Sensorless back electromotive force observation method for permanent magnet synchronous motor

Abstract

The invention belongs to the technical field of motor control, and particularly relates to a sensorless back electromotive force observation method for a permanent magnet synchronous motor. The method comprises the following steps: S1, constructing a linear expansion state observer by taking the back electromotive force of a voltage model of the permanent magnet synchronous motor as an expansion state; s2, introducing an internal model item related to the fundamental frequency of the counter electromotive force into the linear expansion state observer to carry out frequency domain design, and obtaining an initial counter electromotive force observer; and S3, introducing a non-linear adaptive item into the initial back electromotive force observer, constructing a weighting function, activating the non-linear adaptive item by using the weighting function, obtaining a final back electromotive force observer, and realizing observation of the back electromotive force. According to the invention, rotor position observation with high dynamic speed and high steady-state precision can be realized.

Description

Technical Field

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

[0002] Permanent magnet synchronous motors (PMSMs), with their superior efficiency and high power density, have been widely used in electric vehicles, electric ships, and other fields. However, traditional control methods relying on rotor position sensors suffer from drawbacks such as high hardware costs and low reliability in harsh environments like high temperatures, extreme cold, dust, and humidity, severely impacting control accuracy and stability. Traditional sensorless control methods based on linear extended state observers, limited by the finite bandwidth of linear systems, suffer from severe phase lag and poor DC bias suppression. On one hand, the linear extended state observer inevitably introduces phase delay when filtering high-frequency noise, leading to systematic errors in rotor position estimation. On the other hand, pursuing higher dynamic response speeds typically requires increasing the observer bandwidth, but this significantly amplifies measurement noise, resulting in decreased system stability. These drawbacks collectively limit the observation accuracy of traditional linear extended state observers under both steady-state and dynamic conditions. Summary of the Invention

[0003] In view of this, the present invention aims to provide a sensorless back EMF observation method for permanent magnet synchronous motors (PMSMs) to solve the problems of poor reliability and high cost of traditional sensor-based control of PMSMs, and the insufficient observation accuracy and system stability caused by phase lag, weak DC bias suppression, noise amplification, and mutual constraints between dynamic response in traditional linear extended state observers. The present invention can achieve rotor position observation that balances high dynamic speed and high steady-state accuracy.

[0004] To achieve the above objectives, the technical solution created by this invention is implemented as follows: A sensorless back EMF observation method for permanent magnet synchronous motors includes the following steps: S1: Using the back EMF of the voltage model of the permanent magnet synchronous motor as the extended state, construct a linear extended state observer; S2: Introduce an internal mode term related to the fundamental frequency of the back EMF into the linear extended state observer for frequency domain design to obtain the initial back EMF observer; S3: Introduce a nonlinear adaptive term into the initial back potential observer and construct a weight function. Activate the nonlinear adaptive term using the weight function to obtain the final back potential observer and realize the observation of the back potential.

[0005] Furthermore, in step S1, the voltage model of the permanent magnet synchronous motor is: ; in, For differential operators, This is the actual resistance of the stator. For the actual stator inductance, for Stator voltage of a composite shaft system for Stator current of composite shaft system for Back potential of a composite shaft system.

[0006] Furthermore, in step S1, the linearly extended state observer is: ; in, For differential operators, This is an estimate of the current state. For the expansion state estimate, This is the ratio of the estimated stator resistance to the estimated stator inductance. Estimate the resistance of the stator. Estimate the inductance for the stator. and These are the first-term gain and second-term gain of the linearly extended state observer, respectively. It is in the current state. for Stator voltage of a composite shaft system.

[0007] Furthermore, in step S1, the linear expansion state observer estimates the expansion state. To the actual expansion state transfer function for: ; Where s is the Laplace operator, and These are the first-term gain and second-term gain of the linearly extended state observer, respectively. This is the ratio of the actual stator resistance to the actual stator inductance.

[0008] Furthermore, in step S2, the initial back potential observer is: ; in, This is an estimated value for the motor's operating frequency. and These are the first-term gain and second-term gain of the linearly extended state observer, respectively. This is an estimate of the current state. For the expansion state estimate, This is the ratio of the estimated stator resistance to the estimated stator inductance. Estimate the inductance for the stator. for Stator voltage of a composite shaft system It is the extended state derivative The estimated value, For current state error, The derivative of the current state estimate, The derivative of the extended state estimate, It is the second derivative of the extended state estimate.

