A full-order terminal sliding mode speed adaptive observation method for permanent magnet synchronous motor

Abstract

A kind of permanent magnet synchronous motor full-order terminal sliding mode speed adaptive observation method belongs to motor control field.Solve the existing permanent magnet synchronous motor sliding mode observation method when motor high-speed rotation exists observation speed slow, the problem of poor smoothness of observation signal.The present application collects the three-phase current of permanent magnet synchronous motor stator winding, obtains the phase current in two-phase stationary coordinate system;Using the phase current in two-phase stationary coordinate system and the alpha axis component and beta axis component of motor stator winding terminal given voltage, establish the full-order motor model based on extended back electromotive force;Design the observation equation of motor stator current extended back electromotive force;Establish the stator current error equation;Calculate the stator current error, design full-order terminal sliding surface, obtain sliding mode control law;Using Lyapunov function, obtain continuous current observation signal;Design speed adaptive law, obtain the speed of permanent magnet synchronous motor rotor.The present application is suitable for the speed observation of permanent magnet synchronous motor rotor.

Description

Technical Field

[0001] This invention belongs to the field of motor control. Background Technology

[0002] Permanent magnet synchronous motors (PMSMs) rely on permanent magnets to generate excitation flux, offering faster response times, higher efficiency, and better speed regulation compared to traditional AC induction motors. Therefore, PMSMs are widely used in aerospace, industrial, and transportation sectors, especially in the rapidly developing new energy vehicle industry.

[0003] For electric drive systems of new energy vehicles, due to the introduction of the ISO26262 functional safety concept, the failure of the rotary transformer in random hardware failures can threaten the life and property safety of the occupants. Therefore, a sensorless control method for permanent magnet synchronous motors that can strip the failed rotary transformer is needed.

[0004] Sliding mode observers have become a widely used sensorless control method due to their simple structure, strong robustness, and high observation accuracy. However, the presence of a sign function in the control law of a sliding mode observer can lead to chattering in the system output. Traditional sliding mode observers use filters to suppress chattering, but this introduces lag in the observed values, reducing the system's control performance. Using continuous saturation functions instead of discontinuous switching functions can reduce chattering and ensure the smoothness of the observer output, but this reduces the observer's response speed and accuracy, and decreases the system's robustness.

[0005] To address these issues, some scholars have proposed designing sliding mode observers based on a full-order model of the motor. This approach can eliminate the need for filters while retaining the switching function, thus removing lag in the observed values. However, this method still introduces discontinuous switching functions into the control input, which can still cause system chattering. After obtaining the motor's back EMF signal through the observer, a phase-locked loop (PLL) is typically used to extract the speed signal. However, under high-speed conditions, a low bandwidth design in the PLL can cause phase lag in the observed signal, while a high bandwidth can introduce high-frequency interference into the speed signal. This poses a challenge to the accurate observation of the speed. Summary of the Invention

[0006] The purpose of this invention is to solve the problems of slow observation speed and poor smoothness of observation signals in existing sliding mode observation methods for permanent magnet synchronous motors when the motor is rotating at high speed. This invention provides an adaptive observation method for the full-order terminal sliding mode speed of permanent magnet synchronous motors.

[0007] The present invention discloses an adaptive observation method for the full-order terminal sliding mode speed of a permanent magnet synchronous motor, comprising:

[0008] Step 1: Collect the three-phase current i of the stator winding of the permanent magnet synchronous motora i b i c The three-phase current i is transformed by Park transformation. a i b i c By performing a coordinate transformation, the phase current i in the two-phase stationary coordinate system is obtained. α i β ;

[0009] Step 2: Using the phase current i in a two-phase stationary coordinate system α i β A full-order motor model based on extended back electromotive force is established using the α-axis and β-axis components of the given voltage at the stator winding terminals of the motor.

