CN113659904B - SPMSM sensorless vector control method based on nonsingular rapid terminal sliding mode observer - Google Patents

Abstract

The invention discloses a SPMSM sensorless vector control method based on a non-singular fast terminal sliding mode observer, and belongs to the technical field of motor control. The method of the present invention first establishes the voltage mathematical model of the permanent magnet synchronous motor based on the two-phase static coordinate system and reconstructs it into the stator current state equation; secondly, uses the current observation error as the state variable to design an integral non-singular sliding mode surface, and derives The composite control law is derived to obtain the extended back electromotive force; finally, the back electromotive force is reconstructed to implement high-frequency filtering, and the motor rotor position is extracted based on the software phase-locked loop principle. and speed Achieve sensorless control of motors. Compared with the traditional sliding mode observer, the present invention can accurately estimate the motor rotor position and speed information at zero low speed and medium and high speed stages, has strong robustness, can effectively suppress chattering in the control system, and solves the problem of Phase lag problem, the steady-state accuracy and dynamic performance of the system are better.

Description

A SPMSM sensorless vector based on non-singular fast terminal sliding mode observer Control Method

Technical field

The present invention relates to the technical field of motor control, and more specifically, to a SPMSM sensorless vector control method based on a non-singular fast terminal sliding mode observer.

Background technique

Permanent magnet synchronous motors have high energy density, low noise during operation, lower torque ripple than other motors, and are easy to maintain. Therefore, they are widely used in military and commercial drones, as well as in the currently very popular electric vehicles and national defense military applications. They have been widely used, which makes the permanent magnet synchronous motor control and speed regulation system a hot research topic at home and abroad. In practical applications of the system, sensors are generally used to directly obtain rotor position and speed information. However, the installation of such mechanical sensors increases the cost of the entire system and imposes certain requirements on the surrounding working environment, which limits the scope of use of the system and causes some insurmountable problems for the performance of the system. Scholars at home and abroad have conducted a lot of research on sensorless control algorithms to replace traditional mechanical sensors to obtain the motor rotor position and speed.

Permanent magnet synchronous motor sensorless technology is mainly divided into two categories, namely the model observer method for medium and high speeds and the salient pole tracking method for zero and low speeds. The sensorless control method suitable for medium and high speeds uses the back electromotive force of the motor to extract position and speed information. The main methods include the sliding mode observer method, the model adaptive method, the disturbance observer method, etc. The sliding mode observer is designed based on the deviation between the actual value of the stator current and the observed value obtained from the mathematical model of the motor and combined with the sliding mode variable structure theory. However, due to the unique discontinuity of sliding mode control, chattering cannot be completely eliminated, and new methods can only be found to suppress it. Traditional sliding mode observers also have phase lag, which produces high-frequency signals and noise. When estimating the rotor position based on the inverse tangent function, the error will be further amplified. Many scholars have done in-depth research on the chattering problem, phase delay and rotor position estimation of the sliding mode algorithm.

The journal "Journal of Electrical Machines and Control Applications" Issue 03, 2020, pages 28-33, proposes a new sliding mode observer design for sensorless permanent magnet synchronous motors based on improved filters, using an S-shaped function as the switching function to reduce Small buffeting, and at the same time, a cascade filter composed of a low-pass filter and a complex filter is used for high-frequency filtering of the back electromotive force to reduce measurement noise and measurement errors. However, this system uses a low-pass filter when filtering high-frequency buffeting and noise in the back electromotive force, which will cause a certain phase lag and a large error in the identification of the initial rotor position when the motor is started. In addition, the overshoot of the system is large and the dynamic response process is poor. This shortcoming is not further studied in this paper.

The journal "Journal of Xi'an Jiaotong University", Volume 50, Issue 01, Pages 87-91,99, proposes a new non-singular terminal sliding mode observer (NFTSMO) based on a tracking differentiator, and designs an integral non-singular The fast terminal sliding mode surface adopts a tracking differentiator to achieve accurate tracking of the back electromotive force, and at the same time realizes the filtering function. When the motor control system is running in a steady state, it can accurately track the given value and accurately estimate the rotor position. However, the disadvantage of this method is that when a step load torque is applied to the motor, the system cannot follow the given value well, and the anti-disturbance performance is poor. At the same time, the estimation error will further increase after the disturbance is applied. In addition, when designing the tracking differentiator, its mathematical model is relatively complex and also contains symbolic functions, so the designed sliding mode control algorithm has poor system performance.

