A sensorless control method for permanent magnet synchronous motor based on sliding mode observer

Abstract

The application discloses a sensorless control method of a permanent magnet synchronous motor based on a sliding mode observer, and comprises the following steps: collecting three-phase currents and three-phase voltages of the permanent magnet synchronous motor and converting the three-phase currents and three-phase voltages into two-phase current components and two-phase voltage components in a stationary coordinate system; inputting the two-phase current components and two-phase voltage components into a novel sliding mode observer; the novel sliding mode observer adopts a sinusoidal saturation switching function to replace a sign function, and adopts a variable gain function based on speed error and state variable cooperative control; taking the product of the sinusoidal saturation switching function and the variable gain function as an equivalent control quantity to obtain an estimated back electromotive force value; inputting the estimated back electromotive force value into a phase-locked loop structure, and extracting an estimated rotor electric angular velocity and an estimated rotor position angle through the phase-locked loop structure; and realizing sensorless vector control of the permanent magnet synchronous motor by using the estimated rotor electric angular velocity and the estimated rotor position angle. The method solves the problem of phase lag and realizes effective suppression of speed chattering.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of sensorless control of permanent magnet synchronous motor, and more particularly to a sensorless control method of permanent magnet synchronous motor based on a sliding mode observer. BACKGROUND

[0002] In recent years, permanent magnet synchronous motors (PMSM) have been widely used in the field of robotics due to their high power density, excellent dynamic response, and high efficiency. In particular, in industrial robots, service robots, and automation systems, the performance advantages of PMSM make it an ideal driving source. However, traditional control methods often rely on mechanical position sensors such as optical encoders and resolvers, which increase the volume, weight, and cost of the system. At the same time, these sensors are easily affected by external environments such as temperature, humidity, and vibration, reducing the reliability of the system. Therefore, in recent years, research on position sensorless control technology has gradually become a hot topic in the field of robotics.

[0003] In position sensorless control, common improvement strategies include extended sliding mode observers and high-order sliding mode observers. Extended sliding mode observers can directly observe the back electromotive force of the motor, thereby avoiding the problem of system chattering caused by extracting the back electromotive force from the switching function. For example, in the invention patent application with publication number CN118554813A, entitled "Permanent magnet direct drive motor anti-disturbance control method based on extended sliding mode disturbance observer", an extended sliding mode disturbance observer is used to estimate the system disturbance term that cannot be accurately measured in real time, and the observed load torque value is fed forward to the current regulator, effectively improving the dynamic response speed of the system. High-order sliding mode observers can achieve accurate estimation of motor rotor position and speed, such as the invention patent application with publication number CN119341419A, entitled "Permanent magnet synchronous motor adaptive high-order terminal sliding mode observer control method", which designs a current signal control law and a back electromotive force signal control rate based on adaptive gain, extended equation, and high-order terminal sliding mode surface, so that the control system can maintain robustness and high-precision output simultaneously under high dynamic response demand.

[0004] However, the above improvement methods make the observer structure extremely complex, greatly increasing the design engineering quantity, and there are certain challenges in actual application. Therefore, in order to meet the high requirements for control performance in robotics applications, how to optimize the existing sliding mode observer, reduce chattering and improve estimation accuracy is a problem that needs to be solved by those skilled in the art. SUMMARY

[0005] In view of the above problems, the present application provides a sensorless control method of permanent magnet synchronous motor based on a sliding mode observer to at least solve some of the technical problems mentioned in the background.

[0006] To achieve the above object, the application adopts the following technical scheme:

[0007] The application provides a sensorless control method for a permanent magnet synchronous motor based on a sliding mode observer, which is applied to a sensorless control system for a permanent magnet synchronous motor based on a sliding mode observer; wherein the method comprises the following steps:

[0008] S1, collecting three-phase currents and three-phase voltages of the permanent magnet synchronous motor;

[0009] S2, converting the three-phase currents and three-phase voltages into two-phase current components and two-phase voltage components in a stationary coordinate system through coordinate transformation;

[0010] S3, inputting the two-phase current components and two-phase voltage components into a novel sliding mode observer; wherein the novel sliding mode observer adopts a sinusoidal saturation switching function to replace a sign function, and adopts a variable gain function based on speed error and state variable cooperative control;

[0011] S4, taking the product of the sinusoidal saturation switching function and the variable gain function as an equivalent control amount of the novel sliding mode observer, and obtaining an estimated back electromotive force value based on the equivalent control amount;

[0012] S5, inputting the estimated back electromotive force value into a phase-locked loop structure, and extracting an estimated rotor electric angular velocity and an estimated rotor position angle through the phase-locked loop structure;

[0013] S6, realizing sensorless vector control of the permanent magnet synchronous motor by using the estimated rotor electric angular velocity and the estimated rotor position angle.

[0014] Further, the novel sliding mode observer is expressed as:

[0015]

[0016]

[0017]

[0018] wherein i α represents an alpha-axis stator current component in a stationary coordinate system; i β represents a beta-axis stator current component in the stationary coordinate system; represents an observed value of the alpha-axis stator current component in the stationary coordinate system; represents an observed value of the beta-axis stator current component in the stationary coordinate system respectively; p represents a differential operator; R s represents a stator resistance; L s represents a stator inductance; u α represents an alpha-axis stator voltage component in the stationary coordinate system; uβ represents the stator voltage component of the β-axis in the stationary coordinate system; H represents a variable gain function based on the speed error and state variable cooperative control; f(s α represents a sinusoidal saturation switching function acting on the α-axis; f(s β represents a sinusoidal saturation switching function acting on the β-axis.

[0019] Further, the sinusoidal saturation switching function f(s) is represented as:

[0020]

[0021] wherein δ represents a frequency coefficient, and σ represents a boundary layer width; s represents a sliding surface.

[0022] Further, the variable gain function H based on the speed error and state variable cooperative control is represented as:

[0023]

[0024] wherein k b represents a basic gain, and k b > 0; e x represents a speed error, and μ represents a proportional coefficient, and 0 < μ < 1; v represents a decay factor, and v > 0; s represents a sliding surface.

[0025] Further, the basic gain k b needs to satisfy the condition:

[0026]

[0027] wherein e α represents the α-axis back electromotive force; e β represents the β-axis back electromotive force; f(s α ) represents a sinusoidal saturation switching function acting on the α-axis; f(s β ) represents a sinusoidal saturation switching function acting on the β-axis.

[0028] Further, the back electromotive force estimation value is represented as:

[0029]

[0030]

[0031] wherein represents the α-axis back electromotive force estimation value; represents the β-axis back electromotive force estimation value; H represents a variable gain function based on the speed error and state variable cooperative control; f(s α) represents a sinusoidal saturation switching function acting on the α-axis; f(s β ) represents a sinusoidal saturation switching function acting on the β-axis; k b represents a base gain; e x represents a speed error; μ represents a proportional coefficient; v represents a damping factor; s represents a sliding mode surface; s α represents a sliding mode surface acting on the α-axis; s β represents a sliding mode surface acting on the β-axis.

[0032] Further, in the S5, the rotor estimated electrical angular velocity and the rotor estimated position angle extracted by the phase-locked loop structure specifically include:

[0033] When the rotor actual position angle θ and the rotor estimated position angle satisfy the error , the relationship between the rotor actual position angle θ and the rotor estimated position angle is .

[0034] Based on the relationship between the rotor actual position angle θ and the rotor estimated position angle , the back electromotive force difference Δe is calculated:

[0035]

[0036] wherein k represents a back electromotive force estimated value amplitude; represents an α-axis back electromotive force estimated value; represents a β-axis back electromotive force estimated value; Δθ represents an angular error between the rotor actual position angle θ and the rotor estimated position angle .

[0037] The angular error Δθ obtained after the back electromotive force difference Δe is subjected to a gain 1 / k e is sent into a PI controller to obtain the rotor estimated electrical angular velocity .

[0038] The rotor estimated electrical angular velocity is integrated to obtain the final rotor estimated position angle .

[0039] Further, the permanent magnet synchronous motor sensorless control system based on the sliding mode observer adopts a speed-current double closed loop structure.

[0040] Further, the speed-current double closed loop structure includes an outer speed loop and an inner current loop;

[0041] The outer speed loop is according to a preset target rotating speed and the rotor estimated electrical angular velocity The difference of the mechanical rotating speed converted from 30 / πp is generated as a q-axis current command value in a two-rotating coordinate system through a PI regulator ;

[0042] The inner layer current ring receives the q-axis current command value , and receives a d-axis current command value in a two-rotating coordinate system = 0 q , and compares the d-axis feedback current i d , respectively; the comparison results are generated as a q-axis voltage command u q and a d-axis voltage command u d through a PI regulator, respectively

[0043] Based on the q-axis voltage command u q and the d-axis voltage command u d , a permanent magnet synchronous motor is driven to operate through a driving inverter

[0044] According to the above technical solution, compared with the prior art, the application provides a permanent magnet synchronous motor sensorless control method based on a sliding mode observer, which has the following beneficial effects:

[0045] The application proposes a novel sliding mode observer structure aiming at the limitation of the traditional sliding mode observer in speed chattering suppression, replaces a sign function with a sinusoidal saturation function, and cancels the use of a low-pass filter, thereby fundamentally solving the phase lag problem.

[0046] The application designs a dynamic gain function based on speed error and state variable, thereby realizing effective suppression of speed chattering and reducing error.

[0047] The technical solution of the application will be further described in detail below by means of the accompanying drawings and embodiments. DETAILED DESCRIPTION

[0048] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, the accompanying drawings needed to be used in the embodiments or the prior art description will be briefly introduced. Obviously, the accompanying drawings in the following description are only embodiments of the application, and other accompanying drawings can be obtained by those skilled in the art without creative labor on the basis of the provided accompanying drawings.

[0049] Figure 1 The flowchart of the permanent magnet synchronous motor sensorless control method based on a sliding mode observer provided by the embodiment of the application is shown.

[0050] Figure 2 The principle diagram of the speed and position calculation link based on a phase-locked loop provided by the embodiment of the application is shown.

[0051] Figure 3 A schematic diagram of the sensorless control system framework for a permanent magnet synchronous motor based on a sliding mode observer, provided in an embodiment of the present invention. Detailed Implementation

[0052] 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.

[0053] This invention discloses a sensorless control method for permanent magnet synchronous motors based on a sliding mode observer, applicable to a sensorless control system for permanent magnet synchronous motors based on a sliding mode observer; wherein "sensorless" specifically refers to the absence of position sensors; such as Figure 1 As shown, the method specifically includes the following steps:

[0054] S1. Collect the three-phase current and three-phase voltage of the permanent magnet synchronous motor;

[0055] S2. Through coordinate transformation, the three-phase current and three-phase voltage are converted into two-phase current components and two-phase voltage components in a stationary coordinate system;

[0056] S3. Input the two-phase current components and the two-phase voltage components into the new sliding mode observer; wherein, the new sliding mode observer uses a sinusoidal saturation switching function to replace the sign function, and uses a variable gain function based on the coordinated control of speed error and state variables;

[0057] S4. The product of the sinusoidal saturation switching function and the variable gain function is used as the equivalent control quantity of the new sliding mode observer, and the back electromotive force is estimated based on the equivalent control quantity.

[0058] S5. Input the back EMF estimate into a phase-locked loop structure, and extract the rotor's estimated electric angular velocity and rotor's estimated position angle through the phase-locked loop structure.

[0059] S6. Sensorless vector control of permanent magnet synchronous motor is achieved by using rotor to estimate electric angular velocity and rotor to estimate position angle.

[0060] Next, each of the above steps will be explained in detail.

[0061] In step S1, the three-phase current (i) of the permanent magnet synchronous motor is collected. a i b i c ) and three-phase voltage (u a ub , u c );

[0062] In the step S2, the three-phase current and the three-phase voltage are converted into two-phase current components and two-phase voltage components in the stationary coordinate system by coordinate transformation; represented as:

[0063]

[0064]

[0065] In the step S3, the two-phase current components and the two-phase voltage components are input into the novel sliding mode observer; wherein the novel sliding mode observer adopts a sinusoidal saturation switching function to replace the sign function, and adopts a variable gain function based on the speed error and the state variable cooperative control; specifically:

[0066] (1) the novel sliding mode observer is represented as:

[0067]

[0068]

[0069]

[0070] wherein, i α represents the α-axis stator current component in the stationary coordinate system; i β represents the β-axis stator current component in the stationary coordinate system; represents the observed value of the α-axis stator current component in the stationary coordinate system; respectively are the observed values of the β-axis stator current component in the stationary coordinate system; p represents the differential operator; R s represents the stator resistance; L s represents the stator inductance; u α represents the α-axis stator voltage component in the stationary coordinate system; u β represents the β-axis stator voltage component in the stationary coordinate system; H represents the variable gain function based on the speed error and the state variable cooperative control; f(s α ) represents the sinusoidal saturation switching function acting on the α-axis; f(s β ) represents the sinusoidal saturation switching function acting on the β-axis.

[0071] (2) the sinusoidal saturation switching function f(s) is represented as:

[0072]

[0073] wherein, δ represents the frequency coefficient, and ; σ represents the boundary layer width; s represents the sliding surface.

[0074] (3) The variable gain function H based on the cooperative control of the speed error and the state variable is expressed as:

[0075]

[0076] wherein k b represents the basic gain, and k b > 0; e x represents the speed error, and ; μ represents the proportional coefficient, and 0 < μ < 1; v represents the attenuation factor, and v > 0; s represents the sliding surface; e -v|s| represents the exponential function form with the sliding surface; in the embodiment of the application, k b = 181, μ = 0.5, and v = 0.5.

[0077] The above basic gain k b needs to satisfy the condition:

[0078]

[0079] wherein e α represents the α-axis back electromotive force; and e β represents the β-axis back electromotive force.

[0080] In the step S4, the product of the sinusoidal saturation switching function and the variable gain function is taken as the equivalent control quantity of the novel sliding mode observer, and the back electromotive force estimation value is obtained based on the equivalent control quantity; the back electromotive force estimation value is expressed as:

[0081]

[0082]

[0083] wherein, represents the α-axis back electromotive force estimation value; represents the β-axis back electromotive force estimation value; H represents the variable gain function based on the cooperative control of the speed error and the state variable; f(s α ) represents the sinusoidal saturation switching function acting on the α-axis; f(s β ) represents the sinusoidal saturation switching function acting on the β-axis; k b represents the basic gain; e x represents the speed error; μ represents the proportional coefficient; v represents the attenuation factor; s represents the sliding surface; s α represents the sliding surface acting on the α-axis; s β represents the sliding surface acting on the β-axis.

[0084] In step S5, to reduce the observation errors of the observed rotational speed and position angle, a phase-locked loop (PLL) is combined with a sliding mode observer to construct a PLL-based calculation stage for rotational speed and position. Specifically, the estimated back electromotive force is input into a PLL structure, and the estimated rotor electrical angular velocity and estimated rotor position angle are extracted through the PLL structure. Figure 2 As shown, it specifically includes:

[0085] When the actual rotor position angle θ is different from the estimated rotor position angle Error satisfies At that time, the actual rotor position angle θ and the estimated rotor position angle The relationship is ;

[0086] Based on the actual rotor position angle θ and the estimated rotor position angle The relationship is used to calculate the back electromotive force difference Δe:

[0087]

[0088] Where k represents the magnitude of the estimated back electromotive force; This represents the estimated value of the back electromotive force along the α axis; The value represents the estimated back electromotive force of the β-axis; Δθ represents the difference between the actual rotor position angle θ and the estimated rotor position angle. angular error;

[0089] When the back electromotive force difference Δe approaches zero, the rotor estimated position angle Converging to the actual rotor position angle θ; the back electromotive force difference Δe is passed through a gain 1 / k e The obtained angular error Δθ is then fed into the PI controller to obtain the estimated electric angular velocity of the rotor. In a PI controller, K p K is the proportional term. i S is the integral term, and S is the Laplace operator;

[0090] Estimating the electric angular velocity of the rotor Integrating the results yields the final estimated rotor position angle. .

[0091] In step S6, sensorless vector control of the permanent magnet synchronous motor is achieved by using the estimated electric angular velocity of the sub-engine and the estimated position angle of the rotor; this step can be implemented by a sensorless control system for permanent magnet synchronous motors based on a sliding mode observer.

[0092] In this embodiment of the invention, the system adopts a speed-current dual closed-loop structure, such as... Figure 3 As shown, it specifically includes an outer velocity loop and an inner current loop; wherein:

[0093] The outer speed loop receives the preset target speed The rotor estimated electrical angular velocity The difference between the mechanical speed converted by 30 / πp and the rotor estimated electrical angular velocity is processed by a PI regulator to generate the q-axis current command value in the two-rotating coordinate system ;

[0094] The inner current loop receives the q-axis current command value and the d-axis current command value = 0, and compares them with the q-axis feedback current i q and the d-axis feedback current i d respectively; the comparison results are processed by a PI regulator to generate the d-axis voltage command u d and the q-axis voltage command u q respectively; based on the q-axis voltage command u q and the d-axis voltage command u d , the SVPWM drives the inverter to drive the PMSM to operate.

[0095] The key of the system is its sensorless technology. It uses the input voltage commands u α , u β , the actual sampled currents i α , and i β to accurately back-calculate the real-time state of the motor through a sliding mode observer. Through subsequent processing, the system finally obtains the rotor estimated electrical angular velocity and the rotor estimated position angle . These two estimated values are the core of the entire system: the rotor estimated electrical angular velocity is used as the feedback of the speed loop, and the rotor estimated position angle provides an accurate angle reference for the coordinate transformation in the FOC control, thereby realizing complete closed-loop control.

[0096] In summary, the embodiment of the application provides a sensorless control method of a permanent magnet synchronous motor based on a sliding mode observer, first, aiming at the limitation of a traditional sliding mode observer in speed chattering suppression, a novel sliding mode observer structure is proposed, a sine saturation function is used to replace a sign function, and use of a low-pass filter is cancelled, so that the phase lag problem is fundamentally solved; second, a dynamic gain function based on a speed error and a state variable is designed, so that effective suppression of speed chattering is realized, and error is reduced.

[0097] The various embodiments in the specification are described in a progressive manner, and each embodiment focuses on the difference from other embodiments, and the same or similar parts between the various embodiments can be referred to each other.

[0098] The above description of the disclosed embodiments enables a person skilled in the art to implement or use the application. Various modifications to the embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the application. Therefore, the application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for sensorless control of permanent magnet synchronous motor based on sliding mode observer, applied to a sensorless control system of permanent magnet synchronous motor based on sliding mode observer; characterized in that, The method comprises the following steps: S1, collecting three-phase currents and three-phase voltages of the permanent magnet synchronous motor; S2, converting the three-phase currents and three-phase voltages into two-phase current components and two-phase voltage components in a stationary coordinate system through coordinate transformation; S3, inputting the two-phase current components and two-phase voltage components into a sliding mode observer; wherein the sliding mode observer adopts a sinusoidal saturation switching function to replace a sign function, and adopts a variable gain function based on speed error and state variable cooperative control; the variable gain function H based on speed error and state variable cooperative control is expressed as: ； where k b represents a base gain, and k b > 0; e x represents a speed error, and ; μ represents a proportional coefficient, and 0 < μ < 1; v represents a decay factor, and v > 0; s represents a sliding mode surface; S4, taking the product of the sinusoidal saturation switching function and the variable gain function as an equivalent control amount of the sliding mode observer, and obtaining an estimated back electromotive force value based on the equivalent control amount; S5, inputting the estimated back electromotive force value into a phase-locked loop structure, and extracting a rotor estimated electrical angular velocity and a rotor estimated position angle through the phase-locked loop structure; S6, realizing sensorless vector control of the permanent magnet synchronous motor by using the rotor estimated electrical angular velocity and the rotor estimated position angle.

2. The sensorless control method of permanent magnet synchronous motor based on sliding mode observer according to claim 1, characterized in that, The sliding mode observer is expressed as: ； ； ； where i α represents the stator current component of the α-axis in the stationary coordinate system; i β represents the stator current component of the β-axis in the stationary coordinate system; represents the observed stator current component of the α-axis in the stationary coordinate system; represents the observed stator current component of the β-axis in the stationary coordinate system, respectively; p represents a differential operator; R s represents the stator resistance; L s represents the stator inductance; u α represents the stator voltage component of the α-axis in the stationary coordinate system; u β represents the stator voltage component of the β-axis in the stationary coordinate system; H represents a variable gain function based on the speed error and the state quantity cooperative control; f(s α ) represents a sinusoidal saturation switching function acting on the α-axis; f(s β ) represents a sinusoidal saturation switching function acting on the β-axis.

3. The sensorless control method of permanent magnet synchronous motor based on sliding mode observer according to claim 1, characterized in that, The sinusoidal saturation switching function f(s) is expressed as: ； where δ denotes the frequency coefficient, and ; σ denotes the boundary layer width; s denotes the sliding surface.

4. The sensorless control method of permanent magnet synchronous motor based on sliding mode observer according to claim 1, characterized in that, Base gain k b The condition must be met: ； where e α represents the α-axis back electromotive force; e β represents the β-axis back electromotive force; f(s α ) represents a sinusoidal saturation switching function acting on the α-axis; and f(s β ) represents a sinusoidal saturation switching function acting on the β-axis.

5. The sensorless control method of permanent magnet synchronous motor based on sliding mode observer according to claim 1, characterized in that, The estimated back electromotive force value is expressed as: ； ； wherein, represents an α-axis back electromotive force estimation value; represents a β-axis back electromotive force estimation value; H represents a variable gain function based on a speed error and a state quantity cooperative control; f(s α represents a sinusoidal saturation switching function acting on the α-axis; f(s β represents a sinusoidal saturation switching function acting on the β-axis; k b represents a base gain; e x represents a speed error; μ represents a proportional coefficient; v represents a decay factor; s represents a sliding mode surface; s α represents a sliding mode surface acting on the α-axis; s β represents a sliding mode surface acting on the β-axis.

6. The sensorless control method of permanent magnet synchronous motor based on sliding mode observer according to claim 1, characterized in that, In the S5, the rotor estimated electrical angular velocity and the rotor estimated position angle are extracted through the phase-locked loop structure, specifically including: When the rotor actual position angle θ and the rotor estimated position angle satisfy , the relationship between the rotor actual position angle θ and the rotor estimated position angle is ; Based on the actual rotor position angle θ and the estimated rotor position angle The relationship is used to calculate the back electromotive force difference Δe: ； where k represents the back electromotive force estimation value amplitude; represents the α-axis back electromotive force estimation value; represents the β-axis back electromotive force estimation value; Δθ represents the angle error of the rotor actual position angle θ and the rotor estimation position angle θe The back electromotive force difference Δe is passed through a gain 1 / k e The angle error Δθ obtained later is fed into a PI controller to obtain the rotor estimated electrical angular velocity ; estimating an electrical angular velocity of the rotor performing integration to obtain a final rotor estimated position angle .

7. A sensorless control method of permanent magnet synchronous motor based on sliding mode observer according to any one of claims 1-6, characterized in that, The sensorless control system of the permanent magnet synchronous motor based on the sliding mode observer adopts a speed-current double closed loop structure.

8. The sensorless control method of permanent magnet synchronous motor based on sliding mode observer according to claim 7, characterized in that, The speed-current double closed loop structure includes an outer speed loop and an inner current loop; The outer speed loop is according to a preset target rotating speed And the rotor estimated electrical angular velocity The difference value of the mechanical rotating speed converted by 30 / πp is generated by a PI regulator to generate a q-axis current command value in a two-phase rotating coordinate system ; The inner current loop receives the q-axis current command value , and receives a d-axis current command value in a two-phase rotating coordinate system = 0, and compares the command with a q-axis feedback current i q and a d-axis feedback current i d , respectively; and generates a q-axis voltage command u q and a d-axis voltage command u d after PI regulator, respectively; based on the q-axis voltage command u q and a d-axis voltage command u d to drive the permanent magnet synchronous motor in operation by driving the inverter.

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