CN104901529B - Suppress the electromagnetic interference chaotic control method of converters - Google Patents
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Abstract
The present invention proposes a kind of electromagnetic interference chaotic control method for suppressing converters, comprises the following steps：According to the multiple scrolls many wing state of chaotic system equations generation many wing chaos attractors of multiple scrolls, and obtain according to chaos attractor the state variable of many wing chaos systems of multiple scrolls；State variable to many wing chaos systems of multiple scrolls is sampled, to obtain chaos sequence；The chaotic carrier signal of frequency chaos change is obtained according to chaos sequence, wherein, the frequency of chaotic carrier signal is represented by equation below：fc=fr+xi·Δf,xi∈ (1,1), i=1,2 ..., wherein, fcFor the frequency of chaotic carrier signal, frOn the basis of carrier frequency, Δ f be peak frequency undulating value, xiFor chaos sequence；According to chaos pulse-width signal and chaotic carrier signal generation Chaotic-Pulse width modulated pwm control signal, to control converters.The method of the present invention being capable of the more efficiently electromagnetic interference for suppressing converters, the Electro Magnetic Compatibility of raising converters.
Description
Technical field
The present invention relates to electric and electronic technical field, more particularly to a kind of electromagnetic interference for suppressing converters is mixed
Ignorant control method.
Background technology
With the fast development of Power Electronic Technique, converters are had been widely used in production and living.But
It is that electromagnetic interference problem in converters caused by switching device high frequency mo has been similarly obtained extensive concern.
CPWM (Chaotic Pulse Width Modulation, chaos pulsewidth modulation) technology is a kind of based on chaology proposition
New modulation techniques for suppressing converters electromagnetic interference, can effectively reduce converters switch frequency
Rate and its electromagnetic interference (Electromagnetic Interference, the EMI) peak value located for several times again.
At present, existing CPWM is mainly based upon discrete type chaos system, such as logistic maps, tent maps,
Chebyshev mappings etc..But, existing CPWM is limited to converters EMI inhibition, can bring very high
Ambient noise, a large amount of subharmonic are produced at non-switch frequency and its frequency multiplication, low-frequency noise can be also produced, these are to suppress
It is undesirable during converters EMI.
The content of the invention
It is contemplated that at least solving one of technical problem in above-mentioned correlation technique to a certain extent.
Therefore, it is an object of the invention to propose a kind of electromagnetic interference chaos controlling side for suppressing converters
Method, this method being capable of the more efficiently electromagnetic interference for suppressing converters, the electromagnetism of raising converters
Compatibility.
To achieve these goals, embodiments of the invention propose a kind of electromagnetic interference for suppressing converters
Chaotic control method, comprises the following steps：Mixed according to many wings of many wing state of chaotic system equation generation multiple scrolls of multiple scrolls
Ignorant attractor, and obtain according to the chaos attractor state variable of many wing chaos systems of the multiple scrolls；To described many
The state variable of many wing chaos systems of scrollwork is sampled, to obtain chaos sequence；Frequency is obtained according to the chaos sequence
The chaotic carrier signal of chaos change, wherein, the frequency of the chaotic carrier signal is represented by equation below：fc=fr+xi·
Δf,xi∈ (- 1,1), i=1,2 ..., wherein, fcFor the frequency of chaotic carrier signal, frOn the basis of carrier frequency, Δ f is most
Big frequency fluctuation value, xiFor the chaos sequence；According to chaos pulse-width signal and the chaotic carrier signal generation chaos
Pulse width modulation (PWM) control signal, to control the converters.
