Nonlinear flux linkage observation method and system based on virtual injection of stator resistance

Abstract

The application discloses a kind of nonlinear flux linkage observation method and system based on stator resistance virtual injection, including the establishment of surface-mounted permanent magnet synchronous motor electrical dynamic equation and traditional nonlinear flux linkage observer equation, introduce virtual sine signal, replace stator resistance in traditional nonlinear flux linkage observer equation with time-varying equivalent resistance, construct with virtual injection's non-autonomous error dynamics equation, convert periodic high-frequency time-varying term into equivalent damping term in averaged autonomous error dynamics model, further obtain globally asymptotically stable nonlinear flux linkage observer, realize closed-loop vector control of position sensorless motor.

Description

Technical Field

[0001] This invention relates to the field of motor control technology, specifically to a nonlinear flux linkage observation method and system based on stator resistance virtual injection. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) are widely used in electric vehicles, renewable energy systems, robotics, industrial automation, home appliances, aerospace, and other fields due to their high efficiency, high torque density, high power density, ease of maintenance, and excellent performance. High-performance PMSM drive systems require rotor position information. This information is typically obtained through rotor position sensors, such as Hall effect sensors, encoders, and resolvers. However, using sensors increases system size and reduces reliability in harsh environments. Sensorless control technology addresses these issues while reducing system costs, thus attracting widespread attention.

[0003] Sensorless algorithms for permanent magnet synchronous motors are mainly divided into the salient pole effect method (physical signal injection method) and the basic model method. The salient pole effect method extracts the rotor position by injecting a high-frequency voltage signal into the motor, and performs well at zero and low speeds. However, this method is only suitable for motors with obvious salient poles. At the same time, the injection of physical signals will cause significant acoustic noise and torque ripple, which limits its application in applications with low noise requirements.

[0004] Nonlinear flux observers (NFOs), as an advanced fundamental modeling method that does not rely on the precise salient pole effect of the motor, rely on the motor voltage and current model to estimate the rotor flux in real time, thereby extracting position information. Compared to physical signal injection methods, NFOs do not require applying actual high-frequency voltage signals to the motor, thus effectively avoiding acoustic noise and torque ripple, and exhibiting excellent control performance in the medium and high speed domains. However, at extremely low or zero speeds, due to the extremely weak back electromotive force of the motor, traditional NFOs face a severe lack of excitation information, causing the system to be easily limited by an undesirable internal equilibrium point, resulting in complete failure of low-speed position estimation. To achieve the commercialization of sensorless operation across the entire speed domain, improving the stability of NFOs in the zero-low speed domain is essential.

[0005] Virtual injection technology, as an innovative excitation method, focuses on introducing sinusoidal signals only within the software model of the control algorithm (such as in the observer parameters), without applying any physical disturbances to the controlled motor itself. This method not only relies on the weak back EMF information at low speeds but also causes the aforementioned undesired equilibrium point to collapse through software-level signal injection, thereby eliminating the unobservable region at extremely low speeds and restoring the system's observability. Combining virtual injection technology with nonlinear flux observers in the control of surface-mounted permanent magnet synchronous motors can improve the global stability of the motor at extremely low speeds or even zero speeds without significantly increasing system physical noise and torque ripple. Summary of the Invention

[0006] In order to overcome the above-mentioned shortcomings and deficiencies of the prior art, the purpose of this invention is to provide a nonlinear flux linkage observation method and system for surface-mounted permanent magnet synchronous motors based on stator resistance virtual injection.

[0007] This invention addresses the problem that traditional nonlinear flux linkage observers diverge at extremely low speeds due to weak back electromotive force, causing the system to fall into an undesirable equilibrium point. It also overcomes the noise caused by traditional physical high-frequency signal injection methods, enabling highly stable sensorless control of surface-mounted permanent magnet synchronous motors (SPMSMs) under extremely low or even zero-speed conditions.

[0008] The objective of this invention is achieved through the following technical solution:

[0009] A nonlinear flux linkage observation method based on stator resistance virtual injection includes the following steps:

[0010] Establishing a surface-mounted permanent magnet synchronous motor at two-phase stationary conditions The electrical dynamic equations in the coordinate system are used to construct the traditional nonlinear flux observer equations for estimating stator flux based on the electrical dynamic equations.

[0011] Introducing a virtual sinusoidal signal reduces the stator resistance in the traditional nonlinear flux observer equation. Replace with time-varying equivalent resistance A non-autonomous error dynamic equation with virtual injection is constructed, where n is the virtual resistance injection amplitude. The virtual injection angular frequency is t, where t is time.

