CN111726048B - Permanent magnet synchronous motor rotor position and speed estimation method based on sliding-mode observer - Google Patents

Permanent magnet synchronous motor rotor position and speed estimation method based on sliding-mode observer Download PDF

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CN111726048B
CN111726048B CN202010735817.9A CN202010735817A CN111726048B CN 111726048 B CN111726048 B CN 111726048B CN 202010735817 A CN202010735817 A CN 202010735817A CN 111726048 B CN111726048 B CN 111726048B
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CN111726048A (en
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张蔚
翟良冠
王家乐
李帆
金鑫
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Nantong University
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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
    • 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
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/0007—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using sliding mode control
    • 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
    • H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
    • 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
    • H02P6/10—Arrangements for controlling torque ripple, e.g. providing reduced torque ripple
    • 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
    • H02P6/18—Circuit arrangements for detecting position without separate position detecting elements
    • H02P6/182—Circuit arrangements for detecting position without separate position detecting elements using back-emf in windings

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  • Control Of Motors That Do Not Use Commutators (AREA)

Abstract

The invention discloses a sliding-mode observer-based permanent magnet synchronous motor rotor position and speed estimation method, wherein the sliding-mode observer is a sliding-mode observer based on a boundary layer self-adjusting arcsine saturation function, and comprises a current state observer, a current comparator, a boundary layer self-adjusting arcsine saturation function module, an extended Kalman filter and a software phase-locked loop. The invention replaces the sign function in the existing sliding mode observer with a boundary layer-based self-adjusting arcsine function, simultaneously adopts an extended Kalman filter to extract extended back electromotive force, removes a low-pass filter in the existing sliding mode observer, and feeds back the extracted extended back electromotive force to a current state observer for amplitude compensation. Compared with the conventional sliding mode controller, the sliding mode observer based on the boundary layer self-adjusting arcsine function can effectively inhibit torque pulsation, improve the steady-state performance of the system and improve the tracking accuracy of the position and the rotating speed of the rotor.

