阅读说明：本技术 永磁无刷直流电机调速系统的积分终端滑模复合控制系统 (Integral terminal sliding mode composite control system of permanent magnet brushless direct current motor speed regulation system ) 是由 王会明 王雪闯 万谦 陈晓雷 唐贤伦 刘行谋 于 2020-12-10 设计创作，主要内容包括：本发明请求保护一种永磁无刷直流电机调速系统的积分终端滑模复合控制系统,由基于积分终端滑模的反馈控制部分和基于扩张状态观测器的干扰估计及前馈补偿部分构成。包括：永磁无刷直流电机、速度复合控制器、扩张状态观测器I、电流复合控制器、扩张状态观测器II、脉宽调制模块,三相逆变器模块,位置传感器模块,转子区间计算模块以及速度计算模块；基于永磁无刷直流电机系统模型设计双闭环控制器,从而得到速度复合抗干扰控制和电流复合抗干扰控制器。与传统的积分终端滑模控制方法相比,该方法既保留了传统积分终端滑模控制方法中系统状态的快速收敛性能,又可以有效减小系统稳态波动,进一步地提高了系统的抗干扰能力。(The invention provides an integral terminal sliding mode composite control system of a permanent magnet brushless direct current motor speed regulating system, which consists of a feedback control part based on an integral terminal sliding mode and an interference estimation and feedforward compensation part based on an extended state observer. The method comprises the following steps: the system comprises a permanent magnet brushless direct current motor, a speed composite controller, an extended state observer I, a current composite controller, an extended state observer II, a pulse width modulation module, a three-phase inverter module, a position sensor module, a rotor interval calculation module and a speed calculation module; and designing a double closed-loop controller based on a permanent magnet brushless direct current motor system model so as to obtain a speed composite anti-interference controller and a current composite anti-interference controller. Compared with the traditional integral terminal sliding mode control method, the method not only keeps the rapid convergence performance of the system state in the traditional integral terminal sliding mode control method, but also can effectively reduce the steady-state fluctuation of the system, and further improves the anti-interference capability of the system.)

1. An integral terminal sliding mode composite control system of a permanent magnet brushless direct current motor speed regulation system is characterized by comprising: the system comprises a permanent magnet brushless direct current motor, a speed composite controller, an extended state observer I, a current composite controller, an extended state observer II, a pulse width modulation module, a three-phase inverter module, a position sensor module, a rotor interval calculation module and a speed calculation module; wherein the speed composite controller is connected with the current composite controller, the speed composite controller and the current composite controller are both based on integral terminal sliding mode control, the speed composite controller and the current composite controller both internally comprise an extended state observer, the current composite controller module is connected with the pulse width modulation module, the three-phase inverter module is also respectively connected with the permanent magnet brushless direct current motor and the rotor interval calculation module, a position sensor is arranged between the permanent magnet brushless direct current motor and the rotor interval calculation module, the speed calculation module is connected with the speed composite controller module, the permanent magnet brushless direct current motor is used for receiving an output signal of the three-phase inverter to start operation, then a signal is fed back to the position sensor, and the input end of the speed composite controller module is a speed reference value omega._rAnd the difference value of the current and the actual speed omega of the motor is used for obtaining the reference current i at the input end of the current composite controller module after passing through the speed composite controller module_rThe extended state observer I is used to derive a disturbance d₁(t) and then performing disturbance compensation by a speed composite controller, wherein the current composite controller is used for obtaining a reference current i_rAnd obtaining the input voltage u of the pulse width modulation module after inputting the difference value of the obtained actual current i into the current composite controller module, wherein the extended state observer II is used for obtaining the interference d₂(t) estimation, then disturbance compensation by a current complex controllerThe wide modulation module is used for outputting the required pulse width modulation voltage according to the modulation principle after the voltage u passes through the pulse width modulation module, transmitting the required pulse width modulation voltage to the input end of the three-phase inverter and driving the permanent magnet brushless direct current motor to operate under the phase change control of the rotor interval calculation module; the three-phase inverter module is used for converting received direct current into alternating current, the position sensor module is used for detecting position sensor signals installed on the permanent magnet brushless direct current motor, the rotor interval calculation module is used for obtaining an interval where the position of a motor rotor is located and implementing phase change control on the three-phase inverter module, and the speed calculation module is used for receiving numerical values calculated by the position sensor signals through the rotor interval and obtaining the actual speed omega of the motor through calculation.

