integrate the filtered stator EMF to obtain the filtered corrected voltage model estimate of the stator flux linkage. The corrected voltage model estimate of the stator flux linkage is used as the output of the observer.

[0061] Step 4: Using the corrected voltage model-estimated stator flux linkage as the stator flux linkage obtained from the voltage model estimation, return to Step 1 to continue calculating the corrected voltage model-estimated stator flux linkage for the next cycle, until completion. After obtaining the filtered stator flux linkage, it can be combined with algorithms such as effective flux linkage and quadrature phase-locked loops to obtain rotor position and speed information, which is then applied to the vector control system to improve the system's anti-disturbance capability and enhance its operating performance.

[0062] The observation method in this embodiment is mainly applied in the sensorless control system of permanent magnet synchronous motor to suppress and eliminate DC bias and harmonic disturbances of various frequencies in the sensorless algorithm caused by factors such as sampling bias, inverter nonlinearity, dead zone setting and motor body structure.

[0063] Furthermore, in step one, the voltage model of the two-phase stationary axis system (α-β axis) of the permanent magnet synchronous motor is as follows:

[0064]

[0065] In the formula ψ sα_VM For the α-axis stator flux linkage based on the voltage model, ψ sβ_VMFor the β-axis stator flux linkage based on the voltage model, u sα For the α-axis stator voltage, u sβ For the β-axis stator voltage, i sα Let i be the α-axis stator current. sβ R is the β-axis stator current. s This is the stator resistance.

[0066] The ψ obtained in this embodiment sα_VM and ψ sβ_VM The stator flux linkage of the motor is estimated by the voltage model in the initial operating cycle. In subsequent operating cycles, the stator flux linkage estimated by the corrected voltage model of the previous cycle is used as the stator flux linkage estimated by the voltage model in the next cycle.

[0067] In step one, the method for estimating the stator flux linkage of the permanent magnet synchronous motor using the current model is as follows:

[0068] Since calculating the flux linkage in the permanent magnet synchronous motor current model under the α-β axis is quite complex, to simplify the calculation, the stator flux linkage is calculated in a two-phase rotating coordinate system (dq axis):

[0069]

[0070] In the formula ψ sd For the d-axis stator flux linkage, ψ sq For the q-axis stator flux linkage, ψ m For permanent magnet flux linkage, L d For the d-axis inductance, L q For q-axis inductance, i sd For the d-axis stator current, i sq This refers to the q-axis stator current.

[0071] d-axis stator flux linkage ψ sd and q-axis stator flux linkage ψ sq Performing the iPark transformation yields the α-axis stator flux linkage ψ based on the current model. sα_CM and β-axis stator flux linkage ψ based on current model sβ_CM :

[0072]

[0073] In the formula θ e The electric angle is the motor angle.

[0074] The stator flux linkage estimation error in step one is:

[0075]

[0076] In the formula ψ sα_err For the α-axis stator flux linkage estimation error, ψ sβ_err This represents the estimation error of the stator flux linkage along the β-axis.

[0077] Furthermore, the method for calculating the stator electromotive force correction value based on the stator flux estimation error using a proportional-integral controller in step two is as follows:

[0078]

[0079] In the formula e sα_err k is the correction value for the stator electromotive force along the α-axis. p1 k is the proportional gain of the α-axis proportional-integral controller. i1 e is the integral gain of the α-axis proportional-integral controller; sβ_err k is the correction value for the β-axis stator electromotive force. p2 k is the proportional gain of the β-axis proportional-integral controller. i2 This is the integral gain of the β-axis proportional-integral controller.

[0080] The method for estimating the stator electromotive force using the voltage model in step two is as follows:

[0081]

[0082] In the formula e sα_VM For the α-axis stator electromotive force based on the voltage model, e sβ_VM This is the β-axis stator electromotive force based on the voltage model.

[0083] The method for obtaining the corrected stator electromotive force in step two is as follows:

[0084]

[0085] In the formula e sα For the corrected α-axis stator electromotive force, e sβ This is the corrected β-axis stator electromotive force.

