Sensorless Control Method of Brushless DC Motor Based on a Novel Reaching Law Sliding Mode Observer

Abstract

The present invention discloses a sensorless control method for a brushless DC motor based on a novel reaching law sliding mode observer, specifically as follows: Step 1, establish a mathematical model of the brushless DC motor in the three-phase stationary coordinate system, and derive the expression of the line back electromotive force and the state equation of the brushless DC motor; Step 2, establish a mathematical model of the sliding mode observer according to the state equation of the brushless DC motor, and obtain the expression of the observed value of the line back electromotive force through the stator current error equation; Step 3, to improve the convergence speed of the sliding mode observer model and reduce chattering, introduce a novel reaching law to improve the convergence rate of the sliding mode observer and suppress chattering at the same time, and analyze the performance of this reaching law to optimize the observed value of the line back electromotive force; Step 4, calculate the motor speed and position information using the observed value of the line back electromotive force, and add an angle compensation on this basis to make up for the phase delay caused by the low-pass filter.

Description

Technical Field

[0001] The present invention belongs to the technical field of sensorless control of brushless DC motors, and particularly relates to a sensorless control method for brushless DC motors based on a novel reaching law sliding mode observer. Background Art

[0002] A brushless DC motor (BLDC) is a DC commutator motor with an internal-to-external structure that replaces mechanical commutation with electronic commutation, and has the advantages of high efficiency, large torque and power density, low cost, simple structure, good controllability, and large torque-inertia ratio. Usually, the rotor poles of a brushless DC motor use tile-shaped permanent magnets. Through magnetic circuit design, a trapezoidal air-gap magnetic density can be obtained. The stator windings mostly use concentrated full-pitch windings, so a better trapezoidal back electromotive force waveform can be obtained. In a high-performance brushless DC motor control system, a position sensor is usually used to obtain an accurate rotor position signal to achieve commutation and speed regulation of the motor. However, the position sensor affects the reliability, cost, and volume of the control system. In order to reduce the control cost and expand the applicable range, sensorless control technology is often used. Therefore, in recent years, sensorless control of brushless DC motors has become a research hotspot.

[0003] Commonly used sensorless methods for brushless DC motors include back electromotive force methods (including terminal voltage detection method, back electromotive force integration method, back electromotive force third harmonic method, freewheeling diode method, line back electromotive force method), phase-locked loop method, inductance method, flux linkage method, artificial intelligence method, etc. Among them, the back electromotive force method is currently the most mature and widely used position detection method. In the back electromotive force detection algorithm, the commutation moment of the winding is obtained by shifting 30° electrical angle from the zero crossing point of the back electromotive force. The phase shift angle is related to the motor speed. When the speed is very low, the detection accuracy is significantly reduced, which easily causes inaccurate commutation. The line back electromotive force detection algorithm eliminates the calculation of the phase shift angle compared with the back electromotive force detection algorithm, and the commutation moment of the winding is directly obtained from the zero crossing point of the line back electromotive force. After converting the back electromotive force into a line back electromotive force signal, it can be found that the zero crossing point of the line back electromotive force signal is exactly the jump point of the motor Hall sensor, that is, the commutation moment. Therefore, only by detecting the zero crossing point of the line back electromotive force can the correct commutation of the motor be achieved. The algorithm is simple and easy to implement, and its performance is better than that of the back electromotive force detection algorithm.

[0004] The sliding mode observer has excellent robust performance, with advantages such as good dynamic performance, strong anti-interference ability, and low sensitivity to parameter changes. The sliding mode observer has been widely applied in motor control scenarios such as induction motors and permanent magnet synchronous motors. The sliding mode observer can also be applied to brushless DC motors. By detecting the motor current and voltage, a mathematical model of the sliding mode line back electromotive force observer is established. The sliding mode observer estimates the line back electromotive force, and then calculates the rotor speed and position angle. Therefore, the sliding mode observer can be used to estimate the line back electromotive force to achieve sensorless control of brushless DC motors. However, due to the discontinuous characteristic of its sign function, it is easy to cause chattering phenomena in the system; when using a low-pass filter to filter the observed values, phase delay will occur, reducing the rotor position estimation performance of the sliding mode observer. Summary of the Invention

