CN112491319B - Vector control current compensation algorithm and vector control model of direct-current brushless motor - Google Patents

Abstract

The utility model provides a brushless DC motor vector control current compensation algorithm and vector control model, relates to brushless DC motor's control field, and the current compensation algorithm is: I.C. A _de ＝I _dt ，I _qe ＝K _c I _qt ，

Wherein, I _dt For stator currents of a brushless DC motor on the d-axis of a two-phase rotating coordinate system, I _qt The stator current of the brushless DC motor on the q axis of the two-phase rotating coordinate system is shown. The control model is as follows:

wherein the content of the first and second substances,

the invention has the advantages of convenient realization, easy programming, the same hardware control structure as the traditional vector control structure of the permanent magnet synchronous motor, no need of additional hardware support, easy popularization in factories and enterprises and small rotation speed fluctuation.

Description

Current Compensation Algorithm and Vector Control Model for Vector Control of Brushless DC Motor

technical field

The invention relates to the control field of a DC brushless motor, and in detail is a kind of convenient implementation and easy programming, the hardware control structure is the same as that of the traditional permanent magnet synchronous motor vector control structure, no additional hardware support is required, and it is easy to be popularized in factories and enterprises. Current compensation algorithm and vector control model of brushless DC motor vector control with small speed fluctuation.

Background technique

We know that brushless DC motors are widely used due to their high efficiency, such as household appliances, servos, electric vehicles and so on. However, the shortcomings of torque and speed oscillation in the DC brushless motor limit its promotion in high-precision occasions. The traditional commutation method of brushless DC motor is 2-2 commutation or 3-3 commutation, which is discrete and discontinuous.

Document T.Tarczewski, and L.M. Grzesiak, "Constrained State Feedback SpeedControl of PMSM Based on Model Predictive Approach," IEEE Transactions on Industrial Electronics, vol. 63, no.6, pp.3867-3875, 2016. Documented sine wave permanent magnets Motor differential equations for synchronous motors under vector control.

B.K.Bose, "Modern Power Electronics and AC drives," 1987, a classic book on motors, details 2-2 commutation or 3-3 commutation, and proposes a classic brushless DC motor when vector control is not considered. The dynamic model is:

Although this type of brushless DC motor model is accurate, it is more complicated and the rotational speed oscillates greatly. The discontinuity of commutation is one of the reasons why the brushless DC motor produces torque and speed oscillation. Therefore, there are many literatures on improving commutation. You can refer to the journal document Design of Speed Control and Reduction of TorqueRipple in the IEEE database. Factor in BLdc Motor Using Spider Based Controller.

Due to the shortcomings of traditional commutation of brushless DC motors, technicians try to apply vector control to brushless DC motors. Vector control has decoupling properties in motor control. The decoupling characteristic means that we can achieve independent control of the electromagnetic torque and excitation of the motor by controlling the torque current and the excitation current, respectively. At the same time, because vector control can improve the efficiency of the motor, promote energy saving and emission reduction, and can reduce the complexity of the motor model and reduce the motor torque and speed fluctuations, it is widely used in induction motors (asynchronous motors) and sine wave permanent magnet synchronous motors. use. Literature A.V.Sant, and K.R.Rajagopal, "PM Synchronous Motor Speed Control Using Hybrid Fuzzy-PI WithNovel Switching Functions," IEEE Transactions on Magnetics, vol.45, no.10, pp.4672-4675, 2009. and Literature K.D. Carey, N. Zimmerman, and C. Ababei, "Hybrid fieldoriented and direct torque control for sensorless BLDC motors used in aerialdrones," IET Power Electronics, vol.12, no.3, pp.438-449, 2019 and Li Kejing, Xu Jie, Wu Jue, Song Jin, "STM32-based vector control system for brushless DC motors", Electronics and Packaging., 2020-09, pp. 29-34, it is documented in the direct application of vector control to brushless DC motors, And recorded that the traditional brushless DC motor vector control model is (the same as the motor differential equation of the sine wave permanent magnet synchronous motor under vector control):