[0009] Furthermore, by introducing an internal mode term related to the fundamental frequency of the back electromotive force into the linear extended state observer for frequency domain design, the estimated extended state of the linear extended state observer is improved. To the actual expansion state transfer function for: ; in, The operating frequency of the motor. and Let be the first-term gain and the second-term gain of the linearly extended state observer, respectively, and s be the Laplace operator. This is the ratio of the actual stator resistance to the actual stator inductance.

[0010] Furthermore, in step S3, the weighting function is: ; in, For the weight function, Let be the independent variable, and exp be the exponentiation operator. This is the steepness coefficient. , The boundary layer width, .

[0011] Furthermore, in step S3, the final back potential observer is: ; in, The derivative of the current state estimate, The derivative of the extended state estimate, The second derivative of the extended state estimate, To estimate the back electromotive force for the composite shaft system, This is the ratio of the estimated stator resistance to the estimated stator inductance. for Stator voltage of a composite shaft system Estimate the inductance for the stator. This is an estimate of the current state. For the expansion state estimate, and These are the first-term gain and second-term gain of the linearly extended state observer, respectively. For current state error, It is the extended state derivative The estimated value, This is an estimated value for the motor's operating frequency. It is a nonlinear adaptive term. It is the exponent of the nonlinear term. , For symbolic operations, For variables The weighting function.

[0012] Compared with the prior art, the present invention can achieve the following beneficial effects: This invention presents a sensorless back EMF observation method for permanent magnet synchronous motors. It organically integrates the strong nonlinear design of the outer layer with the frequency domain design of the inner layer using a smooth weighting function. The outer layer uses nonlinear terms to improve dynamic performance, effectively overcoming the inherent contradiction between steady-state accuracy and dynamic response speed in traditional linear structures, and avoiding the amplification of measurement noise caused by directly increasing the linear bandwidth. The inner layer, based on a frequency domain design method, tunes the transfer function from the estimated expansion state to the actual expansion state, effectively achieving zero phase lag and zero amplitude attenuation at the operating frequency, and effectively eliminating the DC bias present in the estimated back EMF. In summary, this invention provides a new technical approach for constructing a sensorless control scheme for permanent magnet synchronous motors that combines high dynamic performance and high steady-state observation accuracy. Attached Figure Description

[0013] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 A schematic flowchart of the sensorless back EMF observation method for permanent magnet synchronous motors described in the embodiments of the present invention; Figure 2 A schematic diagram illustrating the principle of the sensorless back EMF observation method for permanent magnet synchronous motors described in the embodiments of the present invention; Figure 3 The experimental results of the conventional linear extended state observer and the back EMF observation method proposed in this invention at a permanent magnet synchronous motor speed of 700 r / min are shown in the embodiments described in this invention; wherein: Figure 3(a) Experimental results of the conventional linear extended state observer described in the embodiment of the present invention at a permanent magnet synchronous motor speed of 700 r / min; Figure 3 (b) Experimental results of the back EMF observation method proposed in this invention under a permanent magnet synchronous motor speed of 700 r / min, as described in the embodiments of this invention; Figure 4 A schematic diagram illustrating the experimental results of the conventional linear extended state observer and the back EMF observation method proposed in this invention at a permanent magnet synchronous motor speed of 1400 r / min, as described in the embodiments of this invention; wherein: Figure 4 (a) Schematic diagram of the experimental results of the conventional linear extended state observer described in the embodiment of the present invention at a permanent magnet synchronous motor speed of 1400 r / min; Figure 4 (b) Schematic diagram of the experimental results of the back EMF observation method proposed in this invention at a speed of 1400 r / min on a permanent magnet synchronous motor, as described in the embodiments of this invention; Figure 5 This is a schematic diagram illustrating the experimental results of the conventional linear extended state observer and the back potential observation method proposed in this invention under dynamic operating conditions, as described in the embodiments of this invention; wherein: Figure 5 (a) Schematic diagram of experimental results of the conventional linear extended state observer described in the embodiment of the present invention under dynamic conditions; Figure 5 (b) Schematic diagram of the experimental results of the back potential observation method proposed in this invention under dynamic operating conditions, as described in the embodiment of this invention. Detailed Implementation

[0014] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and do not constitute a limitation thereof.

