CN108306566B - Linear induction motor secondary flux linkage estimation method based on extended state observer - Google Patents

Linear induction motor secondary flux linkage estimation method based on extended state observer Download PDF

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CN108306566B
CN108306566B CN201810159475.3A CN201810159475A CN108306566B CN 108306566 B CN108306566 B CN 108306566B CN 201810159475 A CN201810159475 A CN 201810159475A CN 108306566 B CN108306566 B CN 108306566B
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flux linkage
mutual inductance
induction motor
linear induction
disturbance
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CN108306566A (en
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徐伟
佃仁俊
刘毅
胡冬
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Huazhong University of Science and Technology
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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
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust 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
    • H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/141—Flux estimation
    • 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
    • H02P25/00—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details
    • H02P25/02—Arrangements or methods for the control of AC motors characterised by the kind of AC motor or by structural details characterised by the kind of motor
    • H02P25/06—Linear motors
    • H02P25/062—Linear motors of the induction type
    • 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
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/01—Asynchronous machines

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Abstract

The invention discloses a linear induction motor secondary flux linkage estimation method based on an extended state observer, which aims at the directional vector control of the secondary flux linkage of a linear induction motor and solves the problem of observation errors of the secondary flux linkage caused by the side effect of the linear induction motor due to mutual inductance and secondary resistance change. The flux linkage observer observes disturbance caused by mutual inductance and secondary resistance change through the improved extended state observer, and performs active compensation in the flux linkage observer, so that robustness of the flux linkage observer to the mutual inductance and the secondary resistance change of the motor is improved.

Description

Linear induction motor secondary flux linkage estimation method based on extended state observer
Technical Field
The invention belongs to the field of alternating current motor control, and particularly relates to a linear induction motor secondary flux linkage estimation method based on an extended state observer.
Background
The linear induction motor is used as a driving device which can directly generate linear motion without an intermediate transmission device and has excellent control performance, and is widely applied to the fields of magnetic suspension, subways, industrial machine tools, electric doors and the like. High performance control of linear induction motors typically employs vector control methods based on secondary flux linkage orientation. Where secondary flux linkage observations are the key to vector control. The observation precision of the traditional flux linkage observer depends on an accurate motor model and motor parameters. Due to the influence of the side end effect, the mutual inductance and the secondary resistance of the linear induction motor are greatly changed under different operating conditions, so that the estimation precision of the secondary flux linkage is influenced, and the control effect of the linear induction motor is influenced. In order to solve the problem, many more accurate linear induction motor models are proposed, but due to the structural diversity of the linear induction motor, the models have no universality, the complexity and the implementation difficulty of an algorithm are increased, and the improvement of the control effect is indirectly influenced. In addition, secondary flux linkage observation methods based on parameter identification exist, but the algorithm is difficult to select proper adaptive parameters, and great difficulty is brought to debugging work.
Disclosure of Invention
Aiming at the defects or the improvement requirements of the prior art, the invention provides a linear induction motor secondary flux linkage estimation method based on an extended state observer, so that the technical problem that the control effect of the linear induction motor is influenced due to the fact that the estimation precision of the conventional secondary flux linkage is low is solved.
In order to achieve the above object, the present invention provides a linear induction motor secondary flux linkage estimation method based on an extended state observer, including:
(1) observing disturbance quantity caused by mutual inductance and secondary resistance change by a primary current extended state observer;
(2) the observed disturbance amount caused by the mutual inductance and the secondary resistance change is compensated into a secondary flux linkage observer to obtain flux linkage amplitude, flux linkage phase angle and synchronous angular velocity.
Preferably, step (1) comprises:
(1.1) establishing a linear induction motor mathematical model based on mutual inductance and secondary resistance change;
(1.2) obtaining a flux linkage differential term according to the mathematical model of the linear induction motor, and determining disturbance quantity caused by mutual inductance and secondary resistance change according to the flux linkage differential term;
(1.3) establishing a primary current extended state observer for a current differential equation in the mathematical model of the linear induction motor to observe disturbance quantity caused by mutual inductance and secondary resistance change.