References A.G.d.Castro, W.C.A.Pereira, T.E.P.d.Almeida, C.M.R.d.Oliveira, J.R.B.d.A. Monteiro, and A.A.d.Oliveira, “Improved Finite Control-Set Model-Based Direct Power Control of BLDC Motor With Reduced Torque Ripple,” IEEE Transactions on Industry Applications, vol. 54, no.5, pp.4476-4484, 2018. In the structure of vector control, the traditional vector control model of brushless DC motor is improved. It adopts a method based on active power and reactive power. The mechanical equations of the brush motor are modeled on a two-phase stationary coordinate system. However, because this method needs to collect the back electromotive force of the DC brushless motor, its structure is more complicated than the traditional structure, and the cost is high, which is not suitable for application.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve the above-mentioned deficiencies of the prior art, and to provide a kind of convenient implementation and easy programming, the hardware control structure is the same as that of the traditional permanent magnet synchronous motor vector control structure, no additional hardware support is required, and it is easy to be popularized in factories and enterprises. Current compensation algorithm and vector control model of brushless DC motor vector control with small speed fluctuation.

The technical scheme adopted by the present invention to solve the above-mentioned deficiencies of the prior art is:

A vector control current compensation algorithm for a brushless DC motor, characterized in that, the equivalent stator current I _de =I _dt of the brushless DC motor on the d-axis of the two-phase rotating coordinate system, and the brushless DC motor is in the two-phase rotating coordinate system. Equivalent stator current I _qe =K _c I _qt on the q-axis,

Among them, I _dt is the stator current of the brushless DC motor on the d-axis of the two-phase rotating coordinate system, and I _qt is the stator current of the brushless DC motor on the q-axis of the two-phase rotating coordinate system. That is, I _dt is the stator current of the brushless DC motor on the d-axis of the two-phase rotating coordinate system in the traditional brushless DC motor vector control method, and I _qt is the traditional brushless DC motor vector control method. The stator current on the q-axis of the two-phase rotating coordinate system.

A vector control model of a brushless DC motor, characterized in that the model is:

in,

In the above formula, I _de is the equivalent stator current of the improved brushless DC motor of the present invention on the d-axis of the two-phase rotating coordinate system, and I _qe is the improved brushless DC motor of the present invention on the two-phase rotating coordinate system q The equivalent stator current on the shaft, ω _e is the synchronous electrical angular velocity of the DC brushless motor, R _s is the stator resistance of the DC brushless motor, L is the equivalent phase inductance of the DC brushless motor stator, and ψ _r is the DC brushless motor. The rotor flux linkage of , p is the number of pole pairs of the DC brushless motor, J is the moment of inertia of the DC brushless motor, U _d is the stator voltage of the DC brushless motor on the d-axis of the two-phase rotating coordinate system, U _q is the DC motor The stator voltage of the brush motor on the q-axis of the two-phase rotating coordinate system, T _L is the load torque of the DC brushless motor, I _dt is the stator current of the traditional brushless DC motor on the d-axis of the two-phase rotating coordinate system, and I _qt is The stator current of a conventional brushless DC motor on the q-axis of a two-phase rotating coordinate system.

A vector control model of a brushless DC motor, characterized in that the model is:

in

In the above formula, I _dt is the stator current of the traditional brushless DC motor on the d-axis of the two-phase rotating coordinate system, I _qt is the stator current of the traditional brushless DC motor on the q-axis of the two-phase rotating coordinate system, and ω _e is the DC The synchronous electrical angular velocity of the brushless motor, R _s is the stator resistance of the brushless DC motor, L is the equivalent phase inductance of the brushless DC motor stator, ψ _r is the rotor flux linkage of the brushless DC motor, and p is the brushless DC motor. The number of pole pairs, J is the moment of inertia of the DC motor, U _d is the stator voltage of the DC brushless motor on the d-axis of the two-phase rotating coordinate system, and U _q is the DC brushless motor on the q-axis of the two-phase rotating coordinate system. Stator voltage, T _L is the load torque of the brushless DC motor,

After the present invention compensates the current obtained in the traditional vector control method of the brushless DC motor, the brushless DC motor can reduce the speed oscillation under the condition that the difference between the output torque and the target torque is small, and is more suitable for It is used in industries that require high rotational speed oscillations such as robot control and electric vehicles. The algorithm of the invention is simple, easy to implement and easy to program, and the hardware control structure is the same as that of the traditional permanent magnet synchronous motor vector control structure, no additional hardware support is required, and it is easy to popularize in factories and enterprises.

Description of drawings

Figure 1 is a diagram of the electromagnetic torque output of the brushless DC motor when four different motor models control the same brushless DC motor.