[0005] The object of the present invention is to provide a sensorless control method for brushless DC motors based on a novel reaching law sliding mode observer, which effectively suppresses the chattering phenomenon of the traditional sliding mode observer and accurately estimates the rotor position of the brushless DC motor.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is: a sensorless control method for brushless DC motors based on a novel reaching law sliding mode observer, which is specifically implemented according to the following steps:

[0007] Step 1, establish a mathematical model of the brushless DC motor in the three-phase stationary coordinate system, and derive the expression of the line back electromotive force and the state equation of the brushless DC motor;

[0008] Step 2, establish a mathematical model of the sliding mode observer according to the state equation of the brushless DC motor, and obtain the expression of the observed value of the line back electromotive force through the stator current error equation;

[0009] Step 3, in order to improve the convergence speed of the sliding mode observer model and reduce chattering, introduce a novel reaching law to improve the convergence rate of the sliding mode observer and suppress chattering at the same time, and analyze the performance of this reaching law to optimize the observed value of the line back electromotive force;

[0010] Step 4, calculate the motor speed and position information using the observed value of the line back electromotive force, and add an angle compensation on this basis to make up for the phase delay caused by the low-pass filter.

[0011] As a preferred technical solution of the present invention, in the said Step 1, establishing the mathematical model of the brushless DC motor is specifically as follows:

[0012] Step 1.1, based on the terminal voltage formula of the brushless DC motor in the three-phase stationary coordinate system as shown below:

[0013]

[0014] In formula (1): u a 、u b 、u c is the winding terminal voltage; i a 、i b 、i c is the phase current; e a 、e b 、e c is the reverse electromotive force; R is the stator resistance; L is the self-inductance of each phase winding of the stator; M is the mutual inductance between every two phase windings of the stator;

[0015] Subtracting the three equations in formula (1) from each other, we can get the three-phase line voltage equation of the brushless DC motor:

[0016]

[0017] In formula (2): u ab 、u bc is the winding line voltage; i ab 、i bc is the phase voltage difference; e ab 、e bc For the line back electromotive force, the three-phase line back electromotive force of the brushless DC motor has the following relationship:

[0018] e ab +e bc +e ca =0 (3).

[0019] As a preferred technical solution of the present invention, in step 1, the expression of line back electromotive force is derived, specifically:

[0020] Step 1.2, write equation (2) into matrix form:

[0021]

[0022] As a preferred technical solution of the present invention, in step 1, the state equation of the brushless DC motor is derived, specifically:

[0023] Step 1.3, replace i in formula (4) ab 、i bc Defined as a state variable, u ab 、u bc Defined as the system input, e ab 、e bc is the system output, from which the state equation of the brushless DC motor can be derived:

[0024]

[0025] As a preferred technical solution of the present invention, in the step 2, a sliding mode observer mathematical model is established according to the brushless DC motor state equation, specifically as follows:

[0026] Step 2.1, establish a sliding mode observer mathematical model according to the brushless DC motor state equation:

[0027]

[0028] In Equation (6), represents the estimated value of the line current, Z ab , Z bc are control functions, and the expressions are as follows:

[0029]

[0030] where K is the sliding mode control gain, and sgn(x) is the sign function, that is:

[0031]

[0032] As a preferred technical solution of the present invention, in the step 2, the expression of the line back electromotive force observation value is obtained through the stator current error equation, specifically as follows:

[0033] Step 2.2, subtract Equation (5) from Equation (6) to obtain the stator current error equation:

[0034]

[0035] In Equation (9), represents the difference between the estimated value and the actual value of the line current;

[0036] Step 2.3, when the system reaches the sliding mode region, it can be considered that the current estimated value is equal to the actual value, and we get:

[0037]

[0038] In this way, the value of the back electromotive force can be obtained as follows:

[0039]

[0040] Equation (11) shows that the motor back electromotive force can be estimated by the observer, but the back electromotive force expressed by this equation is included in the sgn(x) function; this function is not a continuous quantity and there is high-frequency harmonic interference. In order to obtain the true motor back electromotive force, this function needs to be low-pass filtered; the back electromotive force obtained after low-pass filtering is:

[0041]

[0042] In the formula, is the observed value of the line back electromotive force, ω c represents the cut-off frequency of the low-pass filter.