[0010] Step 3: Based on the full-order motor model, design the observation equation for the extended back electromotive force of the motor stator current;

[0011] Step 4: Using the full-order model and the observer equation, establish the stator current error equation; calculate the stator current error;

[0012] Step 5: Based on the stator current error, design the full-order terminal sliding mode surface and obtain the sliding mode control law;

[0013] Step 6: Using the sliding mode control law, and using the Lyapunov function, obtain the range of the gain coefficient of the control law that makes the stator current error and the derivative of the stator current error converge to 0, and obtain a continuous current observation signal.

[0014] Step 7: Based on the current observation signal and the observation equation, design the speed adaptive law to obtain the speed of the permanent magnet synchronous motor rotor.

[0015] Furthermore, in this invention, step two, the process of establishing a full-order motor model based on extended back electromotive force, is as follows:

[0016] Step 2.1 Establish the stator voltage equations of the permanent magnet synchronous motor in the α-β axis system;

[0017] Step 22: Using the stator voltage equation, construct a voltage equation based on the extended back electromotive force;

[0018] Step 23: Using the extended back EMF representation in the voltage equation based on extended back EMF, construct a full-order motor model with stator current and extended back EMF as state variables, which is the full-order motor model based on extended back EMF.

[0019] Furthermore, in this invention, in step two-one, the stator voltage equation is:

[0020]

[0021] In the formula: u α It is the α-axis component of the voltage at the stator winding terminals of the motor, u β It is the β-axis component of the voltage across the stator windings of the motor; i α It is the α-axis component of the phase current of the motor stator winding, i β It is the β-axis component of the phase current of the motor stator winding; R s It is the resistance of the motor stator winding, ω e It is the electric angular velocity of the motor rotor, θ e It is the rotor position angle of the motor; ψ f It is the rotor flux linkage of the motor, p is the differential operator; L α =L0+L1 cos2θ e L β =L0-L1 cos2θ e L αβ =L1 sin2θ e L0 = (L d +L q ) / 2; L1=(L d -L q ) / 2, L α It is the α-axis component of the stator winding inductance of the motor, L β It is the β-axis component of the motor stator winding inductance, L αβ L1 is the α-β axis coupled inductance; L0 is the average inductance of the motor stator winding along the dq axis, and L1 is the differential inductance of the motor stator winding along the dq axis; L d It is the d-axis component of the stator winding inductance of the motor, L q It is the q-axis component of the inductance of the motor stator winding.

[0022] Furthermore, in step two of this invention, the voltage equation based on the extended back electromotive force is as follows:

[0023]

[0024] In the formula, i q i is the q-axis current of the stator winding. d This represents the d-axis current of the stator winding.

[0025] Furthermore, in this invention, in steps two and three, the full-order motor model with stator current and extended back electromotive force as state variables is as follows:

[0026]

[0027] In the formula: i=[i α i β ] T , e = [e α e β] T These are the stator current and extended back electromotive force matrices in the α-β axis system, respectively; These are the stator current derivative matrix and the extended back electromotive force derivative matrix in the α-β axis system, respectively; u=[u α u β ] T The stator voltage matrix in the α-β axis system; Input matrix to the system; As the system state matrix.

[0028] Furthermore, in this invention, in step three, the observation equation for the extended back electromotive force of the motor stator current is:

[0029]

[0030] In the formula: These are the stator current and the observed extended back electromotive force matrix, respectively, observed in the α-β axis system; These are the stator current and the extended back electromotive force derivative matrices observed in the α-β axis system, respectively. Let be the state matrix under the observation equation, where The observed value of the rotor's electric angular velocity; The feedback gain matrix is ​​given by l, where l is the gain coefficient of the back EMF control signal, and l is greater than 0; v = [v α v β ] T It is the control signal input vector of the observer on the α-β axis, also known as the overall control law; It is the observed rotor electric angular velocity.

