Sensorless Control Method of Brushless DC Motor Based on New Flux Linkage Function Method

Abstract

The present invention discloses a sensorless control method for a brushless DC motor based on a novel flux linkage function method, 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 rotor flux linkage of the brushless DC motor; Step 2. According to the relationship between the line back electromotive force and the speed, construct a traditional speed-independent flux linkage function by comparing the expression of the line rotor flux linkage of the brushless DC motor pairwise; Step 3. For the integral structure existing in the traditional speed-independent flux linkage function, use a frequency adaptive filter to replace the pure integrator to suppress harmonic components and DC offsets, construct an improved flux linkage function, and judge the commutation point of the motor through the improved flux linkage function, and at the same time calculate the rotor angular velocity to achieve a sensorless control method. The sensorless control method for a brushless DC motor based on the novel flux linkage function method effectively suppresses the phenomenon of harmonic components and DC offsets generated by using a pure integrator in the traditional flux linkage function.

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 flux linkage function method. Background Art

[0002] A brushless DC motor (BLDC) is a DC commutator motor from inside to outside with electronic commutation replacing brush mechanical commutation, and has advantages such as 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 adopt tile-shaped permanent magnets, and through magnetic circuit design, a trapezoidal air-gap magnetic density can be obtained. The stator windings mostly adopt 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 accurate rotor position signals 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, the 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 the most mature and widely used position detection method at present. In the back electromotive force detection algorithm, the commutation moment of the winding is obtained by shifting 30° electrical angle from the zero crossing of the back electromotive force. The phase shift angle is related to the motor speed, and the detection accuracy is significantly reduced when the speed is very low, which is likely to cause 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 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 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 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 superior to that of the back electromotive force detection algorithm.

[0004] Different from the back electromotive force method, the flux linkage method obtains rotor position information by estimating the flux linkage. Starting from the motor voltage equation, the flux linkage calculation formula is derived. By constructing the flux linkage function of the brushless DC motor, the estimated rotor position error is small. Since only information such as motor voltage, current, motor parameters, and initial flux linkage is required during the estimation process, which is independent of the motor speed, etc., it has the advantage of a wide speed regulation range and is an ideal detection method. However, due to the integral structure existing in the traditional flux linkage function, using a pure integrator to integrate the back electromotive force to calculate the stator flux linkage is easily affected by the DC offset error in the input signal, resulting in poor dynamic and static performance of the motor. Summary of the Invention

[0005] The object of the present invention is to provide a sensorless control method for a brushless DC motor based on a novel flux linkage function method, which effectively suppresses the phenomenon of harmonic components and DC offset generated by the traditional flux linkage function using a pure integrator, 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 a brushless DC motor based on a novel flux linkage function method, 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 line rotor flux linkage expression of the brushless DC motor;

[0008] Step 2, according to the relationship between the line back electromotive force and the speed, construct a traditional speed-independent flux linkage function by comparing the line rotor flux linkage expressions of the brushless DC motor pairwise;

[0009] Step 3, aiming at the integral structure existing in the traditional speed-independent flux linkage function, use a frequency adaptive filter to replace the pure integrator to suppress harmonic components and DC offset, construct an improved flux linkage function, and judge the commutation point of the motor through the improved flux linkage function, and at the same time calculate the rotor angular velocity to realize the sensorless control method.

[0010] As a preferred technical solution of the present invention, in the said Step 1, establishing a mathematical model of the brushless DC motor in the three-phase stationary coordinate system is specifically as follows:

[0011] Step 1.1, the mathematical model of the brushless DC motor is specifically as follows:

[0012] 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 cis 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;

[0015] By subtracting the three equations in Equation (1) pairwise, the three - phase line voltage equations of the motor can be obtained:

[0016]

[0017] 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, and there is a relationship among the three - phase line back electromotive forces of the motor:

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

[0019] As a preferred technical solution of the present invention, in the said Step 1, the expression of the line rotor magnetic flux of the brushless DC motor is derived, specifically:

[0020] Step 1.2, the back electromotive force of the motor is numerically equal to the change rate of the permanent - magnet magnetic flux passing through the winding closed loop with time. Thus, the three - phase magnetic flux expressions are as follows:

[0021]

[0022] In Equation (4), e ab , e bc , e ca is the back electromotive force of the brushless DC motor, and ψ ab , ψ bc , ψ ca is the line rotor magnetic flux of the brushless DC motor.