[0043] As a preferred technical solution of the present invention, in the said step 3, in order to improve the convergence speed of the sliding mode observer model and reduce chattering, a new reaching law is introduced to improve the convergence rate of the sliding mode observer, while suppressing chattering, and the performance of this reaching law is analyzed, so as to optimize the observed value of the line back electromotive force, specifically:

[0044] Step 3.1, select the sliding mode surface as follows:

[0045]

[0046] In formula (13), S is the sliding mode surface; as the system state reaches the sliding mode surface, the stator current error approaches 0, and the expression of the line back electromotive force can be obtained as follows:

[0047]

[0048] Step 3.2, introduce a new type of fast variable reaching law to improve the sliding mode observer, change the constant speed reaching law K in formula (7) to the new reaching law g(x1, S), and obtain the control function Z ab 、Z bc expression:

[0049]

[0050] wherein,

[0051]

[0052] In the formula, k1>0; k2>0; δ>0; 0<ε<1; x1 is the error state variable of the system, and its expression is:

[0053]

[0054] Step 3.3, analyze the performance of this new reaching law as follows:

[0055] When the system state is far from the sliding mode, the value of |x1| increases, and the function value of g(x1, S) is approximately equal to -k2S plays a leading role, which can ensure that the system approaches the sliding mode at a relatively fast speed;

[0056] When the system state is close to the sliding mode, the value of |x1| decreases, and the function value of g(x1, S) is approximately equal to 0, and -g(x1, S) plays a leading role in the convergence rate, making the system reach a stable equilibrium point;

[0057] Through the test of Lyapunov stability theorem, the new reaching law has stability; according to Equation (14), the observed value of the line back electromotive force can be obtained

[0058] As a preferred technical solution of the present invention, in the step 4, the motor speed and position information are calculated by using the observed value of the line back electromotive force, and an angle compensation is added on this basis to make up for the phase delay caused by the low-pass filter, specifically as follows:

[0059] Step 4.1, calculate the motor speed; according to Equation (3), the line back electromotive force e ca is:

[0060] e ca =-e ab -e bc (18)

[0061] When the brushless DC motor rotates, the magnitude of the winding back electromotive force is proportional to the speed; at the same time, since the phase winding back electromotive force of the motor is a trapezoidal wave, at any moment, the maximum value of the line back electromotive force is twice the maximum value of the phase winding back electromotive force, and the electrical angular velocity of the motor is p times the mechanical angular velocity (p is the number of pole pairs), that is:

[0062]

[0063]

[0064] In the formula, is the estimated value of the rotor angular velocity of the motor, is the maximum value of the three estimated line back electromotive forces, and K ω is the back electromotive force constant of the brushless DC motor;

[0065] Step 4.2, calculate the rotor position of the motor. The rotor position of the motor is the integral of the electrical angle, and its specific expression is:

[0066]

[0067] Among them, θ0 is the initial position angle of the motor rotor, and the determination of this initial value is related to the starting function. To simplify the control process, it can be positioned within the range of 0° to 60° in the starting function;

[0068] Step 4.3, perform rotor position angle compensation; because a certain phase delay will be generated after adding the filter, and the smaller the cut-off frequency, the larger the generated phase delay angle, so a certain angle compensation is also required to improve the estimation accuracy of the rotor rotation angle, and the improvement is as follows:

[0069]

[0070] In formula (22), is the estimated angular velocity after phase compensation; is the estimated rotor position angle after phase compensation;

[0071] Then, based on the estimated angular position of the rotor, the brushless DC motor can be driven to operate according to the sequence of the six-step conduction phases of the brushless DC motor. Thus, a sensorless control method for a brushless DC motor based on a novel reaching law sliding mode observer is realized.