[0031] Furthermore, in this invention, in step four, the stator current error equation is:

[0032]

[0033] In the formula: and It is the error between the observed current and the actual current in the α-β axis system; and It is the derivative of the error between the observed current and the actual current in the α-β axis system; and It is the error between the observed back electromotive force and the actual back electromotive force in the α-β axis system.

[0034] Furthermore, in this invention, in step five, the full-order terminal sliding surface is:

[0035]

[0036] In the formula: s is the sliding surface; It is the stator current error matrix; C1 and C2 are the stator current error derivative matrix; p / q are the design coefficients; p and q are the terminal absorption factors, where p and q are odd numbers and satisfy 0 < p / q < 1.

[0037] Furthermore, in this invention, the process of obtaining a continuous current observation signal in step six is ​​as follows:

[0038] First, substitute the stator current error into the full-order terminal sliding surface;

[0039]

[0040] Based on the control law of the full-order terminal sliding surface:

[0041] v = v c +v s

[0042] In the formula: v = [v α v β ] T It is the control law for the full-order terminal sliding surface; v c =[v αc v βc ] T It is an equivalent control law; v s =[v αs v βs ] T It is a switching control law;

[0043] Obtain the equivalent control law and the switching control law:

[0044]

[0045]

[0046] In the formula: v c This is the equivalent control law; v s It is the switching control law; k and η are the designed gain coefficients; ε is the acceleration sliding mode reaching stage coefficient, and k, η and ε are all positive numbers;

[0047] Substitute the equivalent control law and the switching control law into s α s β Obtain the specific development formula of the sliding surface:

[0048]

[0049] Then, calculate the derivative of the sliding surface; obtain the full-order sliding surface derivative:

[0050]

[0051] Then, the sliding surface expansion and its derivative are substituted into the Lyapunov function to make the stator current error and the derivative of the stator current error converge to 0, thereby obtaining a continuous current observation signal.

[0052] Furthermore, in this invention, in step seven, the adaptive rotational speed law is:

[0053]

[0054]

[0055] in, Let be the derivative of the observed electric angular velocity of the motor, and h be the adaptive gain to be designed. The extended back electromotive force α-axis component observed in the α-β axis system. v represents the β-axis component of the extended back electromotive force observed in the α-β axis system. α It is the α-axis component of the total control law of the full-order terminal sliding surface, v β It is the β-axis component of the overall control law of the full-order terminal sliding surface. The observed value of the electric angular velocity of the motor. denoted as the observed motor speed, and p represents the number of pole pairs of the permanent magnet synchronous motor.

[0056] This invention obtains the derivative of the observed electric angular velocity using an adaptive law method, i.e., numerical calculation. After integration, the observed electric angular velocity is obtained, and then the rotational speed signal is derived through a transformation formula, resulting in a smoother rotational speed observation curve. Simultaneously, a full-order terminal sliding mode observer is designed, which provides better speed and smoothness for observing back electromotive force compared to traditional sliding mode observers, ensuring a rapid response in rotational speed observation. Especially under high-speed conditions, it avoids the chattering and lag phenomena in the speed observation signal caused by the bandwidth limitations of the phase-locked loop. Attached Figure Description

[0057] Figure 1 This is a flowchart of the method described in this invention;

[0058] Figure 2 This is a system diagram illustrating the control principle of the method described in this invention;

[0059] Figure 3 This is a waveform diagram of the back electromotive force observed by the method described in this invention;

[0060] Figure 4 These are waveforms showing the actual and observed rotational speeds of the motor as described in this invention.

[0061] Figure 5 These are waveforms of the actual and observed angles of the motor as described in this invention.

[0062] Figure 6 This is a waveform diagram showing the error between the actual and observed motor speeds as described in this invention.

[0063] Figure 7 This is a waveform diagram showing the error between the actual and observed angles of the motor in the method described in this invention. Detailed Implementation

[0064] 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.

