# Patent

## Title
Rotation angle estimation module for sensorless vector control of PMSM

## Abstract

A rotation angle estimation module is provided. The rotation angle estimation module includes: a fixed flux instruction estimation unit calculating a rotating flux (λsd, λsq) and a fixed flux instruction (λsα*, λsβ*) based on a rotation angle θ and the current (Isα, Isβ) of a fixed coordinate system; a fixed flux estimation unit calculating a fixed flux (λsα, λsβ) based on the voltage (Vsα, Vsβ) of the fixed coordinate system, and the current (Isα, Isβ) and fixed flux error (Δsα, Δsβ) of the fixed coordinate system; a fixed flux error estimation unit using the fixed flux instruction (λsα*, λsβ*) and the fixed flux (λsα, λsβ) to calculate the fixed flux error (Δsα, Δsβ) and feed the errors back to the fixed flux estimation unit; and a trigonometric function calculation unit calculating the rotation angle θ based on the rotating flux (λsd, λsq) and the fixed flux (λsα, λsβ).

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
Pursuant to 35 U.S.C. §119(a), this application claims the benefit of earlier filing date and right of priority to Korean Patent Application No. 10-2014-0051180 filed on Apr. 29, 2014, the contents of which are all hereby incorporated by reference herein in its entirety.
BACKGROUND
The present disclosure relates to a sensorless vector control system of a permanent magnet synchronous motor (PMSM), and more particularly, to a rotation angle estimation module for sensorless vector control of a PMSM.
In general, information on the speed and location of a rotor is needed to control drive and control a synchronous motor, and a separate location sensor, such as an encoder or resolver is used for detecting the location.
However, since a method of detecting the speed and location by using a sensor has limitations in the complexity of hardware, an expensive cost, low reliability, and electrical noise, it is insufficient in economy and technology.
Since various sensorless vector control methods have been proposed in order to solve such limitations, a sensor less control method may estimate information on the speed and location of the rotor without installing a separate location sensor.
Typical sensorless vector control methods of a PMSM include a method of using counter electromotive force, a method of using a voltage model, a method of using a model reference controller, a method of using a status estimation module, a Kalman filter, non-linear control, and intellectual control, but since they need a significant amount of calculation and an estimation error occurs in a low-speed region, there was a limitation in that they are not easy to actually use.
Thus, there is a sensorless vector control method of a PMSM that may drastically decrease the amount of calculation and minimize the estimation error.
SUMMARY
Embodiments provide a rotation angle estimation module and a sensorless vector control system of a permanent magnet synchronous motor (PMSM) employing the module that decrease an amount of calculation for the rotation angle estimation of the PMSM and minimize an estimation error, in the sensorless vector control of the PMSM.
In one embodiment, a rotation angle estimation module of a permanent magnetic synchronous motor (PMSM) for sensorless vector control of the PMSM includes: a fixed flux instruction estimation unit calculating a rotating flux (λsd, λsq)and a fixed flux instruction (λsα*, λsβ*) based on a rotation angle θ and the current (Isα, Isβ) of a fixed coordinate system; a fixed flux estimation unit calculating a fixed flux (λsα, λsβ) based on the voltage (Vsα, Vsβ) of the fixed coordinate system, and the current (Isα, Isβ) and fixed flux error (Δsα, Δsβ) of the fixed coordinate system; a fixed flux error estimation unit using the difference between the fixed flux instruction (λsα*, λsβ*) and the fixed flux (λsα, λsβ) to calculate the fixed flux error (Δsα, Δsβ) and feed the errors back to the fixed flux estimation unit; and a trigonometric function calculation unit calculating the rotation angle θ, a distance that a rotor moves, based on the rotating flux (λsd, λsq) and the fixed flux (λsα, λsβ).
The trigonometric function calculation unit may finally calculate the rotation angle θ and feeds a calculated angle back to the fixed flux instruction estimation unit.
The fixed flux instruction estimation unit may calculate the rotating flux (λsd, λsq) based on the current (Isα, Isβ) of the fixed coordinate system, the rotation angle θ, the inductance (Ld, Lq) of a rotary coordinate system, and the flux λPM of a permanent magnet.
