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CN113395028B - Method for forming flux linkage observer based on voltage and current hybrid model - Google Patents

Method for forming flux linkage observer based on voltage and current hybrid model Download PDF

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Publication number
CN113395028B
CN113395028B CN202110854236.1A CN202110854236A CN113395028B CN 113395028 B CN113395028 B CN 113395028B CN 202110854236 A CN202110854236 A CN 202110854236A CN 113395028 B CN113395028 B CN 113395028B
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flux linkage
voltage
model
current
hybrid model
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CN113395028A (en
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张永昌
陈浩
杨海涛
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North China University of Technology
North China Electric Power University
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North China University of Technology
North China Electric Power University
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    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/0017Model reference adaptation, e.g. MRAS or MRAC, useful for control or parameter estimation
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/06Rotor flux based control involving the use of rotor position or rotor speed sensors
    • H02P21/08Indirect field-oriented control; Rotor flux feed-forward control
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/13Observer control, e.g. using Luenberger observers or Kalman filters
    • HELECTRICITY
    • H02GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02PCONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/14Estimation or adaptation of machine parameters, e.g. flux, current or voltage
    • H02P21/141Flux estimation

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  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Control Of Ac Motors In General (AREA)

Abstract

The invention discloses a method for forming a voltage-current hybrid model flux linkage observer, which comprises the following steps of: step A: through the design of PI parameters of a voltage-current hybrid model flux linkage observer, the imaginary part of the characteristic function F(s) is reduced, and meanwhile, the real part of the characteristic function F(s) is ensured to gradually increase from 0 to 1 along with the increase of frequency; and B: and carrying out stability analysis on the improved voltage-current hybrid model flux linkage observer. The method can realize smooth switching of the current model and the voltage model and reduce flux linkage estimation errors, thereby solving the problem of poor robustness of the traditional mixed model flux linkage observer in a medium-speed region. When the motor parameters have errors, the improved hybrid model flux linkage observer can observe accurate rotor flux linkage in a full-speed range, and the problems of amplitude attenuation, phase offset and the like at different rotating speeds are solved.