[0015] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0016] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0017] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0018] The invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0019] like Figure 1 As shown, this invention proposes a sensorless back EMF observation method for permanent magnet synchronous motors, which specifically includes the following steps: S1: Using the back EMF of the voltage model of the permanent magnet synchronous motor as the extended state, construct a linear extended state observer; S2: Introduce an internal mode term related to the fundamental frequency of the back EMF into the linear extended state observer for frequency domain design to obtain the initial back EMF observer; S3: Introduce a nonlinear adaptive term into the initial back potential observer and construct a weight function. Activate the nonlinear adaptive term using the weight function to obtain the final back potential observer and realize the observation of the back potential.

[0020] It should be noted that this invention, by introducing an internal mode term related to the fundamental frequency of the back EMF for frequency domain design, can effectively eliminate the DC bias component in the estimated back EMF, achieving zero phase lag and zero amplitude attenuation at the operating frequency, thus improving the back EMF observation accuracy under steady-state conditions. At the same time, by introducing a nonlinear adaptive term, the back EMF observation accuracy under dynamic conditions such as sudden changes in motor speed or load disturbances is improved. Furthermore, by designing a weighting function, it is ensured that the nonlinear adaptive term is activated only under dynamic conditions with large errors, effectively avoiding the influence of complex nonlinear terms on the frequency domain design of the internal mode.

[0021] Furthermore, firstly, a voltage model of the permanent magnet synchronous motor is established, and a linear extended state observer is constructed to observe the back EMF. The rotor position and operating frequency information are extracted in real time from the observed back EMF using a phase-locked loop. Secondly, an internal mode term related to the fundamental frequency of the back EMF is introduced into the linear extended state observer, and back EMF observation with zero phase lag and zero amplitude attenuation is achieved through frequency domain design. Finally, based on the frequency domain design, a nonlinear adaptive term is further introduced to overcome the limitation of the fixed bandwidth of the linear system. A weighting function is designed to activate the nonlinear adaptive term to ensure that it does not affect the frequency domain design of the internal mode.

[0022] like Figure 2 As shown, This is a reference operating frequency. yes Composite shaft reference current, The symbol is PI, which stands for Proportional-Integral Controller. The sensorless back EMF observation method for permanent magnet synchronous motors provided by this invention obtains the estimated operating frequency of the rotor from the estimated back EMF through a phase-locked loop. and estimated location , This is the estimated back electromotive force for the composite shaft system.

[0023] In step S1, to construct the observation equation for the back electromotive force, the permanent magnet synchronous motor is first established in... The voltage model of the composite shaft system is as follows: (1.1); In the formula: For differential operators, and These are the actual stator resistance and the actual stator inductance, respectively. for Stator voltage of a composite shaft system for Stator current of composite shaft system for Back EMF of a composite axis system. Considering the back EMF as an expanding state, let the current state... Actual expansion state Then equation (1.1) can be further rewritten as: (1.2); In the formula: For the derivative of the extended state, for Let the current states be respectively and expansion state The estimated value is and The linearly extended state observer is constructed as follows: (1.3); In the formula: represent ,in, It is the estimated resistance of the stator. It is the stator estimated inductance. and These are the first and second term gains of the linearly extended state observer. Let the current state error be... The expansion state error is Combining equations (1.2) and (1.3), we get: (1.4); In the formula: Representative parameter mismatch term, satisfying .

[0024] Neglecting parameter mismatch, the linear extended state observer constructed by equation (1.4) estimates the extended state. To the actual expansion state transfer function This can be expressed as: (1.5); In the formula: s represents the Laplace operator. After obtaining the estimated extended state... After obtaining the real-time value, considering that the fundamental frequency of the back EMF is consistent with the motor's operating frequency, the estimated rotor operating frequency and position information can be obtained through a phase-locked loop. Due to the transfer function... Exhibiting low-pass filtering characteristics, significant amplitude attenuation and phase lag occur at the motor's operating frequency. To address this issue, this invention further incorporates frequency domain design.

[0025] In step S2, based on the linear extended state observer, considering the sinusoidal nature of the back EMF, an internal mode term related to the fundamental frequency of the back EMF is introduced and frequency domain design is performed to convert the extended state derivative. Designed as follows: (1.6); In the formula: It is the operating frequency of the motor. This represents an unmodeled disturbance. The internal mode term is formed. Based on the frequency domain design concept, this invention further designs the initial back EMF observer as follows: (1.7); In the formula: It is the extended state derivative The estimated value, This is an estimated value of the motor's operating frequency. Based on equation (1.7), the estimated expansion state after frequency domain design can be obtained. To the actual expansion state transfer function : (1.8); Frequency domain design capabilities are demonstrated by suppressing DC bias and eliminating phase hysteresis, due to There is a zero point at the origin, for constant offsets ( (This is the DC bias amplitude) Applying the final value theorem, we can obtain: (1.9); In the formula: It estimates the DC bias amplitude. It is a time variable.

