CN111497929B - A position sensorless controller for automotive EPS steering system - Google Patents
A position sensorless controller for automotive EPS steering system Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B62—LAND VEHICLES FOR TRAVELLING OTHERWISE THAN ON RAILS
- B62D—MOTOR VEHICLES; TRAILERS
- B62D5/00—Power-assisted or power-driven steering
- B62D5/04—Power-assisted or power-driven steering electrical, e.g. using an electric servo-motor connected to, or forming part of, the steering gear
- B62D5/0457—Power-assisted or power-driven steering electrical, e.g. using an electric servo-motor connected to, or forming part of, the steering gear characterised by control features of the drive means as such
- B62D5/046—Controlling the motor
- B62D5/0463—Controlling the motor calculating assisting torque from the motor based on driver input
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
- H02P21/18—Estimation of position or speed
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
- H02P6/14—Electronic commutators
- H02P6/16—Circuit arrangements for detecting position
- H02P6/17—Circuit arrangements for detecting position and for generating speed information
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Abstract
本发明公开汽车控制领域中的一种汽车EPS转向系统无位置传感器控制器，由EPS状态反馈控制器、带通滤波器、标幺化模块、离散角度判断模块、低通滤波器、两相高频电压计算模块、2s/2r坐标变换模块、3s/2s坐标变换模块、角度初始化模块和低通滤波器组成，EPS状态反馈控制器与两相高频电压计算模块并联后连接EPS转向系统的输入端，EPS转向系统输出端与3s/2s坐标变换模块串联，3s/2s坐标变换模块输出端与第二低通滤波器、2r/2s坐标变换模块、EPS状态反馈控制器依次串联形成局部闭环控制，通过离散角度判断模块，实现对电机位置角度的精度估算，避免系统延迟、抖振等缺陷，通过EPS状态反馈控制器替代传统的串联闭环控制系统，提高系统的控制精度。
The invention discloses a position sensorless controller of an automobile EPS steering system in the field of automobile control, which is composed of an EPS state feedback controller, a band-pass filter, a per-unitization module, a discrete angle judgment module, a low-pass filter, a two-phase high Frequency and voltage calculation module, 2s/2r coordinate transformation module, 3s/2s coordinate transformation module, angle initialization module and low-pass filter. The EPS state feedback controller is connected in parallel with the two-phase high-frequency voltage calculation module and then connected to the input of the EPS steering system The output end of the EPS steering system is connected in series with the 3s/2s coordinate transformation module, and the output end of the 3s/2s coordinate transformation module is connected in series with the second low-pass filter, the 2r/2s coordinate transformation module, and the EPS state feedback controller to form a local closed-loop control. , Through the discrete angle judgment module, the accuracy of the motor position angle can be estimated, avoiding defects such as system delay and chattering, and replacing the traditional series closed-loop control system with the EPS state feedback controller to improve the control accuracy of the system.
Description
Technical Field
The invention belongs to the field of automobile control, and particularly relates to a controller without a position sensor for an EPS (electric power steering) system of an automobile, which is suitable for controlling the EPS system of the automobile.
Background
With the continuous innovative development of the automobile electronic technology and the control technology, the automobile power steering system goes from the traditional pure mechanical power steering system to the gradually developed and perfect hydraulic power steering system and then to the later novel electric control hydraulic power steering system, and the electric power steering system, namely the EPS system, is widely popularized and used nowadays. The EPS system adopts a power-assisted motor to provide steering power assistance, and the power assistance is directly controlled by an electric control system. Compared with the traditional hydraulic power-assisted steering system, the method for controlling the power assistance by the motor can save energy and is very environment-friendly.
The EPS system is provided with a power source by a power-assisted motor, and mainly comprises a torque sensor, the power-assisted motor, a speed reducing mechanism and a motor electronic control unit. The hydraulic system is cancelled, the engine works independently, and the energy consumption is reduced; the EPS system only adopts mechanical connection and electric signal control, has higher efficiency and is beneficial to chassis integrated control; the direct current motor has good starting and speed regulating performance, so that the direct current motor is widely applied to an EPS system, but the sliding contact of the electric brush and the commutator causes mechanical abrasion and sparks to form a radio interference source, so that the direct current motor has many faults and low reliability. The existing permanent magnet synchronous motor has the advantages of small size, high efficiency, high power factor and the like, and is developed into a novel steering motor which replaces an EPS system direct current motor, namely an EPS permanent magnet synchronous motor.