FIG. 2 is an enlarged view of the time period from 0 to 0.0432s in FIG. 1 , and is an enlarged view of the initial interval of each brushless DC motor.

FIG. 3 is an enlarged view of the time period from 0.4742 to 0.4939 s in FIG. 1 , and is an enlarged view of the electromagnetic torque of each brushless DC motor when the load is stable.

FIG. 4 is an error diagram between the actual output speed of each brushless DC motor and the given speed in three control methods of brushless DC motors based on different models.

FIG. 5 is a graph of the actual output rotational speed of each brushless DC motor in three control methods of the brushless DC motor based on different models.

Detailed ways

The theoretical basis of the present invention is as follows:

The dynamic model of the BLDC motor follows the following assumptions: iron losses and magnetic saturation are negligible; the stator windings are centralized, symmetrical and Y-connected.

Also, assume that the back EMF of a BLDC motor is a trapezoidal wave with respect to the rotor position:

和

出自于M.P.Maharajan,and S.A.E.Xavier,“Design ofSpeed Control and Reduction of Torque Ripple Factor in BLdc Motor UsingSpider Based Controller,”IEEE Transactions on Power Electronics,vol.34,no.8,pp.7826-7837,2019。Formula (1) expresses the opposite electromotive force of A, and the opposite electromotive force of phase B and C can be obtained similarly according to formula (1), the difference is that the phase offsets are respectively

and

From MPMaharajan, and SAEXavier, “Design of Speed Control and Reduction of Torque Ripple Factor in BLdc Motor Using Spider Based Controller,” IEEE Transactions on Power Electronics, vol.34, no.8, pp.7826-7837, 2019.

Theoretically, the stator current of the brushless DC motor is a trapezoidal wave; therefore, the A-phase stator current should conform to formula (2):

和

The stator currents of B-phase and C-phase can be deduced according to formula (2), the difference between them is that the phase offset is

and

If the trapezoidal wave Ta(θ) in the formula (2) can be converted into a sine wave Sa(t), then the vector control can be applied to the DC brushless motor. First, square waves and sine waves can be regarded as two independent subspaces of Hilbert spaces. Then, the relationship between them can be established by the L2 norm [0,2π] equidistant co-construction:

Bringing formulas (2, 3) into formula (4), the relationship between I _trp and I _sin can be deduced:

Considering that both the back EMF and the stator current of the brushless DC motor are trapezoidal waves, according to the classical mechanical equation and formula (5) of the brushless DC motor, we can obtain formula (6):

就可以实现直流无刷电机的新型矢量控制。由于从梯形波变换到正弦波是在L2空间中执行的，因此它们之间的转换是可逆的。换言之，它们之间的变换是线性变换，这个变换保证了梯形波包含的功率与正弦波包含的功率是相同的。考虑到电机的电磁转矩是电磁功率对于电角度θ的导数，因此梯形波和正弦波在新型变换中所包含的功率和电磁转矩都是相同的，这也是本发明提出变换的意义所在。Equation (6) shows that we can multiply the I _qt obtained on the vector control of the traditional brushless DC motor by a compensation coefficient

The new vector control of DC brushless motor can be realized. Since the transformation from a trapezoidal wave to a sine wave is performed in L2 space, the transformation between them is reversible. In other words, the transformation between them is a linear transformation, which ensures that the power contained in the trapezoidal wave is the same as that contained in the sine wave. Considering that the electromagnetic torque of the motor is the derivative of the electromagnetic power to the electrical angle θ, the power and electromagnetic torque contained in the new transformation of the trapezoidal wave and the sine wave are the same, which is the meaning of the transformation proposed in the present invention.

Based on the derivation of the above formula, it can be known that a current compensation algorithm in the vector control of the brushless DC motor, the equivalent stator current I _de = I _dt of the brushless DC motor on the d-axis of the two-phase rotating coordinate system, and the brushless DC motor in the two-phase rotating coordinate system. Equivalent stator current I _qe =K _c I _qt on the q-axis of the phase rotation coordinate system,

Among them, I _dt is the stator current of the brushless DC motor on the d-axis of the two-phase rotating coordinate system, and I _qt is the stator current of the brushless DC motor on the q-axis of the two-phase rotating coordinate system. That is, I _dt is the stator current of the brushless DC motor on the d-axis of the two-phase rotating coordinate system in the traditional brushless DC motor vector control method, and I _qt is the traditional brushless DC motor vector control method. The stator current on the q-axis of the two-phase rotating coordinate system.