[0012] Based on the first-order averaging theorem, the non-autonomous error dynamic equation is subjected to nonlinear coordinate transformation, time scale normalization, and first-order averaging, transforming the periodic high-frequency time-varying terms into equivalent damping terms in the averaged autonomous error dynamic model.

[0013] By adjusting the virtual resistance injection amplitude, the equivalent jitter amplitude reaches the critical condition determined by the equilibrium point equation, thereby causing the undesired equilibrium point in the averaged autonomous error dynamics model to undergo saddle bifurcation and disappear, resulting in a globally asymptotically stable nonlinear flux observer.

[0014] The estimated stator flux is based on the output of the globally asymptotically stable nonlinear flux observer. Subtract stator inductance flux The estimated rotor flux linkage is obtained. The estimated rotor electric angular velocity and rotor electric angular position are extracted by PLL, and finally closed-loop vector control of the sensorless motor is realized.

[0015] Furthermore, the surface-mounted permanent magnet synchronous motor is established when both phases are stationary. The electrical dynamic equations in the coordinate system are presented, and based on these equations, a traditional nonlinear flux observer equation for estimating stator flux is constructed, specifically as follows:

[0016] At rest in two phases In the coordinate system, establish the electrical dynamic equations of SPMSM;

[0017] Define the stator flux linkage vector as Utilizing the rotor permanent magnet flux linkage vector The amplitude is constant Based on the characteristics of the gradient descent method, a traditional nonlinear flux observer equation is constructed.

[0018] Furthermore, the introduction of a virtual sinusoidal signal reduces the stator resistance in the traditional nonlinear flux linkage observer equation. Replace with time-varying equivalent resistance Construct a non-autonomous error dynamic equation with virtual injection, specifically as follows:

[0019] To address the problem of observation failure caused by the weak back electromotive force at extremely low speeds, the stator resistance in the traditional nonlinear flux linkage observer equation is reduced. Replace with time-varying equivalent resistance ;

[0020] Define the state observation error, subtract the electrical dynamic equations of SPMSM from the nonlinear flux observer equations after introducing the virtual sinusoidal injection term, and establish the non-autonomous error dynamic equations with virtual sinusoidal injection.

[0021] Furthermore, based on the first-order averaging theorem, the non-autonomous error dynamic equation is subjected to nonlinear coordinate transformation, time-scale normalization, and first-order averaging, transforming the periodic high-frequency time-varying terms into equivalent damping terms in the averaging model, specifically:

[0022] To eliminate the explicit dependence of the rotor's electrical angular position in the physical error differential equations, a nonlinear coordinate transformation involving rotation and scaling is introduced, defining the rotation-scaling coordinate transformation. and the transformed state variables Differentiating with respect to time t, and using the derivative property of the rotation matrix, we obtain:

[0023]

[0024] in, This represents the number of pole pairs of the motor. This refers to the rotor's mechanical angular velocity;

[0025] Substituting the non-autonomous error dynamics equation into the above equation, under the magnetic field orientation control framework, the following is adopted: The SPMSM of the control strategy satisfies the Park transformation relation. The error dynamic equation in matrix form is obtained, and it can be seen that the virtual sinusoidal injection is directly coupled to the quadrature axis current after coordinate transformation.

[0026] Substituting the time transformation law into the matrix form of the error dynamic equation and eliminating the constant coefficients, we obtain the dimensionless non-autonomous error dynamic equation system.

[0027] Since the non-autonomous error dynamics equation with virtual sinusoidal injection has high-frequency time-varying terms, based on the first-order averaging theorem, the non-autonomous error dynamics equation is transformed into an equivalent averaged autonomous error dynamics model.

[0028] Furthermore, the non-autonomous error dynamics equation is transformed into an equivalent averaged autonomous error dynamics model, specifically:

[0029] Define averaged coordinate variables Perform the transformation, where , A is the equivalent jitter amplitude, a fast time variable. According to the first-order averaging theorem, for sufficiently small perturbation parameters... By solving for the average vector field over one period, the non-autonomous error dynamics equation is transformed into an equivalent averaged autonomous error dynamics model:

[0030]

[0031] Among them, the average nonlinear term Supplementary items Corresponding to the equivalent damping provided by virtual injection, it can suppress error divergence.