[0023] Step 1.3, since the mutual inductance M is very small and can be ignored, from Equation (2) and Equation (4), the line back electromotive force of the motor can be obtained as:

[0024]

[0025] The line rotor magnetic flux can be obtained by integrating the line voltage. From Equation (5), the expression of the line rotor magnetic flux of the brushless DC motor is:

[0026]

[0027] As a preferred technical solution of the present invention, in the step 2, according to the relationship between the line back electromotive force and the rotational speed, the line rotor flux linkage expression of the brushless DC motor is used to construct a traditional speed-independent flux linkage function by pairwise comparison, specifically as follows:

[0028] Step 2.1, the line back electromotive force of the motor can be expressed as the product of the back electromotive force coefficient of the motor, the rotational speed of the motor, and the back electromotive force waveform function. Therefore, the three-phase line back electromotive force can be expressed as:

[0029]

[0030] In the formula, k e is the back electromotive force coefficient; ω is the rotational speed of the motor; H(θ) ab , H(θ) bc , H(θ) ca are the line back electromotive force waveform functions related to the rotor position of the brushless DC motor. The line back electromotive force waveform function has the same waveform shape as the line back electromotive force of the brushless DC motor. Therefore, it is a function of the rotor position of the brushless DC motor;

[0031] From this, the expression of the line rotor flux linkage of the brushless DC motor with respect to the rotational speed can be obtained:

[0032]

[0033] The amplitude of the line rotor flux linkage is proportional to the rotational speed of the brushless DC motor. When the rotational speed of the brushless DC motor is small, the amplitude of the line rotor flux linkage is also small, and there will be a large error in the commutation signal obtained by detecting the zero crossing point of the line rotor flux linkage; the traditional flux linkage function method eliminates the influence of the rotational speed by comparing two rotor flux linkages and obtains a function independent of the rotational speed of the brushless DC motor. This function is not affected by the specific parameters of the brushless DC motor and has a one-to-one correspondence with the rotor position of the brushless DC motor;

[0034] Step 2.2, three flux linkage functions independent of the rotational speed of the brushless DC motor can be obtained by adopting different ways of comparing the line rotor flux linkages. The expressions of the three flux linkage functions are:

[0035]

[0036]

[0037]

[0038] In formulas (9), (10), and (11), F1(θ), F2(θ), and F3(θ) are the flux linkage functions of the brushless DC motor.

[0039] As a preferred technical solution of the present invention, in step 3, for the integral structure existing in the traditional speed-independent flux function, a frequency adaptive filter is used to replace the pure integrator to suppress harmonic components and DC offsets, construct an improved flux function, and determine the commutation point of the motor through the improved flux function, while calculating the rotor angular velocity to achieve a sensorless control method, specifically as follows:

[0040] According to the expression of the brushless DC motor flux function, when the line rotor flux is zero, the corresponding flux function value will become infinite, and the zero crossing point of the line rotor flux is the commutation point of the motor. Therefore, the commutation point of the motor can be determined by detecting the extreme point of the flux function;

[0041] However, due to the integral structure existing in the traditional flux function, using a pure integrator to integrate the back electromotive force to calculate the stator flux is easily affected by the DC offset error in the input signal, resulting in poor dynamic and static performance of the motor. Therefore, it is necessary to improve the flux function;

[0042] Step 3.1, introduce a frequency adaptive filter, and its transfer function is as follows:

[0043]

[0044] In formula (12), H(s) is an integral filter cascaded with a band-pass filter (BPF), which acts as a pure integrator at the operating frequency and suppresses other frequency components, such as DC, fifth harmonic, and seventh harmonic. Different bandwidths and phase characteristics can be obtained by selecting μ; using the electrical speed ω r Update the gain ω of this observer n , that is, ω n = ω r , and achieve frequency adaption by updating the gain ω of this observer in real time n ; the absolute value of ω r is used to maintain the stability of operation, even if ω r is negative.