2. The integrated terminal sliding mode composite control system of the permanent magnet brushless direct current motor speed regulation system according to claim 1, characterized in that the speed composite controller is composed of feedback control based on an integrated terminal sliding mode and feedforward control based on an extended state observer I, and the speed composite controller is designed as follows:

let w_rIs a reference velocity signal, the velocity tracking error e₁Can be defined as:

e₁＝w_r-w

to e₁The derivation is as follows:

designing an integral terminal sliding mode surface as follows:

wherein the content of the first and second substances,λ₁> 0, sgn (. SP.) is a sign function, s₁Indicating speedIntegral terminal sliding mode surface of composite controller, lambda₁Is a slip form surface s₁T is the upper limit of the integration time,_a1is a slip form surface s₁The speed composite controller based on the integral terminal sliding mode is designed as follows:

wherein a ═ K_t/J，Representing the torque coefficient, n_pIs the magnetic pole pair number psi_fIs a rotor flux linkage; j is moment of inertia; in the mathematical model of the permanent magnet brushless direct current motor, for the convenience of designing the controller, let a be K_tJ, denotes the current coefficient, k₁＞0，Denotes the derivative of w, i_rThe input of the speed composite controller is speed, and the output is reference current i after internal calculation of the controller_r，To interfere with d₁(t) estimation.

3. The integral terminal sliding mode composite control system of the permanent magnet brushless direct current motor speed regulation system according to claim 2, wherein the model of the extended state observer I is as follows:

wherein eta is₁₁Is an estimate of w, η₁₂Is to the disturbance d₁(t) estimation, p₁Are parameters of the extended state observer I.

4. The integrated terminal sliding mode composite control system of the permanent magnet brushless direct current motor speed regulation system according to claim 3, characterized in that the current composite controller is compounded by feedback control of an integrated terminal sliding mode and feedforward control based on an extended state observer II, and the current composite controller is designed as follows:

i is the actual output current of the motor, let i_rIs a reference current signal, a current tracking error e₂Can be defined as:

e₂＝i_r-i

to e₂The derivation is as follows:

designing an integral terminal sliding mode surface as follows:

wherein the content of the first and second substances,λ₂> 0, sgn (. lambda.) is a sign function, lambda₂，a₂For integral terminal sliding form surface s₂The parameters of (1); τ represents a differential operator; k is a radical of₂Representing the parameters of the current composite controller, the current composite controller based on the integral terminal sliding mode is designed as follows:

wherein, b is 1/L, k₂More than 0, L is stator inductance; in the mathematical model of the permanent magnet brushless direct current motor, for the convenience of designing the controller, b is 1/L, represents a voltage coefficient and is the output of a current composite controller,to interfere with d₂(t) estimation.

5. The integral terminal sliding mode composite control system of the permanent magnet brushless direct current motor speed regulation system according to claim 4, wherein the model of the extended state observer II is as follows:

wherein eta is₂₁Is an estimate of i, η₂₂Is a disturbance d₂(t) estimating the value of the average of the measured values,respectively represent η₂₂And η₂₁Is a parameter of the extended state observer II.

6. The integrated terminal sliding mode composite control system of the speed regulating system of the permanent magnet brushless direct current motor according to any one of claims 1 to 5, wherein a mathematical model of the permanent magnet brushless direct current motor is as follows:

wherein the content of the first and second substances,is a torque coefficient; k_e＝n_pψ_fAlso the torque coefficient; n is_pIs the magnetic pole pair number psi_fIs a rotor flux linkage; w, i and u are the actual rotating speed, the stator current and the stator voltage of the motor respectively; l is a stator inductance; r is a stator resistor; b is a viscous friction coefficient; j is moment of inertia; t is_LIs the load torque.

In order to design a controller for the permanent magnet brushless direct current motor conveniently, a mathematical model of the controller can be simplified into the following form:

wherein a ═ K_t/J，b＝1/L，

7. The integrated terminal sliding mode composite control system of the speed regulating system of the permanent magnet brushless direct current motor according to any one of claims 1 to 5, characterized in that the integrated terminal sliding mode composite control system of the speed regulating system of the permanent magnet brushless direct current motor specifically comprises the following steps:

1) detecting a position sensor signal to obtain an interval where the position of a motor rotor is located and carrying out phase change control on a three-phase inverter module;

2) detecting the bus current to obtain an actual current i required by the current composite controller module;

3) the position sensor signal is subjected to the numerical value calculated by the rotor interval, and the actual speed omega of the motor is obtained by a speed calculation module;

