CN108110761A - Fuzzy High-Order Sliding Mode Control Method of Active Power Filter based on Linearization Feedback - Google Patents

Fuzzy High-Order Sliding Mode Control Method of Active Power Filter based on Linearization Feedback Download PDF

Info

Publication number
CN108110761A
CN108110761A CN201810067129.2A CN201810067129A CN108110761A CN 108110761 A CN108110761 A CN 108110761A CN 201810067129 A CN201810067129 A CN 201810067129A CN 108110761 A CN108110761 A CN 108110761A
Authority
CN
China
Prior art keywords
msub
mrow
mover
centerdot
mtr
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN201810067129.2A
Other languages
Chinese (zh)
Other versions
CN108110761B (en
Inventor
李思扬
费峻涛
梁霄
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Changzhou Campus of Hohai University
Original Assignee
Changzhou Campus of Hohai University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Changzhou Campus of Hohai University filed Critical Changzhou Campus of Hohai University
Priority to CN201810067129.2A priority Critical patent/CN108110761B/en
Publication of CN108110761A publication Critical patent/CN108110761A/en
Application granted granted Critical
Publication of CN108110761B publication Critical patent/CN108110761B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/01—Arrangements for reducing harmonics or ripples
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/20—Active power filtering [APF]

Landscapes

  • Engineering & Computer Science (AREA)
  • Power Engineering (AREA)
  • Feedback Control In General (AREA)
  • Heterocyclic Carbon Compounds Containing A Hetero Ring Having Nitrogen And Oxygen As The Only Ring Hetero Atoms (AREA)

Abstract

The invention discloses a kind of fuzzy High-Order Sliding Mode Control Method of Active Power Filter based on Linearization Feedback, first, establish the mathematical model of Three-Phase Parallel Active Power Filter-APF, when designing controller, dynamic sliding surface is designed first, Linearization Feedback control design case sliding mode controller is recycled, and indeterminate is approached using fuzzy control on the basis of this controller, design adaptive law makes system keep stable state.The validity of the method by simulation results show.This method greatly strengthens the compensation performance and robust performance of system, achievees the purpose that fast and effective harmonic carcellation.