[0045] Step 3.2, use a frequency adaptive filter to replace the pure integrator. At this time, the expression of the line rotor flux is:

[0046]

[0047]

[0048]

[0049] In the formula, μ, ω n are filter parameters.

[0050] Step 3.3: Calculate the ratios of different line-rotor fluxes to obtain the new flux function (M function), and its expression is as follows:

[0051]

[0052]

[0053]

[0054] In Eqs. (16), (17), and (18), M1(θ), M2(θ), and M3(θ) are the M functions of the brushless DC motor.

[0055] Step 3.4: Use the M function to determine the commutation points of the motor, specifically as follows:

[0056] Denote the zero-crossing point of the line-rotor flux ψ ab as θ1. According to the relationship between ψ ab and ψ bc we can obtain:

[0057]

[0058]

[0059] Within one electrical cycle, ψ ab has two zero-crossing points, so there will be two positions where it changes from the positive maximum value to the negative maximum value; since the electrical angle of the line-rotor flux is the commutation point of the motor, the electrical angle of the extreme value of the M function is also the commutation point of the motor. According to the six-step principle of the brushless DC motor, in order to obtain the six commutation signals required for the normal operation of the motor, different M functions need to be selected according to different intervals, so as to realize the rotor position estimation of the brushless DC motor;

[0060] Step 3.5: In order to realize the sensorless control of the brushless DC motor, while obtaining the commutation signals, it is also necessary to estimate the speed to achieve speed closed-loop. The specific scheme for speed estimation is as follows:

[0061] The sensorless control system of the brushless DC motor adopts a double closed-loop control of the speed loop and the current loop. Using the classical PI control algorithm, in order to feedback the speed loop, the rotor speed information needs to be estimated; in Step 3.3, accurate rotor position information has been obtained, and the rotor angular velocity can be calculated as follows:

[0062]

[0063] where, is the rotor position information estimated by the motor, is the estimated value of the rotor angular velocity of the motor;

[0064] Thus, 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. So far, a sensorless control method for brushless DC motors based on a novel flux linkage function method has been realized.

[0065] The beneficial effects of the present invention are as follows: In the sensorless control method for brushless DC motors based on the novel flux linkage function method of the present invention, a frequency adaptive filter is introduced to replace the pure integrator, thereby improving the traditional flux linkage function method. When using the traditional flux linkage function method for sensorless control of brushless DC motors, due to the integral structure of the traditional flux linkage function, a pure integrator is used to integrate the back electromotive force to calculate the stator flux linkage, which is easily affected by the DC offset error in the input signal, resulting in poor dynamic and static performance of the motor. Therefore, a frequency adaptive filter is introduced to replace the pure integrator, thereby improving the traditional flux linkage function method. Compared with the traditional flux linkage method using a pure integrator, this filter cascades a band-pass filter (BPF) and an integral filter, which can effectively suppress harmonic components and DC offsets, improve the accuracy of flux linkage observation, better estimate the rotor speed and position information, and improve the sensorless rotor position estimation performance of brushless DC motors. Description of the Drawings

[0066] Figure 1 is the sensorless control block diagram of a brushless DC motor based on the novel flux linkage function method of the present invention;

[0067] Figure 2 is the structural block diagram of the frequency adaptive filter used in the present invention; Detailed Embodiments

[0068] The sensorless control method for brushless DC motors based on the novel flux linkage function method of the present invention is specifically implemented according to the following steps:

[0069] 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 rotor flux linkage of the brushless DC motor, specifically:

[0070] Step 1.1: The mathematical model of the brushless DC motor is specifically as follows:

[0071] Based on the terminal voltage formula of the brushless DC motor in the three-phase stationary coordinate system as shown below:

[0072]