[0032] Furthermore, by adjusting the injection amplitude of the virtual resistor, the equivalent jitter amplitude reaches the critical condition determined by the equilibrium point equation, thereby causing the undesired equilibrium point in the averaged autonomous error dynamic model to undergo saddle bifurcation and disappear, thus obtaining a globally asymptotically stable nonlinear flux observer. Specifically, this involves establishing a mapping relationship between the equivalent jitter amplitude and physical quantities, and adjusting the virtual injection parameters to trigger saddle bifurcation.

[0033] Furthermore, a mapping relationship between the equivalent jitter amplitude and physical quantities is established, and the virtual injection parameters are adjusted to trigger saddle-node bifurcation. The specific steps are as follows:

[0034] By setting the derivative of the averaged autonomous error dynamic model to zero and introducing scalar parameters for dimensionality reduction, a univariate algebraic equation that determines the system equilibrium point is derived.

[0035] Establish an explicit analytical relationship between the equivalent jitter amplitude and the actual control variables of the system, combined with first-order averaging of small parameters. The physical mapping expression for the equivalent jitter amplitude is derived.

[0036] Based on the current operating speed and quadrature-axis current of the motor, adaptive parameter design and dynamic adjustment are performed to obtain a globally asymptotically stable nonlinear flux observer.

[0037] Furthermore, based on the current operating speed and quadrature-axis current of the motor, adaptive parameter design and dynamic adjustment are performed, specifically as follows:

[0038] First, to ensure the strict validity of the first-order averaging theorem and the dynamic bandwidth of the system, the angular frequency is injected. The selection is at least higher than the observer's cutoff frequency. 10 times higher;

[0039] Secondly, when the motor is in extremely low speed operation When the equivalent jitter amplitude A increases to the threshold, the undesired equilibrium point in the averaged autonomous error dynamics model undergoes a saddle bifurcation and disappears, leaving only the unique global asymptotically stable equilibrium point that makes the error system retain only the zero estimation error.

[0040] Finally, based on the formula To maintain the equivalent jitter amplitude A greater than the threshold condition required to trigger equilibrium point collapse, under load start-up conditions, due to the quadrature axis current amplitude... As the amplitude of the virtual disturbance injection n increases, the required amplitude n is dynamically reduced proportionally, thereby minimizing internal disturbances while maintaining global stable convergence.

[0041] Furthermore, based on the estimated stator flux output by the globally asymptotically stable nonlinear flux observer... Subtract stator inductance flux The estimated rotor flux linkage is obtained. The estimated rotor electrical angular velocity and rotor electrical angular position are extracted using a PLL, specifically:

[0042] Obtain the estimated rotor flux linkage that is globally stable and convergent;

[0043] Construct the PLL phase error function and obtain the estimated electric angular velocity through a proportional-integral controller. and rotor position Ultimately, sensorless vector control of the surface-mounted permanent magnet synchronous motor was achieved.

[0044] A system for implementing the aforementioned nonlinear flux linkage observation method includes a speed controller, a PI controller, a PLL, and a nonlinear flux linkage observer, wherein the virtual sine signal is injected into the nonlinear flux linkage observer.

[0045] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0046] 1. By employing a method of injecting a large-scale virtual disturbance under extremely low-speed conditions, it brings the advantages of completely eliminating the unobservable region at extremely low speeds and achieving stable zero-speed start-up of the motor.

[0047] When the motor is at extremely low speed or zero speed, injecting a virtual sine signal with a large amplitude can directly cause the undesired equilibrium point of the system to collapse, breaking the dead zone limitation from the bottom layer and ensuring the global stable convergence of the observer when the back EMF is extremely weak.

[0048] 2. By adopting the method of adaptively reducing the virtual injection amplitude under low-speed conditions, it brings the advantages of balancing observation stability and driving smoothness.

[0049] As the motor speed gradually increases, the excitation effect of the back electromotive force begins to recover. At this time, the amplitude of the virtual injection is adaptively reduced, which can maintain the system's unique stable equilibrium point and significantly reduce parameter fluctuations on the control algorithm side, thereby improving the quality of the full-speed domain transition.

[0050] 3. By adopting the method of dynamically reducing the virtual injection amplitude under load conditions, it brings the advantage of excellent performance in extremely low-speed heavy-load operation.