The fixed flux instruction estimation unit may compensate for the rotation angle θ by using the rotating flux (λsd, λsq) to calculate a fixed flux instruction (λsα*, λsβ*).
The fixed flux estimation unit may receive the α axis voltage Vsα of the fixed coordinate system, the α axis current Isα of the fixed coordinate system, and the α axis flux error Δsα of the fixed coordinate system to calculate an α axis flux change ratio dλsα/dt of the fixed coordinate system by using an equation dλsα/dt=Vsα−RsIsα+Δsα(Rs: stator resistance), receive the β axis voltage Vsβ of the fixed coordinate system, the β axis current Isβ of the fixed coordinate system, and the β axis flux error Δsβ of the fixed coordinate system to calculate the β axis flux change ratio dλsβ/dt of the fixed coordinate system by using the equation dλsβ/dt=Vsβ−RsIsβ+Δsβ(Rs: stator resistance), integrate the α axis flux change ratio dλsα/dt of the fixed coordinate system to output the α axis flux λsα, and integrate the output of the β axis flux change ratio dλsβ/dt of the fixed coordinate system to output the β axis flux λsβ of the fixed coordinate system.
The fixed flux error estimation unit may calculate the difference between the α axis flux instruction value λsα* of the fixed coordinate system input from the fixed flux instruction estimation unit and the α axis flux λsα input from the fixed flux estimation unit, calculate the difference between the β axis flux instruction value λsβ* of the fixed coordinate system input from the fixed flux instruction estimation unit and the β axis flux λsβ input from the fixed flux estimation unit, receive the difference from the α axis flux λsα to adjust a gain and calculate the α axis flux error Δsα of the fixed coordinate system, and receive the difference from the β axis flux λsβ to adjust a gain and calculate the β axis flux error Δsβ of the fixed coordinate system.
The trigonometric function calculation unit 40 may find angels θdq and θαβ by the applying of a trigonometric function to the rotating flux (λsd, λsq) and the fixed flux (λsα, λsβ), respectively, and output the rotation angle θ based on the angles θdq and θαβ.
The trigonometric function calculation unit 40 may receive the d axis flux λsd of the rotary coordinate system and the q axis flux λsq of the rotary coordinate system from the fixed flux instruction estimation unit to output the angle θdq of λd q based on the d axis by using a trigonometric function arctangent, receive the α axis flux λsα of the fixed coordinate system and the β axis flux λsβ of the fixed coordinate system from the fixed flux estimation unit to output the angle θαβ of λαβ based on the α axis by using the trigonometric function arctangent, and find the difference between the angles θdq and θαβ to output the rotation angle θ.
In another embodiment, an operating method of a rotation angle estimation module of a motor for sensorless vector control of a PMSM includes: calculating a rotating flux (λsd, λsq) and a fixed flux instruction (λsα*, λsβ*) based on the current (Isα, Isβ) of a fixed coordinate system and a rotation angle θ; calculating a fixed flux (λsα, λsβ) based on the voltage (Vsα, Vsβ) of the fixed coordinate system, and the current (Isα, Isβ) and fixed flux error (Δsα, Δsβ) of the fixed coordinate system, through a fixed flux estimation unit; using the difference between the fixed flux instruction (λsα*, λsβ*) and the fixed flux (λsα, sβ) to calculate the fixed flux error (Δsα, Δsβ) and feed the errors back to the fixed flux estimation unit; and calculating the rotation angle θ, a distance that a rotor moves, based on the rotating flux (λsd, λsq) and the fixed flux (λsα, λsβ).
The details of one or more embodiments are set forth in the accompanying drawings and the description below. Other features will be apparent from the description and drawings, and from the claims.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a diagram for explaining vector between the fixed coordinate system and rotary coordinate system of the rotation angle estimation module according to an embodiment.
FIG. 2 is a block diagram representing the general relationships between the components of the rotation angle estimation module according to an embodiment.
FIG. 3 is a block diagram based on a circuit diagram of the rotation angle estimation module according to an embodiment.
FIG. 4 is a block diagram representing a status in which the rotation angle estimation module according to an embodiment is applied to a typical sensorless vector control system of a permanent magnet synchronous motor (PMSM).