[0065] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0066] Specific Implementation Method 1: The following is combined with... Figure 1 This embodiment describes an adaptive observation method for the full-order terminal sliding mode speed of a permanent magnet synchronous motor, comprising:

[0067] Step 1: Collect the three-phase current i of the stator winding of the permanent magnet synchronous motor a i b i c The three-phase current i is transformed by Park transformation. a i b i c By performing a coordinate transformation, the phase current i in the two-phase stationary coordinate system is obtained. α i β ;

[0068] Step 2: Using the phase current i in a two-phase stationary coordinate system α i β A full-order motor model based on extended back electromotive force is established using the α-axis and β-axis components of the given voltage at the stator winding terminals of the motor.

[0069] Step 3: Based on the full-order motor model, design the observation equation for the extended back electromotive force of the motor stator current;

[0070] Step 4: Using the full-order model and the observer equation, establish the stator current error equation; calculate the stator current error;

[0071] Step 5: Based on the stator current error, design the full-order terminal sliding mode surface and obtain the sliding mode control law;

[0072] Step 6: Using the sliding mode control law and Lyapunov function, obtain the continuous current observation signal when the stator current error and the derivative of the stator current error converge to 0.

[0073] Step 7: Based on the current observation signal and the observation equation, design a speed adaptive law, integrate the speed adaptive law, and obtain the speed of the permanent magnet synchronous motor rotor.

[0074] Furthermore, in this invention, step two, the process of establishing a full-order motor model based on extended back electromotive force, is as follows:

[0075] Step 2: 1. Establish the stator voltage equations of the permanent magnet synchronous motor in the α-β axis coordinate system;

[0076] Step 22: Using the stator voltage equation, construct a voltage equation based on the extended back electromotive force;

[0077] Steps 2 and 3: Using the extended back EMF representation in the voltage equation based on extended back EMF, construct a full-order motor model with stator current and extended back EMF as state variables, thus completing the establishment of the full-order motor model based on extended back EMF.

[0078] Furthermore, in this invention, in step two-one, the stator voltage equation is:

[0079]

[0080] In the formula: u α It is the α-axis component of the voltage at the stator winding terminals of the motor, u β It is the β-axis component of the voltage across the stator windings of the motor; i α It is the α-axis component of the phase current of the motor stator winding, i β It is the β-axis component of the phase current of the motor stator winding; R s It is the resistance of the motor stator winding, ω e It is the electric angular velocity of the motor rotor, θ e It is the rotor position angle of the motor; ψ f It is the rotor flux linkage of the motor, p is the differential operator; L α =L0+L1 cos2θ e L β =L0-L1 cos2θ e L αβ =L1 sin2θ e L0 = (L d +L q ) / 2; L1=(L d -L q ) / 2, L α It is the α-axis component of the stator winding inductance of the motor, L β It is the β-axis component of the motor stator winding inductance, L αβ L1 is the α-β axis coupled inductance; L0 is the average inductance of the motor stator winding along the dq axis, and L1 is the differential inductance of the motor stator winding along the dq axis; L dIt is the d-axis component of the stator winding inductance of the motor, L q It is the q-axis component of the inductance of the motor stator winding.

[0081] Furthermore, in this invention, in step two-two, the voltage equation is based on the extended back electromotive force:

[0082]

[0083] In the formula: i q i is the q-axis current of the stator winding. d This represents the d-axis current of the stator winding.

[0084] At this point, the extended back electromotive force takes the following form:

[0085]

[0086] Combining Equation 3, Equation 2 can be rewritten as a state equation with stator current as the state variable:

[0087]

[0088] Considering that the electromagnetic time constant is much smaller than the mechanical time constant, within adjacent calculation periods, it can be assumed that... Then Gong

[0089] Equation 3 yields the following approximate form of the state equation with the extended back electromotive force as the state variable:

[0090]

[0091] Furthermore, in this invention, in steps two and three, the full-order motor model with stator current and extended back electromotive force as state variables is as follows:

[0092]

[0093] In the formula: i=[i α i β ] T , e = [e α e β ] T These are the stator current and extended back electromotive force matrices in the α-β axis system, respectively; These are the stator current derivative matrix and the extended back electromotive force derivative matrix in the α-β axis system, respectively; u=[u α u β ] T The stator voltage matrix in the α-β axis system; Input matrix to the system; As the system state matrix.