Preferably, step (1.1) comprises:
by
Figure BDA0001582501240000021
Establishing a linear induction motor mathematical model based on mutual inductance and secondary resistance change, wherein i1Is a primary current vector u1Is a primary voltage vector, #2Is a secondary flux linkage vector, R1Is a primary resistance, R2Is a secondary resistance, LmIs mutual inductance, L1For primary self-inductance, L2For secondary self-inductance, Ll1For primary leakage inductance, Ll2For secondary leakage inductance, TrIs a secondary time constant, omega is a secondary electric angular velocity, v is a motor rotor velocity, tau is a motor polar distance, sigma is a magnetic leakage coefficient, d is a flux linkage differential term,
Figure BDA0001582501240000022
preferably, step (1.2) comprises:
by
Figure BDA0001582501240000023
Obtaining a flux linkage differential term d, wherein LmNRated value for mutual inductance, TrNIs a nominal value for the secondary time constant,
Figure BDA0001582501240000024
representing the amount of disturbance caused by mutual inductance and secondary resistance change.
Preferably, step (1.3) comprises:
by
Figure BDA0001582501240000031
A primary current extended state observer is established to observe disturbance amounts caused by mutual inductance and secondary resistance change, wherein,
Figure BDA0001582501240000032
a、ω0、krand ξ are the gain parameters, ω, of the primary current extended state observer, respectively1Synchronous angular velocity, L, of a linear induction motor1NRated value, σ, representing the primary self-inductanceNRepresents a rated leakage coefficient, L2NA nominal value representing the secondary self-inductance,
Figure BDA0001582501240000033
representing the estimated primary current, e representing the primary current estimation error,
Figure BDA0001582501240000034
which represents an estimate of the disturbance,
Figure BDA0001582501240000035
which represents the derivative of the primary current estimate,
Figure BDA0001582501240000036
a low-frequency component representing the disturbance estimate,
Figure BDA0001582501240000037
an alternating current component representing an estimate of the disturbance,
Figure BDA0001582501240000038
and
Figure BDA0001582501240000039
is an intermediate variable.
Preferably, step (2) comprises:
(2.1) estimating the amount of disturbance based on the observed changes in the mutual inductance and the secondary resistance
Figure BDA00015825012400000310
Obtaining the estimated value of the flux linkage differential term
Figure BDA00015825012400000311
Wherein the content of the first and second substances,
Figure BDA00015825012400000312
(2.2) integrating the estimated value of the flux linkage differential term to obtain the secondary flux linkage
Figure BDA00015825012400000313
Wherein the content of the first and second substances,
Figure BDA00015825012400000314
(2.3) linking the obtained secondary magnetic flux
Figure BDA00015825012400000315
Sending into phase-locked loop to obtain amplitude of secondary flux linkage
Figure BDA00015825012400000316
And phase angle of secondary flux linkage
Figure BDA00015825012400000317
And the synchronous angular velocity ω of the linear induction motor1。
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects: the secondary flux linkage observer provided by the invention actively observes and compensates disturbance caused by mutual inductance and secondary resistance, improves the flux linkage observation precision, and enhances the robustness to the mutual inductance and secondary flux linkage change.