DETAILED DESCRIPTION OF THE EMBODIMENTS
In the following, the technical features of an embodiment are described in detail with reference to the accompanying drawings.
FIG. 1 shows the principle of the sensorless vector control method of a permanent magnet synchronous motor (PMSM) according to an embodiment, by using a vector diagram.
The vector control method divides and controls currents applied to the motor into a flux current Idse and a torque current Iqse based on a rotary coordinate system.
The vector control method of the PMSM fixes the flux current Idse to match a rotor location θ, and applies the torque current Iqse to the sensorless vector control of the PMSM.
In order to match the flux current Idse with the rotor location θ, there is a need to acquire the rotor location θ from a location sensor.
FIG. 1 represents a flux relationship according to a fixed coordinate system αβ and a rotary coordinate system dq in the vector control of the PMSM, an axis used for a vector control system is divided into the fixed coordinate system and the rotary coordinate system, the fixed coordinate system indicates a coordinate system having a coordinate axis not rotating but fixed, and the rotary coordinate system indicates a coordinate system that rotates at any angular velocity ω.
By using a flux value (λα, λβ) based on the fixed coordinate system αβ and a flux value (λd, λq) based on the rotary coordinate system dq, it is possible to estimate the rotor location θ by subtracting the angle θdq of λdq based on the d axis from the angle θαβ of λαβ based on the α axis.
An embodiment estimates a final rotor location by using stator flux vector λαβ based on the fixed coordinate system αβ and rotor flux vector λdq based on the rotary coordinate system dq along with arctangent tan−1 and information on the estimated rotor location matches the location of an actual motor.
FIG. 2 shows a rotation angle estimation unit 100 estimating a rotation angle θ, a distance that a rotor moves, based on the vector diagram of FIG. 1 and the rotation angle estimation unit 100 includes a fixed flux instruction estimation unit 10, a fixed flux estimation unit 20, a fixed flux error estimation unit 30, and a trigonometric function calculation unit 40.
The fixed flux instruction estimation unit 10 calculates a rotating flux (λsd, λsq) and a fixed flux instruction (λsα*, λsβ*) based on the current (Isα, Isβ) and the rotation angle θ based on the fixed coordinate system αβ. In particular, the fixed flux instruction estimation unit 10 receives the current (Isα, Isβ) and rotation angle θ of the fixed coordinate system αβ and uses a rotor flux equation to calculate the fixed flux instruction (λsα*, λsβ*).
The rotor flux equation firstly calculates a rotating flux (λsd, λsq) and finally calculates the fixed flux instruction (λsα*, λsβ*) by using a calculation result.
The fixed flux estimation unit 20 calculates the fixed flux (λsα, λsβ) based on the voltage (Vsα, Vsβ) of the fixed coordinate system αβ, and the current (Isα, Isβ) and fixed flux error (Δsα, Δsβ) of the fixed coordinate system. In particular, the fixed flux estimation unit 20 receives the voltage (Vsα, Vsβ) of the fixed coordinate system αβ, and the current (Isα, Isβ) and fixed flux error (Δsα, Δsβ) of the fixed coordinate system αβ and uses a stator voltage equation to calculate the fixed flux (λsα, λsβ) of the α and β axes.
The fixed flux error estimation unit 30 uses the difference between the fixed flux instruction (λsα*, λsβ*) and the fixed flux (λsα, λsβ) to calculate the fixed flux error (Δsα, Δsβ) and feeds the errors back to the fixed flux estimation unit. In particular, the fixed flux error estimation unit 30 uses the difference between the fixed flux instruction (λsα*, λsβ*) output by the fixed flux instruction estimation unit 10 and the fixed flux (λsα, λsβ) output by the fixed flux estimation unit 20 to calculate the fixed flux error (Δsα, Δsβ) of the α and β axes and feeds the errors back to the fixed flux estimation unit 20.
The trigonometric function calculation unit 40 calculates the rotation angle θ, a distance that a rotor moves, based on the rotating flux (λsd, λsq) and the fixed flux (λsα, λsβ). In particular, the trigonometric function calculation unit 40 performs calculation on the rotating flux (λsd, λsq) firstly calculated by the rotor flux equation of the fixed flux instruction estimation unit 10 and the fixed flux (λsα, λsβ) output by the fixed flux estimation unit 20 by using trigonometric functions to find angles θdq and θαβ, respectively.
When the angle θdq is finally subtracted from the angle θαβ, it is possible to calculate the rotation angle θ, a distance that a rotor moves, and a calculated rotation angle is fed back to the fixed flux instruction estimation unit 10.