The electromagnetic interference chaotic control method of suppression converters according to embodiments of the present invention, by many whirlpools
The state variable sampling for rolling up many wing chaos systems obtains chaos sequence, and the chaos of frequency chaos change is generated based on chaos sequence
Carrier signal, then modulation wave signal is compared with chaotic carrier signal, Chaotic PWM control signal is produced, to control electric power electricity
Sub- converter switches device, realizes the CPWM technologies based on many wing chaos systems of multiple scrolls.The method of the present invention is opened in reduction
Close frequency and its again for several times EMI peak value while, can reduce in non-switch frequency and its again for several times, particularly low-frequency range is introduced
Subharmonic so that further improve converters Electro Magnetic Compatibility.In addition, this method is controlled suitable for any PWM
In the converters of system, it is easy to accomplish, do not increase hardware cost, and with very strong application.
In addition, the electromagnetic interference chaotic control method according to the above embodiment of the present invention for suppressing converters,
There can also be technical characteristic additional as follows：
In some instances, multi-scroll chaotic system is improves Chua circuits, and many wing chaos systems are two directional spredings
The many wing chaos systems of plane net trellis.
In some instances, the dimensionless state equation of the improvement Chua circuits is：
Wherein, α=10, β=16, ξ=0.3~1 is control parameter, f1(x, ξ) and f2(y) it is ladder wave train, wherein
f1ξ in (x, ξ) is control parameter.
In some instances, when producing even number scrollwork attractor, the f1(x, ξ) and f2(y) specific configuration form
For：
Wherein, A1=A2>0, N >=0, M >=0.
In some instances, the improvement Chua circuits can produce the quantity of scrollwork attractor for (2N+2) × (2M+2) ×
(2N+2), and multi-direction grid scrollwork distribution is presented.
In some instances, when producing odd number scrollwork attractor, the f1(x, ξ) and f2(y) specific configuration form
For：
Wherein, A1=A2>0, N >=1, M >=1.
In some instances, the improvement Chua circuits can produce the quantity of scrollwork attractor for (2N+1) × (2M+1) ×
(2N+1), and multi-direction grid scrollwork distribution is presented.
In some instances, the dimensionless state equation of many wing chaos systems of two directional spredings plane net trellis
For：
Wherein,
Wherein, F0=k, Fi=2A/k, Ei=0.5 (1+i) A/k, A, k, ki, G is coefficient.
In some instances, the producible wing chaos of many wing chaos systems of two directional spredings plane net trellis is inhaled
The quantity of introduction is (2N+2) × (2M+2).
The additional aspect and advantage of the present invention will be set forth in part in the description, and will partly become from the following description
Obtain substantially, or recognized by the practice of the present invention.
Brief description of the drawings
The above-mentioned and/or additional aspect and advantage of the present invention will become from description of the accompanying drawings below to embodiment is combined
Substantially and be readily appreciated that, wherein：
Fig. 1 is the electromagnetic interference chaotic control method of suppression converters according to an embodiment of the invention
Flow chart；
Fig. 2 is that the chaos according to an embodiment of the invention using 2 × 2 × 2 scrollworks for improving Chua circuit evolvings is inhaled
Introduction phasor, respectively x/y plane, yz planes and xz planes；
Fig. 3 is many wing chaos systems generations of two directional spreding plane net trellis of utilization according to an embodiment of the invention
2 × 2 wings chaos attractor phasor；
Fig. 4 is the control principle drawing of PWM controls according to an embodiment of the invention；
Fig. 5 is the topological diagram and its EMI interference path of the Boost according to a specific embodiment of the invention
Figure；And
Fig. 6 is the PWM of the conventional fixed-frequency according to a specific embodiment of the invention, based on scattered date sequence
Boost switching device drain-source voltage under the CPWM and CPWM based on 2 × 2 scroll chaotic systems, this 3 kinds of control modes
VdcSpectrum results comparison diagram.
Embodiment
Embodiments of the invention are described below in detail, the example of the embodiment is shown in the drawings, wherein from beginning to end
Same or similar label represents same or similar element or the element with same or like function.Below with reference to attached
The embodiment of figure description is exemplary, is only used for explaining the present invention, and is not considered as limiting the invention.
