CN109889061A - A kind of high-speed rail low-frequency oscillation suppression method based on extended state observer sliding formwork control - Google Patents
A kind of high-speed rail low-frequency oscillation suppression method based on extended state observer sliding formwork control Download PDFInfo
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Abstract
The present invention discloses a kind of high-speed rail low-frequency oscillation suppression method based on extended state observer sliding formwork control, first constructs EMU net-side rectifier state-space model；Load variation is considered as disturbance again, extended state observer is established to state-space model, obtains bearing power estimated value；In conjunction with control target, the output of control system is chosen, establishes and is based on voltage-controlled two sliding-mode surfaces of outer ring, in conjunction with bearing power estimated value, current on line side reactive component reference value is obtained, completes seeking for sliding-mode surface expression formula；Switch function is sought, then switch function is multiplied with DC voltage, obtains control voltage；It is alpha-beta coordinate system component by control voltage transformation, passes through sinusoidal pulse width modulation output control pulse.All external disturbances are considered as a state variable by the present invention, in the case where load sudden change, are able to maintain the constant of DC voltage, and current on line side can be made to possess smaller total harmonic distortion factor, guarantee the power quality and system stability of vehicle net coupled system.
Description
Technical field
The present invention relates to high-speed rail power supply technique field, specially a kind of high-speed rail based on extended state observer sliding formwork control
Low-frequency oscillation suppression method.
Background technique
With the fast development of Chinese high-speed rail, high speed, heavily loaded, big density have become the important spy of electric railway instantly
Property, therefore, increasingly higher demands are proposed to the power supply reliability of high-speed rail.More and more novel friendships directly hand over transmission locomotive to throw
Enter operation, considerably increases the complexity of tractive power supply system, the low-frequency oscillation of China's tractive power supply system is exactly at this
It is generated under the background of sample, this phenomenon is fundamentally wild effect caused by vehicle network parameters mismatch.Many results of study
The control strategy for showing net-side rectifier is the big key factor for influencing vehicle net system stability.AC drive locomotive, height
Traction convertor used in fast EMU is mainly made of four-quadrant pulse rectifier and traction invertor.Four-quadrant pulse is whole
Stream is net-side rectifier, belongs to PWM rectifier.EMU net-side rectifier generallys use outer voltage and current inner loop combines
Double circle controling mode, current main control mode has transient current testing strategy, variable phase angle control policy, prediction
Direct Current Control Strategy, dq decoupling control policy etc..The control effect of traditional linear control method, which has hardly resulted in, to be mentioned
It rises, therefore nonlinear control method, such as PREDICTIVE CONTROL, Passive Shape Control and sliding formwork control etc. is introduced into the control of current transformer
It is necessary.
Summary of the invention
In view of the above-mentioned problems, the purpose of the present invention is to provide one kind can save cost, it is able to maintain DC voltage
It is constant so that current on line side possesses smaller total harmonic distortion factor, can guarantee the power quality of vehicle net coupled system and be
The high-speed rail low-frequency oscillation suppression method based on extended state observer sliding formwork control for stability of uniting.Technical solution is as follows:
A kind of high-speed rail low-frequency oscillation suppression method based on extended state observer sliding formwork control, comprising the following steps:
Step A: defining current on line side amount of quadrature, and the state for constructing EMU net-side rectifier under d-q rotating coordinate system is empty
Between model；
Step B: load variation is considered as disturbance, extended state observer is established to above-mentioned state-space model, is born
Carry the estimated value of power；
Step C: in conjunction with control target, the output of control system is chosen, establishes and is based on voltage-controlled two sliding formworks of outer ring
Face obtains the reference value of current on line side reactive component in conjunction with the bearing power estimated value that step B is obtained, and completes sliding-mode surface expression
Formula is sought；
Step D: sliding formwork control tendency rate is chosen to above-mentioned two sliding-mode surface, two sliding-mode surfaces that step C is established substitute into
Obtained result is substituted into the state-space model of EMU net-side rectifier under d-q rotating coordinate system by sliding formwork control tendency rate,
Switch function is obtained, which is multiplied with DC voltage, obtains control voltage；
Step E: control voltage obtained in step D is obtained into alpha-beta coordinate system component by coordinate transform, then passes through sine
Non-inverting output controls pulse.