[0073] In formula (1): u a 、u b 、u c are the winding terminal voltages; i a 、i b 、i cis the phase current; e a and e b and e c are the back electromotive forces; 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;

[0074] Subtracting the three equations in Equation (1) pairwise, the three - phase line - voltage equations of the motor can be obtained:

[0075]

[0076] In Equation (2): u ab and u bc are the winding line - voltages; i ab and i bc are the phase - voltage differences; e ab and e bc are the line back - electromotive forces, and there is a relationship among the three - phase line back - electromotive forces of the motor:

[0077] e ab + e bc + e ca = 0 (3);

[0078] Step 1.2, the line back - electromotive force of the brushless DC motor is numerically equal to the change rate of the permanent - magnet magnetic flux passing through the winding closed loop with time. Thus, the three - phase magnetic - flux expressions are as follows:

[0079]

[0080] In Equation (4), e ab and e bc and e ca are the line back - electromotive forces, and ψ ab and ψ bc and ψ ca are the line - rotor magnetic fluxes of the brushless DC motor.

[0081] Step 1.3, since the mutual inductance M is very small and can be ignored, from Equation (2) and Equation (4), the line back - electromotive force of the brushless DC motor can be obtained as:

[0082]

[0083] The line - rotor magnetic flux is obtained by integrating the line voltage. From Equation (5), the expression of the line - rotor magnetic flux of the brushless DC motor is:

[0084]

[0085] Step 2, according to the relationship between the line back - electromotive force and the speed, the line - rotor magnetic - flux expression of the brushless DC motor is constructed into a traditional speed - independent magnetic - flux function by pairwise comparison, specifically:

[0086] Step 2.1, the line back electromotive force of the brushless DC motor can be expressed as the product of the motor back electromotive force coefficient, the motor speed, and the back electromotive force waveform function. Therefore, the three-phase line back electromotive force can be expressed as:

[0087]

[0088] In the formula, k e is the back electromotive force coefficient; ω is the motor speed; H(θ) ab , H(θ) bc , H(θ) ca are the line back electromotive force waveform functions related to the rotor position of the brushless DC motor. The line back electromotive force waveform function has the same waveform shape as the line back electromotive force of the brushless DC motor. Therefore, it is a function of the rotor position of the brushless DC motor;

[0089] From this, the expression of the line rotor magnetic flux of the brushless DC motor with respect to the speed can be obtained:

[0090]

[0091] The amplitude of the line rotor magnetic flux is proportional to the speed of the brushless DC motor. When the speed of the brushless DC motor is small, the amplitude of the line rotor magnetic flux is also small. The commutation signal obtained by detecting the zero-crossing point of the line rotor magnetic flux will have a large error; the traditional magnetic flux function method eliminates the influence of speed by comparing two rotor magnetic fluxes and obtains a function independent of the speed of the brushless DC motor. This function is not affected by the specific parameters of the brushless DC motor and has a one-to-one correspondence with the rotor position of the brushless DC motor;

[0092] Step 2.2, by adopting different ways of comparing the line rotor magnetic fluxes, three magnetic flux functions independent of the speed of the brushless DC motor can be obtained. The expressions of the three magnetic flux functions are:

[0093]

[0094]

[0095]

[0096] In formulas (9), (10), and (11), F1(θ), F2(θ), and F3(θ) are the magnetic flux functions of the brushless DC motor;

[0097] Step 3, aiming at the integral structure existing in the traditional speed-independent magnetic flux function, a frequency adaptive filter is used to replace the pure integrator to suppress harmonic components and DC offsets, construct an improved magnetic flux function, and judge the motor commutation point through the improved magnetic flux function. At the same time, the rotor angular velocity is calculated to realize the sensorless control method, specifically as follows:

[0098] According to the expression of the flux linkage function of the brushless DC motor, it can be known that when the line rotor flux linkage is zero, the corresponding flux linkage function value will become infinite, and the zero crossing point of the line rotor flux linkage is the commutation point of the motor. Therefore, the commutation point of the motor can be determined by detecting the extreme point of the flux linkage function;