Description

Method for forming flux linkage observer based on voltage-current hybrid model
Technical Field
The invention belongs to the field of power electronics, and particularly relates to a method for forming a flux linkage observer based on a voltage-current hybrid model.
Background
The key in an induction motor control system is to accurately obtain the magnitude and spatial position of the rotor flux linkage vector. Direct detection of rotor flux linkage is difficult, and the existing literature indicates that flux linkage estimation mostly adopts a voltage model, a current model, a full-order flux linkage observation model and the like. Because the current model comprises a rotor time constant and mutual inductance parameters, the parameters are greatly influenced when the motor is heated and a magnetic circuit is saturated, and flux linkage observation errors are caused. But in summary, the current model does not need a voltage signal and has no influence of direct current bias, so that the current model is more suitable for a low-speed running state. The voltage model does not contain rotor resistance, and the motor parameter robustness is stronger, so the performance is superior to that of the current model at medium and high speed. However, the voltage model has two main problems in practical application: firstly, the low-speed occasion is sensitive to the resistance change of the stator; and secondly, a pure integration link in the model is easy to cause flux linkage observation errors. The former can reduce the influence of stator resistance parameters through online parameter self-adaptation; in practical application, the problems of direct current bias and integral saturation of a pure integral link caused by electromagnetic interference, sensor measurement and sampling errors and the like are more obvious.
In order to improve the estimation accuracy of the rotor flux linkage observer, a plurality of improved flux linkage observers are proposed in the prior literature. For example, a voltage-current hybrid model rotor flux linkage observer is proposed in document "a New Quick-response And High-efficiency Control structure of index Motor", which makes full use of the advantages of a current model in a low-speed region And the advantages of a voltage model in a High-speed region. In the medium-speed switching region, flux linkage estimation is sensitive to motor parameters due to the influence of factors such as a voltage dead zone, so that the problem of robustness in the medium-speed switching region becomes a key of research.
In order to solve the problem of poor robustness in the intermediate speed region, some scholars propose some solutions, but most of the solutions change the structure of a mixed model. For example, in the document "Novel Rotor-Flux Observer Using Observer guided performance Function in Complex Vector Space For Field-Oriented instruction Motor drivers", an angle compensation module is added based on a traditional hybrid model, which not only increases the calculated amount, but also increases the real-time operation capability of the control system because the expression includes on-line parameters. The inventor also proposes to improve the voltage model in the hybrid model, and add a high-pass filter on the basis of a pure integrator to eliminate the direct-current component in the back electromotive force, so as to solve the direct-current offset problem in the integration result. Although the observation performance of the flux linkage is improved at the medium and high speeds, the observation performance in the low speed region is not improved. At present, no better method can simultaneously meet the following requirements: 1) flux linkage estimation is accurate in a medium-speed switching region; 2) the calculated amount is small; 3) the structure of the hybrid model is not changed. Therefore, a simple and practical method needs to be designed to enable the hybrid model to obtain better flux linkage observation performance in the medium-speed switching region.
Disclosure of Invention
The invention provides an improved voltage-current hybrid model flux linkage observer, which aims at the problems that a traditional hybrid model flux linkage observer is sensitive to motor parameters in a medium-speed switching region and the like. Under the condition of not changing the structure of the hybrid model, through theoretical analysis of the hybrid model characteristic function in the frequency domain, a group of complex coefficient PI parameters are designed to replace the traditional real coefficient PI parameters, so that the imaginary part of the characteristic function is 0, and the real part is gradually increased from 0 to 1 along with the increase of the frequency. The current model and the voltage model are smoothly switched, and flux linkage estimation errors are reduced, so that the problem that the traditional mixed model flux linkage observer is poor in robustness in a medium-speed region is solved. The technical scheme adopted by the invention is as follows:
step A; based on the characteristic function of the traditional mixed model, the imaginary part of the characteristic function is made as small as possible by designing a group of complex coefficient PI parameters, and meanwhile, the real part of the characteristic function is ensured to gradually increase from 0 to 1 along with the increase of frequency;
and B: and C, performing stability analysis on the improved mixed model obtained according to the step A, so that the characteristic root of the improved mixed model is in the left half plane of the complex plane, and ensuring the stability of the system.
In some embodiments, the step a comprises:
According to the characteristic function of the voltage and current hybrid model flux linkage observer:
Figure BDA0003183519930000021
when the motor is in steady operation, let s equal to j omegaeObtaining:
Figure BDA0003183519930000031
order to
Figure BDA0003183519930000032
Wherein, Kp、KiIs the PI parameter, ωeIs the synchronous angular frequency;