Contents of the invention

1. The technical problem to be solved by the invention

Aiming at the permanent magnet synchronous motor control speed regulation system that uses a sliding mode observer to estimate the motor rotor position and speed information, problems such as high-frequency chattering, noise, and phase delay will occur. The present invention proposes a method based on non-singular fast terminal sliding mode observation. The SPMSM sensorless vector control method of the device can realize sensorless vector control of surface-mounted permanent magnet synchronous motors. In practical applications, the position and speed of the motor rotor can be effectively tracked, the operating cost of the motor can be reduced, and the steady-state accuracy and dynamic performance of the system can be improved.

2.Technical solutions

In order to achieve the above objects, the technical solutions provided by the present invention are:

A SPMSM sensorless vector control method based on a non-singular fast terminal sliding mode observer of the present invention, the steps are:

Step 1: Establish the voltage state equation of the permanent magnet synchronous motor based on the two-phase stationary coordinate system αβ, reconstruct it into the stator current state equation, and construct the current state observation equation;

Step 2: Sample the three-phase current i _abc and the three-phase voltage u _abc , and calculate the current error state equation;

Step 3: Use the current observation error as the state variable to design the sliding mode surface function S _(t) of the new non-singular fast terminal sliding mode observer, and design the sliding mode surface equivalent control based on the current error state equation and the sliding mode surface function. The function V _eq and the switching control function V _sw use the Lyapunov function stability criterion to prove their stability;

Step 4: Use the extended Kalman filter to reconstruct the extended back electromotive force and extract the estimated back electromotive force Finally, the motor rotor position is estimated based on the phase-locked loop principle/> and speed/>

3. Beneficial effects

The technical solution provided by the present invention has the following significant effects compared with the existing known technology:

The SPMSM sensorless vector control method based on the non-singular fast terminal sliding mode observer of the present invention effectively suppresses the problems such as high-frequency chattering and large torque pulsation existing in the traditional sliding mode observer. The extended Kalman filter is selected Reconstruct the back electromotive force, smooth the back electromotive force waveform, realize high-frequency filtering, and solve the phase lag problem of existing observers. The system's new sliding mode face has little dependence on motor parameters and strong anti-interference ability. It can accurately estimate the position and speed of the motor rotor at zero low speed and medium and high speed stages. Compared with the traditional singular sliding mode observer, the singularity problem of its system is overcome.

Description of the drawings

Figure 1 is a sensorless vector control block diagram of a surface-mounted permanent magnet synchronous motor (SPMSM) based on NFTSMO in the present invention;

Figure 2 is a schematic diagram of the new non-singular fast terminal sliding mode observer (NFTSMO) in the present invention;

Figure 3 is the schematic diagram of the traditional sliding mode observer (SMO);

Figure 4 is the structural block diagram of the extended Kalman filter (EKF);

Figure 5 is the schematic diagram of PLL;

In Figure 6 (a) is a waveform diagram comparing the predicted speed and the actual speed using the control method of the present invention; (b) is a waveform diagram comparing the predicted speed and the actual speed using a traditional sliding mode observer (SMO);

In Figure 7 (a) is a waveform diagram comparing the error between the predicted speed and the actual speed using the control method of the present invention; (b) is a waveform diagram comparing the error between the predicted speed and the actual speed using a traditional sliding mode observer (SMO);

In Figure 8 (a) is a three-phase current comparison waveform diagram when the control method of the present invention changes from no-load to load; (b) is a comparison of the three-phase current when the traditional sliding mode observer (SMO) changes from no-load to load. Waveform graph;

In Figure 9 (a) is the α-axis back electromotive force waveform diagram after primary filtering of the present invention; (b) is the α-axis back electromotive force waveform diagram after filtering by the extended Kalman filter of the present invention;

In Figure 10 (a) is a comparison waveform diagram between the predicted rotor position and the actual rotor position using the control method of the present invention; (b) is a comparison waveform diagram between the traditional sliding mode observer (SMO) predicted rotor position and the actual rotor position.