[0094] Furthermore, in this invention, in step three, the observation equation for the extended back electromotive force of the motor stator current is:

[0095]

[0096] In the formula: These are the stator current and the observed extended back electromotive force matrix, respectively, observed in the α-β axis system; These are the stator current and the extended back electromotive force derivative matrices observed in the α-β axis system, respectively. Let be the state matrix under the observation equation, where The observed value of the rotor's electric angular velocity; The feedback gain matrix is ​​given by l, where l is the gain coefficient of the back EMF control signal, and l is greater than 0; v = [v α v β ] T It is the control signal input vector of the observer on the α-β axis, also known as the overall control law; It is the observed rotor electric angular velocity.

[0097] Furthermore, in this invention, the method for obtaining the stator current error equation in step four is as follows:

[0098] Consider i α =i d cosθ e -i q sinθ e i β =i d sinθ e +i q cosθ e During stable operation of the motor, i d i q Both are constants; then i α i β Differentiating with respect to time, we get:

[0099]

[0100] Therefore, the stator current error equation is obtained by subtracting the observation equation of the extended back EMF of the motor stator current from the full-order motor model with stator current and extended back EMF as state variables:

[0101]

[0102] In the formula: and It is the error between the observed current and the actual current in the α-β axis system; and It is the derivative of the error between the observed current and the actual current in the α-β axis system; and It is the error between the observed back electromotive force and the actual back electromotive force in the α-β axis system.

[0103] Furthermore, in this invention, in step five, the full-order terminal sliding surface is:

[0104]

[0105] In the formula: s is the sliding surface; It is the stator current error matrix; C1 and C2 are the stator current error derivative matrix; p / q are the design coefficients; p and q are the terminal absorption factors, where p and q are odd numbers and satisfy 0 < p / q < 1.

[0106] Furthermore, in this invention, the process of obtaining a continuous current observation signal in step six is ​​as follows:

[0107] Based on the control law of the full-order terminal sliding surface:

[0108] v = v c +v s Formula 11

[0109] In the formula: v = [v α v β ] T It is the overall control law for the full-order terminal sliding surface; v c =[v αc v βc ] T It is an equivalent control law; v s =[v αs v βs ] T It is a switching control law;

[0110] Obtain the equivalent control law and the switching control law:

[0111]

[0112]

[0113] In the formula: v c This is the equivalent control law; v s It is the switching control law; k and η are the designed gain coefficients; ε is the acceleration sliding mode reaching stage coefficient, and k, η and ε are all positive numbers;

[0114] Substitute the stator current error into the full-order terminal sliding surface;

[0115]

[0116] Substitute the equivalent control law and the switching control law into sα s β Obtain the expanded form:

[0117]

[0118] Then, the derivative of the sliding surface is calculated to obtain the full-order sliding surface derivative:

[0119]

[0120] Then, the sliding surface expansion and its derivative are substituted into the Lyapunov function to make the stator current error and the derivative of the stator current error converge to 0, so as to obtain a continuous current observation signal.

[0121] Specifically:

[0122] Design a Lyapunov function:

[0123] Taking the derivative of the function with respect to time t yields... Where V i =[V iα V iβ ] T V iα V iβ These are Lyapunov functions along the α-β axes, respectively;

[0124] Lyapunov function value V i satisfy At that time, the sliding surface s will converge to 0 in finite time; where, For V i The derivative of Then only Meeting convergence conditions

[0125] Consider the stability of the sliding surface along the α-β axes separately:

[0126]

[0127] make:

[0128]

[0129] Let k ≥ d + f0. In the motor model, L d =0.2e-3,L q =0.47e-3.