[0051] Based on the characteristic that the equivalent jitter amplitude of the system is proportional to the quadrature-axis current, the heavier the motor load, the smaller the required virtual injection amount. This not only overcomes the defect of traditional physical injection methods being prone to failure under heavy loads, but also optimizes the dynamic response and anti-interference capability of the system during load startup to the greatest extent. Attached Figure Description

[0052] Figure 1 This is a structural block diagram of the present invention;

[0053] Figure 2 This is a schematic diagram of the operating waveform of the present invention when the motor is running at full load at 2.67Hz. Specifically, under the nonlinear flux observer with an initial virtual injection frequency of 20Hz and an injection amplitude of 0.4, the load is gradually increased to the rated load, the injection amplitude gradually decreases, and the system remains stable throughout.

[0054] Figure 3 This is a schematic diagram showing that the motor of the present invention operates under a 2.67Hz conventional nonlinear flux linkage observer, and the system diverges after 0.1 times the rated load, with a maximum error angle of -93.6°.

[0055] Figure 4 This is the operating waveform of the motor of the present invention under a sudden load condition of 2Hz, specifically with an initial virtual injection frequency of 7Hz and an injection amplitude of 2.0. A schematic diagram showing the system remaining stable after instantaneous loading and unloading under a nonlinear flux linkage observer.

[0056] Figure 5 This is a waveform diagram of the motor of the present invention operating under a narrow load condition with a 2Hz conventional nonlinear flux observer. Detailed Implementation

[0057] The present invention will be further described in detail below with reference to the embodiments, but the implementation of the present invention is not limited thereto.

[0058] Example

[0059] like Figures 1-5 As shown, a nonlinear flux linkage observation method for surface-mounted permanent magnet synchronous motors based on stator resistance virtual injection includes the following steps:

[0060] S1 establishes the electrical dynamic equations and traditional nonlinear flux linkage observer equations for the surface-mounted permanent magnet synchronous motor, as follows:

[0061] S1.1: At rest in both phases In the coordinate system, establish the electrical dynamic equations of the SPMSM:

[0062] (1)

[0063] in, and These represent the stator voltage and current vectors, respectively; For stator resistance, For stator inductance, The magnitude of the permanent magnet flux linkage; the rotation vector containing position information is defined as... ,in It is a standard antisymmetric matrix.

[0064] S1.2 Define the stator flux linkage vector as Utilizing the rotor permanent magnet flux linkage vector The amplitude is constant Based on the characteristics of the gradient descent method, we construct the equations for a traditional nonlinear flux linkage observer:

[0065]

[0066] in, For the estimated stator flux linkage, This is the observer gain.

[0067] S2 introduces a virtual sinusoidal signal, reducing the stator resistance in the traditional nonlinear flux observer equation. Replace with time-varying equivalent resistance Construct a non-autonomous error dynamic equation with virtual injection, specifically as follows:

[0068] S2.1 addresses the issue of observation failure caused by weak back EMF at extremely low speeds by incorporating the stator resistance in the observer model within the control algorithm. Replace with time-varying equivalent resistance Where n is the virtual resistance injection amplitude, This is a virtual injection of angular frequency.

[0069] S2.2 Define the state observation error as The permanent magnet synchronous motor shown in equation (1) is stationary in two phases. Electrical equations in coordinate system and stator resistance Replace with time-varying equivalent resistance The following formula By subtracting the nonlinear flux linkage observer shown, we obtain the non-autonomous error dynamic equation with virtual sinusoidal injection:

[0070]

[0071] In equation (3), n is the virtual resistance injection amplitude. This is a virtual injection of angular frequency.

[0072] S3 applies a nonlinear coordinate transformation, time-scale normalization, and first-order averaging to the non-autonomous error dynamics equation based on the first-order averaging theorem. The periodic high-frequency time-varying terms are transformed into equivalent damping terms in the averaging model, including the following steps:

[0073] S3.1 To eliminate the physical error in the differential equation regarding the rotor's electrical angular position The explicit dependency introduces nonlinear coordinate transformations involving rotation and scaling. For state variables Taking the derivative with respect to time t, and using the derivative property of the rotation matrix, we can obtain:

[0074]

[0075] in, This represents the number of pole pairs of the motor. ω is the rotor mechanical angular velocity.

[0076] S3.2 The formula (3) in Substitute the expression into the above formula. Under the Field Direction Control (FOC) framework, adopt... The SPMSM of the control strategy satisfies the Park transformation relation. By further combining algebraic relationships, the error dynamic equation in matrix form can be derived:

[0077]

[0078] The core nonlinear term is defined as follows: , It is a second-order identity matrix. Therefore, it can be seen that the virtual sinusoidal injection, after coordinate transformation, is directly coupled to the quadrature-axis current. superior.