in the medium and high frequency band, F (j omega)e) When the voltage-current hybrid model observer only functions as a voltage flux linkage observer, only a is 0, and the following results are obtained:
Ki=-jωeKp
in the low frequency band, want F (j ωe) The real part of (a) rises slowly from 0 to 1, and the following design is made:
Figure BDA0003183519930000033
obtaining:
Figure BDA0003183519930000034
wherein, ω isbBoundary angular frequencies switched for the current model and the voltage model flux linkage observer.
In some embodiments, the step B comprises:
the mathematical model of the voltage-current hybrid model flux linkage observer under a static coordinate system is as follows:
Figure BDA0003183519930000035
wherein,
Figure BDA0003183519930000036
is the rotor time constant; l ism、Lr、Ls、Rs、Rr、ωr、σ、p、
Figure BDA0003183519930000037
Mutual inductance, rotor inductance, stator resistance, rotor angular velocity, leakage inductance, differential operator, current model rotor flux linkage estimation value and voltage model rotor flux linkage estimation value;
and transforming the formula (3-1), wherein the state space equation of the closed-loop voltage-current hybrid model flux linkage observer is as follows:
Figure BDA0003183519930000041
variable of state
Figure BDA0003183519930000042
State matrix
Figure BDA0003183519930000043
The state equation is:
Figure BDA0003183519930000044
the characteristic equation is as follows:
Figure BDA0003183519930000045
because of the fact that
Figure BDA0003183519930000046
Is in the left half plane of the complex plane, so that
Figure BDA0003183519930000047
Figure BDA0003183519930000048
The root of the voltage-current hybrid model magnetic linkage observer is positioned on the left half plane of the complex plane, so that the stability of the improved voltage-current hybrid model magnetic linkage observer is ensured;
in the low frequency range (0 ≦ omega)e<ωb),KpAnd KiThe relationship between them is:
Figure BDA0003183519930000049
combined vertical type (3-4) and (3-5) are obtained:
Figure BDA00031835199300000410
solving the following steps:
Figure BDA0003183519930000051
suppose KpA + b j, adding KpSubstituting into equation (3-7) yields:
Figure BDA0003183519930000052
as can be seen from the equations (3-8), the system is stable and the characteristic function F (j ω) is stable as long as a is guaranteed to be greater than 0e) In the low frequency band, the imaginary part is always 0, and the real part gradually increases from 0 to 1 along with the rise of frequency;
in the medium-high frequency band, KpAnd KiThe relationship between is:
Ki=-jωeKp (3-9)
the combined vertical type (3-4) and (3-5) are as follows:
s2+Kps-jωeKp=0
solving the following steps:
Figure BDA0003183519930000053
suppose KpA + b j, KpSubstituting into the formula (3-10) to ensure that the real part of the characteristic root is less than zero; for convenience of calculation, order
Figure BDA0003183519930000054
Values for a and b were obtained:
Figure BDA0003183519930000055
by adopting the values of a and b in the formula, the obtained characteristic root is in the left half plane of the complex plane, so that the closed-loop voltage-current mixed model system is stable.
The invention has the following characteristics and advantages: compared with the traditional improvement scheme, no additional module is needed, and the calculation amount is small. The current model and the voltage model of the improved mixed model can be smoothly switched in a medium-speed switching region, and flux linkage estimation errors are reduced. The advantages of the current model and the voltage model are fully utilized, so that the hybrid model has good robustness to the change of the motor parameters. When the motor parameters have errors, the improved hybrid model flux linkage observer can observe accurate rotor flux linkage in a full-speed range, and the problems of amplitude attenuation, phase offset and the like at different rotating speeds are solved.
Drawings
FIG. 1 is a real and imaginary part of an improved hybrid model feature function F(s);
FIG. 2 is a block diagram of a sensor model predictive flux linkage control architecture;
FIG. 3 is a comparison of flux linkage estimation waveforms when the rotor resistance is varied;
fig. 4a and 4b are a comparison of estimated rotor flux linkage waveforms at varying rotor resistance, where in fig. 4 a:
Figure BDA0003183519930000061
(300r/min no load); in FIG. 4 b:
Figure BDA0003183519930000062
(300r/min full load);
fig. 5a and 5b are a comparison of flux linkage estimation waveforms at a variable stator resistance, wherein in fig. 5 a:
Figure BDA0003183519930000063
Figure BDA0003183519930000064
(300r/min full load); in fig. 5 b:
Figure BDA0003183519930000065
(300r/min empty);
fig. 6a and 6b are the comparison of flux linkage estimation waveforms when the mutual inductance is changed, wherein, in fig. 6 a:
Figure BDA0003183519930000066
Figure BDA0003183519930000067
(300r/min empty); in fig. 6 b:
Figure BDA0003183519930000068
300r/min full load).
Detailed Description
The following examples are presented to enable those skilled in the art to more fully understand the present invention and are not intended to limit the invention in any way.
The invention provides an improved voltage-current hybrid model flux linkage observer, which comprises the following steps:
step A: through the design of PI parameters of a voltage-current hybrid model flux linkage observer, the imaginary part of a characteristic function F(s) is reduced as much as possible, and meanwhile, the real part of the characteristic function F(s) is ensured to be gradually increased from 0 to 1 along with the increase of frequency;
and B, performing stability analysis on the improved voltage-current hybrid model flux linkage observer.
In some embodiments, step a comprises:
according to the characteristic function of the voltage and current hybrid model flux linkage observer:
Figure BDA0003183519930000069