4) the input end of the speed composite controller module is a speed reference value omega_rObtaining the reference current i at the input end of the current composite controller module after the difference value of the actual speed omega obtained in the step 3) passes through the speed composite controller module_r；

5) Reference current i obtained in step 4)_rObtaining the input voltage u of the pulse width modulation module after the difference value of the actual current i obtained in the step 2) passes through the current composite controller module;

6) and the voltage u passes through the pulse width modulation module, outputs the required pulse width modulation voltage according to the modulation principle, transmits the required pulse width modulation voltage to the input end of the three-phase inverter, and drives the permanent magnet brushless direct current motor to operate under the phase change control of the rotor interval calculation module.

Technical Field

The invention belongs to an interference suppression method of a permanent magnet brushless direct current motor, and particularly relates to a composite control method of an integral terminal sliding mode algorithm of a permanent magnet brushless direct current motor speed regulation system in combination with an extended state observer.

Background

The permanent magnet brushless direct current motor is a novel direct current motor developed along with rapid development of power electronic technology, manufacturing industry and novel materials, and is widely applied to the industrial fields of aerospace, household appliances, instruments and meters, chemical engineering, medical appliances and the like due to a series of advantages of simple structure, reliable operation, convenient maintenance, high efficiency, no excitation loss, good speed regulation performance and the like.

In general, sliding mode control can be divided into two categories, control based on linear sliding mode surfaces and control based on non-linear sliding mode surfaces. The two control systems differ in that the former is asymptotically stable, whereas control based on non-linear sliding surfaces is time-limited stable. Among existing sliding mode control methods, Integral Terminal Sliding Mode Control (ITSMC) is an effective control method based on non-linear sliding mode surfaces. The invention discusses the problem of interference suppression of a speed regulating system of a permanent magnet brushless direct current motor. Firstly, an Integral Terminal Sliding Mode Control (ITSMC) method is introduced for a speed loop, and meanwhile, a closed-loop system can be ensured to have certain anti-interference capability. However, ITSMC may cause the steady state speed of a permanent magnet synchronous motor control system to fluctuate widely in the presence of strong disturbances. Therefore, an integral terminal sliding mode composite control method based on an Extended State Observer (ESO) is provided. The method adopts ESO to estimate the interference of the system and uses feedforward control to compensate the interference. Compared with the traditional integral terminal sliding mode control method, the method has stronger anti-interference performance.

Therefore, the integral terminal sliding mode composite control method of the permanent magnet brushless direct current motor speed regulation system is designed, so that the system maintains the rapid convergence performance and further improves the anti-interference capability.

Disclosure of Invention

The present invention is directed to solving the above problems of the prior art. An integral terminal sliding mode composite control system of a permanent magnet brushless direct current motor speed regulation system is provided. The technical scheme of the invention is as follows:

an integral terminal sliding mode composite control system of a permanent magnet brushless direct current motor speed regulation system comprises: the system comprises a permanent magnet brushless direct current motor, a speed composite controller, an extended state observer I, a current composite controller, an extended state observer II, a pulse width modulation module, a three-phase inverter module, a position sensor module, a rotor interval calculation module and a speed calculation module; wherein the speed composite controller is connected with the current composite controller, the speed composite controller and the current composite controller are both based on integral terminal sliding mode control, the speed composite controller and the current composite controller both internally comprise an extended state observer, the current composite controller module is connected with the pulse width modulation module, the three-phase inverter module is also respectively connected with the permanent magnet brushless direct current motor and the rotor interval calculation module, a position sensor is arranged between the permanent magnet brushless direct current motor and the rotor interval calculation module, the speed calculation module is connected with the speed composite controller module, the permanent magnet brushless direct current motor is used for receiving an output signal of the three-phase inverter to start operation, then a signal is fed back to the position sensor, and the input end of the speed composite controller module is a speed reference value omega._rAnd the difference value of the current and the actual speed omega of the motor is used for obtaining the reference current i at the input end of the current composite controller module after passing through the speed composite controller module_rThe extended state observer I is used to derive a disturbance d₁(t) and then performing disturbance compensation by a speed composite controller, wherein the current composite controller is used for obtaining a reference current i_rAnd obtaining the input voltage u of the pulse width modulation module after inputting the difference value of the obtained actual current i into the current composite controller module, wherein the extended state observer II is used for obtaining the interference d₂(t), then disturbance compensation is carried out through a current composite controller, a pulse width modulation module is used for outputting required pulse width modulation voltage according to a modulation principle after voltage u passes through the pulse width modulation module, the required pulse width modulation voltage is transmitted to the input end of a three-phase inverter, and a permanent magnet brushless direct current motor is driven to operate under the phase change control of a rotor interval calculation module; the three-phase inverter module is used for converting received direct current into alternating current, the position sensor module is used for detecting position sensor signals installed on the permanent magnet brushless direct current motor, the rotor interval calculation module is used for obtaining an interval where the position of a motor rotor is located and implementing phase change control on the three-phase inverter module, and the speed calculation module is used for receiving numerical values calculated by the position sensor signals through the rotor interval and obtaining the actual speed omega of the motor through calculation.