Drawings
Fig. 1 is a schematic flowchart of a method for estimating secondary flux linkage of a linear induction motor based on an extended state observer according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a secondary flux linkage orientation control system of a linear induction motor based on a flux linkage observer according to an embodiment of the present invention;
FIG. 3(a) is a flux linkage estimation simulation result based on the flux linkage observer of the present invention;
FIG. 3(b) is a flux linkage estimation simulation result based on a conventional flux linkage observer;
FIG. 4 is the current observation error of different flux observers when the secondary resistance is deviated by 1.5 times;
FIG. 5 is a graph showing current observation errors of different flux linkage observers at 0.6 times mutual inductance deviation;
FIG. 6(a) is a dynamic curve of d-axis current;
FIG. 6(b) is a dynamic curve of q-axis current;
FIG. 7 is a current observation dynamic variation curve;
FIG. 8(a) is a speed variation dynamic curve;
fig. 8(b) is a thrust dynamics curve.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The invention provides a linear induction motor secondary flux linkage estimation method based on an extended state observer, which aims at directional vector control of a secondary flux linkage of a linear induction motor and solves the problem of observation errors of the secondary flux linkage caused by mutual inductance and secondary resistance change due to the side effect of the linear induction motor. The flux linkage observer observes disturbance caused by mutual inductance and secondary resistance change through the improved extended state observer, and performs active compensation in the flux linkage observer, so that the observation precision of the secondary flux linkage of the linear induction motor is effectively improved, the vector control of the linear induction motor obtains a better dynamic effect, and the robustness of the flux linkage observer to the mutual inductance and the secondary resistance change of the motor is improved.
Fig. 1 is a schematic flow chart of a method for estimating secondary flux linkage of a linear induction motor based on an extended state observer according to an embodiment of the present invention, where the method shown in fig. 1 includes the following steps:
(1) observing disturbance quantity caused by mutual inductance and secondary resistance change by a primary current extended state observer;
in an alternative embodiment, step (1) comprises:
(1.1) establishing a linear induction motor mathematical model based on mutual inductance and secondary resistance change;
in an alternative embodiment, step (1.1) comprises:
by
Figure BDA0001582501240000051
Establishing a linear induction motor mathematical model based on mutual inductance and secondary resistance change, wherein i1＝[i1αi1β]TIs a primary current vector u1＝[u1αu1β]TIs a primary voltage vector, #2＝[ψ2αψ2β]TIs a secondary flux linkage vector, R1Is a primary resistance, R2Is a secondary resistance, LmIs mutual inductance, L1＝Lm+Ll1For primary self-inductance, L2＝Lm+Ll2For secondary self-inductance, Ll1For primary leakage inductance, Ll2For secondary leakage inductance, Tr＝L2/R2Is a secondary time constant, omega-pi v/tau is a secondary electric angular velocity, v is a motor rotor velocity, tau is a motor polar distance,
Figure BDA0001582501240000054
is a magnetic leakage coefficient, d is a flux linkage differential term,
Figure BDA0001582501240000052
(1.2) obtaining a flux linkage differential term according to a mathematical model of the linear induction motor, and determining disturbance quantity caused by mutual inductance and secondary resistance change according to the flux linkage differential term;
in an alternative embodiment, step (1.2) comprises:
by
Figure BDA0001582501240000053
Obtaining a flux linkage differential term d, wherein LmNRated value for mutual inductance, TrNIs the nominal value of the secondary time constant, and the subscript N indicates the nominal value of the corresponding parameter, Δ (—) is the amount of uncertainty caused by the variation of the motor parameter,
Figure BDA0001582501240000061
representing the amount of perturbation w caused by mutual inductance and secondary resistance changes.
(1.3) establishing a primary current extended state observer aiming at a current differential equation in a mathematical model of the linear induction motor to observe disturbance quantity caused by mutual inductance and secondary resistance change.
In an alternative embodiment, step (1.3) comprises:
by
Figure BDA0001582501240000062
A primary current extended state observer is established to observe disturbance amounts caused by mutual inductance and secondary resistance change, wherein,
Figure BDA0001582501240000063
a、ω0、krand ξ are the gain parameters, ω, of the primary current extended state observer, respectively1For synchronous angular velocity of linear induction motors, obtainable by a phase-locked loop, L1NRated value, σ, representing the primary self-inductanceNRepresents a rated leakage coefficient, L2NA nominal value representing the secondary self-inductance,
Figure BDA0001582501240000064
representing the estimated primary current, e representing the primary current estimation error,
Figure BDA0001582501240000065
an estimated value of the disturbance amount is represented,
Figure BDA0001582501240000066
which represents the derivative of the primary current estimate,
Figure BDA0001582501240000067
a low-frequency component representing the disturbance estimate,
Figure BDA0001582501240000068
an alternating current component representing an estimate of the disturbance,
Figure BDA0001582501240000069
and
Figure BDA00015825012400000610
are intermediate variables with no actual physical meaning.