The EPS system, as a torque servo system, requires a motor assist torque with rapid and accurate response, and is very sensitive to the pulsation of the torque, so that the stable and reliable operation of the motor depends on a motor control technology. In practical industrial control systems, especially in high-performance speed regulation occasions, the position sensor is an important element for acquiring a rotor position signal, but the sensor may be in failure under the environments of high and low temperature, humidity and the like, so that the accuracy of the sensor is reduced and even the sensor is damaged, and the operation stability and controllability of the motor are affected. The simultaneous mounting of position sensors increases the cost of the drive system as well as the bulk and complexity of the drive system. Therefore, the research on the control of the motor without a position sensor is very necessary.
The traditional position-sensorless control method is to inject high-frequency signals, a heterodyne demodulation technology is adopted in position sensing control, and because heterodyne demodulation has an inertia link, delay exists in estimation of rotor position signals, and the speed regulation performance of a motor is directly influenced.
Disclosure of Invention
The invention aims to provide a position sensorless controller of an automobile EPS steering system, which can effectively improve the control precision of a motor position sensorless control scheme, particularly high-performance control under transient working conditions, aiming at the defects of the existing position sensorless control scheme of an EPS permanent magnet synchronous motor.
The invention relates to a controller of an automobile EPS steering system without a position sensor, which adopts the technical scheme that: the device consists of an EPS state feedback controller, a band-pass filter, a per-unit module, a discrete angle judgment module, a low-pass filter, a two-phase high-frequency voltage calculation module, a 2s/2r coordinate transformation module, a 3s/2s coordinate transformation module, an angle initialization module and a low-pass filter, wherein the first input of the EPS state feedback controller is a reference angle thetarefThe second input is the fundamental current i under the two-phase rotating coordinate system output by the 2s/2r coordinate transformation moduledq(k) The third input is the final estimated angle theta (k) output by the first low-pass filter, and the EPS state feedback controller outputs a control voltage uαβ(k) (ii) a The input of the two-phase high-frequency voltage calculation module is a high-frequency voltage VinAnd angular frequency ωinThe output is high-frequency injection voltage under a two-phase static coordinate system
The control voltage uαβ(k) And high frequency injection voltage
As two inputs of the EPS steering system, the EPS steering system outputs three-phase current Iabc(k) To a 3s/2s coordinate transformation module, the 3s/2s coordinate transformation module outputs current I under a two-phase static coordinate systemαβ(k) Respectively to a band-pass filter and a second low-pass filter, the band-pass filter outputs high-frequency current under two-phase static coordinate system
To the per unit module, the second low-pass filter outputs fundamental current i under the two-phase static coordinate systemαβ(k) To a 2s/2r coordinate transformation module, the 2s/2r coordinate transformation module outputs fundamental current i under a two-phase rotating coordinate systemdq(k) (ii) a The per-unit module outputs per-unit parameters Kαβ(k) To a discrete angle judgment module as the first input of the discrete angle judgment module, and the second input of the discrete angle judgment module is the angular frequency omegainThe discrete angle judgment module outputs a preliminary estimated angle
The first low-pass filter outputs the final estimated angle theta (k) to the angle initialization module, the 2s/2r coordinate transformation module and the EPS state feedback controller respectively, and the angle initialization module outputs the third input of the discrete angle judgment module3 initialization angles theta1,θ2,θ3。
The invention has the beneficial effects that:
1. according to the invention, the precision estimation of the position angle of the motor is realized through the discrete angle judgment module, so that the position sensor-free control of the EPS steering system is realized, and the defects of increased cost, complex driving system and the like caused by the installation of a position sensor in the traditional control are overcome. Compared with the traditional controller without the position sensor, the controller is efficient and direct, avoids the defects of system delay, buffeting and the like, and realizes the high-precision control of the EPS steering system without the position sensor.