[0099] However, due to the integral structure of the traditional flux linkage function, using a pure integrator to integrate the back electromotive force to calculate the stator flux linkage is easily affected by the DC offset error in the input signal, resulting in poor dynamic and static performance of the motor. Therefore, it is necessary to improve the flux linkage function;

[0100] Step 3.1, introduce a frequency adaptive filter, and its transfer function is as follows:

[0101]

[0102] In Equation (12), H(s) is an integral filter cascaded with a band-pass filter (BPF), which acts as a pure integrator at the operating frequency and suppresses other frequency components, such as DC, fifth harmonic, and seventh harmonic. Different bandwidths and phase characteristics can be obtained by selecting μ; use the electrical speed ω r Update the gain ω of this observer n , that is, ω n = ω r , and achieve frequency adaption by updating the gain ω of this observer in real time n ; the absolute value of ω r is used to maintain the stability of operation, even if ω r is negative;

[0103] Step 3.2, use the frequency adaptive filter to replace the pure integrator. At this time, the expression of the line rotor flux linkage is:

[0104]

[0105]

[0106]

[0107] In the formula, μ, ω n are filter parameters.

[0108] Step 3.3, take the ratio of different line rotor flux linkages to obtain a new flux linkage function (M function), and its expression is as follows:

[0109]

[0110]

[0111]

[0112] In formulas (16), (17), and (18), M1(θ), M2(θ), and M3(θ) are the M functions of the brushless DC motor.

[0113] Step 3.4: Use the M function to determine the commutation point of the motor, specifically as follows:

[0114] Denote the zero-crossing point of the line rotor flux linkage ψ ab as θ1. According to the relationship between ψ ab and ψ bc we can obtain:

[0115]

[0116]

[0117] Within one electrical cycle, ψ ab has two zero-crossing points, so there will be two positions where it changes from the positive maximum value to the negative maximum value; since the electrical angle of the line rotor flux linkage is the commutation point of the motor, the extreme value electrical angle of the M function is also the commutation point of the motor; according to the six-step principle of the brushless DC motor, in order to obtain the six commutation signals required for the normal operation of the motor, different M functions need to be selected according to the different intervals, so as to realize the rotor position estimation of the brushless DC motor;

[0118] Step 3.5: In order to realize the sensorless control of the brushless DC motor, while obtaining the commutation signal, it is also necessary to estimate the speed to achieve speed closed-loop. The specific scheme for speed estimation is as follows:

[0119] The sensorless control system of the brushless DC motor adopts double closed-loop control of the speed loop and the current loop. Using the classical PI control algorithm, in order to feedback the speed loop, the rotor speed information needs to be estimated; in Step 3.3, accurate rotor position information has been obtained, and thus the rotor angular velocity can be calculated as:

[0120]

[0121] where, is the rotor position information estimated by the motor, is the estimated value of the rotor angular velocity of the motor;

[0122] Then, from the estimated angular position of the rotor, the brushless DC motor can be driven to operate according to the six-step conduction phase sequence of the brushless DC motor. Thus, a sensorless control method for the brushless DC motor based on the new flux linkage function method is realized.

[0123] The present invention proposes a sensorless control method for a brushless DC motor based on a novel flux linkage function method, which introduces a frequency adaptive filter to replace the pure integrator, thereby improving the traditional flux linkage function method. Compared with the traditional flux linkage method that uses a pure integrator, this filter cascades a band-pass filter (BPF) and an integration filter, which can effectively suppress harmonic components and DC offsets, improve the accuracy of flux linkage observation, better estimate the rotor speed and position information, and improve the sensorless rotor position estimation performance of the brushless DC motor.