Description

Permanent magnet synchronous motor rotor position and speed estimation method based on sliding-mode observer
Technical Field
The invention relates to the field of electromechanical control, in particular to a method for estimating the position and the speed of a permanent magnet synchronous motor rotor based on a sliding-mode observer.
Background
The control technology without the position sensor samples relevant electric signals in the motor to estimate the position and speed information of the rotor, and a mechanical position sensor is removed, so that the volume and the weight of the system are reduced, the cost and the hardware complexity are reduced, and the running performance of the system is improved.
The permanent magnet synchronous motor position sensorless control method mainly comprises a high-frequency injection method and an observer method, wherein the observer method comprises an extended Kalman filter, model reference self-adaption, a sliding-mode observer and the like. The sliding mode observer is a nonlinear control method, is simple in structure, low in modeling precision requirement and strong in robustness, and also has the problems of large system buffeting, delay of position angle phase and poor steady-state performance.
The traditional sliding mode observer adopts a sign function as a sliding mode surface control function, so that the system buffeting is serious, a large amount of harmonic waves exist in observed back electromotive force, the rotating speed estimation precision is influenced, the torque pulsation is large, the system buffeting can be effectively reduced by adopting a saturation function to replace the sign function, but the boundary layer thickness of the saturation function is always fixed to a constant value, and the steady state performance under certain rotating speed or certain load applying working conditions is poor. The use of a low-pass filter can effectively filter out high-frequency harmonics, but causes the amplitude of the back electromotive force to be reduced and the phase of the position angle to be delayed, and needs additional position compensation. Therefore, the research on the position-free sensor control algorithm which can effectively inhibit torque pulsation, is accurate in tracking the position and the rotating speed of the rotor, has good steady-state performance and is simple in structure has wide development prospect.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the prior art, the method for estimating the position and the speed of the permanent magnet synchronous motor based on the sliding-mode observer is provided, the position and the rotating speed information of the rotor can be accurately tracked, the torque pulsation is restrained, and the steady-state performance of the system is improved.
The technical scheme is as follows: the method for estimating the position and the speed of the permanent magnet synchronous motor rotor based on the sliding-mode observer is characterized in that the sliding-mode observer is based on a boundary layer self-adjusting arcsine saturation function and comprises a current state observer, a current comparator, a boundary layer self-adjusting arcsine saturation function module, an extended Kalman filter and a software phase-locked loop;
the inputs of the current state observer are respectively sampled alpha-axis voltage u and sampled beta-axis voltage uα、uβControl function value z of alpha and beta axis sliding mode surfaceα、zβAnd alpha and beta axis extended back EMF observations
Figure BDA0002604889440000021
The output of the current state observer is estimated values of alpha and beta axis currents
Figure BDA0002604889440000022
The alpha and beta axis current estimates
Figure BDA0002604889440000023
With sampled alpha and beta axis currents iα、iβThe difference value of the first and second boundary layer self-adjusting sine-inversion saturation function modules is input into a boundary layer self-adjusting sine-inversion saturation function module, and the output of the boundary layer self-adjusting sine-inversion saturation function module is alpha and beta axis sliding mode surface control function value zα、zβ(ii) a The alpha and beta axis sliding mode surface control function value zα、zβAnd estimating the rotational speed
Figure BDA0002604889440000024
Inputting the data into an extended Kalman filter, wherein the output of the extended Kalman filter is alpha and beta axis extended back electromotive force observed values
Figure BDA0002604889440000025
Figure BDA0002604889440000026
The alpha and beta axis extended back EMF observations
Figure BDA0002604889440000027
Input to a software phase locked loop, whereby said software phase locked loop outputs an estimated rotor position angle
Figure BDA0002604889440000028
And estimating the rotational speed
Figure BDA0002604889440000029
Further, the current state observer is:
Figure BDA00026048894400000210
wherein R is stator resistance, ω is electrical angular velocity, Ld、LqD and q axis inductance values, respectively;
the alpha and beta axis sliding mode surface control function value zα、zβExpressed as:
Figure BDA00026048894400000211
wherein k issIs the switching gain, ks>max(|Eα|,|Eβ|)，Eα、EβRespectively alpha axis and beta axis extended back electromotive force, Narcsin(s) is a boundary layer self-adjusting arcsine saturation function;
the extended Kalman filter is as follows:
Figure BDA00026048894400000212
wherein k iskFor the adaptive rate of the filter, kk>0；
Figure BDA00026048894400000213
Extending the back emf observation error values for the alpha and beta axes respectively,
Figure BDA00026048894400000214
further, the boundary layer self-adjusting arcsine saturation function is as follows:
Figure BDA00026048894400000215
wherein the content of the first and second substances,
Figure BDA0002604889440000031
sα、sβexpanding the counter electromotive force E for the alpha and beta axes, respectivelyα、EβCorresponding to the slip-form surface, λ is the basic boundary layer thickness.