2. The EPS state feedback controller replaces the traditional series closed-loop control system, so that the defects of the series closed-loop system are avoided, and the control precision of the system is improved.
3. The required control variable and the input variable are easy-to-measure variables, and the control algorithm of the controller can be realized only by modular software programming, thereby being beneficial to engineering realization.
Drawings
FIG. 1 is a block diagram of the present invention;
fig. 2 is a block diagram of the structure of the EPS steering system 2 in fig. 1;
fig. 3 is a block diagram of the structure of the EPS state feedback controller 1 in fig. 1;
in the figure: an EPS state feedback controller; an EPS steering system; 3. a band-pass filter; 4. a per-unit module; 5. a discrete angle judgment module; 6. a first low-pass filter; 7. a two-phase high-frequency voltage calculation module; 8.3s/2r coordinate transformation module; a 9.3s/2s coordinate transformation module; 10. an angle initialization module; 12.2r/2s coordinate transformation module; 13. a feedback voltage controller; 21. a space voltage vector modulation module; 22. a voltage source inverter; 23. a permanent magnet synchronous motor; 24. a speed reduction mechanism.
Detailed Description
As shown in fig. 1, the present invention is composed of an EPS state feedback controller 1, a band pass filter 3, a per unit module 4, a discrete angle determination module 5, a first low pass filter 6, a two-phase high frequency voltage calculation module 7, a 2s/2r coordinate transformation module 8, a 3s/2s coordinate transformation module 9, an angle initialization module 10, and a second low pass filter 11.
The output end of the EPS state feedback controller 1 is connected with a first input end of the EPS steering system 2, and the output end of the two-phase high-frequency voltage calculation module 7 is connected with a second input end of the EPS steering system 2. The output end of the EPS steering system 2 is connected with the input end of a 3s/2s coordinate transformation module 9, the output end of the 3s/2s coordinate transformation module 9 is divided into two paths, one path is sequentially connected with a second low-pass filter 11, a 2s/2r coordinate transformation module 8 and the EPS state feedback controller 1 in series, and the other path is sequentially connected with a band-pass filter 3, a per-unit module 4, a discrete angle judgment module 5 and a first low-pass filter 6 in series. The output end of the first low-pass filter 6 is respectively connected with the angle initialization module 10, the 2s/2r coordinate transformation module 8 and the EPS state feedback controller 1. The output end of the angle initialization module 10 is connected with the discrete angle judgment module 5.
The EPS state feedback controller 1 has three inputs, the first of which is a reference angle thetaref(ii) a The second input is the fundamental current i under the two-phase rotating coordinate system output by the 2s/2r coordinate transformation module 8dq(k) K is a discrete sample sampling index, and
) (ii) a The third input is the final estimated angle θ (k) output by the first low pass filter 6.
The EPS state feedback controller 1 processes the three output values and outputs a control voltage uαβ(k) The control voltage uαβ(k) Is the first input to the EPS steering system 2.
The input of the two-phase high-frequency voltage calculation module 7 is a high-frequency voltage V injected from the outsideinAnd a high frequency voltage VinAngular frequency of (omega)inThe output is high-frequency injection voltage under a two-phase static coordinate system
The high frequency injection voltage
Is an EPS steering system 2To the second input of (a).
High frequency current
Inputting into the per-unit module 4, the per-unit module 4 processes the high-frequency current
Performing per-unit processing to obtain per-unit parameter Kαβ(k) And input to the discrete angle determination module 5 as the first input of the discrete angle determination module 5. The second input of the discrete angle judgment module 5 is the angular frequency omega of the high-frequency voltageinThe third input is the initialized angle theta output by the angle initializing module 101,θ2,θ3The output of the discrete angle judgment module 5 is the preliminary estimated angle
Preliminary estimation of angle
The first low-pass filter 6 outputs the final estimated angle θ (k) through the first low-pass filter 6. The final estimated angle θ (k) is used as an input of the angle initialization module 10, and the angle initialization module 10 outputs the initialized angle θ1,θ2,θ3The initialized angle theta1,θ2,θ3As a third input to the discrete angle determination module 5.