[0124] The sensorless control block diagram of the brushless DC motor based on the novel flux linkage function method is as Figure 1 shown. It adopts a double closed-loop control of speed and current and uses the classical PI control algorithm. The double closed-loop control system of the brushless DC motor chops the DC power supply into a PWM wave through a PWM chopper, thereby changing the average voltage applied across the armature to adjust the speed of the motor. Since the zero-crossing point of the line rotor flux linkage is the commutation moment, Figure 1 a novel flux linkage function method is used for sensorless control. The terminal voltage and phase current of the motor are detected, the line rotor flux linkage is obtained through calculation, the commutation point is estimated using the novel flux linkage function method, and then the rotor speed and position information are calculated to achieve the sensorless control method of the brushless DC motor based on the novel flux linkage function method. The novel flux linkage function method uses a frequency adaptive filter to replace the pure integrator. The structural block diagram of the frequency adaptive filter is as Figure 2 shown. This filter cascades a band-pass filter (BPF) and an integration filter, which can effectively suppress harmonic components and DC offsets, improve the accuracy of flux linkage observation, and better estimate the rotor speed and position information.

Claims

1. A sensorless control method for a brushless DC motor based on a novel flux linkage function method, characterized in that The implementation is specifically carried out according to the following steps: Step 1, establish the mathematical model of the brushless DC motor in the three-phase static coordinate system, and derive the expression of the line rotor flux linkage of the brushless DC motor; Step 2, according to the relationship between the line back electromotive force and the speed, construct the traditional speed-independent flux linkage function by comparing the expressions of the line rotor flux linkage of the brushless DC motor pairwise; Step 3, aiming at the integral structure existing in the traditional speed-independent flux linkage function, use a frequency adaptive filter to replace the pure integrator, suppress the harmonic components and DC offset, construct an improved flux linkage function, and determine the commutation point of the motor through the improved flux linkage function, and at the same time calculate the rotor angular velocity to realize the sensorless control method; In the said Step 3, aiming at the integral structure existing in the traditional speed-independent flux linkage function, use a frequency adaptive filter to replace the pure integrator, suppress the harmonic components and DC offset, construct an improved flux linkage function, and determine the commutation point of the motor through the improved flux linkage function, and at the same time calculate the rotor angular velocity to realize the sensorless control method, specifically as follows: According to the expression of the flux linkage function of the brushless DC motor, it can be known that when the line rotor flux linkage is zero, the corresponding flux linkage function value will become infinite, and the zero crossing point of the line rotor flux linkage is the commutation point of the motor. Therefore, the commutation point of the motor is determined by detecting the extreme point of the flux linkage function; However, due to the integral structure existing in the traditional flux linkage function, using a pure integrator to integrate the back electromotive force to calculate the stator flux linkage is easily affected by the DC offset error in the input signal, resulting in poor dynamic and static performance of the motor. Therefore, it is necessary to improve the flux linkage function; Step 3.1, introduce a frequency adaptive filter, and its transfer function is as follows: (12) In formula (12), is an integrating filter cascaded with a band-pass filter BPF, which acts as a pure integrator at the operating frequency while suppressing other frequency components such as DC, fifth harmonic, and seventh harmonic; different bandwidths and phase characteristics are obtained through the selection of ; the electrical speed is used to update the gain of the observer , that is , and frequency adaption is achieved by updating the gain of the observer in real time; the absolute value of is used to maintain the stability of operation even when is negative; Step 3.2, use a frequency adaptive filter to replace the pure integrator. At this time, the expression of the line rotor flux linkage is: (13) (14) (15) In the formula, , are filter parameters; Step 3.3: Calculate the ratios of different line rotor fluxes to obtain a new flux function, denoted as M function, and its expression is as follows: (16) (17) (18) In formulas (16), (17), and (18), , , are functions of the brushless DC motor; M functions Step 3.4, use M the function to judge the commutation point of the motor, specifically as follows: Denote the zero crossing point of the line rotor flux linkage as . According to the relationship between and , we can obtain: (19) (20) Within one electrical cycle There are two zero-crossing points, so there will be two positions where the positive maximum value changes to the negative maximum value; since the electrical angle of the line rotor flux linkage is the commutation point of the motor, therefore M The electrical angle of the extreme value of the function is also the commutation point of the motor; according to the six-step principle of the brushless DC motor, in order to obtain the six commutation signals required for the normal operation of the motor, different M functions need to be selected according to different intervals, so as to realize the rotor position estimation of the brushless DC motor; Step 3.5, in order to realize the sensorless control of the brushless DC motor, while obtaining the commutation signal, it is also necessary to estimate the speed to realize the speed closed-loop. The specific scheme for speed estimation is as follows: The sensorless control system of the brushless DC motor adopts a double closed-loop control of the speed loop and the current loop, and uses the classical PI control algorithm. In order to feedback the speed loop, it is necessary to estimate the rotor speed information; in Step 3.3, accurate rotor position information has been obtained, and the rotor angular velocity can be calculated as follows: (21) Among them, is the rotor position information estimated for the motor, is the estimated value of the rotor angular velocity of the motor; 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 the new flux linkage function method is realized.