[0086] Furthermore, in step three, the α-axis and β-axis control laws of the second-order generalized integrator with the limit cycle oscillator are the same. The α-axis control law is:

[0087]

[0088] In the formula To estimate the center frequency, ε α For e sα With e′ sα The difference, k is the algorithm gain coefficient, e′ sα The α-axis stator electromotive force is the filtered output of the second-order generalized integrator, where q is the orthogonal component, qe′. sα α is the orthogonal output α-axis stator electromotive force of the second-order generalized integrator, A0 is the convergence radius of the limit loop, s is a complex variable, and Γ is the gain coefficient of the frequency-locked loop.

[0089] The calculation method for estimating the stator flux linkage using the corrected α-axis voltage model in step three is as follows:

[0090]

[0091] In the formula ψ sα Estimate stator flux linkage for the corrected α-axis voltage model.

[0092] Similarly, the treatment of the β-axis is the same as that of the α-axis. The calculation method for estimating the stator flux linkage using the corrected β-axis voltage model in step three is as follows:

[0093] The β-axis control law of a second-order generalized integrator with a limit cycle oscillator is:

[0094]

[0095] ε β For e sβ With e′ sβ The difference, e′ sβ The β-axis stator electromotive force is the filtered output of the second-order generalized integrator.

[0096] The corrected β-axis voltage model estimates the stator flux linkage ψ. sβ for:

[0097]

[0098] The specific process of step four is as follows: estimate the stator flux linkage ψ using the corrected α-axis voltage model. sα And the β-axis voltage model estimates the stator flux linkage ψ sβ The voltage model outputs the stator flux estimate for the next calculation cycle, and steps one through four continue iteratively in the next operation cycle, thereby suppressing the DC bias and harmonic disturbances of the flux observation input. ψ sα and ψ sβ The lieutenant general does not contain any disturbance components, which improves the anti-disturbance capability of the sensorless control algorithm of the flux linkage model.

[0099] Figure 1 This is a block diagram of the method of the present invention applied to the sensorless control of a permanent magnet synchronous motor. Based on the motor vector control, it obtains rotor position information using the method of the present invention, thereby replacing the traditional method of obtaining rotor position and speed information by encoder.

[0100] Figure 1 The control system employs vector control, with speed and position obtained using a flux linkage observer in conjunction with a phase-locked loop (PLL). A dual-closed-loop control method is used, with an outer speed loop and an inner current loop. Both the current and speed loops are controlled by proportional-integral (PI) controllers. This invention replaces position sensors. The final obtained ψ... sα and ψsβ It can filter out DC bias and harmonic disturbances in voltage and current signals, thus improving the anti-disturbance capability of the flux observer algorithm.

[0101] Considering the possibility of algorithm divergence, the convergence interval of the method of this invention can be designed from the perspective of convergence. Figure 4 Let k be the design convergence interval. Specific implementation examples:

[0103] The effectiveness of the method of the present invention will be verified through the following examples:

[0104] The effectiveness of the flux linkage observation method based on the limiting loop oscillator proposed in this invention for suppressing harmonic disturbances was verified on a permanent magnet synchronous motor (PMSM) tractor platform. The experimental platform parameters were set as follows: motor rated power 2.2 kW, stator resistance 2.53 Ω, d-axis inductance 22.38 mH, q-axis inductance 51.75 mH, magnetic flux 0.5 Wb, number of pole pairs 3, switching frequency and sampling frequency 6 kHz, and control parameters k = 1.414, Γ = 1000, and A0 = 1.

[0105] Depend on Figure 5 and Figure 6 As can be seen from the waveform diagram, without the method of this invention, the rotor position estimation error varies significantly with changes in load. Fourier analysis reveals abundant harmonic content at various frequencies in the stator electromotive force. Figure 7 and Figure 8 As can be seen from the waveform diagram, after adopting the method of the present invention, the rotor position estimation error changes less with the load. At the same time, Fourier analysis shows that the harmonic components of each frequency in the stator electromotive force are significantly suppressed.