As shown in fig. 2, the EPS steering system 2 is composed of a space voltage vector modulation module 21, a voltage source inverter 22, a permanent magnet synchronous motor 23, and a speed reduction mechanism 24, which are connected in series in this order. Control voltage u of EPS steering system 2 in two-phase stationary coordinate systemαβ(k) And high frequency injection voltage
As input, three-phase current I is outputabc(k) In that respect Space voltage vector modulation module 21 to control voltage uαβ(k) And high frequency injection voltage
The sum is used as input to output a switching pulse signal Ta、Tb、TcThe voltage source inverter 22 switches the pulse signal Ta、Tb、TcAs input, three-phase current I is outputabc(k) The permanent magnet synchronous motor 23 is driven by three-phase current Iabc(k) For input, output torque TeTo the speed reducing mechanism 24.
As shown in fig. 3, the EPS state feedback controller 1 is composed of a 2r/2s coordinate transformation module 12 and a feedback voltage controller 13. Current i in two-phase rotating coordinate systemdq(k) And a reference angle thetarefAnd the estimated angle theta (k) as input to the feedback voltage controller 13, the feedback voltage controller 13 outputting a control voltage u in a two-phase rotation coordinate systemdq(k) The control voltage udq(k) As a first input of the 2r/2s coordinate transformation module 12, a second input of the 2r/2s coordinate transformation module 12 is an estimated angle θ (k), and the coordinate transformation by the 2r/2s coordinate transformation module 12 is performedAfter conversion, the control voltage u under the two-phase static coordinate system is outputαβ(k) The control voltage uαβ(k) Is the output of the EPS state feedback controller 1.
The expression of the feedback voltage controller 12 is:
wherein X is ═ id(k),iq k(k),θ(k),Eθ]TAnd is a state variable matrix of the system. i.e. id(k),iq(k) In order to synchronize the currents in the rotating coordinate system,
and k is the integral of the rotating speed error, k is a discrete sampling index, and T is a sampling period. The gain coefficient matrix of the feedback voltage controller 12 with P being 2 × 4, according to the actual parameters and the working condition of the EPS steering system 2, the gain coefficient matrix of the feedback voltage controller 1 is:
the input of the two-phase high-frequency voltage calculation module 7 is high-frequency voltage VinAnd angular frequency omega of high frequency voltageinThe output is high-frequency injection voltage under a two-phase static coordinate system
The input-output relationship of the two-phase high-frequency voltage calculation module 7 is as follows:
where k is the discrete sampling index and T is the sampling period.
Three-phase current I output by EPS steering system 2abc(k) Converted into a two-phase static coordinate system by a 3s/2s coordinate conversion module 9Current I ofαβ(k) Respectively passing through a band-pass filter 3 and a second low-pass filter 11 to output high-frequency current in a two-phase stationary coordinate system
And a fundamental current iαβ(k)。
The per-unit module 4 outputs the high-frequency current to the band-pass filter 3
Per-unit, outputting per-unit parameter Kαβ(k) The expression of (a) is:
in the formula, Ld、LqIs the stator inductance under the rotating coordinate system,
the angle initialization module 10 inputs the estimated angle theta (k) and outputs 3 initialization angles theta (k)1,θ2,θ3. The angle initialization module 10 first performs delay processing on the estimated angle θ (k) to obtain the estimated angle θ (k-1) of the previous period, and calculates 3 initialization angles θ (k-1) according to the estimated angle θ (k-1)1,θ2,θ3Respectively is as follows:
the discrete angle judgment module 5 pairs the per unit parameter Kαβ(k) Angular frequency omegain3 initialization angles theta1,θ2,θ3Processing, making discrete angle judgment, and outputting the angle estimation value of current time
Discrete angleThe judgment process of judgment is as follows:
(1) initializing 3 angles theta1,θ2,θ3Are respectively recorded as 3 iteration angles theta'1,θ′2,θ′3Setting an iteration termination coefficient lambda;
(2) respectively iterating the angles theta'1,θ′2,θ′3Combined per unit parameter Kαβ(k) Angular frequency omegainAnd calculating 3 cost functions Q by the sampling period T1,Q2,Q3The cost function calculation formula is as follows:
if the estimated rotor angle is completely accurate, the corresponding cost function value Q1，Q2，Q3Is 0 and therefore the magnitude of the cost function value represents the accuracy of the rotor position signal.