[0072] The beneficial effects of the present invention are as follows: A sensorless control method for a brushless DC motor based on a novel reaching law sliding mode observer according to the present invention introduces a novel reaching law to improve the traditional sliding mode observer, which can suppress chattering while increasing the convergence speed of the observer. When using the traditional sliding mode observer for sensorless control of a brushless DC motor, due to the discontinuous characteristic of the sign function, chattering of the system is likely to occur. At the same time, when using a low-pass filter to filter the observed value, phase delay will be generated, reducing the rotor position estimation performance of the sliding mode observer. Therefore, a novel reaching law is introduced to improve the traditional sliding mode observer. Since this reaching law is a smooth function, compared with the traditional sliding mode observer, the sliding mode observer using the novel reaching law effectively suppresses the chattering of the back electromotive force observed value, increases the convergence speed, and has strong robustness and stability. At the same time, angle compensation is added during the calculation of the rotor position, which can effectively compensate for the influence of the phase delay caused by the low-pass filter and improve the sensorless rotor position estimation performance of the brushless DC motor. Description of the Drawings

[0073] Figure 1 is the schematic diagram of a sensorless control method for a brushless DC motor based on a novel reaching law sliding mode observer according to the present invention;

[0074] Figure 2 is the structural block diagram of the sliding mode observer using the novel reaching law in the present invention. Detailed Embodiments

[0075] A sensorless control method for a brushless DC motor based on a novel reaching law sliding mode observer according to the present invention is characterized in that it is specifically implemented according to the following steps:

[0076] Step 1: Establish the mathematical model of the brushless DC motor in the three-phase stationary coordinate system, and derive the expression of the line back electromotive force and the state equation of the brushless DC motor, specifically as follows:

[0077] Step 1.1: Establish the mathematical model of the brushless DC motor in the three-phase stationary coordinate system:

[0078] Based on the terminal voltage formula of the brushless DC motor in the three-phase stationary coordinate system as shown below:

[0079]

[0080] In Equation (1): u a , u b , u c is the winding terminal voltage; i a , i b , i c is the phase current; e a , e b , e c is the back electromotive force; R is the stator resistance; L is the self - inductance of each phase winding of the stator; M is the mutual inductance between every two phase windings of the stator;

[0081] By subtracting the three equations of Equation (1) from each other pairwise, the three - phase line voltage equation of the brushless DC motor can be obtained:

[0082]

[0083] In Equation (2): u ab , u bc is the winding line voltage; i ab , i bc is the phase voltage difference; e ab , e bc is the line back electromotive force. There is a relationship among the three - phase line back electromotive forces of the brushless DC motor:

[0084] e ab +e bc +e ca = 0 (3).

[0085] Step 1.2, derive the expression of the line back electromotive force:

[0086] Write Equation (2) in matrix form:

[0087]

[0088] Step 1.3, derive the state equation of the brushless DC motor:

[0089] Define i ab , i bc in Equation (4) as state variables, u ab , u bc as system input variables, and e ab , e bc as system output variables. Thus, the state equation of the brushless DC motor can be derived:

[0090]

[0091] Step 2: Establish the mathematical model of the sliding mode observer according to the state equation of the brushless DC motor. Through the stator current error equation, obtain the expression of the estimated value of the line back electromotive force, specifically as follows:

[0092] Step 2.1: Establish the mathematical model of the sliding mode observer according to the state equation of the brushless DC motor:

[0093]

[0094] In formula (6), represents the estimated value of the line current, and Z ab , Z bc are control functions, and the expressions are as follows:

[0095]

[0096] Among them, K is the sliding mode control gain, and sgn(x) is the sign function, that is:

[0097]

[0098] Step 2.2: Subtract formula (5) from formula (6) to obtain the stator current error equation:

[0099]

[0100] In formula (9), represents the difference between the estimated value and the actual value of the line current;

[0101] Step 2.3: When the system reaches the sliding mode region, it can be considered that the estimated current value is equal to the actual value, and we get:

[0102]

[0103] In this way, the value of the back electromotive force can be obtained as follows:

[0104]

[0105] Formula (11) shows that the motor back electromotive force can be estimated by the observer, but the back electromotive force expressed by this formula is included in the sgn(x) function; this function is not a continuous quantity and there is high-frequency harmonic interference. In order to obtain the true motor back electromotive force, this function needs to be low-pass filtered; the back electromotive force obtained after low-pass filtering is:

[0106]

[0107] In the formula, is the observed value of the line back electromotive force, and ω c represents the cut-off frequency of the low-pass filter;

[0108] Step 3. To improve the convergence speed of the sliding mode observer model and reduce chattering, a new reaching law is introduced to increase the convergence rate of the sliding mode observer while suppressing chattering, and the performance of this reaching law is analyzed to optimize the observed value of the line back electromotive force, specifically as follows:

[0109]

[0110] In Equation (13), S is the sliding mode surface; as the system state reaches the sliding mode surface, the stator current error approaches 0, and the expression of the line back electromotive force can be obtained as follows:

[0111]

[0112] Step 3.2. A new type of fast variable reaching law is introduced to improve the sliding mode observer. The constant speed reaching law K in Equation (7) is changed to the new reaching law g(x1, S), and the control functions Z ab and Z bc are obtained as follows:

[0113]

[0114] where

[0115]

[0116] In the formula, k1>0; k2>0; δ>0; 0<ε<1; x1 is the error state variable of the system, and its expression is:

[0117]

[0118] Step 3.3. Analyze the performance of this new reaching law as follows:

[0119] When the system state is far from the sliding mode, the value of |x1| increases, and the function value of g(x1, S) is approximately equal to -k2S plays a dominant role, which can ensure that the system approaches the sliding mode at a relatively fast speed;

[0120] When the system state is close to the sliding mode, the value of |x1| decreases, and the function value of g(x1, S) is approximately equal to 0. -g(x1, S) plays a dominant role in the convergence rate, making the system reach a stable equilibrium point;

[0121] Through the Lyapunov stability theorem test, this new reaching law has stability; according to Equation (14), the observed value of the line back electromotive force can be obtained

[0122] Step 4: Calculate the motor speed and position information using the observed line back electromotive force (back-EMF) values, and add an angle compensation on this basis to make up for the phase delay caused by the low-pass filter. Specifically:

[0123] Step 4.1: Calculate the motor speed; according to Equation (3), the line back-EMF e can be calculated as: ca as follows:

[0124] e ca =-e ab -e bc (18)

[0125] When the brushless DC motor rotates, the magnitude of the winding back-EMF is proportional to the speed; at the same time, since the phase winding back-EMF of the motor is a trapezoidal wave, at any moment, the maximum value of the line back-EMF is twice the maximum value of the phase winding back-EMF, and the electrical angular velocity of the motor is p times the mechanical angular velocity (p is the number of pole pairs), that is:

[0126]

[0127]

[0128] In the formula, is the estimated value of the motor rotor angular velocity, is the maximum value of the three estimated line back-EMFs, and K ω is the back-EMF constant of the brushless DC motor;

[0129] Step 4.2: Calculate the motor rotor position. The rotor position of the motor is the integral of the electrical angle, and its specific expression is:

[0130]

[0131] where θ0 is the initial position angle of the motor rotor. The determination of this initial value is related to the starting function. To simplify the control process, it can be positioned within the range of 0° to 60° in the starting function;

[0132] Step 4.3: Perform rotor position angle compensation; since the phase will have a certain delay after adding the filter, and the smaller the cut-off frequency, the larger the phase delay angle generated, so a certain angle compensation is also required to improve the estimation accuracy of the rotor rotation angle. The improvement is as follows:

[0133]

[0134] In Equation (22), is the estimated angular velocity after phase compensation; is the estimated rotor position angle after phase compensation;

[0135] Therefore, the estimated rotor angular position can be used to drive the brushless DC motor according to the sequence of its six-step conduction phases. Thus, a sensorless control method for a brushless DC motor based on a new reaching law sliding mode observer has been realized.

[0136] This paper proposes a sensorless control method for brushless DC motors based on a novel reaching-law sliding-mode observer. This method improves upon the traditional sliding-mode observer by introducing a novel reaching-law. Compared to the traditional sliding-mode observer, the improved sliding-mode observer using the novel reaching-law effectively suppresses chattering in the back-electromotive force (BEM) observations, demonstrating greater robustness and stability. Furthermore, angle compensation is incorporated into the rotor position calculation to effectively compensate for phase delay.