when the motor is in steady operation, let s equal to j omegaeAnd obtaining:
Figure BDA0003183519930000071
order to
Figure BDA0003183519930000072
Wherein, Kp、KiIs a PI parameter; omegaeIs the synchronous angular frequency.
In the medium and high frequency band, F (j omega)e) The voltage-current hybrid model observer having 1 only functions as a voltage flux linkage observer, and in this case, a may be set to 0. Obtaining:
Ki=-jωeKp
in the low frequency band, want F (j ωe) The real part of (a) rises slowly from 0 to 1, and the following design is made:
Figure BDA0003183519930000073
obtaining:
Figure BDA0003183519930000074
wherein, ω isbBoundary angle for switching between current model and voltage model flux linkage observersFrequency.
In some embodiments, step B comprises:
the mathematical model of the voltage-current hybrid model flux linkage observer under a static coordinate system is as follows:
Figure BDA0003183519930000075
wherein,
Figure BDA0003183519930000076
is the rotor time constant; l ism、Lr、Ls、Rs、Rr、ωr、σ、p、
Figure BDA0003183519930000077
Figure BDA0003183519930000078
The rotor flux linkage estimation method comprises the following steps of mutual inductance, rotor inductance, stator resistance, rotor angular velocity, leakage inductance, differential operator, current model rotor flux linkage estimation value and voltage model rotor flux linkage estimation value.
And transforming the formula (3-1), wherein the state space equation of the closed-loop voltage-current hybrid model flux linkage observer is as follows:
Figure BDA0003183519930000079
variable of state
Figure BDA00031835199300000710
State matrix
Figure BDA00031835199300000711
The state equation is:
Figure BDA0003183519930000081
The characteristic equation is as follows:
Figure BDA0003183519930000082
because of the fact that
Figure BDA0003183519930000083
Root of (2) is in the left half plane of the complex plane, so that only the
Figure BDA0003183519930000084
Figure BDA0003183519930000085
The root of the voltage-current hybrid model flux linkage observer is positioned on the left half plane of the complex plane, so that the stability of the improved voltage-current hybrid model flux linkage observer can be ensured.
In the low frequency range (0 ≦ omega)e<ωb),KpAnd KiThe relationship between is:
Figure BDA0003183519930000086
the combined vertical type (3-4) and (3-5) are as follows:
Figure BDA0003183519930000087
solving the following steps:
Figure BDA0003183519930000088
suppose KpA + b j, and KpSubstituting into equation (3-7) yields:
Figure BDA0003183519930000089
as can be seen from equation (18), as long as a is guaranteed to be greater than 0, the system is stable and the characteristic function F (j ω) is stablee) In the low frequency band, the imaginary part is always 0, and the real part gradually increases from 0 to 1 as the frequency rises.
In the medium-high frequency band, KpAnd KiThe relationship between is:
Ki=-jωeKp (3-9)
the combined vertical type (3-4) and (3-5) are as follows:
s2+Kps-jωeKp=0
solving the following steps:
Figure BDA00031835199300000810
suppose KpA + b j, KpAnd (5) substituting the real part of the characteristic root into the formula (3-10) to ensure that the real part of the characteristic root is less than zero. To facilitate the calculation, can be
Figure BDA00031835199300000811
Values for a and b were obtained:
Figure BDA00031835199300000812
the solutions of a and b are not unique. By adopting the values of a and b in the formula, the obtained characteristic root is in the left half plane of the complex plane, so that the closed-loop voltage-current mixed model system can be stable.
The invention is further described below in conjunction with the appended drawings, wherein the feasibility of the improved model is verified in conjunction with model predictive flux control, but is only used to illustrate the invention, and is not used to limit the scope of the invention.
FIG. 1 is a characteristic function F (j ω) of an improved hybrid model at steady state of the motore) Real and imaginary variation cases.
Fig. 2 is a block diagram of a voltage-current hybrid model structure. The voltage-current hybrid model consists of a current model, a voltage model and a PI regulator. The PI regulator is controlled to enable the current model to play a main role in a low-speed area and enable the voltage model to play a main role in a medium-speed area and a high-speed area, and therefore accurate rotor flux linkage is obtained in a full-speed range.
FIG. 3 is a block diagram of model predictive flux linkage control. The effectiveness of the proposed method can be derived by comparing the simulation results of fig. 4a, 4b, 5a, 5b, 6a and 6 b. As can be seen from fig. 4a and 4 b: when there is an error in the rotor resistance, the estimated flux linkage of the hybrid model and the new and improved hybrid model presented herein can follow the actual flux linkage in both the unloaded and fully loaded cases. But the improved hybrid model of the present invention has better observed performance compared to the two. As can be seen from fig. 5a and 5 b: when the stator resistance has errors, the estimated flux linkage of the hybrid model has errors in amplitude and phase compared with the actual flux linkage under the conditions of no load and full load. The estimated flux linkage of the improved hybrid model of the invention can keep up with the actual flux linkage and has better observation performance. As can be seen from fig. 6a and 6 b: in both the no-load and full-load conditions, when there is an error in the mutual inductance, the estimated flux linkage of the hybrid model has an error in both amplitude and phase compared to the actual flux linkage. And the estimated flux linkage of the improved hybrid model of the invention can keep up with the actual flux linkage.
Those skilled in the art will appreciate that the above embodiments are only exemplary embodiments and that various changes, substitutions, and alterations can be made without departing from the spirit and scope of the application.