(3) Will iterate an angle of θ'1,θ′2,θ′3Corresponding 3 cost function values Q1,Q2,Q3Comparing, and taking the iteration angle corresponding to the minimum cost function value as the optimal angle thetaop。
(4) Make theta'1＝θop，θ′2＝θop+2π/3·2-n，θ′3＝θop-2π/3·2-nAnd n is the current iteration number.
(5) If (theta'2-θ′1) If lambda is less than lambda, the iteration is terminated, otherwise, the step (2) is returned.
(6) After the iteration is ended, outputting an angle estimated value
Estimated angle of output from the discrete angle judgment module 5
As a first low passThe final estimated angle theta (k) is output by the filter 6, and is used as the input of the EPS state feedback controller 1, the 2s/2r coordinate transformation module 8 and the angle initialization module 10.
As shown in figure 1, an EPS state feedback controller 1 and a two-phase high-frequency voltage calculation module 7 are connected in parallel and then connected with an input end of an EPS steering system 2, an output end of the EPS steering system 2 is connected with a 3s/2s coordinate transformation module 9 in series, an output end of the 3s/2s coordinate transformation module 9 is connected with a second low-pass filter 11, a 2r/2s coordinate transformation module 8 and the EPS state feedback controller 1 in series in sequence to form local closed-loop control, and meanwhile, the output end of the EPS state feedback controller is connected with a band-pass filter 3, a per unit module 4, a discrete angle judgment module 5 and a first low-pass filter 6 in series to finally form an EPS steering system position-sensor-free controller, so that position-sensor-free control of the EPS steering system is realized. The EPS state feedback controller 1 replaces a traditional series closed-loop control system, so that the defects of the series closed-loop system are overcome, and the control precision of the system is improved. The two-phase high-frequency voltage calculation module 7 realizes the low-speed control of the permanent magnet synchronous motor by introducing high-frequency voltage. The per unit module 4 eliminates the adverse effect of the motor parameter change on the control. The invention overcomes the defects of increased cost, complex driving system and the like caused by installing the position sensor in the traditional control method, and avoids the control delay caused by the traditional phase-locked loop control technology without the position sensor. The defects of angle estimation precision, system delay, buffeting and the like are improved through discrete angle iterative optimization. Meanwhile, the EPS state feedback controller replaces the traditional series closed-loop control, and the control accuracy and the control structure are improved, so that the high-accuracy EPS steering system is controlled without a position sensor.
Claims (7)
1. The utility model provides a car EPS a steering system does not have position sensor controller which characterized by: the device is composed of an EPS state feedback controller (1), a band-pass filter (3), a per unit module (4), a discrete angle judgment module (5), a first low-pass filter (6), a two-phase high-frequency voltage calculation module (7), a 2s/2r coordinate transformation module (8), a 3s/2s coordinate transformation module (9), an angle initialization module (10) and a second low-pass filter (11), wherein the first input of the EPS state feedback controller (1) is a reference angleDegree thetarefThe second input is the fundamental current i under the two-phase rotating coordinate system output by the 2s/2r coordinate transformation module (8)dq(k) The third input is the final estimated angle theta (k) output by the first low-pass filter (6), and the EPS state feedback controller (1) outputs a control voltage uαβ(k) (ii) a The input of the two-phase high-frequency voltage calculation module (7) is a high-frequency voltage VinAnd angular frequency ωinThe output is high-frequency injection voltage under a two-phase static coordinate system
The control voltage uαβ(k) And high frequency injection voltage
As two inputs of the EPS steering system (2), the EPS steering system (2) outputs a three-phase current Iabc(k) To a 3s/2s coordinate transformation module (9), the 3s/2s coordinate transformation module (9) outputs a current I under a two-phase static coordinate systemαβ(k) Respectively to a band-pass filter (3) and a second low-pass filter (11), the band-pass filter (3) outputs high-frequency current under a two-phase static coordinate system
To the per unit module (4), the second low pass filter (11) outputs the fundamental current i under the two-phase static coordinate systemαβ(k) To a 2s/2r coordinate transformation module (8), the 2s/2r coordinate transformation module (8) outputs fundamental current i under a two-phase rotating coordinate systemdq(k) (ii) a The per-unit module (4) outputs a per-unit parameter Kαβ(k) To a discrete angle judgment module (5) as a first input of the discrete angle judgment module (5), and a second input of the discrete angle judgment module (5) is the angular frequency omegainThe discrete angle judgment module (5) outputs a preliminary estimated angle
To the first low-pass filter (6), the first low-pass filter (6) outputs the final estimated angle theta (k) to the angle initialization module (10) respectively,A 2s/2r coordinate transformation module (8) and an EPS state feedback controller (1), wherein the angle initialization module (10) outputs 3 initialization angles theta which are used as the third input of the discrete angle judgment module (5)1,θ2,θ3And k is a discrete sampling index.