Further, detailed process is as follows by the step A:
For single-phase two level topological structure, by ac-side current inIt is expressed as iα, exchange side electromotive force enIt is expressed as uα,
Building and iα、uαOrthogonal virtual amount iβ、uβ, principle is converted according to the constant power that coordinate transform follows, is obtained
uαiα+uβiβ=Udcidc
In formula, UdcFor DC side burning voltage, idcFor DC side steady load electric current；
Define uα=SαUdc, uαIt is uabComponent on α axis, uβ=SβUdc, uβIt is uabComponent on β axis, uabIt is whole
Flow bridge port voltage；Sα、SβIt is the perfect switch function under alpha-beta coordinate system；Obtain idcExpression formula:
In formula, udcFor DC side load voltage；
In conjunction with the KVL equation of exchange side, of ac, virtual orthographic amount are indicated in same equation group, obtained
In formula, L and R are respectively the equivalent leakage inductance and ohmic leakage to secondary side of mobile transformer, and C is DC side support electricity
Hold；eαExchange side electromotive force en, eβFor enObtained after rotating clockwise 90 degree and enOrthogonal voltage vector, ilFor load electricity
Stream；Two-phase stationary coordinate system is carried out to the coordinate transform of two-phase rotating coordinate system, obtains EMU net side under d-q rotating coordinate system
The mathematical model of rectifier:
In formula, ed、eqRespectively net side electromotive force and virtual orthographic component point of d axis and q axis in the rotated coordinate system respectively
Amount；id、iqRespectively net side electromotive force and virtual orthographic component distinguish d, q component in the rotated coordinate system；According to definition, d axis point
Amount indicates that active component, q axis component indicate reactive component, SdUdc、SqUdcIt is then uabCorresponding component is expressed as state space mould
The matrix form of type:
Obtain the mathematical model of EMU net-side rectifier matrix form under two-phase rotating coordinate system.
Further, detailed process is as follows by the step B: enabling
Wherein, PdqFor above-mentioned edidWith eqiqSum, i.e., exchange side power；Pl=ilRlIt is actual loading power, RlFor etc.
Imitate load resistance；Easy, the x for expression1And x2Respectively representWith PlState variable；It will be moved under d-q rotating coordinate system
The third formula of the mathematical model of vehicle group net-side rectifierSimplify are as follows:
To design extended state observer, above formula is indicated are as follows:
Wherein, f (t) indicates x2Derivation；
Then a linear extended state observer is expressed as follows:
Wherein, z1And z2Respectively x1And x2Estimated value, obtained by extended state observer, β1And β2To pass through Hull
The dimension positive parameter that hereby stable theory acquires.
Further, detailed process is as follows by the step C:
Select Udc、iqFor the output of control system, ifThenAccording to d- obtained in step A
The matrix form of EMU net-side rectifier state-space model under q rotating coordinate system, standard type can be controlled by releasing it
Wherein, ω is power grid a-c cycle angular speed；udc、iq、Error amounteφIt respectively indicates are as follows:
Wherein,For the reference value of DC voltage；For iqReference value, φrefFor the reference value of φ.
Establish two sliding-mode surface s1、s2Respectively with Udc、iqIt is corresponding:
Wherein, α, α1、α2For gain amplifier, and replaced with βFeedback factor as sliding formwork control；
By error amounteφExpression substitute into above formula, obtain:
By the mathematical model of EMU net-side rectifier under d-q rotating coordinate system and DC voltage reference valueGeneration
Enter above formula to obtain:
By idSeparation, obtains
In formula, C,It is known constant, udc、iq、ilIt being measured by corresponding measuring tool, β is preset parameter,
SdWith SqIt is switch function, it willAs idReference value；
According to following power principle of invariance under d-q rotating coordinate system
udid+uqiq=Udcidc
According to control target, reactive current component iq=0, then
udid=Udcidc
Define ud=SdUdc, due to ud=ed-Rid, above formula is expressed as
(ed-Rid)id=UdcSdid
Then SdExpression formula be
By the mathematical model of EMU net-side rectifier under d-q rotating coordinate system
Since the resistance R of the biggish transformer of capacity is minimum, therefore ignore, and because in the ideal case,eq=
0, then
It obtains
Above formula is substituted into idReference valueExpression formula, obtain
Then
Wherein, ilIt is by the z in step B2/Udc=ilIt obtains, then it is available by above formulaExpression formula
Sliding-mode surface is rewritten are as follows:
Further, detailed process is as follows by the step D:
To upper described two sliding-mode surface s1、s2Exponential approach rate is chosen, is obtained
Wherein, ε1For constant, indicate that system mode point levels off to sliding-mode surface s1(x)=0 rate, rate and ε1Size
It is directly proportional；-k1S is exponential approach item, represents the process by sliding-mode surface of system mode approach sliding-mode surface；For sliding-mode surface s1's
Derivation；
The expression formula of sliding-mode surface is substituted into
Due toIt is in the ideal situation constant, thereforeThen above formula is expressed as
The state-space model for substituting into EMU net-side rectifier under d-q rotating coordinate system, obtains
By switch function Sd、SqIt shows
It obtains controlling voltage needed for pulse width modulation
The beneficial effects of the present invention are:
1) it is proposed by the present invention suitable for EMU net-side rectifier based on extended state observer sliding mode control strategy
Because itself being the characteristic of variable-structure control, meeting PWM rectifier in itself is also the feature of variable structure system, improves this
The robust performance of system can damp the problem of Traction networks-EMU electrical quantity vibrates.
2) present invention can overcome EMU net side reorganizer response speed and the contradiction between the overshoot time, and based on outer
The robustness of system can be improved in the extended state observer part of Interference Estimation in ring.
3) information content required for the present invention is less, can use the identical control target of less information realization, and can save
Save the economic expenditure and space hold of sensor.
4) all external disturbances are considered as a state variable by the present invention, so that comparing in the case where load sudden change
It cannot keep the constant of DC voltage in former sliding mode controller, this method can be kept.
5) present invention can make current on line side possess smaller total harmonic distortion factor, this is to the electric energy for guaranteeing vehicle net coupled system
Quality and system stability are of great significance.
Detailed description of the invention
Fig. 1 is control structure figure of the invention.
Fig. 2 is rectifier equivalent circuit diagram of the invention.
The position Fig. 3 rectifier of the invention includes the simplified electrical circuit diagram of switch function.
Fig. 4 is DC voltage comparison of wave shape figure.
Simulation model figure Fig. 5 of the invention；From and Goto label is mutually all one group, indicates two signals actually phase
Even.
Fig. 6 is controller simulation illustraton of model of the invention；The non-repeat mark of this figure of label occurred in Fig. 5.
Fig. 7 a is DC voltage Udc waveform diagram of the present invention.
Fig. 7 b ac-side current in, ac-side current un waveform diagram.
Fig. 7 c accesses 5 motor-cars at the 0s moment for vehicle net of the present invention cascade emulation first, then at 3s, 6s and 9s moment
1 motor-car is increased separately, accesses voltage on line side u, the current on line side i waveform diagram of 8 motor-cars altogether；EMU refers to an EMU.
Specific embodiment
The present invention is described in further details in the following with reference to the drawings and specific embodiments.The present embodiment is with CRH5 type motor-car
For group.
Step A: defining current on line side amount of quadrature, and the state for constructing EMU net-side rectifier under d-q rotating coordinate system is empty
Between model.
For EMU net-side rectifier using four-quadrant pulse rectifier, this patent is directed to single-phase two level topology
Structure.Pantograph takes stream from contact net, and as the input of rectifier after mobile transformer is depressured, rectifier is then by the list of input
Phase alternating current buckling changes steady dc voltage into.
By ac-side current inIt is expressed as iα, exchange side electromotive force enIt is expressed as uα, building and iα、uαOrthogonal virtual amount
iβ、eβ, principle is converted according to the constant power that coordinate transform follows, can be obtained
uαiα+uβiβ=Udcidc
In formula, UdcFor DC side burning voltage, idcFor DC side steady load electric current.
Define uα=SαUdc, uαIt is uabComponent on α axis, uβ=SβUdc, uβIt is uabComponent on β axis, Sα、SβIt is
Perfect switch function under alpha-beta coordinate system.Obtain idcExpression formula:
As shown in Fig. 2, by writing KVL equation to exchange side column, and of ac, virtual orthographic amount are indicated in same equation
In group, the mathematical model of EMU net-side rectifier under d-q rotating coordinate system can get
In formula, L and R are respectively the equivalent leakage inductance and ohmic leakage to secondary side of mobile transformer, and C is DC side support electricity
Hold.In EMU net-side rectifier, corresponding parameter value is respectively as follows: Traction networks network pressure virtual value Un=27500V, net side electricity
Hinder R=0.145 Ω, net side inductance L=0.0054H, DC side Support Capacitor C=0.009F, DC side load equivalent resistance R=
25Ω.Given DC voltage Udc=3600V.
Two-phase stationary coordinate system is carried out to the coordinate transform of two-phase rotating coordinate system to above formula, d-q rotational coordinates can be obtained
It is the mathematical model of lower EMU net-side rectifier
In formula, ed、eqRespectively net side electromotive force and virtual orthographic component point of d axis and q axis in the rotated coordinate system respectively
Amount, similarly, id、iqRespectively net side electromotive force and virtual orthographic component distinguish d, q component in the rotated coordinate system.According to definition,
D axis component indicates that active component, q axis component indicate reactive component.
Step B: P is enableddq=edid+eqiq,x2=Pl.Wherein Pl=ilRlIt is actual loading power.Therefore
The third formula of the mathematical model of EMU net-side rectifier can be reduced under d-q rotating coordinate systemFor
Extended state observer is established, all disturbances and unknown quantity be considered as a new state variable.For motor-car networking
Side rectifier, actual loading power be not it is constant, so being considered as external disturbance.Therefore, to design extended state observer,It is represented by
And a linear extended state observer is then as follows
Wherein, z1And z2It is obtained by extended state observer, they are x respectively1And x2Estimated value.
All external disturbances are considered as a state variable by the present embodiment, so that comparing in the case where load sudden change
It cannot keep the constant problem of DC voltage in former sliding mode controller, party's rule can keep holding the perseverance of DC voltage
It is fixed.As shown in Figure 4.
Step C: in conjunction with control target, the output of control system is chosen, establishes and is based on voltage-controlled two sliding formworks of outer ring
Face obtains the reference value of current on line side reactive component, completes seeking for sliding-mode surface expression formula.It is specific as follows:
Select Udc、iqFor the output of control system.IfThenAccording to d- obtained in step A
The matrix form of EMU net-side rectifier state-space model under q rotating coordinate system, standard type can be controlled by releasing it
According to the two of EMU net-side rectifier control targets: first, guaranteeing that network pressure net stream keeps power factor close
In 1；Second, guaranteeing that DC-side Voltage Stabilization in the fluctuation range of permission, selects Udc、iqFor the output of control system.udc、
iq、Error amounteφIt is expressed as
Establish two sliding-mode surface s1、s2Respectively with two control target, that is, Udc、iqIt is corresponding
Wherein, α, α1、α2For gain amplifier, and replaced using βFor the feedback factor of sliding formwork control.
The DC voltage ginseng by the mathematical model of EMU net-side rectifier under d-q rotating coordinate system and being artificially arranged
Examine valueSubstituting into above formula can obtain, and herein due to the rated value 3600V of CRH5 type vehicle DC voltage, then control target and want direct current
Side voltage is fluctuated in a certain range near the 3600V.
By idSeparation, obtains
Wherein, ilIt is by the z in step B2/Udc=ilIt obtains, then it is available by above formulaExpression formula
C in formula,It is known constant, udc、iq、ilIt can be measured by corresponding measuring tool, β is to need to design
The parameter of person's design, SdWith SqIt is switch function, it willAs idReference value.
According to following power principle of invariance under d-q rotating coordinate system
udid+uqiq=Udcidc
According to control target, reactive current component iq=0, then
udid=Udcidc
Define ud=SdUdc, u can be obtained according to electric circuit knowledged=ed-Rid, obtain SdExpression formula
By the mathematical model of EMU net-side rectifier under d-q rotating coordinate system.And transformer biggish for capacity,
Resistance R is minimum, can ignore, and because in the ideal case,eq=0, then
Above formula is substituted into idReference valueExpression formula, obtain
Then
Wherein, ilIt is by the z in step B2/Udc=ilIt obtains, then it is available by above formulaExpression formula
Sliding-mode surface can be rewritten into following simple form
Step C: sliding formwork control tendency rate is chosen to above-mentioned two sliding-mode surface, two sliding-mode surfaces that step B is established substitute into
Obtained result is substituted into the state-space model of EMU net-side rectifier under d-q rotating coordinate system by sliding formwork control tendency rate,
Switch function is obtained, which is multiplied with DC voltage, obtains control voltage.
To acquired two sliding-mode surface s above1、s2Exponential approach rate is chosen, is obtained
ε1For constant, indicate that system mode point levels off to sliding-mode surface s1(x)=0 rate, rate and ε1Size at just
Than；-k1S is exponential approach item, represents the process by sliding-mode surface of system mode approach sliding-mode surface；For sliding-mode surface s1Derivation
Value；ε2、s2、-k2s2、Meaning rule is same as above.
The expression formula of sliding-mode surface is substituted into
Due toIt is all constant, soAbove formula is represented by
The state-space model for substituting into EMU net-side rectifier under d-q rotating coordinate system, obtains
By switch function Sd、SqIt shows
It obtains controlling voltage needed for pulse width modulation
D. control voltage obtained in step C is obtained into alpha-beta coordinate system component by coordinate transform, then passes through sinusoidal pulsewidth
Modulate output control pulse.
Finally build simulation model in Matlab/Simulink as shown in figure 5, gained voltage, current waveform such as Fig. 7 a,
Shown in 7b, institute's loading is nominal load, and equivalent resistance is R=25 Ω.Waveform shows that DC voltage overshoot is 0, does not have
Time to peak, regulating time 0.05s, voltage fluctuation 60V.It is obtained compared to performance indicator for common traditional proportional_integral control
Improve to preferable, alternating current only needs 3 cycles from stabilization is started to, and THD is reduced.
The sliding mode control algorithm is applied in Traction networks-EMU cascade simulation model, access Traction networks are successively increased
EMU quantity, under traditional transient state Direct Current Control, access EMU EMU and supply conductor voltage when reaching 8,
Apparent fluctuation occurs for electric current, and generates vehicle net low-frequency oscillation.It is being based on sliding formwork control high-speed rail low-frequency oscillation suppression method
Control under, for access EMU when meeting or exceeding 8, electrical quantity is basicly stable, as shown in Figure 7 c, low-frequency oscillation does not occur
Problem.
Claims (5)
1. a kind of high-speed rail low-frequency oscillation suppression method based on extended state observer sliding formwork control, which is characterized in that including with
Lower step:
Step A: defining current on line side amount of quadrature, constructs the state space mould of EMU net-side rectifier under d-q rotating coordinate system
Type；
Step B: load variation is considered as disturbance, extended state observer is established to above-mentioned state-space model, obtains load function
The estimated value of rate；
Step C: in conjunction with control target, choosing the output of control system, establishes and is based on voltage-controlled two sliding-mode surfaces of outer ring, knot
The bearing power estimated value that step B is obtained is closed, the reference value of current on line side reactive component is obtained, completes asking for sliding-mode surface expression formula
It takes；
Step D: sliding formwork control tendency rate is chosen to above-mentioned two sliding-mode surface, two sliding-mode surfaces that step C is established substitute into sliding formwork
Tendency rate is controlled, obtained result is substituted into the state-space model of EMU net-side rectifier under d-q rotating coordinate system, is obtained
The switch function is multiplied by switch function with DC voltage, obtains control voltage；
Step E: control voltage obtained in step D is obtained into alpha-beta coordinate system component by coordinate transform, then passes through sinusoidal pulsewidth
Modulate output control pulse.
2. the high-speed rail low-frequency oscillation suppression method according to claim 1 based on extended state observer sliding formwork control,
It is characterized in that, detailed process is as follows by the step A:
For single-phase two level topological structure, by ac-side current inIt is expressed as iα, exchange side electromotive force enIt is expressed as uα, building with
iα、uαOrthogonal virtual amount iβ、uβ, principle is converted according to the constant power that coordinate transform follows, is obtained
uαiα+uβiβ=Udcidc
In formula, UdcFor DC side burning voltage, idcFor DC side steady load electric current；
Define uα=SαUdc, uαIt is uabComponent on α axis, uβ=SβUdc, uβIt is uabComponent on β axis, uabFor rectifier bridge end
Mouth voltage, Sα、SβIt is the perfect switch function under alpha-beta coordinate system；Obtain idcExpression formula:
In formula, udcFor DC side load voltage；
In conjunction with the KVL equation of exchange side, of ac, virtual orthographic amount are indicated in same equation group, obtained
In formula, L and R are respectively the equivalent leakage inductance and ohmic leakage to secondary side of mobile transformer, and C is DC side Support Capacitor；eαI.e.
Exchange side electromotive force en, eβFor enObtained after rotating clockwise 90 degree and enOrthogonal voltage vector, ilFor load current；It carries out
Two-phase stationary coordinate system obtains EMU net-side rectifier under d-q rotating coordinate system to the coordinate transform of two-phase rotating coordinate system
Mathematical model:
In formula, ed、eqRespectively net side electromotive force and virtual orthographic the component component of d axis and q axis in the rotated coordinate system respectively；
id、iqRespectively net side electromotive force and virtual orthographic component distinguish d, q component in the rotated coordinate system；According to definition, d axis component
Indicate that active component, q axis component indicate reactive component, SdUdc、SqUdcIt is then uabCorresponding component, is expressed as state-space model
Matrix form:
Obtain the mathematical model of EMU net-side rectifier matrix form under two-phase rotating coordinate system.
3. the high-speed rail low-frequency oscillation suppression method according to claim 2 based on extended state observer sliding formwork control,
It is characterized in that, detailed process is as follows by the step B: enabling
Pdq=edid+eqiq,x2=Pl；
Wherein, PdqTo exchange side power；Pl=ilRlIt is actual loading power, RlFor equivalent load resistance；Easy, the x for expression1With
x2Respectively representWith PlState variable；The then mathematical model of EMU net-side rectifier under d-q rotating coordinate system
Third formulaSimplify are as follows:
To design extended state observer, above formula is indicated are as follows:
Wherein, f (t) indicates x2Derivation；
Then a linear extended state observer is expressed as follows:
Wherein, z1And z2Respectively x1And x2Estimated value, obtained by extended state observer, β1And β2To be tieed up hereby by Hull
The positive parameter that stable theory acquires.
4. the high-speed rail low-frequency oscillation suppression method according to claim 3 based on extended state observer sliding formwork control,
It is characterized in that, detailed process is as follows by the step C:
Select Udc、iqFor the output of control system, ifThenIt is revolved according to d-q obtained in step A
The matrix form for turning EMU net-side rectifier state-space model under coordinate system, standard type can be controlled by releasing it
Wherein, ω is power grid a-c cycle angular speed；udc、iq、Error amounteφIt respectively indicates are as follows:
Wherein,For the reference value of DC voltage；For iqReference value, φrefFor the reference value of φ；
Establish two sliding-mode surface s1、s2Respectively with Udc、iqIt is corresponding:
Wherein, α, α1、α2For gain amplifier, and replaced with βFeedback factor as sliding formwork control；
By error amounteφExpression substitute into above formula, obtain
By the mathematical model of EMU net-side rectifier under d-q rotating coordinate system and DC voltage reference valueIn substitution
Formula obtains
By idSeparation, obtains
In formula, C,It is known constant, udc、iq、ilIt is measured by corresponding measuring tool, β is preset parameter, SdWith Sq
It is switch function, it willAs idReference value；
According to following power principle of invariance under d-q rotating coordinate system
udid+uqiq=Udcidc
According to control target, reactive current component iq=0, then
udid=Udcidc
Define ud=SdUdc, due to ud=ed-Rid, above formula is expressed as
(ed-Rid)id=UdcSdid
Then SdExpression formula be
By the mathematical model of EMU net-side rectifier under d-q rotating coordinate system
Since the resistance R of the biggish transformer of capacity is minimum, therefore ignore, and because in the ideal case,eq=0,
Then
It obtains
Above formula is substituted into idReference valueExpression formula, obtain
Then
Wherein, ilIt is by the z in step B2/Udc=ilIt obtains, then it is available by above formulaExpression formula
Sliding-mode surface is rewritten are as follows:
5. the high-speed rail low-frequency oscillation suppression method according to claim 4 based on extended state observer sliding formwork control,
It is characterized in that, detailed process is as follows by the step D:
To upper described two sliding-mode surface s1、s2Exponential approach rate is chosen, is obtained
Wherein, ε1For constant, indicate that system mode point levels off to sliding-mode surface s1(x)=0 rate, rate and ε1Size at just
Than；-k1S is exponential approach item, represents the process by sliding-mode surface of system mode approach sliding-mode surface；For sliding-mode surface s1Derivation；
The expression formula of sliding-mode surface is substituted into
Due toIt is in the ideal situation constant, thereforeThen above formula is expressed as
The state-space model for substituting into EMU net-side rectifier under d-q rotating coordinate system, obtains
By switch function Sd、SqIt shows
It obtains controlling voltage needed for pulse width modulation
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| CN111049160A (en) * | 2019-12-24 | 2020-04-21 | 西南交通大学 | SMC-based performance improvement method for vehicle network system under multi-working-condition operation |
| CN111262460A (en) * | 2020-02-16 | 2020-06-09 | 河南理工大学 | Five-level rectifier sliding mode PIR control method based on coupling inductor |
| CN111293942A (en) * | 2020-03-07 | 2020-06-16 | 西南交通大学 | Performance improvement method for vehicle network system under multi-working-condition operation |
| CN113852102A (en) * | 2021-09-27 | 2021-12-28 | 湖南工业大学 | Traction network low-frequency oscillation suppression method based on exponential approximation law sliding mode control |
| CN114221557A (en) * | 2021-10-20 | 2022-03-22 | 西南交通大学 | Motor train unit rectifier control method and system based on sliding-mode observer |
| CN115224960A (en) * | 2022-07-26 | 2022-10-21 | 株洲中车时代电气股份有限公司 | Current transformer load power observation method, current loop feedforward control method and current loop feedforward control system |
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| CN113852102B (en) * | 2021-09-27 | 2024-02-02 | 湖南工业大学 | Traction network low-frequency oscillation suppression method based on exponential approach law sliding mode control |
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