[0137] like Figure 1 As shown, the present invention proposes a sensorless control method for a brushless DC motor based on a novel reaching law sliding mode observer. This method uses dual closed-loop speed and current control and utilizes the classic PI control algorithm. The dual closed-loop control system of the brushless DC motor uses a PWM chopper to chop the DC power supply into a PWM wave, thereby changing the average voltage applied to the armature to adjust the motor speed. Since the zero crossing point of the line back electromotive force is the commutation moment, Figure 1 The line back electromotive force method is used for sensorless control. The terminal voltage and phase current of the motor are detected, and the line voltage and line current are calculated. The line back electromotive force is estimated by using the improved sliding mode observer, and then the speed and position information of the rotor are calculated. The sensorless control method of the brushless DC motor based on the improved sliding mode observer is realized. The structural block diagram of the improved sliding mode observer is shown in the figure. Figure 2 As shown in the figure, a new reaching law is used to replace the traditional constant velocity reaching law. Since the reaching law is a smooth function, it can effectively reduce the chattering. When calculating the rotor position, angle compensation is added to reduce the phase error caused by the low-pass filter.

Claims

1. A sensorless control method for a brushless DC motor based on a novel reaching law sliding mode observer, characterized in that, The implementation is specifically carried out according to the following steps: Step 1: Establish a mathematical model of the brushless DC motor in the three-phase static coordinate system, and derive the expression of the line back electromotive force and the state equation of the brushless DC motor; Step 2: Establish a mathematical model of the sliding mode observer according to the state equation of the brushless DC motor, and obtain the expression of the observed value of the line back electromotive force through the stator current error equation; Step 3: To improve the convergence speed of the sliding mode observer model and reduce chattering, a new reaching law is introduced to improve the convergence rate of the sliding mode observer and suppress chattering at the same time, and the performance of this reaching law is analyzed to optimize the observed value of the line back electromotive force; Step 4: Calculate the motor speed and position information using the observed value of the line back electromotive force, and add an angle compensation on this basis to make up for the phase delay caused by the low-pass filter; In the said Step 1, the mathematical model of the brushless DC motor is established as follows: Step 1.1: Based on the terminal voltage formula of the brushless DC motor in the three-phase static coordinate system as follows: (1) In Equation (1): , , are the winding terminal voltages; , , are the phase currents; , , are the back electromotive forces; R is the stator resistance; L is the self-inductance of each stator phase winding; M is the mutual inductance between every two stator windings; Subtract the three equations in Equation (1) from each other in pairs to obtain the three-phase line voltage equation of the brushless DC motor: (2) In Equation (2): and are the winding line voltages; and are the phase voltage differences; and are the line back electromotive forces. There is a relationship among the three-phase line back electromotive forces of the brushless DC motor: (3)； In the said Step 1, the expression of the line back electromotive force is derived as follows: Step 1.2: Write Equation (2) in matrix form: (4)； In the said Step 1, the state equation of the brushless DC motor is derived as follows: Step 1.3, take the and in Equation (4) as state variables, and as system input variables, and as system output variables. Thus, the state equation of the brushless DC motor can be derived: (5)。 2. The sensorless control method of the brushless DC motor based on the novel reaching law sliding mode observer according to claim 1, wherein In the said Step 2, the mathematical model of the sliding mode observer is established according to the state equation of the brushless DC motor as follows: Step 2.1: Establish a mathematical model of the sliding mode observer according to the state equation of the brushless DC motor: (6) In formula (6), , represent the predicted values of line currents, , are control functions, and the expressions are as follows: (7) Among them, K is the sliding mode control gain, is the sign function, that is: (8)。 3. The sensorless control method for a brushless DC motor based on a novel reaching law sliding mode observer according to claim 2, wherein In the said Step 2, the expression of the observed value of the line back electromotive force is obtained through the stator current error equation as follows: Step 2.2: Subtract Equation (6) from Equation (5) to obtain the stator current error equation: (9) In formula (9), and represent the difference between the predicted value and the actual value of the line current; Step 2.3: When the system reaches the sliding mode region, it can be considered that the estimated current value is equal to the actual value, and we get: (10) In this way, the value of the back electromotive force is obtained as follows: (11) Equation (11) shows that the back electromotive force of the motor is estimated by the observer, but the back electromotive force expressed by this equation is included in the function; This function is not a continuous quantity and there is high-frequency harmonic interference. In order to obtain the true back electromotive force of the motor, this function needs to be low-pass filtered; the back electromotive force obtained after low-pass filtering is: (12) In the formula, and are the observed values of the line back electromotive force, represents the cut-off frequency of the low-pass filter.