[0130] Under ideal simulation conditions considering steady-state conditions, the maximum error in observing the electric angular velocity is 2.09 rad / s, the maximum error in observing the α-β axis current derivative is 150°, and the estimation error of the back electromotive force derivative is... The maximum value is 0.5. Therefore, the maximum value of d is d. maxThe maximum value of f0 0max They are 300 and 2400 respectively.

[0131]

[0132] So, by Then, as the sliding surface s approaches 0, then:

[0133]

[0134] At this point, the full-order terminal sliding surface converges to 0 in a finite time, and the time t for the sliding surface s(t) = 0 is... r Represented as:

[0135]

[0136] at this time, and It will also reach 0 within a finite time, and the sign function in the control law, after integration, can be used to obtain a continuous current observation signal through the observation equation.

[0137] Furthermore, in this invention, in step seven, the adaptive rotational speed law is:

[0138]

[0139]

[0140] in, Let be the derivative of the observed electric angular velocity of the motor, and h be the adaptive gain to be designed. The extended back electromotive force α-axis component observed in the α-β axis system. v represents the β-axis component of the extended back electromotive force observed in the α-β axis system. α It is the α-axis component of the total control law of the full-order terminal sliding surface, v β It is the β-axis component of the overall control law of the full-order terminal sliding surface. The observed value of the electric angular velocity of the motor. denoted as the observed motor speed, and p represents the number of pole pairs of the permanent magnet synchronous motor.

[0141] The specific derivation process is as follows:

[0142] consider consider Differentiating with respect to time:

[0143]

[0144]

[0145] set up Taking the derivative with respect to time t, we get:

[0146]

[0147] At this point:

[0148]

[0149] Speed ​​adaptive law:

[0150]

[0151] By integrating the speed adaptive law, the electric angular velocity of the permanent magnet synchronous motor rotor can be obtained, and the motor speed is then known.

[0152] When a sliding mode occurs, it can be considered that If we assume that the observed speed tracks the actual speed of the motor, then we can approximate it as... Much smaller than ω e e β Then, the stability of the speed adaptive law and the accuracy of the observations are verified:

[0153] Combining Equations 8 and 21, Equation 23 can be approximated as follows:

[0154]

[0155] The Lyapunov functions for back electromotive force and electric angular velocity error are defined as follows:

[0156]

[0157] Differentiating Equation 27 with respect to time t yields:

[0158]

[0159] Substituting formulas 24 and 26 into formula 28, we get:

[0160]

[0161] Substituting the adaptive law designed in Formula 25 into it, we get:

[0162]

[0163] It can be known and It will asymptotically converge to z. α and z β , It will also gradually converge to ω e z αβ In The term will gradually approach 0, that is, z αβ=e αβ .

[0164] Furthermore, since the convergence characteristics of the back EMF affect the convergence speed of the speed adaptive law, an analysis of the back EMF convergence characteristics is performed. Subtracting Equation 6 from Equation 7 yields the back EMF error equation:

[0165]

[0166] When the observation system is stable, s=0 is considered Right now Considering again Formula 14 can then be simplified to:

[0167]

[0168] Substituting formula 32 into formula 31 yields the formula for the second-order homogeneous differential equation.

[0169]

[0170] Applying the Laplace transform to the formula for the second-order homogeneous differential equation yields the characteristic equation as follows:

[0171]

[0172] Solving the characteristic equation of formula 33 yields a pair of conjugate eigenvalues, as follows:

[0173]

[0174] Since the real part -l < ​​0, we know that the eigenvalues ​​are in the left half-plane, and the system is a homogeneous equation. Therefore, it can be proved that... It gradually converges to 0, but as the motor speed increases, its imaginary response increases, which can cause unnecessary oscillations in the system. Therefore, l is designed in the following form:

[0175]

[0176] Where l0>0, σ>0, The term σ can avoid system oscillations and accelerate the convergence of back EMF error to 0. The term σ prevents the back EMF signal from tracking too slowly when the speed is low. The existence of σ ensures the speed observation speed.