Wherein a ═ LmN/(σNL1NL2N)。
(2) The observed disturbance amount caused by the mutual inductance and the secondary resistance change is compensated into a secondary flux linkage observer to obtain flux linkage amplitude, flux linkage phase angle and synchronous angular velocity.
In an alternative embodiment, step (2) comprises:
(2.1) estimating the amount of disturbance based on the observed changes in the mutual inductance and the secondary resistance
Figure BDA0001582501240000071
Obtaining the estimated value of the flux linkage differential term
Figure BDA0001582501240000072
Wherein the content of the first and second substances,
Figure BDA0001582501240000073
(2.2) integrating the estimated value of the flux linkage differential term to obtain the secondary flux linkage
Figure BDA0001582501240000074
Wherein the content of the first and second substances,
Figure BDA0001582501240000075
(2.3) linking the obtained secondary magnetic flux
Figure BDA0001582501240000076
Sending into phase-locked loop to obtain amplitude of secondary flux linkage
Figure BDA0001582501240000077
And phase angle of secondary flux linkage
Figure BDA0001582501240000078
And the synchronous angular velocity ω of the linear induction motor1。
Fig. 2 is a schematic structural diagram of a vector control system of a linear induction motor based on an improved flux linkage observer according to an embodiment of the present invention, which includes a current sensor module, a speed measurement module, an abc/αβ coordinate transformation module, a αβ/dq coordinate transformation module, a dq/αβ coordinate transformation module, a current loop PI control module, a speed loop PI control module, a flux linkage loop PI control module, a space voltage vector modulation (SVPWM) module, and the flux linkage observer module provided in the present invention, and the specific implementation procedures are as follows:
(a) sampling the stator current of the linear induction motor through a current sensor to obtain ia、ibBy means of abc/αβ coordinate transformation module, froma、ibTo obtain iα、iβ；
(b) Obtaining the motor speed v by a speed measurement model, and calculating the electrical angular speed omega of the motor according to the motor speed v;
(c) voltage u outputted by dq/αβ coordinate transformation moduleα、uβ，iα、iβAnd omega is input into the proposed flux linkage observation module to calculate flux linkage amplitude
Figure BDA0001582501240000079
Phase angle of flux linkage
Figure BDA00015825012400000710
And synchronous angular velocity ω1。
(c) The specific implementation process is as follows:
defining variables:
Figure BDA00015825012400000711
wherein the content of the first and second substances,
Figure BDA00015825012400000712
according to the following formula, input uα、uβ、iα、iβAnd ω, establishing stator current i1And a primary current extended state observer of disturbance w:
Figure BDA0001582501240000081
wherein a ═ LmN/(σNL1NL2N)，ω0、krAnd ξ are the gain parameters, ω, of the primary current extended state observer, respectively1Is the synchronous angular velocity of the motor;
based on the observed disturbance amount estimated value caused by parameter change
Figure BDA0001582501240000082
An estimate of the derivative of the flux linkage is determined, wherein,
Figure BDA0001582501240000083
integrating to obtain the secondary flux linkage according to the estimated value of the flux linkage derivative
Figure BDA0001582501240000084
Secondary flux linkage to be obtained
Figure BDA0001582501240000085
Inputting the phase-locked loop, and calculating to obtain the amplitude of the secondary flux linkage
Figure BDA0001582501240000086
Angle of sum
Figure BDA0001582501240000087
And synchronous angular velocity ω of the motor1。
(d) Secondary flux linkage amplitude to be obtained
Figure BDA0001582501240000088
Inputting the magnetic chain loop PI module with a given magnetic chain amplitude psi to obtain a given d-axis current
Figure BDA0001582501240000089
Inputting the given rotating speed v and the actual rotating speed v into a rotating speed ring PI module to obtain the given current of the q axis