Description

Fuzzy High-Order Sliding Mode Control Method of Active Power Filter based on Linearization Feedback
Technical field
It is more particularly to a kind of high based on Linearization Feedback adaptive fuzzy the present invention relates to active power filtering technology is belonged to The Control Method of Active Power Filter of rank sliding formwork.
Background technology
It is a kind of the effective of inhibition harmonic pollution using harmonic current caused by power filter device absorption harmonic source Measure.Active Power Filter-APF has fast-response and high controllability, can not only compensate each harmonic, can also compensate for Reactive power inhibits flickering etc..Non-linear and uncertain due to electric system, adaptive and intelligent control has the modeling simple The advantages that list, control accuracy are high, non-linear adaptive is strong can apply harmonious for utility power quality control in active filter Ripple is administered, and has important research significance and market value.
The principle of parallel three phase Active Power Filter-APF is had extensively studied herein, on this basis founding mathematical models, profit With Three-Phase Parallel Active Power Filter-APF linear state equations, Linearization Feedback high_order sliding mode control method is added.Research Active Power Filter-APF model reference self-adapting control, it is proposed that Linearization Feedback High-Order Sliding Mode fuzzy adaptivecontroller algorithm, Harmonic compensation applied to Three-Phase Parallel Active Power Filter-APF controls.It is emulated by MATLAB, demonstrates increase linearisation The self-adaptation control method of feedback High-Order Sliding Mode fuzzy control is suitble to compensation circuit harmonic wave, improves power quality.
The content of the invention
The present invention carries to inhibit the influence of extraneous unknown disturbance and modeling error to active power filter system performance Go out a kind of Control Method of Active Power Filter that High-Order Sliding Mode is obscured based on Linearization Feedback, further improve system Shandong Stick.
The present invention solves its technical problem and is achieved through the following technical solutions：
Fuzzy High-Order Sliding Mode Control Method of Active Power Filter based on Linearization Feedback, includes the following steps：
(1) Active Power Filter-APF mathematical model is established；
(2) controller is designed：Dynamic sliding surface is designed first, recycles Linearization Feedback control design case sliding mode controller, And indeterminate is approached using fuzzy control on the basis of sliding mode controller, design adaptive law makes system keep stablizing shape State.
Further, the Active Power Filter-APF mathematical model of foundation is in the step (1)：
Wherein, x is instruction current,For the derivative of x, Device inputs u in order to control, and b is constant, LcFor inductance, RcFor resistance, vdcFor DC capacitor voltage, vkIt is filtered for three phase active electric power Ripple device terminal voltage, ikElectric current, d are compensated for three-phasekFor on off state function, dkIt is defined as follows：Then dkIt relies on It is the nonlinear terms of system in the on off operating mode of kth phase IGBT；ck、cmFor switch function, m, k are the constant more than 0.
Further, secondary derivation, active electric power filter are carried out to the Active Power Filter-APF mathematical model that step (1) obtains Ripple device mathematical model can be defined as：
For the derivative of f (x),For the derivative of u,ForDerivative；IfWherein f1(x) to be unknown Nonlinear function, then the Active Power Filter-APF mathematical model can be defined as：
Further, concretely comprising the following steps for high_order sliding mode control rule is designed in the step (2)：
Definition is used for the tracking error e of input：
E=x-xd
Wherein, x is instruction current, xdFor reference current,
Secondary derivation is carried out to tracking error：
Wherein,ForDerivative,For xdDerivative；
Define sliding-mode surface：
L=e+k2∫e
Wherein k2For constant, ∫ e are the integration to tracking error；
To sliding-mode surface derivation：
WhereinFor the derivative of e；
Define High-Order Sliding Mode face s：
Wherein,To be more than 0 constant,
To the derivation of High-Order Sliding Mode face：
WhereinForDerivative,For the derivative of s；
According to Linearization Feedback technology,
BecauseSo make g1(x)=b,
RX=ξ-ρ sgn (s)
Wherein ρ is constant more than 0, and ρ >=| D |, D is the upper bound constant of ρ, and sgn is sign function, ξ and RXBe in order to Simplify the intermediate variable of Process Design,
Because：
So：
Therefore, system design of control law is：
Further, restraining the fuzzy control law of design addition according to the high_order sliding mode control of design is：
Wherein,ForFuzzy close function,For f (xk) fuzzy close function,For ρ sgn (s) fuzzy close function, xkFor the scalar form of x, skFor the scalar form of High-Order Sliding Mode face s.
Further, in the step (2) concretely comprising the following steps for adaptive law design is carried out using Li Ya spectrum promise husband functions：
If Liapunov function：
Because
Wherein,WithRespectively V1And V2Derivative, sTFor the transposition of s, γ1And γ2To be more than 0 constant,For letter NumberFuzzy parameter,For functionFuzzy parameter,ForTransposition,ForTransposition,For Derivative,ForDerivative, δT(xk) and φT(hk) be respectivelyWithMembership function,ForEstimate,For functionIdeal value,For function h (sk) ideal value, ω is fuzzy The approximate error of system, f (xk) it is actual value；
Because：
So
Wherein, ωkFor the scalar form of ω,For ωkDerivative, γ1, γ2For constant,For dkDerivative, Jin Ershe The adaptive law of meter systems is：
Wherein, η is the constant more than 0；
By (2), (3), (4) are brought (1) into and are obtained：
WhenWhen,It sets up,
Wherein, | | sk| | it is skNorm, wherein, | ωmax| for the absolute value of the maximum of ω.
Beneficial effects of the present invention are：
Compared with prior art, the present invention has extensively studied the principle of parallel three phase Active Power Filter-APF, basic herein Upper founding mathematical models using Three-Phase Parallel Active Power Filter-APF linear state equations, add Linearization Feedback high-order Sliding-mode control.Study Active Power Filter-APF model reference self-adapting control, it is proposed that Linearization Feedback High-Order Sliding Mode mould Self-adaptive fuzzy control algolithm, the harmonic compensation applied to Three-Phase Parallel Active Power Filter-APF control.It is emulated by MATLAB, The self-adaptation control method for demonstrating increase Linearization Feedback High-Order Sliding Mode fuzzy sliding mode tracking control is suitble to compensation circuit harmonic wave, improves Power quality.
Description of the drawings
Fig. 1 is the structure diagram of the present invention；
Fig. 2 is Linearization Feedback High-Order Sliding Mode fuzzy adaptive controller block diagram of the present invention；
Fig. 3 is the oscillogram of source current；
Fig. 4 is the datagram of systematic error；
Fig. 5 is the oscillogram of DC voltage.
Specific embodiment
Below by specific embodiment, the invention will be further described, and following embodiment is descriptive, is not limit Qualitatively, it is impossible to which protection scope of the present invention is limited with this.