The electromagnetic interference chaos control of suppression converters according to embodiments of the present invention is described below in conjunction with accompanying drawing
Method processed.
Fig. 1 is the electromagnetic interference chaotic control method of the suppression converters according to one embodiment of the invention
Flow chart.As shown in figure 1, this method comprises the following steps：
Step S101, many wing chaos attractors of multiple scrolls are generated according to many wing state of chaotic system equations of multiple scrolls,
And the state variable of many wing chaos systems of multiple scrolls is obtained according to chaos attractor.
Wherein, in this step, multi-scroll chaotic system is, for example, to improve Chua circuits, and many wing chaos systems are, for example,
Two directional spreding plane net trellis many wings (Shimizu-Morioka, S-M) chaos systems.
More specifically, the dimensionless state equation of improvement Chua circuits is, for example,：
Wherein, α=10, β=16, ξ=0.3~1 is control parameter, f1(x, ξ) and f2(y) it is ladder wave train, wherein
f1ξ in (x, ξ) is control parameter.
Further, in above formula, if produce even number scrollwork attractor, f1(x, ξ) and f2(y) specific structure
Appearance formula is：
Wherein, A1=A2>0, N >=0, M >=0.
Further, using the formula, the quantity that scrollwork attractor can be produced in Chua circuits are improved is (2N+2) × (2M
+ 2) × (2N+2), and multi-direction grid scrollwork distribution is presented.
On the other hand, if produce odd number scrollwork attractor, the f1(x, ξ) and f2(y) specific configuration form
For：
Wherein, A1=A2>0, N >=1, M >=1.Further, using the formula, scrollwork can be produced in Chua circuits are improved and inhaled
The quantity of introduction is (2N+1) × (2M+1) × (2N+1), and multi-direction grid scrollwork distribution is presented.
As specific example, work as N=0 as shown in Fig. 2 illustrating, during M=0, using above-mentioned formula generate 2 × 2 ×
The chaos attractor phasor of 2 scrollworks, Fig. 2 (a), Fig. 2 (b) and Fig. 2 (c) correspond respectively to x/y plane, yz planes and xz planes
As a result.
Further, the dimensionless state equation of the two many wing S-M chaos systems of directional spreding plane net trellis is：
Wherein,
Wherein, in above formula, F0=k, Fi=2A/k, Ei=0.5 (1+i) A/k, A, k, ki, G is coefficient.
Further, it can be produced using the state equation of the above-mentioned many wing S-M chaos systems of two directional spredings plane net trellis
The quantity of raw wing chaos attractor is (2N+2) × (2M+2).As specific example, work as N=as shown in figure 3, illustrating
When 0, M=0, the chaos attractor phasor of 2 × 2 wings generated using above-mentioned formula.
Step S102, the state variable to many wing chaos systems of multiple scrolls is sampled, to obtain chaos sequence.In tool
In body example, in this step, for example, sample frequency is set to fs.It should be noted that the difference of sample frequency, chaos sequence
Distribution it is different, applied in CPWM, the inhibition to converters electromagnetic interference also can be different.
Step S103, the chaotic carrier signal of frequency chaos change is obtained according to chaos sequence, wherein, chaotic carrier signal
Frequency represented by equation below：
fc=fr+xi·Δf,xi∈ (- 1,1), i=1,2 ...,
Wherein, fcFor the frequency of chaotic carrier signal, frOn the basis of carrier frequency, Δ f be peak frequency undulating value, xiFor
Chaos sequence.In this example, x hereiniA scale operation is have passed through, makes xi∈(-1,1)。
Step S104, is controlled according to chaos pulse-width signal and chaotic carrier signal generation Chaotic-Pulse width modulated PWM
Signal processed, to control converters.Specifically, chaos pulse-width signal is compared with chaotic carrier signal
Compared with to produce Chaotic PWM control signal, according to Chaotic PWM control signal control converters switching device, with this reality
CPWM technologies now based on many wing chaos systems of multiple scrolls.