4. The sensorless control method of a brushless DC motor based on a novel reaching law sliding mode observer according to claim 3, characterized in that, In the said Step 3, to improve the convergence speed of the sliding mode observer model and reduce chattering, a new reaching law is introduced to improve the convergence rate of the sliding mode observer and suppress chattering at the same time, and the performance of this reaching law is analyzed to optimize the observed value of the line back electromotive force as follows: Step 3.1: Select the sliding mode surface as follows: (13) In Equation (13), is the sliding mode surface; as the system state reaches the sliding mode surface, the stator current error approaches 0, and the expression of the line back electromotive force can be obtained as follows: (14) Step 3.2, introduce a new type of fast variable reaching law to improve the sliding mode observer, and change the constant velocity reaching law in Equation (7) K to the new reaching law , and obtain the expressions of the control functions and under the new variable velocity reaching law: (15) Where, (16) In the formula, ; ; ; ; is the error state variable of the system, and its expression is: (17) Step 3.3: Analyze the performance of this new reaching law as follows: When the system state is far from the sliding mode, the value of increases, and the function value of is approximately equal to which plays a dominant role and can ensure that the system approaches the sliding mode at a relatively fast speed; When the system state is close to the sliding mode, the value of decreases, and the function value of is approximately equal to 0, which plays a dominant role in the convergence rate and makes the system reach a stable equilibrium point; It is verified by the Lyapunov stability theorem that the new reaching law has stability; the observation value of the line back electromotive force can be obtained according to Equation (14). , .

5. The sensorless control method for a brushless DC motor based on a novel reaching law sliding mode observer according to claim 4, wherein In the said Step 4, calculate the motor speed and position information using the observed value of the line back electromotive force, and add an angle compensation on this basis to make up for the phase delay caused by the low-pass filter as follows: Step 4.1, calculate the motor speed; according to Equation (3), the back electromotive force of the wire can be calculated as follows: (18) When the brushless DC motor rotates, the magnitude of the back electromotive force of the winding is proportional to the rotational speed; at the same time, since the back electromotive force of the motor phase winding is a trapezoidal wave, at any moment, the maximum value of the line back electromotive force is twice the maximum value of the phase winding back electromotive force, and the electrical angular velocity of the motor is p times that of the mechanical angular velocity, that is: (19) (20) In the formula, is the estimated value of the angular velocity of the motor rotor, is the maximum value of the three line back electromotive forces estimated, is the back electromotive force constant of the brushless DC motor; Step 4.2: Calculate the rotor position of the motor; the rotor position of the motor is the integral of the electrical angle, and its specific expression is: (21) Among them, is the initial position angle of the motor rotor. The determination of this initial value is related to the starting function. To simplify the control process, it can be positioned within the range of 0° to 60° in the starting function. Step 4.3: Perform rotor position angle compensation; because the phase will produce a certain delay after adding the filter, and the smaller the cut-off frequency, the larger the phase delay angle generated, so a certain angle compensation is also required to improve the estimation accuracy of the rotor rotation angle, and the improvement is as follows: (22) In formula (22), is the estimated angular velocity after phase compensation; is the estimated rotor position angle after phase compensation; Then, based on the estimated angular position of the rotor, the brushless DC motor is driven to operate according to the sequence of the six-step conduction phases of the brushless DC motor. Thus, a sensorless control method for the brushless DC motor based on a novel reaching law sliding mode observer is realized.

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