The rotation angle estimation unit 100 continues to calculate the rotation angle θ by feedback between the fixed flux error estimation unit 30 and the fixed flux estimation unit 20, between the fixed flux estimation unit 20 and the trigonometric function calculation unit 40, and between the fixed flux instruction estimation unit 10 and the trigonometric function calculation unit 40.
Each component of the rotation angle estimation unit is described in detail by using FIG. 3 that is a block diagram representing a particular circuit configuration of the rotation angle estimation unit 100.
<Fixed Flux Instruction Estimation Unit 10>
The fixed flux instruction estimation unit 10 includes a first rotary coordinate conversion unit 101, a second rotary coordinate conversion unit 102, a first rotating flux calculation unit 103, a second rotating flux calculation unit 104, a first fixed coordinate conversion unit 105, and a second fixed coordinate conversion unit 106.
The first rotary coordinate conversion unit 101 receives the α axis current Isα of the fixed coordinate system and the rotation angle θ in order to use a rotor flux equation and coordinate-converts into the d axis current value Isd of the rotary coordinate system.
The second rotary coordinate conversion unit 102 receives the β axis current Isβ of the fixed coordinate system and the rotation angle θ and coordinate-converts into the q axis current value Isq of the rotary coordinate system.
The first rotating flux calculation unit 103 receives the d axis current Isd of the first rotary coordinate conversion unit 101 and uses the rotor flux equation, λsd=LdIsd+λPM (Ld: d axis inductance of the rotary coordinate system, λPM: flux by a permanent magnet) to calculate the d axis flux λsd of the rotary coordinate system.
The second rotating flux calculation unit 104 receives the q axis current Isq of the second rotary coordinate conversion unit 102 and uses the rotor flux equation, λsq=LqIsq (Lq: q axis inductance of the rotary coordinate system) to calculate the q axis flux λsq of the rotary coordinate system.
The d axis flux λsd and q axis flux λsq of the rotary coordinate system are input to the trigonometric function calculation unit 40.
The first fixed coordinate conversion unit 105 is a compensator compensating for a value coordinate-converted in order to use the rotor flux equation, compensates for the rotation angle θ by using the output of the first rotating flux calculation unit 103 to coordinate-convert into the fixed coordinate system, and outputs the α axis flux instruction value λsα* of the fixed coordinate system.
The second fixed coordinate conversion unit 106 compensates for the rotation angle θ by using the output of the second rotating flux calculation unit 104 to coordinate-convert into the fixed coordinate system, and outputs the β axis flux instruction value λsβ* of the fixed coordinate system.
<Fixed Flux Estimation Unit 20>
The fixed flux estimation unit 20 includes a first fixed flux change ratio calculation unit 201, a second fixed flux change ratio calculation unit 202, a first integrator 203, and a second integrator 204.
The first fixed flux change ratio calculation unit 201 receives the α axis voltage Vsα of the fixed coordinate system, the α axis current Isα of the fixed coordinate system, and the α axis flux error Δsα of the fixed coordinate system, term-converts the stator voltage equation, Vsα=RsIsα+dλsα/dt (Rs: stator resistance) into the equation dλsα/dt=Vsα−RsIsα+Δsα (Rs: stator resistance), and calculates the α axis flux change ratio dλsα/dt of the fixed coordinate system.
The second fixed flux change ratio calculation unit 202 receives the β axis voltage Vsβ of the fixed coordinate system, the β axis current Isβ of the fixed coordinate system, and the β axis flux error Δsβ of the fixed coordinate system, term-converts the stator voltage equation, Vsβ=RsISβ+dλsβ/dt (Rs: stator resistance) into the equation dλsβ/dt=Vsβ−RsIsβ+Δsβ (Rs: stator resistance), and calculates the β axis flux change ratio dλsβ/dt of the fixed coordinate system.
The first integrator 203 integrates the outputs of the first fixed flux change ratio calculation unit 201 to output the α axis flux λsα of the fixed coordinate system.
The second integrator 204 integrates the outputs of the second fixed flux change ratio calculation unit 202 to output the β axis flux λsβ of the fixed coordinate system.
The α axis flux λsα and β axis flux λsβ output by the first integrator 203 and the second integrator 204 are input to the trigonometric function calculation unit 40.
<Fixed Flux Error Estimation Unit 30>
The fixed flux error estimation unit 30 includes a first subtractor 301, a second subtractor 302, a first controller 303 and a second controller 304 and performs the function of compensating for the estimated fixed coordinate system α-β axis flux, and an error is compensated for by a PI controller and input to the fixed flux estimation unit 20.
The first subtractor 301 calculates the difference between the α axis flux instruction value λsα* of the fixed coordinate system input from the fixed flux instruction estimation unit 10 and the α axis flux λsα input from the fixed flux estimation unit 20.