Has the advantages that: the invention replaces the symbolic function in the existing sliding-mode observer with a boundary layer-based self-adjusting arcsine function, simultaneously adopts an extended Kalman filter to extract extended back electromotive force, removes a low-pass filter in the existing sliding-mode observer, and feeds back the extracted extended back electromotive force to a current state observer for amplitude compensation; compared with the conventional sliding mode controller, the sliding mode observer based on the boundary layer self-adjusting arcsine function can effectively inhibit torque pulsation, improve the steady-state performance of the system and improve the tracking accuracy of the position and the rotating speed of the rotor. The rotor position and speed estimation method provided by the invention can effectively reduce the system buffeting, improve the rotor position and speed estimation precision and inhibit the torque pulsation, and meets the requirements of the permanent magnet synchronous motor driving fields such as a high-speed hydrogen pump and an air compressor on the system reliability and efficiency.
Drawings
FIG. 1 is a control block diagram of a vector control system of an embodiment of the present invention;
FIG. 2 is a structural block diagram of a sliding-mode observer based on a boundary layer self-adjusting arcsine saturation function according to an embodiment of the invention;
FIG. 3 is a block diagram of a software phase locked loop according to an embodiment of the present invention;
FIG. 4 is a static experimental result of a sliding-mode observer of an embodiment of the present invention; wherein, (a) is an expanded counter electromotive force observation value, (b) is an estimated value, an actual value and an error value thereof of the rotation speed, and (c) is an estimated value, an actual value and an error value thereof of the rotor position angle.
FIG. 5 is a dynamic experimental result of a sliding mode observer according to an embodiment of the present invention; wherein, (a) is the estimated value, the actual value and the error value and the torque of the rotating speed under the condition of the rotating speed abrupt change, and (b) is the estimated value, the actual value and the error value and the torque of the rotating speed under the condition of the torque abrupt change.
Detailed Description
The invention is further explained below with reference to the drawings.
The vector control system of fig. 1 is composed of links such as a speed PI regulator, d-and q-axis current PI regulators, inverse Park coordinate transformation, SVPWM (space vector pulse width modulation), a three-phase inverter, a permanent magnet synchronous motor, Clarke coordinate transformation, Park coordinate transformation, a sliding mode observer based on a boundary layer self-adjusting arcsine saturation function, and a Software Phase Locked Loop (SPLL). The system is a speed (outer loop) and current (inner loop) double closed loop structure. A sliding-mode observer based on a boundary layer self-adjusting arcsine saturation function and a software phase-locked loop are used for estimating the position and the speed of a motor rotor in real time to replace a mechanical position sensor.
The estimated rotor position angle is used for Park coordinate transformation and inverse Park coordinate transformation in a vector control system, and the estimated speed is used as a feedback value of a speed loop. Sliding mode observer based on boundary layer self-adjusting arcsine saturation function for estimating rotating speed
Figure BDA0002604889440000041
Alpha and beta axis voltages uα、uβAnd alpha and beta axis currents iα、iβExpanding counter electromotive force observed value with output quantity of alpha and beta axis as input quantity
Figure BDA0002604889440000042
The input quantity of the software phase-locked loop is alpha and beta axis expansion counter electromotive force observed value
Figure BDA0002604889440000043
The output being the estimated rotor position angle
Figure BDA0002604889440000044
And rotational speed
Figure BDA0002604889440000045
As shown in FIG. 2, the sliding-mode observer based on the boundary layer self-adjusting arcsine saturation function comprises a current state observer, a current comparator, a boundary layer self-adjusting arcsine saturation function module, an extended Kalman filter and a software phase-locked loop. The current state observer is connected with a boundary layer self-adjusting arcsine saturation function module, the boundary layer self-adjusting arcsine saturation function module is connected with an extended Kalman filter and a current state observer module, the extended Kalman filter module is connected with a software phase-locked loop module and the current state observer module, and the software phase-locked loop module is connected with the extended Kalman filter module.
The inputs of the current state observer are the sampled alpha and beta axis voltages u, respectivelyα、uβControl function value z of alpha and beta axis sliding mode surfaceα、zβAnd alpha and beta axis extended back EMF observations
Figure BDA0002604889440000046
The output of the current state observer is the alpha and beta axis current estimates
Figure BDA0002604889440000047
Alpha and beta axis current estimates
Figure BDA0002604889440000048
With sampled alpha and beta axis currents iα、iβThe difference value of the first and second boundary layer is input into a boundary layer self-adjusting arcsine saturation function, and the output of the boundary layer self-adjusting arcsine saturation function is alpha and beta axis sliding mode surface control function value zα、zβ. Alpha and beta axis sliding mode surface control function value zα、zβAnd estimating the rotational speed
Figure BDA0002604889440000049
Inputting the data into an extended Kalman filter, wherein the output of the extended Kalman filter is an alpha-axis extended back electromotive force observed value and a beta-axis extended back electromotive force observed value
Figure BDA00026048894400000410
Alpha and beta axis extended back EMF observations
Figure BDA00026048894400000411
Input to a software phase locked loop, whereby the software phase locked loop outputs an estimated rotor position angle
Figure BDA00026048894400000412
And estimating the rotational speed
Figure BDA00026048894400000413
The design process of the current state observer and the boundary layer self-adjusting arcsine saturation function in the estimation method comprises the following steps:
the stator voltage equation in the α β coordinate system is:
Figure BDA00026048894400000414