Figure BDA00015825012400000810
(e) Based on the obtained secondary flux linkage phase angle
Figure BDA00015825012400000811
And iα、iβAnd dq axis currents id and i are obtained through an αβ/dq coordinate transformation moduleq；
(f) Given value according to dq axis
Figure BDA00015825012400000812
With the actual value i of the dq-axis currentd、iqInputting the current loop PI regulator to obtain dq axis voltage ud、uq；
(g) Based on the obtained secondary flux linkage phase angle
Figure BDA00015825012400000813
D to be obtainedqAxial voltage ud、uqThe input dq/αβ coordinate transformation module obtains the voltage u on the αβ coordinate axisα、uβ；
(h) The obtained voltage uα、uβAn input space voltage vector modulation module (SVPWM) module generates corresponding PWM pulses and sends the PWM pulses to a switching device, and an inverter is controlled to generate corresponding voltage so as to drive a motor.
The present invention will be described in detail with reference to specific examples.
Example 1
Embodiment 1 of the present invention compares the secondary flux estimation method of the linear induction motor of the present invention with a method based on a conventional flux observer, based on a 3kW linear induction motor driving platform. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The parameters of the linear induction motor used are as follows: r1＝1.21Ω，R2＝2.4Ω，Ll1＝11.41mH，Ll2＝4.32mH，Lm35.21mH,. tau.148.5 mm, 4 pole pair number p, andthe machine mass M is 100kg, and the friction viscosity coefficient mu is 0.001 N.s/M. Fig. 3 shows flux linkage observations of the flux linkage observer of the present invention and a conventional flux linkage observer, respectively, using different mutual inductances and secondary resistances under steady-state conditions: fig. 3(a) shows the flux linkage observation result of the flux linkage observer proposed by the present invention, and it can be seen that when the observer adopts different mutual inductance and secondary resistance to perform flux linkage estimation, the difference from the actual flux linkage is very small; fig. 3(b) shows a flux linkage estimation method based on a conventional extended state observer, which shows that there is a large deviation compared with the actual flux linkage when flux linkage estimation is performed by using different mutual inductance and secondary resistance. Fig. 4 shows the current observation error under the condition that the secondary resistance used by the flux linkage observer is 1.5 times of the actual value, and it can be seen that the current observation error is smaller by adopting the method provided by the invention. Fig. 5 shows the current observation error when the mutual inductance used by the flux linkage observer is 0.6 times of the actual value, and it can be seen that the current error is smaller by adopting the flux linkage observation method provided by the invention compared with the traditional method.
FIG. 6 shows the variation of the dq-axis current in a dynamic process; FIG. 7 shows a current estimation error variation curve in a dynamic process; fig. 8 shows the variation curves of speed and electromagnetic thrust in the dynamic process. As can be seen from fig. 6(a), in the dynamic process, the flux linkage observer provided by the present invention has a higher excitation current during vector control; it can be seen from fig. 6(b) that the time required for the q-axis current to enter in the method proposed by the present invention is reduced from 6.1s of the conventional method to about 5.9 s. It can be seen from fig. 7 that the current observation error is smaller by adopting the method of the invention. From fig. 8(a), it can be seen that the dynamic condition time of the speed tracking is smaller and the speed rises faster by adopting the method proposed by the present invention; it can be seen from fig. 8(b) that the thrust output during the dynamic adjustment process is greater by the method proposed by the present invention.