Further, the speed composite controller is composed of feedback control based on an integral terminal sliding mode and feedforward control based on an extended state observer I, and is designed as follows:

let w_rIs a reference velocity signal, the velocity tracking error e₁Can be defined as:

e₁＝w_r-w

to e₁The derivation is as follows:

designing an integral terminal sliding mode surface as follows:

wherein the content of the first and second substances,λ₁＞0，sgn(is a sign function, s)₁Integral terminal sliding mode surface, lambda, representing a velocity complex controller₁Is a slip form surface s₁T is the upper limit of the integration time,_a1is a slip form surface s₁The speed composite controller based on the integral terminal sliding mode is designed as follows:

wherein a ═ K_t/J，Representing the torque coefficient, n_pIs the magnetic pole pair number psi_fIs a rotor flux linkage; j is moment of inertia; in the mathematical model of the permanent magnet brushless direct current motor, for the convenience of designing the controller, let a be K_tJ, denotes the current coefficient, k₁＞0，Denotes the derivative of w, i_rThe input of the speed composite controller is speed, and the output is reference current i after internal calculation of the controller_r，To interfere with d₁(t) estimation.

Further, the extended state observer I is modeled as follows:

wherein eta is₁₁Is an estimate of w, η₁₂Is to the disturbance d₁(t) estimation, p₁Are parameters of the extended state observer I.

Further, the current composite controller is formed by compounding feedback control of an integral terminal sliding mode and feedforward control based on an extended state observer II, and is designed as follows:

i is the actual output current of the motor, let i_rIs a reference current signal, a current tracking error e₂Can be defined as:

e₂＝i_r-i

to e₂The derivation is as follows:

designing an integral terminal sliding mode surface as follows:

wherein the content of the first and second substances,λ₂> 0, sgn (. lambda.) is a sign function, lambda₂，a₂For integral terminal sliding form surface s₂The parameters of (1); τ represents a differential operator; k is a radical of₂Representing the parameters of the current composite controller, the current composite controller based on the integral terminal sliding mode is designed as follows:

wherein, b is 1/L, k₂More than 0, L is stator inductance; in the mathematical model of the permanent magnet brushless direct current motor, for the convenience of designing the controller, b is 1/L, represents a voltage coefficient and is the output of a current composite controller,to interfere with d₂(t) estimation.

Further, the extended state observer II is modeled as follows:

wherein eta is₂₁Is an estimate of i, η₂₂Is a disturbance d₂(t) estimating the value of the average of the measured values,respectively represent η₂₂And η₂₁Is a parameter of the extended state observer II.

Further, the mathematical model of the permanent magnet brushless dc motor is:

wherein the content of the first and second substances,is a torque coefficient; k_e＝n_pψ_fAlso the torque coefficient; n is_pIs the magnetic pole pair number psi_fIs a rotor flux linkage; w, i and u are the actual rotating speed, the stator current and the stator voltage of the motor respectively; l is a stator inductance; r is a stator resistor; b is a viscous friction coefficient; j is moment of inertia; t is_LIs the load torque.

In order to design a controller for the permanent magnet brushless direct current motor conveniently, a mathematical model of the controller can be simplified into the following form:

wherein a ═ K_t/J，b＝1/L，

Further, the integral terminal sliding mode composite control system of the permanent magnet brushless direct current motor speed regulation system specifically comprises the following steps:

1) detecting a position sensor signal to obtain an interval where the position of a motor rotor is located and carrying out phase change control on a three-phase inverter module;

2) detecting the bus current to obtain an actual current i required by the current composite controller module;

3) the position sensor signal is subjected to the numerical value calculated by the rotor interval, and the actual speed omega of the motor is obtained by a speed calculation module;

4) the input end of the speed composite controller module is a speed reference value omega_rObtaining the reference current i at the input end of the current composite controller module after the difference value of the actual speed omega obtained in the step 3) passes through the speed composite controller module_r；

5) Reference current i obtained in step 4)_rObtaining the input voltage u of the pulse width modulation module after the difference value of the actual current i obtained in the step 2) passes through the current composite controller module;

6) and the voltage u passes through the pulse width modulation module, outputs the required pulse width modulation voltage according to the modulation principle, transmits the required pulse width modulation voltage to the input end of the three-phase inverter, and drives the permanent magnet brushless direct current motor to operate under the phase change control of the rotor interval calculation module.