Claims (1)

1. A forming method of a voltage and current hybrid model flux linkage observer is characterized by comprising the following steps:
step A: through the design of PI parameters of a voltage-current hybrid model flux linkage observer, the imaginary part of the characteristic function F(s) is reduced, and meanwhile, the real part of the characteristic function F(s) is ensured to gradually increase from 0 to 1 along with the increase of frequency;
and B, step B: performing stability analysis on the improved voltage-current hybrid model flux linkage observer;
wherein the step A comprises the following steps:
according to the characteristic function of the voltage-current hybrid model flux linkage observer:
Figure FDA0003658675500000011
when the motor is in steady operation, let s be j omegaeObtaining:
Figure FDA0003658675500000012
order to
Figure FDA0003658675500000013
Wherein, Kp、KiIs the PI parameter, ωeIs the synchronous angular frequency;
in the medium and high frequency band, F (j omega)e) When the voltage-current hybrid model observer only functions as a voltage flux linkage observer, only a is 0, and the following results are obtained:
Ki=-jωeKp
in the low frequency band, want F (j ωe) The real part of (a) rises slowly from 0 to 1, and the following design is made:
Figure FDA0003658675500000021
obtaining:
Figure FDA0003658675500000022
wherein, ω isbBoundary angular frequency for switching of the current model and the voltage model flux linkage observer;
The step B comprises the following steps:
the mathematical model of the voltage and current mixed model flux linkage observer in a static coordinate system is as follows:
Figure FDA0003658675500000023
wherein,
Figure FDA0003658675500000024
is the rotor time constant; l ism、Lr、Ls、Rs、Rr、ωr、σ、p、
Figure FDA0003658675500000025
Mutual inductance, rotor inductance, stator resistance, rotor angular velocity, leakage inductance, differential operator, current model rotor flux linkage estimation value and voltage model rotor flux linkage estimation value;
and (3) converting the formula (3-1), wherein the state space equation of the closed-loop voltage-current hybrid model flux linkage observer is as follows:
Figure FDA0003658675500000026
variable of state
Figure FDA0003658675500000027
State matrix
Figure FDA0003658675500000028
The state equation is:
Figure FDA0003658675500000031
the characteristic equation is as follows:
Figure FDA0003658675500000032
because of the fact that
Figure FDA0003658675500000033
Is in the left half plane of the complex plane, so that
Figure FDA0003658675500000034
Figure FDA0003658675500000035
The root of the improved voltage-current hybrid model flux linkage observer is positioned on the left half plane of the complex plane, so that the stability of the improved voltage-current hybrid model flux linkage observer is ensured;
in the low frequency range (0 ≦ omega)e<ωb),KpAnd KiThe relationship between is:
Figure FDA0003658675500000036
the combined vertical type (3-4) and (3-5) are as follows:
Figure FDA0003658675500000037
solving the following steps:
Figure FDA0003658675500000038
suppose KpA + b j, and KpSubstituting into equation (3-7) yields:
Figure FDA0003658675500000039
as can be seen from the equations (3-8), the system is stable and the characteristic function F (j ω) is stable as long as a is guaranteed to be greater than 0e) In the low frequency bandThe imaginary part is always 0, and the real part gradually increases from 0 to 1 along with the rise of the frequency;
in the medium-high frequency band, KpAnd KiThe relationship between is:
Ki=-jωeKp (3-9)
Combined vertical type (3-4) and (3-5) are obtained:
s2+Kps-jωeKp=0
solving the following steps:
Figure FDA0003658675500000041
suppose KpA + b j, KpSubstituting into the formula (3-10) to ensure that the real part of the characteristic root is less than zero; for convenience of calculation, order
Figure FDA0003658675500000043
Values for a and b were obtained:
Figure FDA0003658675500000042
by adopting the values of a and b in the formula, the obtained characteristic root is on the left half plane of the complex plane, so that the closed-loop voltage-current mixed model system is stable.
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