Detailed ways

In order to further understand the content of the present invention, the present invention will be described in detail with reference to the accompanying drawings and embodiments.

Example 1

This embodiment is a SPMSM sensorless vector control method based on a non-singular fast terminal sliding mode observer. Figure 1 is a sensorless vector control block diagram of a surface-mounted permanent magnet synchronous motor (SPMSM) based on NFTSMO provided in this embodiment. As shown in Figure 1, ASR is the speed regulator and ACR is the current regulator. It adopts the PI regulator double closed-loop vector control scheme of speed outer loop and current inner loop. After PI adjustment and Park inverse transformation, the αβ axis given voltage u _α is obtained. u _β is used as the input value of the voltage space vector modulation SVPWM. The on and off of the inverter thyristor is controlled by adjusting the duty cycle of the PWM waveform, thereby achieving Permanent magnet synchronous motor double closed-loop speed regulation.

The sampled three-phase current i _abc and three-phase voltage u _abc are transformed into two-phase stationary coordinate values i _αβ after Park coordinate transformation. The deviation from the stator current observation value is used as the state variable for designing the non-singular fast terminal sliding mode surface function. Then combine the terminal attractor function to design the sliding mode control law, use the extended Kalman filter to reconstruct the extended back electromotive force and perform secondary filtering, and finally predict the speed of the motor through the software phase-locked loop (PLL) principle. and rotor position/> The specific steps are:

Step 1. Establish the voltage state equation of the permanent magnet synchronous motor (PMSM) based on the two-phase stationary coordinate system αβ, reconstruct it into the stator current state equation, and construct the current state observation equation:

In order to simplify the analysis, assuming that the three-phase PMSM is an ideal motor, its three-phase voltage equation in the natural coordinate system ABC can be known. Through Clark coordinate transformation, the voltage state equation in the two-phase stationary coordinate system can be obtained:

Among them, L _d and L _q are the dq-axis components of the stator inductance, R _s is the stator resistance, ω _e is the electrical angular velocity, is the differential operator, [u _α u _β ] ^T is the component of the stator voltage on the αβ axis, [i _α i _β ] ^T is the component of the stator current on the αβ axis, [E _α E _β ] ^T is the extended back electromotive force (EMF) on αβ axis component, and satisfies:

In the formula, θ _e is the electrical angle of the rotor position, is the rotor flux linkage, [i _d i _q ] ^T is the stator current component in the dq axis.

Transform equation (1) and reconstruct it into the stator current state equation:

This embodiment is for research on the surface-mounted three-phase permanent magnet synchronous motor (SPMSM), that is: L _d = L _q = L _s , L _s is the stator inductance, and all formulas thereafter are expressed in L _s .

In order to obtain the estimated value of the extended back electromotive force, the current state observer equation is constructed as:

In the formula, is the current state observation value, [u _α u _β ] ^T is the control input of the observer, [V _α V _β ] ^T is the αβ axis component of the sliding mode surface control law function.

Step 2: Sample the three-phase current i _abc and the three-phase voltage u _abc . After Clark coordinate transformation, obtain the current i _αβ and voltage u _αβ in the two-phase stationary coordinate system αβ. Calculate the current error according to the stator current state equation and current state observation equation. Equation of state:

Combined with Figure 2, it can be seen from the traditional sliding mode surface design idea that the current error is used as the state variable of the sliding mode surface function. The new non-singular sliding mode surface function is designed based on the traditional sliding mode observer. . This embodiment uses a given speed outer ring,/> Double closed-loop speed control system with double current inner loops. The deviation between the given current and the feedback current is adjusted by PI to obtain the direct-axis voltage/> and quadrature axis voltage/> After Park inverse transformation, the voltage values u _α and u _β in the two-phase stationary coordinate system are obtained, which are input to the voltage space vector modulation SVPWM. By adjusting the duty cycle of the PWM waveform, the on and off of the inverter thyristor is controlled, thereby realizing permanent magnet Synchronous motor double closed loop speed regulation.