As specific example, the principle of pwm control signal generation is as shown in Figure 4.Mixed using modulation wave signal and frequency
The carrier signal of ignorant change compares, and obtains the driving letter of Chaotic PWM control signal, i.e. converters switching device
Number.Thus chaos controlling signal control converters work in chaos state, you can realize and be based on many wings of multiple scrolls
The CPWM technologies of chaos system.
Method for the ease of being better understood from the embodiment of the present invention, below with widely used in converters
Come the electromagnetic interference chaos controlling side of the suppression converters of the simulating, verifying embodiment of the present invention exemplified by Boost
Validity of the method for suppression converters EMI.
Specifically, the schematic diagram of Boost is as shown in Figure 5.Can according to the Boost EMI principles produced
Know, the drain-source voltage V of switching devicedcFor electromagnetic interference source, then to VdcCarry out spectrum analysis, you can obtain Boost
Electromagnetic interference situation.
First, choose exemplified by 2 × 2 scroll chaotic systems, using formula (1), work as N=0, during M=0, generate 2 × 2 × 2 whirlpools
The chaos attractor of volume, carries out sampling to state variable x and obtains chaos sequence, sample frequency is 1000Hz.By this chaos sequence
It is added in the CPWM of Boost controls, and to its VdcFrequency spectrum is measured.Wherein, Boost emulation platform is joined
Number is as shown in table 1 below：
Table 1
In this example, for example, building emulation platform using Matlab/Simulink softwares, and realize based on multiple scrolls
The suppression converters electromagnetic interference chaotic control method of many wing chaos systems.To contrast the base of the embodiment of the present invention
Where the advantage of the suppression converters electromagnetic interference chaotic control method of many wing chaos systems of multiple scrolls, imitative
Realized respectively in very conventional fixed-frequency PWM, the CPWM based on scattered date sequence (logistic chaotic maps) and
Based on the CPWM of 2 × 2 scroll chaotic systems, more than under 3 kinds of control modes, switching device drain-source voltage V is measured respectivelydcFrequency
Spectrum, obtains spectrum results comparing result as shown in Figure 6.
As shown in fig. 6, lines 1 are the Boost V under PWM (T-PWM) controls of conventional fixed-frequencydcSpectrogram,
Lines 2 are the Boost V under CPWM (TCF-PWM) controls based on scattered date sequence (logistic chaotic maps)dc
Spectrogram, lines 3 are the Boost V under CPWM (SCF-PWM) controls based on 2 × 2 scroll chaotic systemsdcSpectrogram.
The Boost under T-PWM controls is contrasted, TCF-PWM and SCF-PWM can reduce switching frequency and its again EMI for several times
Peak value.But under TCF-PWM controls, reducing switching frequency and its while EMI peak value for several times again, can in switching frequency and
Its times produces a wide range of, subharmonic of amplitude around for several times, particularly in low-frequency range, this will be unfavorable for Boost EMI
Suppression.And the SCF-PWM of the embodiment of the present invention can solve this problem to a certain extent, opened in significantly more efficient reduction
Close frequency and its again for several times EMI peak value while, only in switching frequency and its again for several times near a small range have harmonic amplitude
Increase, it is to avoid the generation of low-frequency noise.From being analyzed above, the controls of the CPWM based on 2 × 2 scroll chaotic systems invented
Method processed has more preferable effect in terms of converters EMI is suppressed.
Further, not only 2 × 2 scroll chaotic systems can suppress converters applied to CPWM controls
More preferable effect is obtained in terms of EMI, 2 × 2 scroll chaotic systems can also be expanded to many wing chaos systems of other multiple scrolls,
Using different systems, the influence for EMI spectrum distributions is also different, accordingly to EMI inhibitions also by difference.