The Clarke and Park transformation formulas in classical vector control are as follows:

与公式(8)结合，补偿的Park变换为：When the compensation coefficient

Combined with formula (8), the compensated Park transform is:

The motor differential equation of traditional brushless motor under vector control is:

According to formula (9), the equivalent current of the d-q axis in the DC brushless motor is:

where I _d and I _q represent the dq-axis current of the brushless DC motor before compensation.

The compensation method in the formula (11) of the present invention is very simple, practical and easy to implement.

According to formula (10) and formula (11), the vector control model of the brushless DC motor of the present invention is obtained:

The traditional brushless DC motor vector control model is:

According to Equation (11) and Equation (13), Equation (12) can be rewritten as:

in

When K _c =1, formula (14) is the same as formula (13). Considering that the back EMF and current of the DC brushless motor are both trapezoidal waves, and the back EMF and current of the permanent magnet synchronous motor are both sine waves, the direct application of vector control to the DC brushless motor is obtained and the vector control is applied to the permanent magnet. The same formula (13) as the motor equation on the magnetic synchronous motor is obviously inaccurate, and the new brushless DC motor vector control motor equation (14) proposed by the present invention considers the trapezoidal wave and the motor equation (13) on the basis of the motor equation. The relationship between the sine waves (from the motor equation is reflected in the addition of Δ ₁ and Δ ₂ ), so the new BLDC motor vector control model is more accurate than the traditional BLDC motor vector control model.

The specific application of the brushless DC motor vector control current compensation algorithm proposed by the present invention in the vector control of the DC brushless motor is as follows:

For speed servo, the DC brushless motor vector control system is a double closed-loop structure, including a speed loop, an excitation current I _de loop and an electromagnetic torque current I _qe loop; although there are three closed loops, the overall can be divided into It is a speed loop and a current loop, so this control structure is also called a double closed-loop structure; the controller in the double closed-loop structure is generally a PID controller.

In the above-mentioned BLDC motor vector control system, the speed reference of the speed loop is an external reference, which is related to actual needs and can be changed artificially; the excitation current reference of the excitation current loop is also an external reference, which is given under normal conditions. If it is 0, it can be given as a negative value if the field weakening is required; the I _qe given of the electromagnetic torque current loop is connected to the output of the speed loop; the adjustment of the PID controller parameters is well known.

把I_de和I_qe分别反馈到励磁电流环和电磁转矩电流环进行反馈。In addition to the above-mentioned given values, the speed of the speed loop and the current of the current loop in the above-mentioned brushless DC motor vector control system also need a feedback amount; the feedback of the speed loop requires a speed sensor to measure the speed of the brushless DC motor, or according to the code The controller obtains the derivation of the rotor position information to obtain the speed of the brushless DC motor, or the position information obtained according to the non-inductive technology to obtain the speed of rotation; the feedback steps of the two current loops are: first, use the current sensor to measure the brushless DC motor Stator three-phase currents I _a , I _b and I _c , and then perform Clarke transformation and Park transformation on them to obtain I _dt and I _qt , and finally use the DC brushless motor vector control current compensation algorithm proposed by the present invention to calculate the improved I _de and I _qe of the equivalent stator current on the dq axis of the two-phase rotating coordinate system,

Feedback I _de and I _qe to the excitation current loop and the electromagnetic torque current loop respectively for feedback.

The output of the three controllers in the double closed loop in the DC brushless motor vector control system is introduced as follows: the output of the speed loop is connected to the electromagnetic torque current loop as a given value of I _qe ; the output of the excitation current loop is U _d , the output of the electromagnetic torque current loop is U _q . After U _d and U _q are processed by coordinate transformation and SVPWM, a PWM signal is sent to drive the inverter to obtain three-phase voltage signals U _a , U _b and U _c , which are respectively connected to the three phases of the stator of the brushless DC motor. This process known.

The brushless DC motor vector control model proposed by the present invention can be applied to the design of some brushless DC motor controllers, such as the design of the predictive controller, which needs to use the brushless DC motor model, and the traditional brushless motor model is difficult to use In the design of the controller, the vector control model of the brushless DC motor proposed by the present invention can be used to design the controller.