[0026] Equation (1.9) shows that the initial back EMF observer provided by this invention can completely eliminate DC bias. Furthermore, at the operating frequency... place ( (Imaginary number), the factors in the denominator of equation (1.8) The transfer function disappears, and it simplifies to an exact unit complex gain. This ensures zero amplitude attenuation at the operating frequency; while at the motor operating frequency... At this point, the phase angle of the transfer function is zero, which means there is no phase delay between the estimated back EMF and the true back EMF. This characteristic directly solves the estimation delay problem commonly found in traditional nonlinear back EMF observers, and this advantage is achieved by introducing an internal mode term that is operationally relevant. This is achieved by using frequency domain design to make the closed-loop transfer function have an ideal frequency response at the target frequency.

[0027] In step S3, the frequency domain design effectively eliminates the DC bias component in the estimated back EMF and achieves observations of zero phase hysteresis and zero amplitude attenuation at the operating frequency. To address the bandwidth limitation problem of traditional linear structures, a nonlinear adaptive term is further introduced based on the frequency domain design. Firstly, a weighting function for activating the nonlinear adaptive function is provided. : (1.10); In the formula: It is the independent variable, and exp represents exponentiation. It's an absolute value operation. This is the steepness coefficient. It is the boundary layer width. The weight function is applied when... Greater than When it is close to 1, Less than The current rapidly decays to zero. Let the current state error... Using as the independent variable, the final back potential observer of this invention is constructed as follows: (1.11); In the formula: It is a nonlinear term. It is the exponent of the nonlinear term, satisfying , This represents symbolic computation. Due to the weight function... Only in the independent variable Greater than It plays a role in time, through reasonable settings The size of the value ensures that the back EMF observer constructed in this invention is activated only under dynamic conditions with large errors. This improves the convergence of the estimated back EMF while effectively avoiding the influence of complex nonlinear terms on the frequency domain design of the inner model, thus maintaining the integrity of the inner frequency domain design.

[0028] Experimental results of a traditional linear extended state observer and the back EMF observation method provided in this embodiment of the invention at a permanent magnet synchronous motor speed of 700 r / min are as follows: Figure 3 As shown, from top to bottom are: shaft and The study includes waveforms of the back EMF estimation, total harmonic distortion (THD) analysis of the back EMF, waveforms of the estimated rotor position and actual position, and waveforms of the estimated position error. It is evident that compared to traditional linear extended state observers, this invention effectively suppresses the DC bias at zero frequency, reducing the total THD from 6.66% to 1.20%, attenuating the fluctuation amplitude from 0.22 rad to only 0.02 rad, and achieving an average estimated position error close to zero, thus achieving excellent observation with zero phase lag and zero amplitude attenuation.

[0029] Experimental results of a traditional linear extended state observer and the back EMF observation method provided in this embodiment of the invention at a permanent magnet synchronous motor speed of 1400 r / min are as follows: Figure 4 As shown, from top to bottom are: shaft and The waveforms of the back EMF estimation, THD analysis of the back EMF, the waveforms of the rotor's estimated and actual positions, and the waveform of the estimated position error are presented. It is evident that compared to traditional linearly extended state observers, this invention effectively suppresses the DC bias at zero frequency, reducing the total THD from 5.37% to 2.32%, decreasing the fluctuation amplitude from 0.06 rad to 0.03 rad, and achieving an average position error close to zero. This demonstrates that even at high speeds, this invention can still achieve excellent observations with zero phase lag and zero amplitude attenuation.

[0030] Experimental results of the traditional linear extended state observer and the back potential observation method provided in this embodiment of the invention under dynamic operating conditions are as follows: Figure 5 As shown, the initial motor speed is 600 r / min, which increases to 1000 r / min at 2 seconds and further increases to 1400 r / min at 4 seconds. From top to bottom, the waveforms are the estimated and actual rotor speeds, the estimated speed error waveform, and the estimated position error waveform. It can be seen that compared to the traditional linear expansion state observer, this invention exhibits significantly smaller maximum speed and position errors in both acceleration phases, and demonstrates near-zero average position error estimation at different steady-state speeds throughout the process, thus improving the position observation accuracy under both dynamic and steady-state conditions.