2. The position sensorless controller for an EPS steering system of an automobile according to claim 1, wherein: the EPS state feedback controller (1) consists of a 2r/2s coordinate transformation module (13) and a feedback voltage controller (12), and the current i under a two-phase rotating coordinate systemdq(k) And a reference angle thetarefAnd the estimated angle theta (k) is used as the input of a feedback voltage controller (12), and the feedback voltage controller (12) outputs a control voltage u under a two-phase rotating coordinate systemdq(k) The control voltage udq(k) As the first input of the 2r/2s coordinate transformation module (13), the second input of the 2r/2s coordinate transformation module (13) is an estimated angle theta (k), and a control voltage u under a two-phase static coordinate system is output through the 2r/2s coordinate transformation module (13)αβ(k)。
3. The position sensorless controller for an EPS steering system of an automobile as claimed in claim 2, wherein: the expression of the feedback voltage controller (12) is:
X＝[id(k),iq k(k),θ(k),Eθ]Tthe state variable matrix, which is the state variable matrix of the system,
and k is a discrete sampling index, T is a sampling period, and P is a gain coefficient matrix of the feedback voltage controller of 2 multiplied by 4.
4. The position sensorless controller for an EPS steering system of an automobile according to claim 1, wherein: the input and output relation of the two-phase high-frequency voltage calculation module (7) is as follows:
k is the discrete sampling index and T is the sampling period.
5. The position sensorless controller for an EPS steering system of an automobile according to claim 1, wherein: per-unit parameters output by the per-unit module (4)
Ld、LqIs the stator inductance under the rotating coordinate system,
6. the position sensorless controller for an EPS steering system of an automobile according to claim 1, wherein: 3 initialization angles are
θ (k-1) is the estimated angle of the last cycle.
7. The position sensorless controller for an EPS steering system of an automobile according to claim 6, wherein: the discrete angle judgment module (5) initializes 3 angles theta1,θ2,θ3Respectively recorded as 3 iteration angles theta1',θ2',θ3', respectively calculating 3 corresponding cost functions
Taking the iteration angle corresponding to the minimum cost function value as the optimal angle thetaopOf # o'1＝θop，θ′2＝θop+2π/3·2-n，θ′3＝θop-2π/3·2-nN is the current iteration number, k is the discrete sampling index, T is the sampling period, if (theta'2-θ′1)<λ, then the angle estimation value is output
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| CN102616272B (en) * | 2012-05-21 | 2015-05-06 | 株洲易力达机电有限公司 | Position control method for sensorless steering wheel |
| JP6022951B2 (en) * | 2013-01-18 | 2016-11-09 | トヨタ自動車株式会社 | Electric power steering device |
| CN106464185B (en) * | 2014-04-29 | 2020-03-20 | 三菱电机株式会社 | AC rotating electric machine control device and electric power steering device provided with same |
| JP6445937B2 (en) * | 2015-07-03 | 2018-12-26 | 日立オートモティブシステムズ株式会社 | Electric power steering device |
| CN109951117B (en) * | 2019-03-27 | 2020-11-03 | 江苏大学 | Position sensor-free permanent magnet synchronous motor control system |
| CN110112922B (en) * | 2019-05-22 | 2023-12-08 | 湖南大学 | Double-active-bridge converter based on EPS control and phase shift angle extraction method thereof |
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2020
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