[0106] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for observing flux linkage of a permanent magnet synchronous motor based on a limit cycle oscillator, characterized in that... include, Step 1: Estimate the stator flux linkage of the permanent magnet synchronous motor using the voltage model and current model respectively, and subtract the stator flux linkage obtained by the two algorithms to obtain the stator flux linkage estimation error; Step 2: The stator electromotive force correction value is calculated based on the stator flux estimation error using a proportional-integral controller; the stator electromotive force correction value is then compensated into the stator electromotive force estimated by the voltage model to obtain the corrected stator electromotive force. Step 3: The corrected stator electromotive force is processed by a second-order generalized integrator with a limit loop oscillator to obtain the corrected voltage model estimate of the stator flux linkage; Step 4: Use the stator flux estimated by the corrected voltage model as the stator flux estimated by the voltage model, return to Step 1 to continue the calculation of the stator flux estimated by the corrected voltage model for the next cycle, until the end; The method for calculating the stator electromotive force correction value based on the stator flux estimation error using a proportional-integral controller in step two is as follows: ， In the formula This is the correction value for the stator electromotive force along the α-axis. The proportional gain of the α-axis proportional-integral controller. The integral gain of the α-axis proportional-integral controller; This is the correction value for the β-axis stator electromotive force. The proportional gain of the β-axis proportional-integral controller. The integral gain of the β-axis proportional-integral controller; For the α-axis stator flux linkage estimation error, This represents the estimation error of the stator flux linkage along the β-axis. The method for obtaining the corrected stator electromotive force in step two is as follows: ， In the formula This is the corrected α-axis stator electromotive force. This is the corrected β-axis stator electromotive force; The α-axis stator electromotive force is based on the voltage model. The β-axis stator electromotive force is based on the voltage model; In step three, the α-axis and β-axis control laws of the second-order generalized integrator with the limit cycle oscillator are the same. The α-axis control law is: ， In the formula To estimate the center frequency, for and The difference, This is the algorithm gain coefficient. The α-axis stator electromotive force is the filtered output of the second-order generalized integrator. For orthogonal components, Let be the radius of convergence of the limiting cycle. For complex variables, This refers to the gain coefficient of the frequency-locked loop; The calculation method for estimating the stator flux linkage using the corrected α-axis voltage model in step three is as follows: ， In the formula To estimate the stator flux linkage for the corrected α-axis voltage model; The calculation method for estimating the stator flux linkage using the corrected β-axis voltage model in step three is as follows: The β-axis control law of a second-order generalized integrator with a limit cycle oscillator is: ， for and The difference, For the filtered output of the second-order generalized integrator Shaft stator electromotive force; Then after correction Shaft voltage model for estimating stator flux for: 。 2. The method for observing the flux linkage of a permanent magnet synchronous motor based on a limit cycle oscillator according to claim 1, characterized in that, In step one, the voltage model of the two-phase stationary shaft system of the permanent magnet synchronous motor is as follows: ， In the formula For the α-axis stator flux linkage based on the voltage model, For the β-axis stator flux linkage based on the voltage model, The stator voltage along the α-axis. This is the β-axis stator voltage. For the α-axis stator current, R is the β-axis stator current. s This is the stator resistance.

3. The method for observing the flux linkage of a permanent magnet synchronous motor based on a limit cycle oscillator according to claim 2, characterized in that, In step one, the method for estimating the stator flux linkage of the permanent magnet synchronous motor using the current model is as follows: Calculate the stator flux linkage in a two-phase rotating coordinate system: ， In the formula For the d-axis stator flux linkage, For q-axis stator flux linkage, For permanent magnet flux linkage, L d For the d-axis inductance, L q It is the q-axis inductance. The stator current is the d-axis current. This refers to the q-axis stator current. d-axis stator flux and q-axis stator flux Performing the iPark transformation yields the α-axis stator flux linkage based on the current model. and β-axis stator flux based on current model : ， In the formula The electric angle is the motor angle.

4. The method for observing the flux linkage of a permanent magnet synchronous motor based on a limit cycle oscillator according to claim 3, characterized in that, The stator flux estimation error in step one is: 。 5. The method for observing the flux linkage of a permanent magnet synchronous motor based on a limit cycle oscillator according to claim 4, characterized in that, The method for estimating the stator electromotive force using the voltage model in step two is as follows: 。

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