The invention has the following advantages and beneficial effects:

1. compared with the traditional integral terminal sliding mode control method, the method not only keeps the rapid convergence performance of the system state in the traditional integral terminal sliding mode control method, but also can effectively reduce the steady-state fluctuation of the system, and further improves the anti-interference capability of the system.

2. The invention has the innovation points that a speed controller and a current controller are designed according to an integral terminal sliding mode surface, and then the speed composite controller and the current composite controller are designed by combining an extended state observer.

3. The system reference speed is input into the speed composite controller, the output reference current is used as the input of the current composite controller after internal calculation, and the output voltage enters the pulse width modulation module after internal calculation. The two controllers are internally provided with the extended state observers, so that the control effect is higher in anti-interference capability and better in dynamic and steady-state performance compared with that of general control.

Drawings

FIG. 1 is a schematic diagram of a control system according to a preferred embodiment of the present invention;

FIG. 2 is a detailed functional block diagram of the control system of the present invention;

FIG. 3 is a block diagram of a speed composite controller incorporating ESOI with integral termination sliding mode of the present invention;

FIG. 4 is a schematic block diagram of the integrated terminal sliding mode combined ESOII current composite controller of the present invention;

FIG. 5 is a system speed profile for two control regimes;

FIG. 6 is a system current curve under the integral terminal sliding mode control mode;

FIG. 7 is a system current curve for the proposed control of the present invention;

FIG. 8 is a system voltage curve for two control modes;

FIG. 9 is an output curve of the extended state observer I in the recommended control mode of the invention;

fig. 10 is an output curve of the extended state observer Π in the preferred control scheme of the present invention.

Detailed Description

The technical solutions in the embodiments of the present invention will be described in detail and clearly with reference to the accompanying drawings. The described embodiments are only some of the embodiments of the present invention.

The technical scheme for solving the technical problems is as follows:

the mathematical model of the permanent magnet brushless direct current motor is as follows:

wherein the content of the first and second substances,is a torque coefficient; k_e＝n_pψ_fAlso the torque coefficient; n is_pIs the magnetic pole pair number psi_fIs a rotor flux linkage; w, i and u are the actual rotating speed, the stator current and the stator voltage of the motor respectively; l is a stator inductance; r is a stator resistor; b is a viscous friction coefficient; j is moment of inertia; t is_LIs the load torque.

In general, to design a controller for a permanent magnet brushless dc motor, a mathematical model thereof can be simplified into the following form:

wherein a ═ K_t/J，b＝1/L，

Fig. 1 is a schematic diagram of the control system of the present invention, and fig. 2 is a detailed schematic block diagram of the control system of the present invention, from which, as will be readily appreciated,

the implementation comprises the following steps:

1) detecting a position sensor signal to obtain an interval where the position of a motor rotor is located and carrying out phase change control on a three-phase inverter module;

2) detecting the bus current to obtain an actual current i required by the current composite controller module;

3) the position sensor signal is subjected to the numerical value calculated by the rotor interval, and the actual speed omega of the motor is obtained by a speed calculation module;

4) the input end of the speed composite controller module is a speed reference value omega_rObtaining the reference current at the input end of the current composite controller module after the difference value of the actual speed omega obtained in the step 3) passes through the speed composite controller modulei_r；

5) Reference current i obtained in step 4)_rObtaining the input voltage u of the pulse width modulation module after the difference value of the actual current i obtained in the step 2) passes through the current composite controller module;

6) and the voltage u passes through the pulse width modulation module, outputs the required pulse width modulation voltage according to the modulation principle, transmits the required pulse width modulation voltage to the input end of the three-phase inverter, and drives the permanent magnet brushless direct current motor to operate under the phase change control of the rotor interval calculation module.