The vector control model of the brushless DC motor proposed by the present invention can be applied in the simulation of the brushless DC motor. As a mathematical model of the brushless DC motor, if it is inconvenient to build a traditional model, the vector control model of the brushless DC motor proposed by the present invention can also be used. The control model is used to simulate the DC brushless motor as the control object.

When using vector control, the classic dynamic model of a BLDC motor is:

(15)

(15)

的角度差。Among them, E _a , E _b , E _c are the back electromotive force of the trapezoidal wave, and they have mutual

angle difference.

Comparing Equation (12) and Equation (15), Equation (12) is more concise and clear. In order to better compare them and some other methods of BLDC motor modeling, we will perform further simulation in MATLAB/Simulink below. Compare.

MATLAB/SIMULINK simulation analysis

The parameters of the brushless DC motor in the simulation are as follows:

Table 1: BLDC Motor Parameters

In order to avoid the influence of the closed-loop controller to verify the validity of the motor model, we adopt open-loop to verify different BLDC motor models. From these models, we have to consider not only their accuracy but also their complexity, and then select the optimal motor model.

At 0.3 seconds, a 10N.M load is added to the DC brushless motor.

As shown in Figures 1-3, the electromagnetic torque Te1 of the standard brushless DC motor is obtained according to formula (15), which is used to simulate the real torque of the brushless DC motor.

References A.G.d.Castro, W.C.A.Pereira, T.E.P.d.Almeida, C.M.R.d.Oliveira, J.R.B.d.A.Monteiro, and A.A.d.Oliveira, “Improved Finite Control-Set Model-Based Direct Power Control of BLDC Motor With Reduced Torque Ripple,” IEEE Transactions on Industry Applications, vol. 54, no.5, pp.4476-4484, 2018. A method based on active power P and reactive power Q is proposed to model and control the brushless DC motor. The brushless DC motor calculated by this method, etc. The effective electromagnetic torque is Te2.

The electromagnetic torque Te3 is calculated by formula (13), which is the electromagnetic torque obtained by the traditional BLDC motor vector control model.

The electromagnetic torque Te4 is calculated by formula (12), which is the electromagnetic torque obtained by adopting the vector control model of the brushless DC motor proposed by the present invention.

The comparison diagrams of Te1, Te2, Te3, and Te4 are shown in Figure 1-Figure 3.

By comparing Te3 and Te1 in Figure 1-Figure 3, it can be seen that the gap between them is relatively large, which means that the motor model obtained directly using vector control for brushless DC motors cannot accurately reflect the actual situation. Working performance of brushless DC motors (dynamic and loaded). The difference between Te2 and Te1 is minimal, but considering the need for additional sensors and peripheral circuits and the need to perform complex calculations, this approach increases cost in practical applications. The difference between Te4 and Te1 is smaller.

For different models of brushless DC motors, the specific control methods are different. Taking speed control as an example, for the traditional brushless DC motor model, the speed and current double closed-loop control based on 2-2 commutation or 3-3 commutation is a well-known control method, denoted as C1; for direct use of vector control to DC The control method of the model obtained by the brushless motor is the same as that of the well-known permanent magnet synchronous motor vector control double closed-loop control structure, which is denoted as C2; for the vector control model of the brushless DC motor of the present invention, the control method can refer to the above-mentioned "DC without DC motor". The current compensation algorithm of brush motor vector control is specifically applied in the vector control of brushless DC motor", denoted as C3.

Figure 4 and Figure 5 are comparison diagrams of the effects of using the above three different brushless DC motor speed control, the obtained output speed data map of the brushless DC motor and the error data map between the output speed and a given speed.

It can be seen from Figure 4 and Figure 5 that when the C2 control mode is used, there is a large error between the stable speed of the motor and the given speed of 600rpm, while the improved C3 mode and the traditional C1 mode based on the present invention are used for the brushless DC motor. During the control, the error between the stable speed and the given speed is very small, but after zooming in, it can be seen that when the C3 mode is used, the speed oscillation is obviously smaller than that of the traditional C1 mode.