[0031] It should be understood that the various forms of processes shown above can be used to reorder, add, or delete steps. For example, the steps described in this invention disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this invention can be achieved, and this is not limited herein.

[0032] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A sensorless back EMF observation method for a permanent magnet synchronous motor, characterized in that: Specifically, the steps include the following: S1: Using the back EMF of the voltage model of the permanent magnet synchronous motor as the extended state, construct a linear extended state observer; S2: Introduce an internal mode term related to the fundamental frequency of the back EMF into the linear extended state observer for frequency domain design to obtain the initial back EMF observer; S3: Introduce a nonlinear adaptive term into the initial back potential observer and construct a weight function. Activate the nonlinear adaptive term using the weight function to obtain the final back potential observer and realize the observation of the back potential.

2. The sensorless back EMF observation method for permanent magnet synchronous motors according to claim 1, characterized in that: In step S1, the voltage model of the permanent magnet synchronous motor is: ； in, For differential operators, This is the actual resistance of the stator. For the actual stator inductance, for Stator voltage of a composite shaft system for Stator current of composite shaft system for Back potential of a composite shaft system.

3. The sensorless back EMF observation method for permanent magnet synchronous motors according to claim 1, characterized in that: In step S1, the linearly extended state observer is: ； in, For differential operators, This is an estimate of the current state. For the expansion state estimate, Estimate the resistance of the stator Stator estimated inductance The ratio, Estimate the resistance of the stator. Estimate the inductance for the stator. and These are the first-term gain and second-term gain of the linearly extended state observer, respectively. It is in the current state. for Stator voltage of a composite shaft system.

4. The sensorless back EMF observation method for permanent magnet synchronous motors according to claim 1, characterized in that: In step S1, the linear expansion state observer estimates the expansion state. To the actual expansion state transfer function for: ； Where s is the Laplace operator, and These are the first-term gain and second-term gain of the linearly extended state observer, respectively. This is the ratio of the actual stator resistance to the actual stator inductance.

5. The sensorless back EMF observation method for permanent magnet synchronous motors according to claim 1, characterized in that: In step S2, the initial back potential observer is: ； in, This is an estimated value for the motor's operating frequency. and These are the first-term gain and second-term gain of the linearly extended state observer, respectively. This is an estimate of the current state. For the expansion state estimate, This is the ratio of the estimated stator resistance to the estimated stator inductance. Estimate the inductance for the stator. for Stator voltage of a composite shaft system It is the extended state derivative The estimated value, For current state error, The derivative of the current state estimate, The derivative of the extended state estimate, It is the second derivative of the extended state estimate.

6. The sensorless back EMF observation method for permanent magnet synchronous motors according to claim 1, characterized in that: After introducing an internal mode term related to the fundamental frequency of the back electromotive force into the linear extended state observer for frequency domain design, the estimated extended state of the linear extended state observer is improved. To the actual expansion state transfer function for: ； in, The operating frequency of the motor. and Let be the first-term gain and the second-term gain of the linearly extended state observer, respectively, and s be the Laplace operator. This is the ratio of the actual stator resistance to the actual stator inductance.

7. The sensorless back EMF observation method for permanent magnet synchronous motors according to claim 1, characterized in that: In step S3, the weighting function is: ； in, For the weight function, Let be the independent variable, and exp be the exponentiation operator. This is the steepness coefficient. , The boundary layer width, .

8. The sensorless back EMF observation method for permanent magnet synchronous motors according to claim 1, characterized in that: In step S3, the final back potential observer is: ； in, The derivative of the current state estimate, The derivative of the extended state estimate, The second derivative of the extended state estimate, To estimate the back electromotive force for the composite shaft system, This is the ratio of the estimated stator resistance to the estimated stator inductance. for Stator voltage of a composite shaft system Estimate the inductance for the stator. This is an estimate of the current state. For the expansion state estimate, and These are the first-term gain and second-term gain of the linearly extended state observer, respectively. For current state error, It is the extended state derivative The estimated value, This is an estimated value for the motor's operating frequency. It is a nonlinear adaptive term. It is the exponent of the nonlinear term. , For symbolic operations, For variables The weighting function.

Images