The second subtractor 302 calculates the difference between the β axis flux instruction value λsβ* of the fixed coordinate system input from the fixed flux instruction estimation unit 10 and the β axis flux λsβ input from the fixed flux estimation unit 20.
The first controller 303 receives the difference from the first subtractor 301, performs proportional-integral (PI) control by the equation KPα+KIα/S (KPα: proportional gain, KIα: integral gain, S: complex variable) to adjust a gain and calculates the α axis flux error Δsα of the fixed coordinate system.
The second controller 304 receives the difference from the second subtractor 302, performs PI control by the equation KPβ+KIβ/S (KPβ: proportional gain, KIβ: integral gain, S: complex variable) to adjust a gain and calculates the β axis flux error Δsβ of the fixed coordinate system.
The α axis flux error Δsα and β axis flux error Δsβ are fed back to the fixed flux estimation unit 20.
<Trigonometric Function Calculation Unit 40>
The trigonometric function calculation unit 40 includes a first arctangent unit 401, a second arctangent unit 402, and a rotation angle subtraction unit 403.
The first arctangent unit 401 receives the d axis flux λsd of the rotary coordinate system and the q axis flux λsq of the rotary coordinate system from the fixed flux instruction estimation unit 10 and outputs the angle θdq of λdq based on the d axis by using a trigonometric function arctangent.
The second arctangent unit 402 receives the α axis flux λsα of the fixed coordinate system and the β axis flux λsβ of the fixed coordinate system from the fixed flux estimation unit 20 and outputs the angle θαβ of λαβ based on the α axis by using the trigonometric function arctangent.
The rotation angle subtraction unit 403 finds the difference between the angles θαβ and θdq to output the rotation angle θ, and the rotation angle θ is fed back to the fixed flux instruction estimation unit 10.
When the rotation angle θ is found, it is possible to find the speed We of a rotor and thus the sensorless vector control system of the PMSM according to an embodiment receives the rotation angle θ and the speed We from the rotation angle estimation unit 100 and controls the PMSM.
FIG. 4 is a block diagram representing a state in which the rotation angle estimation unit 100 according to an embodiment is applied to a sensorless vector control system inverter-controlling a typical PMSM, through which it is possible to understand how the outputs of the rotation angle estimation unit 100, the rotation angle θ and the speed We are input to a PMSM control unit 1.
The technical scope of an embodiment includes the sensorless vector control system of the PMSM to which the rotation angle estimation unit 100 is applied.
Since the embodiment describes a method of finding the stator flux vector and the rotor flux vector, the flux equation of a rotor circuit is coordinate-converted into the stator flux equation by the applying of the voltage equation of a stator circuit and the flux equation of the rotor circuit and then the stator flux vector is compensated for to finally find the stator flux vector and the rotor flux vector.
The angles θαβ and θdq are found by the applying of the trigonometric function tan−1 to the final stator flux vector and rotor flux vector and the location θ information on the PMSM is estimated by using the equation θ=θαβ−θdq.
Since the method is easy to implement, it is easy to actually apply it to a product and since the stator voltage equation and the rotor equation are together used, an estimated error in location information at low and high speeds is minimized.
Also, the rotation angle estimation unit 100 according to an embodiment may also be applied to a vector control system having location and speed sensors as a backup in addition to the sensorless vector control system of the PMSM.
According to an embodiment, since the stator voltage equation and the rotor equation are together used, it is possible to rapidly and accurately estimate the rotation angle of a rotor at low and high speeds and by applying the estimated rotation angle to perform the sensorless vector control of the PMSM, it is possible to provide a more reliable and economical sensorless vector control system of the PMSM.
Although embodiments have been described with reference to a number of illustrative embodiments thereof, it should be understood that numerous other modifications and embodiments can be devised by those skilled in the art that will fall within scope of the principles of this disclosure. More particularly, various variations and modifications are possible in the component parts and/or arrangements of the subject combination arrangement within the scope of the disclosure, the drawings and the appended claims. In addition to variations and modifications in the component parts and/or arrangements, alternative uses will also be apparent to those skilled in the art.