To sum up, the electromagnetic interference chaotic control method of suppression converters according to embodiments of the present invention, passes through
State variable sampling to many wing chaos systems of multiple scrolls obtains chaos sequence, and frequency chaos change is generated based on chaos sequence
Chaotic carrier signal, then modulation wave signal is compared with chaotic carrier signal, produces Chaotic PWM control signal, to control
Converters switching device, realizes the CPWM technologies based on many wing chaos systems of multiple scrolls.The method of the present invention exists
Reduce switching frequency and its again for several times EMI peak value while, can reduce in non-switch frequency and its again for several times, particularly low frequency
The subharmonic that section is introduced, so as to further improve the Electro Magnetic Compatibility of converters.In addition, this method is suitable for any
In the converters of PWM controls, it is easy to accomplish, do not increase hardware cost, and with very strong application.
In the description of the invention, it is to be understood that term " " center ", " longitudinal direction ", " transverse direction ", " length ", " width ",
" thickness ", " on ", " under ", "front", "rear", "left", "right", " vertical ", " level ", " top ", " bottom " " interior ", " outer ", " up time
The orientation or position relationship of the instruction such as pin ", " counterclockwise ", " axial direction ", " radial direction ", " circumference " be based on orientation shown in the drawings or
Position relationship, is for only for ease of the description present invention and simplifies description, rather than indicate or imply that the device or element of meaning must
There must be specific orientation, with specific azimuth configuration and operation, therefore be not considered as limiting the invention.
In addition, term " first ", " second " are only used for describing purpose, and it is not intended that indicating or implying relative importance
Or the implicit quantity for indicating indicated technical characteristic.Thus, define " first ", the feature of " second " can express or
Implicitly include at least one this feature.In the description of the invention, " multiple " are meant that at least two, such as two, three
It is individual etc., unless otherwise specifically defined.
In the present invention, unless otherwise clearly defined and limited, term " installation ", " connected ", " connection ", " fixation " etc.
Term should be interpreted broadly, for example, it may be fixedly connected or be detachably connected, or integrally；Can be that machinery connects
Connect or electrically connect；Can be joined directly together, can also be indirectly connected to by intermediary, can be in two elements
The connection in portion or the interaction relationship of two elements, unless otherwise clear and definite restriction.For one of ordinary skill in the art
For, the concrete meaning of above-mentioned term in the present invention can be understood as the case may be.
In the present invention, unless otherwise clearly defined and limited, fisrt feature can be with "above" or "below" second feature
It is that the first and second features are directly contacted, or the first and second features pass through intermediary mediate contact.Moreover, fisrt feature exists
Second feature " on ", " top " and " above " but fisrt feature are directly over second feature or oblique upper, or be merely representative of
Fisrt feature level height is higher than second feature.Fisrt feature second feature " under ", " lower section " and " below " can be
One feature is immediately below second feature or obliquely downward, or is merely representative of fisrt feature level height less than second feature.
In the description of this specification, reference term " one embodiment ", " some embodiments ", " example ", " specifically show
The description of example " or " some examples " etc. means to combine specific features, structure, material or the spy that the embodiment or example are described
Point is contained at least one embodiment of the present invention or example.In this manual, to the schematic representation of above-mentioned term not
Identical embodiment or example must be directed to.Moreover, specific features, structure, material or the feature of description can be with office
Combined in an appropriate manner in one or more embodiments or example.In addition, in the case of not conflicting, the skill of this area
Art personnel can be tied the not be the same as Example or the feature of example and non-be the same as Example or example described in this specification
Close and combine.
Although embodiments of the invention have been shown and described above, it is to be understood that above-described embodiment is example
Property, it is impossible to limitation of the present invention is interpreted as, one of ordinary skill in the art within the scope of the invention can be to above-mentioned
Embodiment is changed, changed, replacing and modification.