Therefore, it is necessary to obtain the current error value. By sampling the three-phase current i _abc and the three-phase voltage u _abc output by the three-phase permanent magnet synchronous motor, the current i _αβ and voltage u _αβ in the two-phase stationary coordinate system are obtained through Clark coordinate transformation. u _αβ serves as the input of the current state observer, and the current state observation value The current observation error compared with the two-phase current i _αβ is used as the input for designing a new non-singular fast terminal sliding mode surface. After making the difference between formula (2) and formula (3), the stator current error state equation is obtained:

In the formula, is the current observation error, [V _α V _β ] ^T is the αβ axis component of the sliding mode surface control law function.

Step 3: Use the current observation error as the state variable to design the sliding mode surface function S _(t) of the new non-singular fast terminal sliding mode observer. Based on the current error state equation and the sliding mode surface function, design the sliding mode surface equivalent control function V _eq and switching control function V _sw , and use Lyapunov stability criterion to prove its stability:

The current observation error is used as the state variable to design a new non-singular fast terminal sliding mode surface. At the same time, the concept of terminal attractor is introduced, and a new non-singular fast terminal sliding mode surface function is designed based on the terminal attractor function.

The terminal attractor function is After deforming this function and then integrating both sides of it, we get:

In the formula: p>q and is a positive odd number, x ₍₀₎ is the initial state of the system state variable x, t _(r) is the time required for the state variable x in the terminal attractor to reach the equilibrium point x=0 from the initial state. The terminal attractor model shows that the system state can converge to the equilibrium point within a limited time, and the terminal attractor has the characteristic of accelerating convergence near the equilibrium point. In this embodiment, an integral link is added when designing a new sliding mode surface, which can smooth the torque pulsation and have the effect of weakening chattering, and the second-order derivative of the state variable will not appear when designing the sliding mode control law.

Design a new non-singular fast terminal sliding mode surface function as:

in, is a saturation function,/> is the hyperbolic tangent function, δ,γ>0,/> And p>q are all positive odd numbers, Δ is the thickness of the boundary layer,/>

When the system state enters the sliding mode, there is Right now:

Transform equation (8) into:

It can be seen from equation (9) that when the error state is far from the equilibrium point, the state convergence rate is determined by the linear term Plays a major role, and a saturation function is added to make the current error have saturation characteristics, and the system can quickly converge to the sliding mode surface on the predetermined control trajectory; when the error state is closer to the equilibrium point, the state convergence rate is determined by the nonlinear term/> is a main factor. therefore,

In the sliding stage, the non-singular fast terminal sliding mode surface (7) can achieve global fast convergence, and It does not contain the state where the index is negative, avoiding strange phenomena.

It can be seen from formula (2) that the extended back electromotive force needs to obtain the value of the back electromotive force before extracting the motor rotor position and speed information. Therefore, the sliding mode control law V of the new sliding mode observer must be obtained. The sliding mode control law consists of the equivalent control function V _eq and the switching control function V _sw . The equivalent control function assumes that the system modeling is accurate and has no influence from other factors and there is no external disturbance, and the system is in the ideal sliding mode area. Under the premise of , solve the obtained average control quantity. It can be seen from equations (5) and (7) that the equivalent control function is:

In the formula, a, b∈R ⁺ .

The switching control function V _sw forces the system state to switch near the sliding mode surface to achieve robust control of uncertainty and disturbance. The switching control function V _sw is composed of the fast power reaching law and the terminal attractor function, that is:

V _sw ＝-k|S| ^μ h(S)-ε|S| ^υ (11)

In the formula, k>0, 0<μ<1, 0<ε<1.

From equation (10) and equation (11), the sliding mode control law function can be obtained as:

When analyzing sliding mode variable structure control, certain control characteristics need to be met. From the above analysis, it can be seen that the system state variables can converge within a certain period of time. In order to ensure the stability of the system, the Lyapunov function is selected to determine the stability of the system:

Taking V _α as an example, the derivative of V _α is:

Within {|S _α |≤(min(|E _α |/k) ^1/μ (|E _α |/ε) ^1/υ }, It is negative definite and can be proved by the same logic/> It is also negative definite, which proves that the system is stable.