Figure BDA00026048894400000415
wherein u isα、uβAlpha and beta axis voltages, respectively; i.e. iα、iβAlpha and beta axis currents, respectively; thetaeIs the rotor position angle; eα、EβExpanded back emf for the alpha and beta axes, respectively; r is stator resistance, and omega is electrical angular velocity; l isd、LqD and q axis inductance values, respectively; i.e. id、iqD and q axis currents, respectively; psifIs a permanent magnet flux linkage.
Equation (1) is rewritten as a state equation with α and β axis currents as state variables:
Figure BDA0002604889440000051
selecting a sliding mode surface on a stator current track, namely:
Figure BDA0002604889440000052
wherein the content of the first and second substances,
Figure BDA0002604889440000053
current estimates for the alpha and beta axes, respectively;
Figure BDA0002604889440000054
current error values for the alpha and beta axes, respectively.
In order to obtain the extended back electromotive force and reduce the influence of filtering on the amplitude of the extended back electromotive force, the extended back electromotive force value observed value is fed back to the current observation loop, and the current state observer is designed as follows:
Figure BDA0002604889440000055
in the formula (I), the compound is shown in the specification,
Figure BDA0002604889440000056
is a sliding mode surface control function; k is a radical ofsIs the switching gain, ks>max(|Eα|,|EβI)); narcsin(s) is a boundary layer self-adjusting arcsine saturation function, s is a sliding mode surface parameter, and the expression is as follows:
Figure BDA0002604889440000057
wherein the content of the first and second substances,
Figure BDA0002604889440000058
sα、sβexpanding the counter electromotive force E for the alpha and beta axes, respectivelyα、EβCorresponding to the slip-form surface, λ is the basic boundary layer thickness.
As can be seen from the formula (6), the Narcsin function can adjust the boundary layer in real time according to the slip form surface error, the control speed cannot be influenced by overlarge thickness of the boundary layer due to the small slip form surface error, and meanwhile, the slip form surface error is indirectly influenced by the change of the rotating speed, the torque or other parameter values, so that the Narcsin function is suitable for implementing adjustment under various working conditions.
Alpha and beta axes in the estimation methodSliding mode surface control function value zα、zβThe calculation process of (2) is as follows:
the stator current error equation obtained by subtracting the equations (5) and (3) is:
Figure BDA0002604889440000059
the extended back emf available from the equivalent control principle is:
Figure BDA00026048894400000510
alpha and beta axis extended back EMF observations in an estimation method
Figure BDA0002604889440000061
Controlling function value z by alpha and beta axis sliding mode surfacesα、zβThe filter is obtained after the filter processing of an extended Kalman filter, and the extended Kalman filter is as follows:
Figure BDA0002604889440000062
wherein k iskFor the adaptive rate of the filter, kk>0；
Figure BDA0002604889440000063
Extending the back emf observation error values for the alpha and beta axes respectively,
Figure BDA0002604889440000064
Eα、Eβextending the back emf for the alpha and beta axes, respectively.
Since the mechanical time constant is much larger than the electromagnetic time constant, the rotational speed is assumed to be constant in one estimation period, which can be obtained from equation (9):
Figure BDA0002604889440000065
to demonstrate the stability of equation (10), the lyapunov function is defined:
Figure BDA0002604889440000066
obtained by substituting formula (10) for formula (11):
Figure BDA0002604889440000067
the extended kalman filter is therefore stable.
The estimation method estimates the position angle and the speed of the rotor through a software phase-locked loop and estimates the position angle of the rotor
Figure BDA0002604889440000068
And estimating the rotational speed
Figure BDA0002604889440000069
The calculation process of (2) is as follows:
Figure BDA00026048894400000610
wherein, Kp/KiRespectively proportional/integral coefficients. The structure block diagram of the software phase-locked loop is shown in fig. 3.
According to the control block diagram shown in fig. 1, experimental verification is performed based on a dSPACE semi-physical simulation experiment platform, and the parameters of the permanent magnet synchronous motor are selected as follows: the rated power is 600W, the rated rotation speed is 750r/min, the rated torque is 7.6 N.m, the pole pair number is 14, the amplitude of the permanent magnet flux linkage is 0.0679Wb, the resistance of an armature winding is 2.3 omega, the alternating-direct axis inductance is 2.22mH and 2.23mH respectively, and the rotational inertia is 0.004 kg.m2The friction torque viscosity coefficient was 0.0004N · m · s. FIG. 4 shows the experimental results at a given rotation speed of 200r/min, FIG. 5(a) shows the experimental results of the motor suddenly changing from 100r/min to 200r/min when no load is applied, and FIG. 5(b) shows the experimental results of the motor suddenly changing from no load to 4 N.m when 100r/min is applied. As can be seen from fig. 4(a), the extended back emf observations of the method of the present invention have a high sinusoid and the back emf observations have a low harmonic THD. As can be seen from fig. 4(b) and 5(a),the estimated value of the rotating speed of the method can well track the actual value, the error of the rotating speed is about +/-3 r/min and only accounts for 1.5 percent of the given rotating speed, and as can be seen from figure 4(c), the estimated rotor position angle and the actual value of the method basically keep consistent and almost have no phase delay. As can be seen from FIG. 5(b), the rotational speed fluctuation of the method of the present invention is maintained substantially constant after the application of 4 N.m, and the torque ripple is small. Experimental results show that the method has the advantages of accurate estimation of the position and the rotating speed of the rotor, quick response of the rotating speed, good robustness and small torque pulsation.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.