As shown in Figure 1, the fuzzy High-Order Sliding Mode Control Method of Active Power Filter based on Linearization Feedback, including following Step：
(1) Active Power Filter-APF model is established
The basic functional principle of Active Power Filter-APF is：The voltage and current of target compensation is detected, is transported through instruction current The command signal that circuit counting draws compensation electric current is calculated, the compensated current occuring circuit amplification of the signal draws compensation electric current, mends Electric current and the harmonic wave to be compensated in load current and idle grade current cancelings are repaid, finally obtains desired source current.
Equation below can obtain according to Circuit theory and Kirchhoff's theorem：
v1, v2, v3Respectively three phase active electric power filter terminal voltage, i1, i2, i3Respectively three-phase compensation electric current,Table Show electric current i1To the derivative of time,Represent electric current i2To the derivative of time,Represent electric current i3To the derivative of time, v1M, v2M,v3M,vMNRepresent that M points are to a, b, c, N point voltages in figure one respectively.M points are the cathode points of power supply, and a, b, c, N are in circuit Each node.LcFor inductance, RcFor resistance, ikElectric current is compensated for three-phase.
Assuming that exchange side supply voltage is stablized, can obtain
Wherein, m is constant more than 0, vmMFor v above-mentioned1M, v2M, v3M, vMN。
And define ckFor switch function, indicate the working condition of IGBT, be defined as follows：
Wherein, k=1,2,3.
Meanwhile vkM=ckvdc, wherein, vkMFor v above-mentioned1M, v2M, v3M, vMN。
So (1) can be rewritten as
vdcFor DC capacitor voltage.
We define dkFor on off state function, it is defined as follows：
Then dkIt is the nonlinear terms of system dependent on the on off operating mode of kth phase IGBT；cmFor switch function.
And have
So (4) can be rewritten as
So (7) can be rewritten into following form
WhereinX is instruction current,For the derivative of x, b For constant, device inputs u in order to control.
(2) Linearization Feedback high_order sliding mode control
Define tracking error e：
E=x-xd
Wherein, xdFor reference current.
First derivative is asked to tracking error e：
WhereinFor xdDerivative
Second dervative is asked to tracking error e：
WhereinForDerivative,ForDerivative
Secondary derivation is carried out to system model：
For the derivative of f (x),For the derivative of u,
IfWherein f1(x) it is unknown nonlinear function.
So master mould can be defined as：
Define sliding-mode surface：
L=e+k2∫e
Wherein k2For constant, ∫ e are the integration to error.
To sliding-mode surface derivation：
WhereinFor the derivative of e,
Define High-Order Sliding Mode face s：
Wherein,To be more than 0 constant.
To the s derivations of High-Order Sliding Mode face：
WhereinForDerivative,For the derivative of s.
According to Linearization Feedback technology：
RX=ξ-ρ sgn (s)
Wherein ρ is constant more than 0, and ρ >=| D |, D is the upper bound constant of ρ, and sgn is sign function,For the second order of x Derivative, ξ and RXIt is to simplify the intermediate variable of Process Design.
Because：
So：
Therefore, system design of control law is：
(3) Linearization Feedback High-Order Sliding Mode fuzzy control
Ri:If x1 isand....xn isthen y is Bi(i=1,2 ..., N)
Wherein,For xjThe membership function of (j=1,2 ..., n).
The then output of fuzzy system is：
Wherein δ=[δ1(x) δ2(x) ... δN(x)]TFor membership function,For degree of membership letter The value of each small component in number,For fuzzy parameter,For the component in fuzzy parameter.
For the fuzzy close of f (x, y), using the form for approaching f (1) and f (2) respectively, corresponding Design of Fuzzy Systems For：
Ambiguity in definition function is following form：
Wherein,ψ be fuzzy system output, ψ1And ψ2For the scalar in output.For mould The sum of the component in parameter is pasted, N is the sum of component,ForIn minimum value,ForThe sum of middle minimum value.
Define best approximation constant
Ω is in formulaSet.
Then：
ω is the approximate error of fuzzy system, δTFor the transposition of δ,ForTransposition.For given arbitrarily small constant ω (ω ＞ 0), as lower inequality is set up：|f(x,y)-ξT(x)θ*|≤ω makesAnd cause
Controller design is：
Wherein,ForFuzzy close function,For f (xk) fuzzy close function,For ρ sgn (s) fuzzy close function, xkFor the scalar form of x, skFor the scalar form of s.
Stability proves：
If Liapunov function：
Because
Wherein,WithRespectively V1And V2Derivative, sTFor the transposition of s, γ1And γ2To be more than 0 constant,For letter NumberFuzzy parameter,For functionFuzzy parameter,ForTransposition,ForTransposition,For Derivative,ForDerivative, δT(xk) and φT(hk) be respectivelyWithMembership function,For h (sk) estimateFor functionIdeal value,For function h (sk) ideal value, ω is fuzzy system The approximate error of system, f (xk) it is actual value.
So
Wherein, ωkFor the scalar form of ω,For ωkDerivative, γ1, γ2For constant,For dkDerivative.
The adaptive law of design system is：
By (19), (20), (21) are brought (18) into and are obtained：
Wherein, | | sk| | it is skNorm, whenWhen,It sets up.
Wherein, | ωmax| for the absolute value of the maximum of ω, must demonstrate,prove.
(4) simulating, verifying
In order to verify the feasibility of above-mentioned theory, emulation experiment has been carried out under Matlab.Simulation results show is set Count the effect of controller.
Simulation parameter is chosen as follows：
Fig. 3, Fig. 4 show respectively source current and systematic error.Have by a small margin during from figure three as can be seen that at 0.04 second Fluctuation, but sine wave can be restored at 0.05 second or so rapidly, and keep smooth waveform.Illustrate the power supply of system Electric current is relatively stablized, and can also keep sine wave when circuitous resistance changes within 0.1 second and 0.2 second, illustrates system robust Property is stronger.From figure four as can be seen that systematic error amplitude is smaller, without larger fluctuation, and at 0.05 second always just later Stable state is kept, can also preferably be tracked even if at the time of load changes and quickly recover to be in line.Illustrate be The tracking effect of system is preferable and tracking velocity is very fast.
Fig. 5 is expressed as the DC voltage figure of Linearization Feedback High-Order Sliding Mode fuzzy control.As seen from the figure, voltage can be It just ramps and stablizes at 1000 volts before 0.05 second, after 0.1 and 0.2 second adds in load, can also recover quickly And 1000 or so are always held at, effect is preferable.
Specific example the results show that the present invention design it is self-adaptive controlled based on Linearization Feedback High-Order Sliding Mode fuzzy control The Control Method of Active Power Filter of system can effectively overcome the influences such as non-linear factor, external disturbance, to improving active filter The stability and dynamic property of ripple device system, it is feasible to improve power transmission and distribution, power grid security guarantee and power quality.
The above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications also should It is considered as protection scope of the present invention.