The results show that the secondary flux linkage observation method provided by the invention has better parameter robustness for mutual inductance and secondary resistance, and has higher response speed in a dynamic process, thereby showing the superiority of the method.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (3)

1. A linear induction motor secondary flux linkage estimation method based on an extended state observer is characterized by comprising the following steps:
(1) observing disturbance quantity caused by mutual inductance and secondary resistance change by a primary current extended state observer;
(2) compensating the observed disturbance quantity caused by mutual inductance and secondary resistance change into a secondary flux linkage observer to obtain flux linkage amplitude, flux linkage phase angle and synchronous angular velocity;
the step (1) comprises the following steps:
(1.1) establishing a linear induction motor mathematical model based on mutual inductance and secondary resistance change;
(1.2) obtaining a flux linkage differential term according to the mathematical model of the linear induction motor, and determining disturbance quantity caused by mutual inductance and secondary resistance change according to the flux linkage differential term;
(1.3) establishing a primary current extended state observer for a current differential equation in the mathematical model of the linear induction motor to observe disturbance quantities caused by mutual inductance and secondary resistance changes;
the step (1.2) comprises the following steps:
by
Figure FDA0002259577110000011
Obtaining a flux linkage differential term d, wherein LmNRated value for mutual inductance, TrNRated value for the secondary time constant, i1Is the primary current vector, ω is the secondary electrical angular velocity, Ψ2Representing the secondary flux linkage vector, LmIs mutual inductance, TrIs a time constant of the secondary stage,
Figure FDA0002259577110000012
representing disturbances caused by mutual inductance and secondary resistance changesThe amount of the compound (A) is,
Figure FDA0002259577110000013
the step (1.3) comprises the following steps:
by
Figure FDA0002259577110000021
A primary current extended state observer is established to observe disturbance amounts caused by mutual inductance and secondary resistance change, wherein,
Figure FDA0002259577110000022
a、ω0、krand ξ are the gain parameters, ω, of the primary current extended state observer, respectively1Synchronous angular velocity, L, of a linear induction motor1NRated value, σ, representing the primary self-inductanceNRepresents a rated leakage coefficient, L2NA nominal value representing the secondary self-inductance,
Figure FDA0002259577110000023
representing the estimated primary current, e representing the primary current estimation error,
Figure FDA0002259577110000024
which represents an estimate of the disturbance,
Figure FDA0002259577110000025
which represents the derivative of the primary current estimate,
Figure FDA0002259577110000026
a low-frequency component representing the disturbance estimate,
Figure FDA0002259577110000027
an alternating current component representing an estimate of the disturbance,
Figure FDA0002259577110000028
Figure FDA0002259577110000029
and
Figure FDA00022595771100000210
is the intermediate variable(s) of the variable,
Figure FDA00022595771100000211
represents an estimate of the secondary flux linkage, u1Is a primary voltage vector, R1Is the primary resistance.
2. The method of claim 1, wherein step (1.1) comprises:
by
Figure FDA00022595771100000212
Establishing a linear induction motor mathematical model based on mutual inductance and secondary resistance change, wherein L1For primary self-inductance, L2The secondary self-inductance is, and σ is the magnetic leakage coefficient.
3. The method of claim 1, wherein step (2) comprises:
(2.1) estimating the amount of disturbance based on the observed changes in the mutual inductance and the secondary resistance
Figure FDA0002259577110000031
Obtaining the estimated value of the flux linkage differential term
Figure FDA0002259577110000032
Wherein the content of the first and second substances,
Figure FDA0002259577110000033
(2.2) integrating the estimated value of the secondary flux linkage according to the estimated value of the flux linkage differential term
Figure FDA0002259577110000034
Wherein，
Figure FDA0002259577110000035
(2.3) estimating the obtained secondary flux linkage
Figure FDA0002259577110000036
Sending into phase-locked loop to obtain amplitude of secondary flux linkage
Figure FDA0002259577110000037
And phase angle of secondary flux linkage
Figure FDA0002259577110000038
And the synchronous angular velocity ω of the linear induction motor1。
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