[0079] S3.3 To further simplify system parameters, a dimensionless slow time scale s is introduced, and the time step is defined as mapped as follows: and normalized speed Substituting the time transformation law into the matrix equation and eliminating the constant coefficients, we obtain the dimensionless non-autonomous error dynamics equations:

[0080]

[0081] Among them, the high-frequency injection gain is equivalently parameterized as Normalized injection frequency is defined as .

[0082] S3.4: Due to the presence of high-frequency injection terms, define an averaged coordinate variable. Perform the transformation, where , A is the equivalent jitter amplitude, a fast time variable. According to the first-order averaging theorem, for sufficiently small perturbation parameters... By solving for the average vector field over one period, the non-autonomous error dynamics equation is transformed into an equivalent averaged autonomous error dynamics model:

[0083] According to the first-order averaging theorem, for sufficiently small perturbation parameters, the non-autonomous error dynamics equations can be transformed into an equivalent averaged autonomous error dynamics model by solving for the average vector field over one period.

[0084]

[0085] Among them, the average nonlinear term Supplementary items Corresponding to the equivalent damping provided by virtual injection, this term can suppress error divergence.

[0086] S4 adjusts the virtual resistance injection amplitude n so that the equivalent jitter amplitude A reaches the critical condition determined by the equilibrium point equation, thereby causing the undesired equilibrium point in the averaged autonomous error dynamics model to undergo saddle bifurcation and disappear, resulting in a globally asymptotically stable nonlinear flux observer.

[0087] Specifically, the steps include the following:

[0088] S4.1: Set the derivative of the averaged autonomous error dynamics model in S3.4 to zero, and introduce scalar parameters. By reducing the dimensionality, we derive the univariate algebraic equation that determines the system's equilibrium point:

[0089]

[0090] S4.2: Establish an explicit analytical relationship between the equivalent jitter amplitude A and the actual control variables of the system. Combining the first-order averaged small parameter, the physical mapping expression for the equivalent jitter amplitude A can be derived as follows:

[0091] (9)

[0092] S4.3: Based on the current operating speed and quadrature-axis current of the motor, perform adaptive parameter design and dynamic adjustment: First, to ensure the strict validity of the first-order averaging theorem and the dynamic bandwidth of the system, inject angular frequency. The selection is at least higher than the observer's cutoff frequency. 10 times higher; secondly, when the motor is in extremely low-speed operation. As the equivalent jitter amplitude A increases to the threshold, the discriminant sign of the core polynomial equation flips, and the undesirable equilibrium point in the averaged autonomous error dynamics model undergoes a saddle-node bifurcation and disappears, leaving the error system with only a unique globally asymptotically stable equilibrium point corresponding to the zero estimation error; finally, based on the formula... To maintain A above the threshold condition required to trigger equilibrium point collapse, under load start-up conditions, due to the amplitude of the quadrature-axis current... As the amplitude of the virtual perturbation injection n increases, the required amplitude of n is dynamically reduced proportionally, thereby minimizing the internal perturbation of the algorithm while maintaining global stable convergence.

[0093] S5. Estimated stator flux based on the output of the globally asymptotically stable nonlinear flux observer. Subtract stator inductance flux The estimated rotor flux linkage is obtained. The estimated rotor electric angular velocity and rotor position are extracted through PLL, ultimately realizing closed-loop vector control of the sensorless motor.

[0094] S5.1: Obtain the estimated rotor flux that is globally stable and convergent .

[0095] S5.2: Constructing the PLL phase error function The estimated electric angular velocity is obtained through a proportional-integral (PI) controller. and rotor position Ultimately, full-speed-domain sensorless closed-loop vector control of the surface-mounted permanent magnet synchronous motor was achieved.

[0096] Based on the above, the nonlinear flux observation method for surface-mounted permanent magnet synchronous motors based on stator resistance virtual disturbance in this embodiment is beneficial to completely eliminate the extremely low-speed unobservable region of traditional methods from the bottom topology without generating physical noise and additional torque pulsation, and to achieve global stable observation under zero-speed heavy-load conditions.