Claims (6)

1. the fuzzy High-Order Sliding Mode Control Method of Active Power Filter based on Linearization Feedback, it is characterised in that：Including as follows Step：
(1) Active Power Filter-APF mathematical model is established；
(2) controller is designed：It designs dynamic sliding surface first, recycles Linearization Feedback control design case sliding mode controller, and Indeterminate is approached using fuzzy control on the basis of sliding mode controller, design adaptive law makes system keep stable state.
2. the fuzzy High-Order Sliding Mode Control Method of Active Power Filter based on Linearization Feedback as described in claim 1, It is characterized in that：The Active Power Filter-APF mathematical model of foundation is in the step (1)：
<mrow> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>b</mi> <mi>u</mi> <mo>+</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> </mrow>
Wherein, x is instruction current,For the derivative of x,U is Controller inputs, and b is constant, LcFor inductance, RcFor resistance, vdcFor DC capacitor voltage, vkFor three phase active electric power filter Terminal voltage, ikElectric current, d are compensated for three-phasekFor on off state function, dkIt is defined as follows：Then dkDependent on The on off operating mode of k phases IGBT is the nonlinear terms of system；ck、cmFor switch function, m, k are the constant more than 0.
3. the fuzzy High-Order Sliding Mode Control Method of Active Power Filter based on Linearization Feedback as claimed in claim 2, It is characterized in that：Secondary derivation, Active Power Filter-APF mathematics are carried out to the Active Power Filter-APF mathematical model that step (1) obtains Model can be defined as：
<mrow> <mover> <mi>x</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>=</mo> <mover> <mi>f</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>b</mi> <mover> <mi>u</mi> <mo>&amp;CenterDot;</mo> </mover> </mrow>
For the derivative of f (x),For the derivative of u,ForDerivative；IfWherein f1(x) to be unknown non-thread Property function, then the Active Power Filter-APF mathematical model can be defined as：
<mrow> <mover> <mi>x</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>=</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>b</mi> <mover> <mi>u</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>.</mo> </mrow>
4. the fuzzy High-Order Sliding Mode Control Method of Active Power Filter based on Linearization Feedback as claimed in claim 3, It is characterized in that：Design high_order sliding mode control rule concretely comprises the following steps in the step (2)：
Definition is used for the tracking error e of input：
E=x-xd
Wherein, x is instruction current, xdFor reference current,
Secondary derivation is carried out to tracking error：
<mrow> <mover> <mi>e</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>=</mo> <mover> <mi>x</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> </mrow>
Wherein,ForDerivative,For xdDerivative；
Define sliding-mode surface：
L=e+k2∫e
Wherein k2For constant, ∫ e are the integration to tracking error；
To sliding-mode surface derivation：
<mrow> <mover> <mi>l</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mi>e</mi> </mrow>
WhereinFor the derivative of e；
Define High-Order Sliding Mode face s：
<mrow> <mi>s</mi> <mo>=</mo> <mover> <mi>l</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <mo>&amp;part;</mo> <mi>l</mi> <mo>=</mo> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mi>e</mi> <mo>+</mo> <mo>&amp;part;</mo> <mi>e</mi> <mo>+</mo> <mo>&amp;part;</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>&amp;Integral;</mo> <mi>e</mi> </mrow>
Wherein,To be more than 0 constant,
To the derivation of High-Order Sliding Mode face：
<mrow> <mover> <mi>s</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mover> <mi>e</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <mo>&amp;part;</mo> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <mo>&amp;part;</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mi>e</mi> </mrow>
WhereinForDerivative,For the derivative of s；
According to Linearization Feedback technology,
BecauseSo make g1(x)=b,
<mrow> <mover> <mi>u</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mfrac> <mrow> <msub> <mi>R</mi> <mi>X</mi> </msub> <mo>-</mo> <msub> <mi>f</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>g</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <msub> <mi>R</mi> <mi>X</mi> </msub> <mo>-</mo> <mover> <mi>f</mi> <mo>&amp;CenterDot;</mo> </mover> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> </mrow> <mi>b</mi> </mfrac> </mrow>
<mrow> <mi>&amp;xi;</mi> <mo>=</mo> <mover> <mi>x</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>-</mo> <mover> <mi>s</mi> <mo>&amp;CenterDot;</mo> </mover> </mrow>
RX=ξ-ρ sgn (s)
Wherein ρ is constant more than 0, and ρ >=| D |, D is the upper bound constant of ρ, and sgn is sign function, ξ and RXIt is to simplify The intermediate variable of journey design,