## Claims

1. A vector control system for sensorless vector control of a motor, the system comprising:
a rotation angle estimation module;
a permanent magnetic synchronous motor (PMSM); and
a permanent magnetic synchronous motor control unit receiving a rotation angle and speed of a rotor of a fixed coordinate system and controlling the PMSM based on the rotation angle and speed,
wherein the rotation angle estimation module comprises:
a fixed flux instruction estimation unit calculating a rotating flux and a fixed flux instruction based on the rotation angle and a current of the fixed coordinate system;
a fixed flux estimation unit calculating a fixed flux based on a voltage, the current and a fixed flux error of the fixed coordinate system;
a fixed flux error estimation unit calculating the fixed flux error using a difference between the calculated fixed flux instruction and the calculated fixed flux and feeding the calculated fixed flux error back to the fixed flux estimation unit; and
a trigonometric function calculation unit calculating the rotation angle based on the calculated rotating flux and the calculated fixed flux and feeding the calculated rotation angle back to the fixed flux instruction estimation unit,
wherein the rotation angle is a distance that the rotor moves, and
wherein calculating the rotation angle comprises:
applying a trigonometric function to the calculated rotating flux to determine a first angle;
applying the trigonometric function to the calculated fixed flux to determine a second angle;
receiving a d-axis flux of a rotary coordinate system and a q-axis flux of the rotary coordinate system from the fixed flux instruction estimation unit;
using a trigonometric function arctangent to output the first angle based on the d-axis flux;
receiving a α-axis flux of the fixed coordinate system and a β-axis flux of the fixed coordinate system from the fixed flux estimation unit;
using the trigonometric function arctangent to output the second angle based on the α-axis flux;
determining a difference between the first angle and second angle; and
outputting the rotation angle.

2. The system of claim 1, wherein the fixed flux instruction estimation unit calculates the rotating flux based on the current of the fixed coordinate system, the rotation angle of the fixed coordinate system, an inductance of the rotary coordinate system, and a flux of a permanent magnet.

3. The system of claim 1, wherein calculating the fixed flux comprises:
receiving a stator resistance Rs;
receives a α-axis voltage Vsα of the fixed coordinate system, a α-axis current Isα of the fixed coordinate system, and a α-axis flux error Δsα of the fixed coordinate system;
calculating a α-axis flux change ratio dλsα/dt of the fixed coordinate system according to an equation dλsα/dt=Vsα−RsIsα+Δsα;
receiving a β-axis voltage Vsβ of the fixed coordinate system, a β-axis current Isβ of the fixed coordinate system, and the β-axis flux error Δsβ of the fixed coordinate system;
calculating a β-axis flux change ratio dλsβ/dt of the fixed coordinate system according to and equation dλsβ/dt=Vsβ−RsIsβ+Δsβ;
integrating the calculated α-axis flux change ratio to output a α-axis flux λsα of the fixed coordinate system; and
integrating the calculated β-axis flux change ratio to output the β-axis flux λsβ of the fixed coordinate system.