[0097] This embodiment further illustrates the nonlinear flux linkage observation method for surface-mounted permanent magnet synchronous motors based on stator resistance virtual injection proposed in this invention. The following detailed description, in conjunction with the accompanying drawings, outlines the structure of the sensorless control system built based on this method and the experimental results. Figure 1 As shown, this embodiment constructs a sensorless closed-loop vector control system for a surface-mounted permanent magnet synchronous motor based on a virtual resistance injection nonlinear flux linkage observer. By introducing a virtual sine injection term into the traditional nonlinear flux linkage observer, the stability of the flux linkage observation error dynamic system under extremely low-speed conditions is improved. Figures 2-5 The operating results of the method of this invention and the traditional nonlinear flux linkage observation method under low-speed gradual load and low-speed sudden load conditions are presented respectively, which are used to verify the stability of flux linkage estimation and rotor position tracking capability of the method of this invention under extremely low-speed load conditions.

[0098] like Figure 1As shown, this embodiment adopts a sensorless closed-loop vector control structure for a surface-mounted permanent magnet synchronous motor based on stator resistance virtual injection. It mainly includes a speed controller, a PI controller, a PLL (phase-locked loop), a nonlinear flux observer, a space vector pulse width modulation module (SVPWM), and a surface-mounted permanent magnet synchronous motor.

[0099] The working process of this method is as follows: given a target speed, the output is obtained through PID control in the speed loop and current loop, and inverse Park transformation. and The dead-time compensation signal is superimposed and then modulated by SVPWM to drive the motor. After the current sampling module samples the phase current of the motor, it undergoes Clarke transformation and is sent along with the voltage command to a nonlinear flux linkage observer superimposed with virtual injection to calculate the rotor flux linkage vector. Finally, the PLL extracts the estimated electrical angle and rotational speed and feeds them back to the control backbone to achieve complete sensorless FOC closed-loop control.

[0100] like Figure 2 As shown, when the motor operates at an electrical frequency of 2.67 Hz, the virtual injection nonlinear flux linkage observation method of this invention is used to gradually load the motor to its rated load, and then gradually unload it. In the initial stage of the experiment, the virtual resistance injection amplitude n is set to 0.4. As the load increases, the quadrature axis current... As the current gradually increases, the amplitude of the virtual resistance injection, n, decreases proportionally to the current quadrature-axis current, with a minimum value of approximately 0.05. When the load decreases, the quadrature axis current... As the voltage decreases, the amplitude of the virtual resistance injection, n, increases accordingly. During the entire loading and unloading process, the rotor electrical angular position is estimated. Capable of continuously tracking the rotor electrical angular position measured by the encoder No continuous increase or loss of synchronization in angle estimation was observed. These experimental results demonstrate that the method of this invention can maintain stable rotor flux linkage and rotor position estimation under extremely low-speed, gradually changing load conditions, while simultaneously reducing the virtual resistance injection amplitude according to the load current.

[0101] To further explain, Figure 2 middle For encoder angle, For the nonlinear flux observer angle, The difference between the two is the error. is the q-axis current, and n is the virtual injection amplitude.

[0102] like Figure 3As shown, a load test was conducted using the traditional nonlinear flux linkage observation method without virtual resistance injection when the motor operated at an electrical frequency of 2.67 Hz. After the load increased, the back EMF excitation was weak under extremely low-speed conditions, making it difficult to estimate the rotor electrical angle position. Gradually deviating from the rotor electrical angular position measured by the encoder Rotor electrical angular position error It continued to increase and reached -93.6°. Simultaneously, the rotor flux was estimated. Axial components The waveform divergence indicates that the traditional nonlinear flux observer is experiencing instability in flux and rotor position observation. Figure 3 The results show that, without the introduction of virtual resistance injection, the traditional nonlinear flux observer may be affected by the undesired equilibrium point under extremely low speed and load conditions, making it difficult to maintain stable rotor flux and rotor position estimation.

[0103] like Figure 4 As shown, when the motor operates at an electrical frequency of 2Hz, the virtual injection nonlinear flux linkage observation method of this invention is used to conduct sudden load and unload experiments. The initial frequency of the virtual injection signal is set to 7Hz, and the initial value of the virtual resistance injection amplitude is set to 2. And based on the motor speed and quadrature axis current Dynamic adjustment is performed. When a sudden change in load occurs, the quadrature-axis current... The rotor electrical angular position is estimated by the corresponding step change that occurs with the load variation. A short-term dynamic deviation occurs, but the encoder rotor electrical angular position is still maintained. Tracking, rotor electrical angular position error No sustained divergence was observed. After the load change ended, the estimated rotor electrical angle position re-entered a stable tracking state. These experimental results demonstrate that the method of this invention can improve the dynamic stability of the nonlinear flux observer under extremely low-speed, abrupt load conditions.