Claims (8)
1. a kind of electromagnetic interference chaotic control method for suppressing converters, it is characterised in that for realizing that reduction is opened
Frequency and its multiple subharmonic amplitude are closed, and avoids the generation of low-frequency noise and subharmonic noise, is comprised the following steps：
According to many wing state of chaotic system equation generation many wing chaos attractors of multiple scrolls of multiple scrolls, and according to the chaos
Attractor obtains the state variable of many wing chaos systems of the multiple scrolls, wherein, multi-scroll chaotic system is electric to improve Chua
Road, many wing chaos systems are the two many wing chaos systems of directional spreding plane net trellis；
State variable to many wing chaos systems of the multiple scrolls is sampled, and sets suitable sample frequency fs, to be mixed
Ignorant sequence；
The chaotic carrier signal of frequency chaos change is obtained according to the chaos sequence, wherein, the frequency of the chaotic carrier signal
Rate is represented by equation below：
fc=fr+xi·Δf,xi∈ (- 1,1), i=1,2 ...,
Wherein, fcFor the frequency of chaotic carrier signal, frOn the basis of carrier frequency, Δ f be peak frequency undulating value, xiTo be described
Chaos sequence；
According to chaos pulse-width signal and the chaotic carrier signal generation Chaotic-Pulse width modulated pwm control signal, with
Control the converters.
2. the electromagnetic interference chaotic control method according to claim 1 for suppressing converters, it is characterised in that
The dimensionless state equation of the improvement Chua circuits is：
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Wherein, α=10, β=16, ξ=0.3~1 is control parameter, f1(x, ξ) and f2(y) it is ladder wave train, wherein f1
ξ in (x, ξ) is control parameter.
3. the electromagnetic interference chaotic control method according to claim 2 for suppressing converters, it is characterised in that
Wherein, when producing even number scrollwork attractor, the f1(x, ξ) and f2(y) specific configuration form is：
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4. the electromagnetic interference chaotic control method according to claim 3 for suppressing converters, it is characterised in that
The quantity that the improvement Chua circuits can produce scrollwork attractor is (2N+2) × (2M+2) × (2N+2), and multi-direction net is presented
Lattice scrollwork is distributed.
5. the electromagnetic interference chaotic control method according to claim 2 for suppressing converters, it is characterised in that
Wherein, when producing odd number scrollwork attractor, the f1(x, ξ) and f2(y) specific configuration form is：
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<mn>0</mn>
</mrow>
<mi>N</mi>
</munderover>
<mi>sgn</mi>
<mo>&lsqb;</mo>
<mi>x</mi>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>4</mn>
<mi>i</mi>
<mo>-</mo>
<mn>2</mn>
<mo>)</mo>
</mrow>
<msub>
<mi>A</mi>
<mn>1</mn>
</msub>
<mo>&rsqb;</mo>
<mo>}</mo>
</mrow>
<mrow>
<msub>
<mi>f</mi>
<mn>2</mn>
</msub>
<mrow>
<mo>(</mo>
<mi>y</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>A</mi>
<mn>2</mn>
</msub>
<mo>{</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>M</mi>
</munderover>
<mi>sgn</mi>
<mo>&lsqb;</mo>
<mi>y</mi>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<msub>
<mi>A</mi>
<mn>2</mn>
</msub>
<mo>&rsqb;</mo>
<mo>+</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>j</mi>
<mo>=</mo>
<mn>0</mn>
</mrow>
<mi>M</mi>
</munderover>
<mi>sgn</mi>
<mo>&lsqb;</mo>
<mi>y</mi>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mn>2</mn>
<mi>j</mi>
<mo>-</mo>
<mn>1</mn>
<mo>)</mo>
</mrow>
<msub>
<mi>A</mi>
<mn>2</mn>
</msub>
<mo>&rsqb;</mo>
<mo>}</mo>
<mo>,</mo>
</mrow>
1
Wherein, A1=A2>0, N >=1, M >=1.
6. the electromagnetic interference chaotic control method according to claim 5 for suppressing converters, it is characterised in that
The quantity that the improvement Chua circuits can produce scrollwork attractor is (2N+1) × (2M+1) × (2N+1), and multi-direction net is presented
Lattice scrollwork is distributed.