According to the attached figure 3, the integral terminal sliding mode speed composite controller comprises speed feedback control and interference estimation eta based on interference₁₂By analyzing the principle block diagram of the integral terminal sliding mode speed composite controller, the feedforward control can obtain the expression of the speed composite controller as follows:

wherein a ═ K_t/J，λ₁＞0，k₁＞0，To interfere with d₁(t) estimation, e₁The error is tracked for velocity.

According to fig. 4, the integrated terminal sliding mode current composite controller comprises current feedback control and interference estimation eta based on the current feedback control₂₂The feedforward control of (1); by analyzing the principle block diagram of the integral terminal sliding mode current composite controller, the expression of the current controller can be obtained as follows:

wherein, b is 1/L, k₂＞0，To interfere with d₂(t) estimation，e₂Is the current tracking error.

In the present invention, the observers I and II are Extended State Observers (ESOs);

the expression of the Extended State Observer (ESO) I is:

wherein eta is₁₁Is an estimate of w, η₁₂Is to the disturbance d₁(t) estimation, p₁Are parameters of the extended state observer I.

The expression of the Extended State Observer (ESO) II is:

wherein eta is₂₁Is an estimate of i, η₂₂Is to the disturbance d₂(t) estimation, p₂To expand the parameters of the state observer II.

As shown in fig. 5, comparing the integral terminal sliding mode composite control method of the permanent magnet brushless dc motor speed regulation system of the present invention with the Integral Terminal Sliding Mode Control (ITSMC) method, it can be known that the control method of the present invention enables the permanent magnet brushless dc motor speed regulation system to rapidly reach a steady state value after starting, the overshoot of the system is small, and the regulation time is short; when the load is applied when t is 8s, the system is quickly recovered to a steady-state value in the case of load disturbance, and the regulation time is extremely short.

As shown in fig. 6, it is a curve of the actual system current and the reference current in the ITSMC control mode;

as shown in fig. 7, it is a curve of the actual current and the reference current of the system under the control mode recommended by the present invention;

comparing the two graphs, it can be seen that the recommended control mode of the invention makes the actual current of the system better track the reference current, which is basically consistent with the reference current, and after the system applies a load when t is 8s, the recommended control mode of the invention makes the system almost have no overshoot, the adjusting time is extremely short, and the current rapidly reaches the steady-state value.

As shown in fig. 8, the voltage curve of the system under two control modes, compared with ITSMC, can be seen from the figure, the control method proposed by the present invention can make the speed regulating system of the permanent magnet brushless dc motor reach a steady state value quickly after starting, the overshoot of the system is small, and the regulating time is short; and when t is 8s, the load is applied, the system has almost no overshoot, the regulation time is extremely short, and the voltage is quickly enabled to reach a steady-state value.

Fig. 9 shows an output curve of the extended state observer I in the control mode recommended by the present invention. The curves shown in graph (a) are w and its estimate η, respectively₁₁It can be seen that the time-varying trend of the graph is consistent with that of fig. 5, and the observed value η₁₁The observer can accurately observe the change of the speed loop of the speed regulating system of the permanent magnet brushless direct current motor in real time, including the condition that the system is interfered by an external load when t is 8 s. The curve shown in the graph (b) is the observed value η₁₂，d₁(t) is the interference experienced by subsystem I (speed loop).

Fig. 10 shows an output curve of the extended state observer Π in the control mode recommended by the present invention. The curves shown in graph (a) are i and its estimated η, respectively₂₁It can be seen that the time-varying trend of the graph is consistent with that of fig. 7, and the observed value η₂₁The observer can accurately observe the change of a current loop of the speed regulating system of the permanent magnet brushless direct current motor in real time, including the condition that the system is interfered by an external load when t is 8 s. The curve shown in the graph (b) is the observed value η₂₂，d₂And (t) is the interference on the subsystem pi (current loop).

The systems, devices, modules or units illustrated in the above embodiments may be implemented by a computer chip or an entity, or by a product with certain functions. One typical implementation device is a computer. In particular, the computer may be, for example, a personal computer, a laptop computer, a cellular telephone, a camera phone, a smartphone, a personal digital assistant, a media player, a navigation device, an email device, a game console, a tablet computer, a wearable device, or a combination of any of these devices.

Computer-readable media, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), Digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device. As defined herein, a computer readable medium does not include a transitory computer readable medium such as a modulated data signal and a carrier wave.

It should also be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.

The above examples are to be construed as merely illustrative and not limitative of the remainder of the disclosure. After reading the description of the invention, the skilled person can make various changes or modifications to the invention, and these equivalent changes and modifications also fall into the scope of the invention defined by the claims.