Because：
<mrow> <mover> <mi>s</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mover> <mi>e</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <mo>&amp;part;</mo> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <mo>&amp;part;</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mi>e</mi> </mrow>
<mrow> <mover> <mi>e</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>=</mo> <mover> <mi>x</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> </mrow>
So：
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>&amp;xi;</mi> <mo>=</mo> <mover> <mi>x</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>-</mo> <mover> <mi>s</mi> <mo>&amp;CenterDot;</mo> </mover> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mover> <mi>x</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>-</mo> <mrow> <mo>(</mo> <mover> <mi>e</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <mo>&amp;part;</mo> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <mo>&amp;part;</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mi>e</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> <mo>-</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>-</mo> <mo>&amp;part;</mo> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>-</mo> <mo>&amp;part;</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mi>e</mi> </mrow> </mtd> </mtr> </mtable> </mfenced>
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>R</mi> <mi>X</mi> </msub> <mo>=</mo> <mi>&amp;xi;</mi> <mo>-</mo> <mi>&amp;rho;</mi> <mi>sgn</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> <mo>-</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>-</mo> <mo>&amp;part;</mo> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>-</mo> <mo>&amp;part;</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mi>e</mi> <mo>-</mo> <mi>&amp;rho;</mi> <mi>sgn</mi> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>
Therefore, system design of control law is：
<mrow> <mover> <mi>u</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <mi>b</mi> </mfrac> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> <mo>-</mo> <mo>(</mo> <mrow> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>+</mo> <mo>&amp;part;</mo> </mrow> <mo>)</mo> <mo>(</mo> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>+</mo> <mi>b</mi> <mi>u</mi> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> </mrow> <mo>)</mo> <mo>-</mo> <mo>&amp;part;</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mi>e</mi> <mo>-</mo> <mi>&amp;rho;</mi> <mi>sgn</mi> <mo>(</mo> <mi>s</mi> <mo>)</mo> <mo>-</mo> <mover> <mi>f</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>(</mo> <mi>x</mi> <mo>)</mo> <mo>)</mo> </mrow> <mo>.</mo> </mrow>
5. the fuzzy High-Order Sliding Mode Control Method of Active Power Filter based on Linearization Feedback as claimed in claim 4, It is characterized in that：Restraining the fuzzy control law of design addition according to the high_order sliding mode control of design is：
<mrow> <mover> <mi>u</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>=</mo> <mfrac> <mn>1</mn> <mi>b</mi> </mfrac> <mrow> <mo>(</mo> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> <mo>-</mo> <mo>(</mo> <mrow> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>+</mo> <mo>&amp;part;</mo> </mrow> <mo>)</mo> <mo>(</mo> <mrow> <mover> <mi>f</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>b</mi> <mi>u</mi> <mo>-</mo> <msub> <mover> <mi>x</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>d</mi> </msub> </mrow> <mo>)</mo> <mo>-</mo> <mo>&amp;part;</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mi>e</mi> <mo>-</mo> <mover> <mi>h</mi> <mo>^</mo> </mover> <mo>(</mo> <msub> <mi>s</mi> <mi>k</mi> </msub> <mo>)</mo> <mo>-</mo> <mover> <mover> <mi>f</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>^</mo> </mover> <mo>(</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>)</mo> <mo>)</mo> </mrow> </mrow>
Wherein,ForFuzzy close function,For f (xk) fuzzy close function,For ρ sgn's (s) Fuzzy close function, xkFor the scalar form of x, skFor the scalar form of High-Order Sliding Mode face s.
6. the fuzzy High-Order Sliding Mode Control Method of Active Power Filter based on Linearization Feedback as claimed in claim 5, It is characterized in that：In the step (2) concretely comprising the following steps for adaptive law design is carried out using Li Ya spectrum promise husband functions：
If Liapunov function：
<mrow> <msub> <mi>V</mi> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msup> <mi>s</mi> <mi>T</mi> </msup> <mo>&amp;CenterDot;</mo> <mi>s</mi> </mrow>
Because
Wherein,WithRespectivelyWithDerivative, sTFor the transposition of s, γ1And γ2To be more than 0 constant,For functionFuzzy parameter,For functionFuzzy parameter,ForTransposition,ForTransposition,For's Derivative,ForDerivative, δT(sk) and φT(hk) be respectivelyWithMembership function,For h (sk) Estimate,For function f (xk) ideal value,For function h (sk) ideal value, ω is fuzzy system Approximate error, f (xk) it is actual value；