[0104] like Figure 5 As shown, a sudden load test was conducted using the traditional nonlinear flux linkage observation method without virtual resistance injection when the motor was operating at an electrical frequency of 2Hz. After the load change, the rotor electrical angle position was estimated. Gradually deviating from the rotor electrical angular position measured by the encoder Rotor electrical angular position error Significantly increased, estimated rotor flux linkage Axial components The amplitude and phase divergence ultimately led to instability in the rotor position observation. Figure 4 and Figure 5A comparison shows that, under the same extremely low-speed abrupt load conditions, traditional nonlinear flux linkage observers may experience instability in flux linkage and rotor position estimation. However, the method of this invention improves the stability of flux linkage observation and the adaptability to load disturbances under extremely low-speed abrupt load conditions by introducing a time-varying virtual resistance term inside the observer.

[0105] Those skilled in the art will readily understand that the above description is merely an embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A nonlinear flux linkage observation method based on stator resistance virtual injection, characterized in that, Includes the following steps: Establishing a surface-mounted permanent magnet synchronous motor at two-phase stationary conditions The electrical dynamic equations in the coordinate system are used to construct the traditional nonlinear flux observer equations for estimating stator flux based on the electrical dynamic equations. Introducing a virtual sinusoidal signal reduces the stator resistance in the traditional nonlinear flux observer equation. Replace with time-varying equivalent resistance A non-autonomous error dynamic equation with virtual injection is constructed, where n is the virtual resistance injection amplitude. The virtual injection angular frequency is t, where t is time. The non-autonomous error dynamics equation is subjected to nonlinear coordinate transformation, time scale normalization, and first-order averaging to transform the periodic high-frequency time-varying terms into equivalent damping terms in the averaged autonomous error dynamics model. By adjusting the virtual resistance injection amplitude, the equivalent jitter amplitude reaches the critical condition determined by the equilibrium point equation, thereby causing the undesired equilibrium point in the averaged autonomous error dynamics model to undergo saddle bifurcation and disappear, resulting in a globally asymptotically stable nonlinear flux observer. The estimated stator flux is based on the output of the globally asymptotically stable nonlinear flux observer. Subtract stator inductance flux The estimated rotor flux linkage is obtained. The estimated rotor electric angular velocity and rotor electric angular position are extracted by PLL, and finally closed-loop vector control of the sensorless motor is realized.

2. The nonlinear flux linkage observation method according to claim 1, characterized in that, The surface-mounted permanent magnet synchronous motor is established when both phases are stationary. The electrical dynamic equations in the coordinate system are presented, and based on these equations, a traditional nonlinear flux observer equation for estimating stator flux is constructed, specifically as follows: At rest in two phases In the coordinate system, establish the electrical dynamic equations of SPMSM; Define the stator flux linkage vector as Utilizing the rotor permanent magnet flux linkage vector The amplitude is constant Based on the characteristics of the gradient descent method, a traditional nonlinear flux observer equation is constructed.

3. The nonlinear flux linkage observation method according to claim 2, characterized in that, The introduction of a virtual sinusoidal signal reduces the stator resistance in the traditional nonlinear flux observer equation. Replace with time-varying equivalent resistance Construct a non-autonomous error dynamic equation with virtual injection, specifically as follows: To address the problem of observation failure caused by the weak back electromotive force at extremely low speeds, the stator resistance in the traditional nonlinear flux linkage observer equation is reduced. Replace with time-varying equivalent resistance ; Define the state observation error, subtract the electrical dynamic equations of SPMSM from the nonlinear flux observer equations after introducing the virtual sinusoidal injection term, and establish the non-autonomous error dynamic equations with virtual sinusoidal injection.

4. The nonlinear flux linkage observation method according to claim 1, characterized in that, The non-autonomous error dynamic equations are subjected to nonlinear coordinate transformation, time-scale normalization, and first-order averaging to transform the periodic high-frequency time-varying terms into equivalent damping terms in the averaged autonomous error dynamic model, specifically: To eliminate the explicit dependence of the rotor's electrical angular position in the physical error differential equations, a nonlinear coordinate transformation involving rotation and scaling is introduced, defining the rotation-scaling coordinate transformation. and the transformed state variables Differentiating with respect to time t, and using the derivative property of the rotation matrix, we obtain: in, This represents the number of pole pairs of the motor. This refers to the rotor's mechanical angular velocity; Substituting the non-autonomous error dynamics equation into the above equation, under the magnetic field orientation control framework, the following is adopted: The SPMSM of the control strategy satisfies the Park transformation relation. The error dynamic equation in matrix form is obtained, and it can be seen that the virtual sinusoidal injection is directly coupled to the quadrature axis current after coordinate transformation. Substituting the time transformation law into the matrix form of the error dynamic equation and eliminating the constant coefficients, we obtain the dimensionless non-autonomous error dynamic equation system. Since the non-autonomous error dynamics equation with virtual sinusoidal injection has high-frequency time-varying terms, based on the first-order averaging theorem, the non-autonomous error dynamics equation is transformed into an equivalent averaged autonomous error dynamics model.