Symbol Description

Claims (3)

1. A DC brushless motor vector control current compensation algorithm is characterized in that, the equivalent stator current of the DC brushless motor on the d-axis of the two-phase rotating coordinate system I _de =I _dt , the equivalent stator current I _qe =K _c I _qt of the brushless DC motor on the q-axis of the two-phase rotating coordinate system,

Among them, I _dt is the stator current of the brushless DC motor on the d-axis of the two-phase rotating coordinate system, and I _qt is the stator current of the brushless DC motor on the q-axis of the two-phase rotating coordinate system; The specific application of the current compensation algorithm in the vector control of the brushless DC motor in the vector control of the brushless DC motor is as follows: The brushless DC motor vector control system is a double closed-loop structure, and the controller in the double closed-loop structure is a PID controller; among them, the speed of the speed loop is given externally, and the excitation current of the excitation current loop is also given externally. , the I _qe of the electromagnetic torque current loop is given to the output of the speed loop; the speed of the speed loop and the excitation current of the excitation current loop require feedback in addition to the above given values; the feedback of the speed loop requires a speed sensor Measure the speed of the brushless DC motor, or derive the rotor position information obtained according to the encoder to obtain the speed of the brushless DC motor, or derive the position information obtained according to the non-inductive technology to obtain the speed; the feedback steps of the two current loops For: firstly use the current sensor to measure the three-phase currents I _a , I _b and I _c of the brushless DC motor stator, then perform Clarke transformation and Park transformation on them to obtain I _dt and I _qt , and finally use the brushless DC motor vector I _de and I _qe of the equivalent stator current on the dq axis of the improved two-phase rotating coordinate system are calculated by the control current compensation algorithm,

Feedback I _de and I _qe to the excitation current loop and the electromagnetic torque current loop respectively for feedback; The outputs of the three controllers in the double closed loop in the DC brushless motor vector control system are as follows: the output of the speed loop is connected to the electromagnetic torque current loop as a given value of I _qe ; the output of the excitation current loop is U _d , the output of the electromagnetic torque current loop is U _q ; after U _d and U _q are processed by coordinate transformation and SVPWM, a PWM signal is sent to drive the inverter to obtain three-phase voltage signals U _a , U _b and U _c , which are respectively connected to Three-phase in the stator of the brushless DC motor. 2. A brushless DC motor vector control model, characterized in that the model is:

in,

In the above formula, I _de is the equivalent stator current of the improved brushless DC motor on the d-axis of the two-phase rotating coordinate system, and I _qe is the equivalent stator current of the improved brushless DC motor on the q-axis of the two-phase rotating coordinate system. Effective stator current, ω _e is the synchronous electrical angular velocity of the brushless DC motor, R _s is the stator resistance of the brushless DC motor, L is the equivalent phase inductance of the stator of the brushless DC motor, ψ _r is the rotor flux linkage of the brushless DC motor , p is the number of pole pairs of the DC brushless motor, J is the moment of inertia of the DC brushless motor, U _d is the stator voltage of the DC brushless motor on the d-axis of the two-phase rotating coordinate system, U _q is the DC brushless motor in the The stator voltage on the q-axis of the two-phase rotating coordinate system, T _L is the load torque of the brushless DC motor, I _dt is the stator current of the brushless DC motor on the d-axis of the two-phase rotating coordinate system, and I _qt is the brushless DC motor. The stator current on the q-axis of the two-phase rotating coordinate system; the method for obtaining the I _dt and I _qt is: use a current sensor to measure the three-phase currents I _a , I _b and I _c of the brushless DC motor stator, and then measure them Clarke transform and Park transform are performed to obtain I _dt and I _qt . 3. A brushless DC motor vector control model, characterized in that the model is:

in

In the above formula, I _dt is the stator current of the brushless DC motor on the d-axis of the two-phase rotating coordinate system, I _qt is the stator current of the brushless DC motor on the q-axis of the two-phase rotating coordinate system, and ω _e is the brushless DC motor. The synchronous electrical angular velocity of the motor, R _s is the stator resistance of the brushless DC motor, L is the equivalent phase inductance of the brushless DC motor stator, ψ _r is the rotor flux linkage of the brushless DC motor, p is the pole pair of the brushless DC motor number, J is the moment of inertia of the brushless DC motor, U _d is the stator voltage of the brushless DC motor on the d-axis of the two-phase rotating coordinate system, and U _q is the stator of the brushless DC motor on the q-axis of the two-phase rotating coordinate system voltage, _TL is the load torque of the brushless DC motor; the method for obtaining the I _dt and I _qt is: use a current sensor to measure the three-phase currents I _a , I _b and I _c of the brushless DC motor stator, and then measure them Clarke transform and Park transform are performed to obtain I _dt and I _qt .

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