[0177] At high motor speeds, the observed values ​​of this invention can quickly track the actual values, ensuring that regardless of changes in the speed setpoint, especially at high motor speeds, this invention effectively improves the speed observation signal's speed and smoothness. Traditional methods using PLLs cannot effectively extract speed at high motor speeds. The method described in this invention effectively avoids the problem of slow tracking speed and poor smoothness of the observed signal reducing the speed, stability, and control accuracy of the sensorless motor control system. Simulation verification shows that... Figure 3 The observed back electromotive force signal shows that it has a high sinusoidal degree and a smooth curve. Figure 4 and Figure 6 These are the waveforms of the actual rotational speed, the observed rotational speed, and the rotational speed observation error, respectively. Figure 5 and Figure 7 The waveforms are for the true angle, the observed angle, and the angle observation error, respectively. As can be seen from the waveforms above, the observed signal obtained by the method described in this invention can quickly track the actual signal, and its observation error is relatively small.

[0178] While the invention has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of the invention. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A method for adaptive observation of the full-order terminal sliding mode speed of a permanent magnet synchronous motor, characterized in that, include: Step 1: Collect the three-phase current of the stator winding of the permanent magnet synchronous motor , , The three-phase current is subjected to Park transformation. , , By performing a coordinate transformation, the phase currents in the two-phase stationary coordinate system are obtained. , ; Step 2: Utilize the phase current in a two-phase stationary coordinate system , A full-order motor model based on extended back electromotive force is established using the α-axis and β-axis components of the given voltage at the stator winding terminals of the motor. Step 3: Based on the full-order motor model, design the observation equation for the extended back electromotive force of the motor stator current; Step 4: Using the full-order motor model and the observation equation, establish the stator current error equation; calculate the stator current error; Step 5: Based on the stator current error, design the full-order terminal sliding mode surface and obtain the sliding mode control law; Step 6: Using the sliding mode control law and Lyapunov function, obtain the continuous current observation signal when the stator current error and the derivative of the stator current error converge to 0. Step 7: Based on the current observation signal and the observation equation, design a speed adaptive law, integrate the speed adaptive law, and obtain the speed of the permanent magnet synchronous motor rotor; In step five, the full-order terminal sliding surface is: In the formula: It is a sliding surface; It is the stator current error matrix; It is the stator current error derivative matrix; and It is the error between the observed current and the actual current in the α-β axis system; and It is the derivative of the error between the observed current and the actual current in the α-β axis system; and It is a design coefficient; It is the terminal absorption factor. and It is an odd number and satisfies ; In step six, the process of obtaining continuous current observation signals is as follows: First, the stator current error is substituted into the full-order terminal sliding surface to obtain the specific expansion formula of the sliding surface; Based on the control law of the full-order terminal sliding surface: In the formula: It is the control law for the full-order terminal sliding surface; It is an equivalent control law; It is a switching control law; Obtain the equivalent control law and the switching control law: In the formula: This is an equivalent control law; It is a switching control law; and It is the gain coefficient of the design; It is the coefficient that accelerates the sliding mode to reach the stage, and , and All are positive numbers; Substituting the equivalent control law and the switching control law... , Obtain the expanded form: Then, for the sliding surface components , Find the derivative; obtain the full-order sliding surface derivative: ； Finally, the sliding surface expansion and its derivative are substituted into the Lyapunov function to make the stator current error and the derivative of the stator current error converge to 0, thus obtaining a continuous current observation signal. In step seven, the adaptive speed law is: in, The derivative of the observed electric angular velocity of the motor, For the adaptive gain to be designed, The extended back electromotive force α-axis component observed in the α-β axis system. The extended back electromotive force β-axis component observed in the α-β axis system. It is the α-axis component of the overall control law of the full-order terminal sliding surface. It is the β-axis component of the overall control law of the full-order terminal sliding surface. The observed value of the electric angular velocity of the motor. denoted as the observed motor speed, and p represents the number of pole pairs of the permanent magnet synchronous motor.