5. The nonlinear flux linkage observation method according to claim 4, characterized in that, The non-autonomous error dynamics equation is transformed into an equivalent averaged autonomous error dynamics model, specifically as follows: Define averaged coordinate variables Perform the transformation, where , A is the equivalent jitter amplitude, a fast-time variable. According to the first-order averaging theorem, for sufficiently small perturbation parameters... By solving for the average vector field over one period, the non-autonomous error dynamics equation is transformed into an equivalent averaged autonomous error dynamics model: Among them, the average nonlinear term Supplementary items Corresponding to the equivalent damping provided by virtual injection, it can suppress error divergence.

6. The nonlinear flux linkage observation method according to claim 1, characterized in that, The process involves adjusting the injection amplitude of the virtual resistor to make the equivalent jitter amplitude reach the critical condition determined by the equilibrium point equation, thereby causing the undesired equilibrium point in the averaged autonomous error dynamics model to undergo saddle bifurcation and disappear, resulting in a globally asymptotically stable nonlinear flux observer. Specifically, this involves establishing a mapping relationship between the equivalent jitter amplitude and physical quantities, and adjusting the virtual injection parameters to trigger saddle bifurcation.

7. The nonlinear flux linkage observation method according to claim 6, characterized in that, Establish the mapping relationship between equivalent jitter amplitude and physical quantity, and adjust the virtual injection parameters to trigger saddle node bifurcation. The specific steps are as follows: By setting the derivative of the averaged autonomous error dynamic model to zero and introducing scalar parameters for dimensionality reduction, a univariate algebraic equation that determines the system equilibrium point is derived. Establish an explicit analytical relationship between the equivalent jitter amplitude and the actual control variables of the system, combined with first-order averaging of small parameters. The physical mapping expression for the equivalent jitter amplitude is derived. Based on the current operating speed and quadrature-axis current of the motor, adaptive parameter design and dynamic adjustment are performed to obtain a globally asymptotically stable nonlinear flux observer.

8. The nonlinear flux linkage observation method according to claim 7, characterized in that, Based on the current operating speed and quadrature-axis current of the motor, adaptive parameter design and dynamic adjustment are performed, specifically as follows: First, to ensure the strict validity of the first-order averaging theorem and the dynamic bandwidth of the system, the angular frequency is injected. The selection is at least higher than the observer's cutoff frequency. 10 times higher; Secondly, when the motor is in extremely low speed operation When the equivalent jitter amplitude A increases to the threshold, the undesired equilibrium point in the averaged autonomous error dynamics model undergoes a saddle bifurcation and disappears, leaving only the unique global asymptotically stable equilibrium point that makes the error system retain only the zero estimation error. Finally, based on the formula To maintain the equivalent jitter amplitude A greater than the threshold condition required to trigger equilibrium point collapse, under load start-up conditions, due to the quadrature axis current amplitude... As the amplitude of the virtual disturbance injection n increases, the required amplitude n is dynamically reduced proportionally, thereby minimizing internal disturbances while maintaining global stable convergence.

9. The nonlinear flux linkage observation method according to claim 1, characterized in that, The estimated stator flux is based on the output of the globally asymptotically stable nonlinear flux observer. Subtract stator inductance flux The estimated rotor flux linkage is obtained. The estimated rotor electrical angular velocity and rotor electrical angular position are extracted using a PLL, specifically: Obtain the estimated rotor flux linkage that is globally stable and convergent; Construct the PLL phase error function and obtain the estimated electric angular velocity through a proportional-integral controller. and rotor position Ultimately, sensorless vector control of the surface-mounted permanent magnet synchronous motor was achieved.

10. A system for implementing the nonlinear flux linkage observation method according to any one of claims 1-9, characterized in that, It includes a speed controller, a PI controller, a PLL, and a nonlinear flux linkage observer, wherein the virtual sine signal is injected into the nonlinear flux linkage observer.

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