2. The sensorless control method for a brushless DC motor based on the novel flux linkage function method according to claim 1, characterized in that In the said Step 1, establish the mathematical model of the brushless DC motor in the three-phase static coordinate system, specifically as follows: Step 1.1, the mathematical model of the brushless DC motor is specifically as follows: Based on the terminal voltage formula of the brushless DC motor in the three-phase static coordinate system as shown below: (1) In Equation (1): , , are the winding terminal voltages; , , are the phase currents; , , are the counter 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 of Equation (1) pairwise to obtain the three-phase line voltage equation of the motor: (2) In Equation (2): and are the winding line voltages; and are the phase voltage differences; and are the line back electromotive forces, and there is a relationship among the three-phase line back electromotive forces of the motor: (3)。 3. The sensorless control method for a brushless DC motor based on the novel flux linkage function method according to claim 2, wherein In the said Step 1, derive the expression of the line rotor flux linkage of the brushless DC motor, specifically as follows: Step 1.2, the line back electromotive force of the brushless DC motor is numerically equal to the change rate of the permanent magnet flux through the winding closed loop with time. Thus, the three-phase flux expressions are as follows: (4) In formula (4), , , are the line back electromotive force, , , are the line rotor fluxes of the brushless DC motor; Step 1.3, due to the mutual inductance M is very small and can be ignored. From Equations (2) and (4), the line back electromotive force of the brushless DC motor is obtained as follows: (5) The line rotor flux is obtained by integrating the line voltage. From Equation (5), the expression of the line rotor flux of the brushless DC motor is: (6)。 4. The sensorless control method for a brushless DC motor based on the novel flux linkage function method according to claim 3, wherein In the said Step 2, according to the relationship between the line back electromotive force and the speed, the line rotor flux expression of the brushless DC motor is used to construct a traditional speed-independent flux function by pairwise comparison, specifically: Step 2.1, the line back electromotive force of the brushless DC motor is expressed as the product of the motor back electromotive force coefficient, the motor speed, and the back electromotive force waveform function. Therefore, the three-phase line back electromotive forces are expressed as: (7) wherein, is the back electromotive force coefficient; is the motor speed; , , are the line back electromotive force waveform functions related to the rotor position of the brushless DC motor. The line back electromotive force waveform function has the same waveform shape as the line back electromotive force of the brushless DC motor. Therefore, it is a function of the rotor position of the brushless DC motor; Thus, the expression of the line rotor flux of the brushless DC motor with respect to the speed is obtained: (8) The amplitude of the line rotor flux is proportional to the speed of the brushless DC motor. When the speed of the brushless DC motor is relatively small, the amplitude of the line rotor flux is also relatively small, and there will be a large error in the commutation signal obtained by detecting the zero crossing of the line rotor flux; the traditional flux function method eliminates the influence of the speed by comparing two rotor fluxes and obtains a function independent of the speed of the brushless DC motor. This function is not affected by the specific parameters of the brushless DC motor and has a one-to-one correspondence with the rotor position of the brushless DC motor; Step 2.2, three flux functions independent of the speed of the brushless DC motor are obtained by using different ways of comparing the line rotor fluxes. The expressions of the three flux functions are: (9) (10) (11) In formulas (9), (10), and (11), , , are the flux linkage functions of the brushless DC motor.

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