4. The system of claim 1, wherein calculating the fixed flux error comprises:
receiving a α-axis flux instruction value of the fixed coordinate system and α-axis flux from the fixed flux estimation unit;
receiving a β-axis flux instruction value of the fixed coordinate system and a β-axis flux from the fixed flux estimation unit;
calculating a first difference between the received α-axis flux instruction value and the received α-axis flux;
calculating a second difference between the received β-axis flux instruction value and the received β-axis flux;
using the first difference to adjust a gain and calculate a α-axis flux error of the fixed coordinate system; and
using the second difference to adjust a gain and calculate a β-axis flux error of the fixed coordinate system.

5. The system of claim 2, wherein the fixed flux instruction estimation unit calculates the fixed flux instruction by using the calculated rotating flux to compensate for the rotation angle of the fixed coordinate system.

6. A operating method for sensorless vector control of a permanent magnetic synchronous motor (PMSM) in a sensorless vector control system, the method comprising:
receiving a rotation angle and speed of a rotor of a fixed coordinate system;
calculating a rotating flux and a fixed flux instruction based on the rotation angle and a current of the fixed coordinate system;
calculating a fixed flux based on a voltage, the current and a fixed flux error of the fixed coordinate system;
calculating the fixed flux error using a difference between the calculated fixed flux instruction and the calculated fixed flux and feeding the calculated fixed flux error back for calculating the fixed flux;
calculating the rotation angle based on the calculated rotating flux and the calculated fixed flux and feeding the calculated rotation angle back for calculating the rotating flux;
controlling PMSM based on the rotation angle and speed,
wherein the rotation angle is a distance that the rotor moves, and
wherein calculating the rotation angle comprises:
applying a trigonometric function to the calculated rotating flux to determine a first angle;
applying the trigonometric function to the calculated fixed flux to determine a second angle;
receiving a d-axis flux of a rotary coordinate system and a q-axis flux of the rotary coordinate system;
using a trigonometric function arctangent to output the first angle based on the d-axis flux;
receiving a α-axis flux of the fixed coordinate system and a β-axis flux of the fixed coordinate system;
using the trigonometric function arctangent to output the second angle based on the α-axis flux;
determining a difference between the first angle and second angle; and
outputting the rotation angle.

7. The method according to claim 6, wherein the rotating flux is calculated based on the current of the fixed coordinate system, the rotation angle of the fixed coordinate system, an inductance of the rotary coordinate system, and a flux of a permanent magnet.

8. The method according to claim 6, wherein calculating the fixed flux comprises:
receiving a stator resistance Rs;
receiving the α-axis voltage Vsα of the fixed coordinate system, the α-axis current Isα of the fixed coordinate system, and a α axis flux error Δsα of the fixed coordinate system;
calculating a α-axis flux change ratio dλsα/dt of the fixed coordinate system according to an equation dλsα/dt=Vsα−RsIsα+Δsα;
receiving a β-axis voltage Vsβ of the fixed coordinate system, the β-axis current Isβ of the fixed coordinate system, and the β-axis flux error Δsβ of the fixed coordinate system;
calculating a β-axis flux change ratio dλsβ/dt of the fixed coordinate system according to an equation dλsβ/dt=Vsβ−RsIsβ+Δsβ;
integrating the calculated α axis flux change ratio to output the α axis flux λsα of the fixed coordinate system; and
integrating the calculated β axis flux change ratio to output the β axis flux λsβ of the fixed coordinate system.

9. The method according to claim 6, wherein calculating the fixed flux error comprises:
receiving a α-axis flux instruction value of the fixed coordinate system and α-axis flux;
receiving a β-axis flux instruction value of the fixed coordinate system and a β-axis flux;
calculating a first difference between the received α-axis flux instruction value the received α-axis flux;
calculating a second difference between the received β-axis flux instruction value and the received β-axis flux;
using the first difference to adjust a gain and calculate a α-axis flux error of the fixed coordinate system; and
using the second difference to adjust a gain and calculate a β-axis flux error of the fixed coordinate system.

10. The method according to claim 7, wherein the fixed flux instruction is calculated by using the calculated rotating flux to compensate for the rotation angle of the fixed coordinate system.