Claims (1)

1. The method for estimating the position and the speed of the permanent magnet synchronous motor rotor based on the sliding-mode observer is characterized in that the sliding-mode observer is based on a boundary layer self-adjusting arcsine saturation function and comprises a current state observer, a current comparator, a boundary layer self-adjusting arcsine saturation function module, an extended Kalman filter and a software phase-locked loop;
the inputs of the current state observer are respectively sampled alpha-axis voltage u and sampled beta-axis voltage uα、uβControl function value z of alpha and beta axis sliding mode surfaceα、zβAnd alpha and beta axis extended back EMF observations
Figure FDA0003285139540000011
The output of the current state observer is estimated values of alpha and beta axis currents
Figure FDA0003285139540000012
The alpha and beta axis current estimates
Figure FDA0003285139540000013
With sampled alpha and beta axis currents iα、iβDifference of (2)The value is input into a boundary layer self-adjusting arcsine saturation function module, and the output of the boundary layer self-adjusting arcsine saturation function module is alpha and beta axis sliding mode surface control function value zα、zβ(ii) a The alpha and beta axis sliding mode surface control function value zα、zβAnd estimating the rotational speed
Figure FDA0003285139540000014
Inputting the data into an extended Kalman filter, wherein the output of the extended Kalman filter is alpha and beta axis extended back electromotive force observed values
Figure FDA0003285139540000015
Figure FDA0003285139540000016
The alpha and beta axis extended back EMF observations
Figure FDA0003285139540000017
Input to a software phase locked loop, whereby said software phase locked loop outputs an estimated rotor position angle
Figure FDA0003285139540000018
And estimating the rotational speed
Figure FDA0003285139540000019
The current state observer is:
Figure FDA00032851395400000110
wherein R is stator resistance, ω is electrical angular velocity, Ld、LqD and q axis inductance values, respectively;
the alpha and beta axis sliding mode surface control function value zα、zβExpressed as:
Figure FDA00032851395400000111
wherein k issIs the switching gain, ks>max(|Eα|,|Eβ|)，Eα、EβRespectively alpha axis and beta axis extended back electromotive force, Narcsin(s) is a boundary layer self-adjusting arcsine saturation function;
the extended Kalman filter is as follows:
Figure FDA00032851395400000112
wherein k iskFor the adaptive rate of the filter, kk>0；
Figure FDA00032851395400000113
Extending the back emf observation error values for the alpha and beta axes respectively,
Figure FDA0003285139540000021
the software phase-locked loop estimates the rotor position angle
Figure FDA0003285139540000022
And estimating the rotational speed
Figure FDA0003285139540000023
The calculation process of (2) is as follows:
Figure FDA0003285139540000024
wherein, Kp、KiRespectively are proportional and integral coefficients;
the boundary layer self-adjusting arcsine saturation function is as follows:
Figure FDA0003285139540000025
wherein the content of the first and second substances,
Figure FDA0003285139540000026
sα、sβexpanding the counter electromotive force E for the alpha and beta axes, respectivelyα、EβAnd (3) corresponding to the sliding mode surface, wherein lambda is the thickness of the basic boundary layer, and s is a parameter of the sliding mode surface.
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