7. the electromagnetic interference chaotic control method according to claim 1 for suppressing converters, it is characterised in that
The dimensionless state equation of many wing chaos systems of two directional spredings plane net trellis is：
<mrow>
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<mtable>
<mtr>
<mtd>
<mrow>
<mover>
<mi>x</mi>
<mo>&CenterDot;</mo>
</mover>
<mo>=</mo>
<mi>y</mi>
<mo>-</mo>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>y</mi>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mover>
<mi>y</mi>
<mo>&CenterDot;</mo>
</mover>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mn>1</mn>
<mo>-</mo>
<mi>z</mi>
<mo>)</mo>
</mrow>
<mi>sgn</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>a</mi>
<mrow>
<mo>(</mo>
<mi>y</mi>
<mo>-</mo>
<mi>g</mi>
<mo>(</mo>
<mi>y</mi>
<mo>)</mo>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mover>
<mi>z</mi>
<mo>&CenterDot;</mo>
</mover>
<mo>=</mo>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mi>b</mi>
<mi>z</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
</mrow>
Wherein,
<mrow>
<mi>f</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<msub>
<mi>F</mi>
<mn>0</mn>
</msub>
<msup>
<mi>x</mi>
<mn>2</mn>
</msup>
<mo>-</mo>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>i</mi>
<mo>=</mo>
<mn>1</mn>
</mrow>
<mi>N</mi>
</munderover>
<msub>
<mi>F</mi>
<mi>i</mi>
</msub>
<mo>&lsqb;</mo>
<mn>1</mn>
<mo>+</mo>
<mn>0.5</mn>
<mi>sgn</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>-</mo>
<msub>
<mi>E</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>-</mo>
<mn>0.5</mn>
<mi>sgn</mi>
<mrow>
<mo>(</mo>
<mi>x</mi>
<mo>+</mo>
<msub>
<mi>E</mi>
<mi>i</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>&rsqb;</mo>
<mo>,</mo>
</mrow>
<mrow>
<mi>g</mi>
<mrow>
<mo>(</mo>
<mi>y</mi>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mi>G</mi>
<munderover>
<mo>&Sigma;</mo>
<mrow>
<mi>m</mi>
<mo>=</mo>
<mo>-</mo>
<mi>M</mi>
</mrow>
<mi>M</mi>
</munderover>
<mi>sgn</mi>
<mrow>
<mo>(</mo>
<mi>y</mi>
<mo>-</mo>
<mn>2</mn>
<mi>m</mi>
<mi>G</mi>
<mo>)</mo>
</mrow>
<mo>.</mo>
</mrow>
Wherein, F0=k, Fi=2A/k, Ei=0.5 (1+i) A/k, A, k, ki, G is coefficient.
8. the electromagnetic interference chaotic control method according to claim 7 for suppressing converters, it is characterised in that
The quantity of the producible wing chaos attractor of many wing chaos systems of two directional spredings plane net trellis be (2N+2) ×
(2M+2)。
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| CN106301303B (en) * | 2016-08-26 | 2018-12-11 | 北京交通大学 | New and effective hybrid chaos spread spectrum pulse duration modulation method and system |
| CN107248898B (en) * | 2017-05-27 | 2019-06-04 | 佛山科学技术学院 | Multiline message chaos encrypting method and its device based on multireel wave signal |
| CN107404223B (en) * | 2017-08-11 | 2019-08-23 | 广州大学 | A kind of switching converter EMI suppressing method based on chaotic signal driving |
| CN107994766B (en) * | 2017-12-19 | 2019-10-25 | 北京交通大学 | Period based on ladder wave train spreads PWM control method and device |
| CN114079375B (en) * | 2021-10-28 | 2023-06-20 | 广州大学 | Fractional order chaos radiation inhibition method, system, computer equipment and storage medium |
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