Step 4: Use the extended Kalman filter (EKF) to reconstruct the extended back electromotive force (EMF) and extract the estimated value of the back electromotive force Finally, the motor rotor position is estimated based on the phase locked loop principle (PLL)/> and speed/>

When designing a sliding mode control system, a switching control function with low chattering is used instead of an absolute value function. However, when the sliding mode switching motion is performed on the sliding mode surface, some high-frequency signals and high-order harmonics will also be generated. Here, The ripple in the estimated back EMF is larger based on the estimated extended back EMF. Therefore, when designing the non-singular sliding mode surface, an integration link is added to filter the back electromotive force waveform once, and a smoother back electromotive force waveform is obtained.

However, in practical applications, high-frequency signals are often accompanied by a large amount of system noise and measurement noise. The ripple component of the back electromotive force cannot be filtered out by the integration link. At the same time, the use of low-pass filters in traditional sliding mode observers will cause phase Delay. Therefore, in order to suppress noise interference and remove high-frequency ripple components, the delayed phase can be eliminated at the same time, and the electrical angle identification accuracy of the rotor position is higher. Combined with Figure 4, the Kalman filter is introduced to perform secondary filtering on the back electromotive force obtained after filtering by the integrator. In fact, the Kalman filter is equivalent to a reconstruction of the back electromotive force. The double filtered back electromotive force is used as the sliding The input of the model observer can adaptively adjust the control system, which can suppress chattering and reduce estimation errors to the maximum extent.

Derivating equation (2) we get:

In the formula, [V _α V _β ] ^T is the αβ axis component of the sliding mode surface control law function, ω _e is the electrical angular velocity, θ _e is the electrical angle of the rotor position, is the rotor flux linkage,/> is the motor speed change rate. The system sampling frequency is much larger than the motor speed change rate, so it can be approximated to zero.

Simplify equation (15) to:

From equation (15) and equation (16), the mathematical expression of the Kalman filter can be deduced as:

In the formula, is the αβ axis component of the back electromotive force filtered by the Kalman filter, and k _k is the filter coefficient of the Kalman filter.

After reconstruction, the new sliding mode observer equation is:

In the formula, m is a real number.

Since sliding mode control is accompanied by the generation of high-frequency signals in the sliding mode, the back electromotive force obtained in the traditional sliding mode observer has phase delay and high-frequency noise. In the traditional sliding mode observer, the rotor is obtained based on the arctangent function. Position and speed, the high-frequency signal is directly introduced into the back electromotive force. After dividing the back electromotive force, the arc tangent value is taken to estimate the rotor position, resulting in the electrical angle error being amplified in one step. In order to overcome this shortcoming, the rotor position and speed information is modulated from the back electromotive force based on the phase-locked loop principle, as shown in Figure 5. The double-filtered back electromotive force is used as the input of the phase-locked loop,

When estimating the rotor position The difference from the measured rotor position θ _e is very small, that is:/> At this time it can be considered Simplifying equation (19) we get:

Adjusting the parameters of the PI regulator based on the phase-locked loop principle (PLL) can accurately estimate the rotor position electrical angle and electrical angular velocity.

The method design process of this embodiment was simulated and verified through the Matlab/Simulink simulation platform. The SPMSM sensorless vector control system based on the traditional sliding mode observer (SMO) and the new non-singular fast terminal sliding mode observer (NFTSMO) is compared through simulation. The permanent magnet synchronous motor parameters are: given speed Stator resistance R _s =0.258Ω, cross-direction axis inductance L _d =L _q =0.827mH, rotor flux linkage/> The number of pole pairs P=4, the damping coefficient B=0N·m·s, and the moment of inertia J=0.0065kg·m ² . The motor starts with no load (T _m = 0N·m), and the system given speed is/> When the motor control system is running at 0.1s, the load torque suddenly changes from the no-load operating state to T _m =10N·m, and the system given speed remains unchanged. The simulation running time is 0.2s.

From the analysis of Figure 6, it can be seen that the given speed of the system when it starts running under no-load condition is When , both control algorithms can reach the given value very quickly. It can be seen from the local amplified waveform diagram at the early stage of the response process that the given value is reached. The overshoot of the new sliding mode observer control system is as small as about 4.8%. , the overshoot of the traditional observer control system is about 5.6%. A load torque of T _m = 10N·m is applied to the system at 0.1s. It can be seen from Figure 6 that the motor speed basically does not change when the new sliding mode observer control system suddenly adds a load disturbance, and the speed amplitude jump range is ± 3rad/min quickly stabilizes near the given value, and the response process is fast; the traditional sliding mode observer control system has a large step amplitude (±30rad/min) in the motor speed when a sudden load disturbance is added, and the The rotational speed will decrease after applying load disturbance.