Because：
<mfenced open='' close=''> <mtable> <mtr> <mtd> <mover> <mi>s</mi> <mo>.</mo> </mover> <mo>=</mo> <mover> <mi>e</mi> <mrow> <mo>.</mo> <mo>.</mo> </mrow> </mover> <mo>+</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mover> <mi>e</mi> <mo>.</mo> </mover> <mo>+</mo> <mo>&amp;PartialD;</mo> <mover> <mi>e</mi> <mo>&amp;CenterDot;</mo> </mover> <mo>+</mo> <mo>&amp;PartialD;</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mi>e</mi> </mtd> </mtr> <mtr> <mtd> <mo>=</mo> <mover> <mi>f</mi> <mo>.</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mover> <mover> <mi>f</mi> <mo>.</mo> </mover> <mo>^</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>+</mo> <mo>&amp;PartialD;</mo> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>f</mi> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mover> <mi>f</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>x</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>+</mo> <mo>&amp;PartialD;</mo> <mo>)</mo> </mrow> <msub> <mi>d</mi> <mi>k</mi> </msub> <mo>-</mo> <mover> <mi>h</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <msub> <mi>s</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mover> <mi>d</mi> <mo>.</mo> </mover> <mi>k</mi> </msub> </mtd> </mtr> </mtable> </mfenced>
So
Wherein, ωkFor the scalar form of ω,For ωkDerivative, γ1, γ2For constant,For dkDerivative, and then design department The adaptive law of system is：
<mrow> <mover> <mi>h</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>s</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mi>&amp;eta;</mi> <mo>+</mo> <mi>&amp;rho;</mi> <mo>)</mo> </mrow> <mi>sgn</mi> <mrow> <mo>(</mo> <mi>&amp;sigma;</mi> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
Wherein, η is the constant more than 0；
By (2), (3), (4) are brought (1) into and are obtained：
<mfenced open = "" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mover> <mi>V</mi> <mo>&amp;CenterDot;</mo> </mover> <mn>2</mn> </msub> <mo>=</mo> <msup> <mi>s</mi> <mi>T</mi> </msup> <mo>&amp;CenterDot;</mo> <mrow> <mo>(</mo> <msub> <mover> <mi>&amp;omega;</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>k</mi> </msub> <mo>+</mo> <mo>(</mo> <mrow> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>+</mo> <mo>&amp;part;</mo> </mrow> <mo>)</mo> <msub> <mi>&amp;omega;</mi> <mi>k</mi> </msub> <mo>-</mo> <mi>h</mi> <mo>(</mo> <mrow> <msub> <mi>s</mi> <mi>k</mi> </msub> <mo>|</mo> <msubsup> <mi>&amp;theta;</mi> <mrow> <mi>h</mi> <mi>k</mi> </mrow> <mo>*</mo> </msubsup> </mrow> <mo>)</mo> <mo>+</mo> <mo>(</mo> <mrow> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>+</mo> <mo>&amp;part;</mo> </mrow> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> <mo>+</mo> <msub> <mover> <mi>d</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>k</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <msub> <mi>s</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <msub> <mover> <mi>&amp;omega;</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>k</mi> </msub> <mo>+</mo> <mo>(</mo> <mrow> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>+</mo> <mo>&amp;part;</mo> </mrow> <mo>)</mo> <msub> <mi>&amp;omega;</mi> <mi>k</mi> </msub> <mo>-</mo> <mo>(</mo> <mrow> <mi>&amp;rho;</mi> <mo>+</mo> <mi>&amp;eta;</mi> </mrow> <mo>)</mo> <mo>&amp;CenterDot;</mo> <mi>sgn</mi> <mo>(</mo> <msub> <mi>s</mi> <mi>k</mi> </msub> <mo>)</mo> <mo>+</mo> <mo>(</mo> <mrow> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>+</mo> <mo>&amp;part;</mo> </mrow> <mo>)</mo> <mo>&amp;CenterDot;</mo> <msub> <mi>d</mi> <mi>k</mi> </msub> <mo>+</mo> <msub> <mover> <mi>d</mi> <mo>&amp;CenterDot;</mo> </mover> <mi>k</mi> </msub> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;le;</mo> <msub> <mi>s</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>+</mo> <mo>&amp;part;</mo> <mo>)</mo> </mrow> <msub> <mi>&amp;omega;</mi> <mi>k</mi> </msub> <mo>-</mo> <mi>&amp;eta;</mi> <mo>|</mo> <mo>|</mo> <msub> <mi>s</mi> <mi>k</mi> </msub> <mo>|</mo> <mo>|</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>&amp;le;</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>s</mi> <mi>k</mi> </msub> <mo>|</mo> <mo>|</mo> <mrow> <mo>(</mo> <mo>(</mo> <mrow> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>+</mo> <mo>&amp;part;</mo> </mrow> <mo>)</mo> <msub> <mi>&amp;omega;</mi> <mi>k</mi> </msub> <mo>-</mo> <mi>&amp;eta;</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mfenced>
WhenWhen,It sets up,
Wherein, | | sk| | it is skNorm, wherein, | ωmax| for the absolute value of the maximum of ω.
CN201810067129.2A 2018-01-24 2018-01-24 Fuzzy high-order sliding mode active power filter control method based on linearization feedback Active CN108110761B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201810067129.2A CN108110761B (en) 2018-01-24 2018-01-24 Fuzzy high-order sliding mode active power filter control method based on linearization feedback