2. The adaptive observation method for the full-order terminal sliding mode speed of a permanent magnet synchronous motor according to claim 1, characterized in that, In step two, the process of establishing a full-order motor model based on extended back electromotive force is as follows: Step 2:

1. Establish the stator voltage equations of the permanent magnet synchronous motor in the α-β axis coordinate system; Step 22: Using the stator voltage equation, construct a voltage equation based on the extended back electromotive force; Steps 2 and 3: Using the extended back EMF representation in the voltage equation based on extended back EMF, construct a full-order motor model with stator current and extended back EMF as state variables, thus completing the establishment of the full-order motor model based on extended back EMF.

3. The adaptive observation method for the full-order terminal sliding mode speed of a permanent magnet synchronous motor according to claim 2, characterized in that, In step two, the stator voltage equation is: In the formula: It is the α-axis component of the voltage at the stator winding terminals of the motor. It is the β-axis component of the voltage at the stator winding terminals of the motor; It is the α-axis component of the phase current of the motor stator winding. It is the β-axis component of the phase current of the motor stator winding; It is the resistance of the motor stator winding. It is the electric angular velocity of the motor rotor. It is the rotor position angle of the motor. is the rotor flux linkage of the motor, and p is the differential operator; ; ; ; ; ; It is the α-axis component of the stator winding inductance of the motor. It is the β-axis component of the stator winding inductance of the motor. It is an α-β axis coupled inductor; It is the average inductance of the motor stator winding along the dq axis. It is the differential inductance of the dq axis of the motor stator winding; It is the d-axis component of the motor stator winding inductance. It is the q-axis component of the inductance of the motor stator winding.

4. The adaptive observation method for the full-order terminal sliding mode speed of a permanent magnet synchronous motor according to claim 3, characterized in that, In step 22, the voltage equation based on the extended back electromotive force is: In the formula: , This refers to the q-axis current of the stator winding. This represents the d-axis current of the stator winding.

5. The adaptive observation method for the full-order terminal sliding mode speed of a permanent magnet synchronous motor according to claim 4, characterized in that, In steps two and three, the full-order motor model with stator current and extended back electromotive force as state variables is as follows: In the formula: , These are the stator current and extended back electromotive force matrices in the α-β axis system, respectively; , These are the stator current derivative matrix and the extended back electromotive force derivative matrix in the α-β axis system, respectively; The stator voltage matrix in the α-β axis system; Input matrix to the system; , , All of these are used as system state matrices.

6. The adaptive observation method for the full-order terminal sliding mode speed of a permanent magnet synchronous motor according to claim 5, characterized in that, In step three, the observation equation for the extended back electromotive force of the motor stator current is: In the formula: , These are the stator current and the observed extended back electromotive force matrix, respectively, observed in the α-β axis system; , These are the stator current and the extended back electromotive force derivative matrices observed in the α-β axis system, respectively. , Let be the state matrix under the observation equation, where The observed value of the rotor's electric angular velocity; Let l be the feedback gain matrix, where l is the gain coefficient of the back EMF control signal, and l is greater than 0. It is the control signal input vector of the observer on the α-β axis, also known as the overall control law; It is the observed rotor electric angular velocity.

7. The adaptive observation method for the full-order terminal sliding mode speed of a permanent magnet synchronous motor according to claim 6, characterized in that, In step four, the stator current error equation is: In the formula: and It is the error between the observed back electromotive force and the actual back electromotive force in the α-β axis system.

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