Analyzing Figure 7(a), when the motor is running at no-load or in steady-state operation with load, the speed error of the new sliding mode control is very small. When a load disturbance is suddenly added, the speed error of the motor is almost the same as in steady-state operation. It can be seen from Figure 7(b) that under the traditional sliding mode observer, the rotational speed error has a large range of deviation in the zero low speed stage when the motor is started, and the rotational speed error is also large during steady-state operation. It can be known from this that the sensorless control system based on the new non-singular fast terminal sliding mode observer can effectively suppress the chattering existing in the sliding mode control system.

It can be seen from Figure 8 that under the control of the low-bounce switching function, the three-phase current fluctuations under the new sliding mode observer are very small, and the three-phase stator current can quickly reach a stable state after the load disturbance is applied in 0.1S; from Figure 9 It can be seen that the back electromotive force undergoes primary filtering by the integral sliding mode observer and high-order filtering after reconstructing the back electromotive force, and a smooth estimated value of the back electromotive force is obtained.

It can be seen from Figure 10 that when estimating the rotor position based on the non-singular fast terminal sliding mode observer (NFTSMO), the initial rotor position identification is more accurate during the zero-low speed stage of motor startup, and the rotor position is accurately tracked during the medium-high speed steady-state operation stage. , its tracking accuracy is 0.01052%; the traditional sliding mode observer (SMO) has a large error in estimating the motor rotor position during the zero and low speed stages of motor startup, and will also produce phase lag. Its tracking accuracy in the medium-high-speed steady-state operation stage is 0.02514%.

The present invention and its embodiments are schematically described above. This description is not limiting. What is shown in the drawings is only one embodiment of the present invention, and the actual structure is not limited thereto. Therefore, if a person of ordinary skill in the art is inspired by the invention and without departing from the spirit of the invention, can devise structural methods and embodiments similar to the technical solution without inventiveness, they shall all fall within the protection scope of the invention. .

Claims (5)

1. A SPMSM sensorless vector control method based on a non-singular fast terminal sliding mode observer, which is characterized in that the steps are: Step 1: Establish the voltage state equation of the permanent magnet synchronous motor based on the two-phase stationary coordinate system αβ, reconstruct it into the stator current state equation, and construct the current state observation equation; Step 2: Sample the three-phase current i _abc and the three-phase voltage u _abc , and calculate the current error state equation; Step 3: Use the current observation error as the state variable to design the sliding mode surface function S _(t) of the new non-singular fast terminal sliding mode observer, and design the sliding mode surface equivalent control based on the current error state equation and the sliding mode surface function. The function V _eq and the switching control function V _sw use the Lyapunov function stability criterion to prove their stability; Step 4: Use the extended Kalman filter to reconstruct the extended back electromotive force and extract the estimated back electromotive force Finally, the motor rotor position is estimated based on the phase-locked loop principle/> and speed/> In the third step described, the current observation error is used as the state variable to design a new non-singular fast terminal sliding mode surface, and the concept of terminal attractor is introduced at the same time, and the new non-singular fast terminal sliding mode surface function is designed based on the terminal attractor function; The terminal attractor function is After deforming this function and then integrating both sides of it, we get: In the formula: p>q and is a positive odd number, x ₍₀₎ is the initial state of the system state variable x, t _r is the time required for the state variable x in the terminal attractor to reach the equilibrium point x=0 from the initial state; Design a new non-singular fast terminal sliding mode surface function as: in, is a saturation function,/> is the hyperbolic tangent function, δ,γ>0,/> And p>q are all positive odd numbers, Δ is the thickness of the boundary layer,/> In the described step three, when the system state enters the sliding mode, there is Transform equation (8) into: It can be seen from equation (9) that when the error state is far from the equilibrium point, the state convergence rate is determined by the linear term Plays a major role, and a saturation function is added to make the current error have saturation characteristics, and the system can quickly converge to the sliding mode surface on the predetermined control trajectory; when the error state is closer to the equilibrium point, the state convergence rate is determined by the nonlinear term/> is a main factor; In the third step, the equivalent control function V _eq and the switching control function V _sw form the sliding mode control law V. From equations (5) and (7), it can be seen that the equivalent control function is: In the formula, a,b∈R ⁺ ; The switching control function V _sw is composed of the fast power reaching law and the terminal attractor function, that is: V _sw ＝-k|S| ^μ h(S)-ε|S| ^υ (11) In the formula, k>0, 0<μ<1, 0<ε<1; From equation (10) and equation (11), the sliding mode control law function can be obtained as: In the third step described, the Lyapunov function is selected to determine the stability of the system: The derivative of V _α is: Within {|S _α |≤(min(|E _α |/k) ^1/μ (|E _α |/ε) ^1/υ }, It is negative definite, and can be proved in the same way/> It is also negative definite, which proves that the system is stable. 2. A SPMSM sensorless vector control method based on a non-singular fast terminal sliding mode observer according to claim 1, characterized in that: in the step one, three-phase permanent magnet synchronization is obtained through Clark coordinate transformation The voltage state equation of the motor in the two-phase stationary coordinate system is as shown in Equation (1), Among them, L _d and L _q are the dq-axis components of the stator inductance, R _s is the stator resistance, ω _e is the electrical angular velocity, is the differential operator, [u _α u _β ] ^T is the component of the stator voltage on the αβ axis, [i _α i _β ] ^T is the component of the stator current on the αβ axis, [E _α E _β ] ^T is the extended back electromotive force (EMF) on αβ axis component, and satisfies: In the formula, θ _e is the electrical angle of the rotor position, is the rotor flux linkage, [i _d i _q ] ^T is the stator current component in the dq axis; Transform equation (1) and reconstruct it into the stator current state equation: In the surface-mounted three-phase permanent magnet synchronous motor, L _d =L _q =L _s is the stator inductance; In order to obtain the estimated value of the extended back electromotive force, the current state observer equation is constructed as: In the formula, is the current state observation value, [u _α u _β ] ^T is the control input of the observer, [V _α V _β ] ^T is the αβ axis component of the sliding mode surface control law function. 3. A SPMSM sensorless vector control method based on a non-singular fast terminal sliding mode observer according to claim 2, characterized in that: in the second step, the three-phase output of the three-phase permanent magnet synchronous motor is collected. From the current i _abc and the three-phase voltage u _abc , the current i _αβ and voltage u _αβ in the two-phase stationary coordinate system are obtained through Clark coordinate transformation; use u _αβ as the input of the current state observer, and compare the current state observation values and current i _αβ are defined as the current observation error. According to equations (3) and (4), the stator current error state equation is deduced as: In the formula, is the current observation error, [V _α V _β ] ^T is the αβ axis component of the sliding mode surface control law function. 4. A SPMSM sensorless vector control method based on a non-singular fast terminal sliding mode observer according to claim 3, characterized in that: in the fourth step, formula (2) is derived by deriving: In the formula, [V _α V _β ] ^T is the αβ axis component of the sliding mode surface control law function, ω _e is the electrical angular velocity, θ _e is the electrical angle of the rotor position, is the rotor flux linkage,/> is the motor speed change rate; Simplify equation (15) to: From equation (15) and equation (16), the mathematical expression of the Kalman filter can be deduced as: In the formula, is the αβ axis component of the back electromotive force filtered by the Kalman filter, and k _k is the filter coefficient of the Kalman filter; After reconstruction, the new sliding mode observer equation is: In the formula, m is a real number. 5. A SPMSM sensorless vector control method based on a non-singular fast terminal sliding mode observer according to claim 4, characterized in that: in the step four, the double-filtered back electromotive force is used as a phase-locked loop As input, the motor back electromotive force difference equation output by the phase locked loop is: When estimating the rotor position The difference from the measured rotor position θ _e is very small, that is/> At this time it can be considered Simplify equation (19) to get Adjusting the parameters of the PI regulator based on the phase-locked loop principle can accurately estimate the rotor position electrical angle and electrical angular velocity.