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201810067129.2A CN108110761B (en) 2018-01-24 2018-01-24 Fuzzy high-order sliding mode active power filter control method based on linearization feedback

Publications (2)

Publication Number Publication Date
CN108110761A true CN108110761A (en) 2018-06-01
CN108110761B CN108110761B (en) 2021-06-01

Family

ID=62220643

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201810067129.2A Active CN108110761B (en) 2018-01-24 2018-01-24 Fuzzy high-order sliding mode active power filter control method based on linearization feedback

Country Status (1)

Country Link
CN (1) CN108110761B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107834560A (en) * 2017-11-16 2018-03-23 河海大学常州校区 Control Method of Active Power Filter based on integer rank High-Order Sliding Mode fuzzy control

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103441499A (en) * 2013-07-24 2013-12-11 河海大学常州校区 Linearization feedback neural sliding-mode control method for three-phase parallel-connection active power filter
CN104917436A (en) * 2015-07-08 2015-09-16 沈阳工业大学 Adaptive second-order terminal sliding-mode control system and method of permanent magnet linear synchronous motor
CN106019938A (en) * 2016-06-03 2016-10-12 长春工业大学 ACC system dispersion second-order slip form control system based on data driving and method thereof
CN106374488A (en) * 2016-09-13 2017-02-01 河海大学常州校区 Fractional order terminal sliding mode-based AFNN control method of active power filter
CN107147120A (en) * 2017-06-29 2017-09-08 河海大学常州校区 Active Power Filter-APF RBF amphineura network adaptive sliding-mode observer methods

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103441499A (en) * 2013-07-24 2013-12-11 河海大学常州校区 Linearization feedback neural sliding-mode control method for three-phase parallel-connection active power filter
CN104917436A (en) * 2015-07-08 2015-09-16 沈阳工业大学 Adaptive second-order terminal sliding-mode control system and method of permanent magnet linear synchronous motor
CN106019938A (en) * 2016-06-03 2016-10-12 长春工业大学 ACC system dispersion second-order slip form control system based on data driving and method thereof
CN106374488A (en) * 2016-09-13 2017-02-01 河海大学常州校区 Fractional order terminal sliding mode-based AFNN control method of active power filter
CN107147120A (en) * 2017-06-29 2017-09-08 河海大学常州校区 Active Power Filter-APF RBF amphineura network adaptive sliding-mode observer methods

Non-Patent Citations (6)

* Cited by examiner, † Cited by third party
Title
JUNTAO FEI: "ADAPTIVE FUZZY BACKSTEPPING CONTROL OF THREE-PHASE ACTIVE POWER FILTER", 《2014 11TH IEEE INTERNATIONAL CONFERENCE ON CONTROL&AUTOMATION》 *
RUI LING: "Second-Order Sliding-Mode Controlled Three-Level Buck DC–DC Converters", 《IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS》 *
TOUFIC AL CHAER: "Linear Feedback Control of a Parallel Active Harmonic Conditioner in Power Systems", 《IEEE TRANSACTIONS ON POWER ELECTRONICS》 *
XIAO LIANG, SIYANG LI, AND JUNTAO FEI: "Adaptive Fuzzy Global Fast Terminal Sliding Mode Control for Mic", 《IEEE ACCESS》 *
ZHONG TANG: "Research of APF Based On Fuzzy-Sliding Mode Variable Structure Control Strategy", 《CICED 2010 PROCEEDINGS》 *
刘金琨: "滑模变结构控制理论及其算法研究与进展", 《控制理论与应用》 *

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107834560A (en) * 2017-11-16 2018-03-23 河海大学常州校区 Control Method of Active Power Filter based on integer rank High-Order Sliding Mode fuzzy control
CN107834560B (en) * 2017-11-16 2020-09-29 河海大学常州校区 Active power filter control method based on integer order high-order sliding mode fuzzy control

Also Published As

Publication number Publication date
CN108110761B (en) 2021-06-01

Similar Documents

Publication Publication Date Title
Fu et al. Control of single-phase grid-connected converters with LCL filters using recurrent neural network and conventional control methods
CN104730921B (en) Method for controlling fuzzy neural network of active power filter based on terminal sliding mode
CN106374488B (en) Active Power Filter-APF AFNN control method based on fractional order terminal sliding mode
CN105610162B (en) A kind of Active Power Filter-APF adaptive fuzzy sliding mode RBF neural control method
CN106707763A (en) Fuzzy-neural global rapid terminal sliding-mode control method of photovoltaic grid-connected inverter
Fang et al. Adaptive backstepping fuzzy neural controller based on fuzzy sliding mode of active power filter
CN105978373A (en) Three-phase inverter backstepping sliding mode control method and system for achieving stabilization of micro-grid
CN107069723B (en) Active Power Filter-APF fractional order PIλAnd active disturbance rejection mixing control method
CN103336866A (en) Processing method for negative resistance containing branch in electromagnetic transient simulation
CN104009477B (en) The robust Model reference adaptive current control method of active power filter system
Wang et al. Modeling and simulation of full-bridge series resonant converter based on generalized state space averaging
CN107611971A (en) For the net side inverter resonance full-order sliding mode control method of Voltage Harmonic distortion operating mode
CN103441499B (en) The Linearization Feedback neural network sliding mode control method of Three Phase Shunt Active Filter
CN103441502A (en) Parallel single-phase H-bridge cascade type active electric power filter control device and method thereof
Shen et al. Novel design of adaptive neural network controller for a class of non-affine nonlinear systems
CN106374490A (en) Active power filter control method based on dynamic surface fuzzy sliding mode control
CN108110761A (en) Fuzzy High-Order Sliding Mode Control Method of Active Power Filter based on Linearization Feedback
CN104467741B (en) Active filter Intelligent current tracking and controlling method based on T S obscurity model buildings
CN106292283A (en) A kind of adaptive fuzzy integral sliding mode control method of photovoltaic combining inverter
CN111262466B (en) Modeling control method of modular multilevel converter based on singular perturbation
Fei et al. Adaptive fuzzy control with supervisory compensator for three-phase active power filter
CN110138241B (en) Single-phase voltage source stability analysis method based on Jacobi theory
CN115940675A (en) Model-free prediction current control method and system for rectifier
CN107834560A (en) Control Method of Active Power Filter based on integer rank High-Order Sliding Mode fuzzy control
Dai et al. Discrete modelling and state‐mutation analysis for sliding mode controlled non‐isolated grid‐connected inverter with H6‐type

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant