CN106936408A - Filtering method, device and electronic equipment - Google Patents
Filtering method, device and electronic equipment Download PDFInfo
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- CN106936408A CN106936408A CN201710168838.5A CN201710168838A CN106936408A CN 106936408 A CN106936408 A CN 106936408A CN 201710168838 A CN201710168838 A CN 201710168838A CN 106936408 A CN106936408 A CN 106936408A
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03H—IMPEDANCE NETWORKS, e.g. RESONANT CIRCUITS; RESONATORS
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- H03H21/0012—Digital adaptive filters
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Abstract
The invention provides a kind of filtering method, device and electronic equipment, it is related to technical field of filtering.Filtering method includes:Set up global interval two types T S fuzzy time-delay systems models;Set up global interval two pattern paste filter model;Filtering error model is set up according to interval two types T S fuzzy time-delay systems models and interval two pattern paste filter model, and is filtered according to filtering error model.Filtering method, device and the electronic equipment that the present invention is provided can preferably process the nonlinear system with parameter uncertainty, complete the design of filter parameter, filtering is more stablized.
Description
Technical field
The present invention relates to technical field of filtering, in particular to a kind of filtering method, device and electronic equipment.
Background technology
In recent years, T-S fuzzy models are received and widely paid close attention to, and T-S fuzzy models are by one by nonlinear smearing weight
The world model that array of linear submodel is smoothly connected, it is non-that it with arbitrary accuracy can approach arbitrary smooth in convex compacting
Linear function, T-S fuzzy models are all sent out at aspects such as the stability analysis of fuzzy system, controller synthesis and wave filter designs
Wave huge effect and achieve plentiful and substantial theoretical result.
It is worth noting that, the above results are based on a pattern fuzzy logic, these traditional type T-S fuzzy controls are led to
Often unascertained information is not included to assume fuzzy weighted values.But in actual applications, not only with non-linear but also often companion
With uncertainty, once the system for considering is the nonlinear system with Parameter uncertainties, the T-S based on a pattern fuzzy logic
Fuzzy control method can not be directly applied.
Therefore, the nonlinear system with parameter uncertainty how has preferably been processed, setting for filter parameter has been completed
Meter, makes error filtering system stabilization, is a problem demanding prompt solution in the prior art.
The content of the invention
In view of this, the purpose of the embodiment of the present invention is to provide a kind of filtering method, device and electronic equipment to improve
Above mentioned problem.
In a first aspect, the embodiment of the invention provides a kind of filtering method, the filtering method includes:
Set up global interval two types T-S fuzzy time-delay systems models;
Set up global interval two pattern paste filter model;
Set up according to the interval two types T-S fuzzy time-delay systems model and the interval two patterns paste filter model
Filtering error model, and be filtered according to the filtering error model.
Second aspect, the embodiment of the invention provides a kind of filter, and the filter includes:
First sets up module, the interval two types T-S fuzzy time-delay systems models for setting up the overall situation;
Second sets up module, and interval two pattern for setting up the overall situation pastes filter model;
3rd sets up module, according to the interval two types T-S fuzzy time-delay systems model and the interval two patterns paste
Filter model sets up filtering error model;
Filtration module, for being filtered according to the filtering error model.
The third aspect, the embodiment of the invention provides a kind of electronic equipment, and the electronic equipment includes:
Memory;
Processor;And
Filter, the filter is installed in the memory and is held by the processor including one or more
Capable software function module, the filter includes:
First sets up module, the interval two types T-S fuzzy time-delay systems models for setting up the overall situation;
Second sets up module, and interval two pattern for setting up the overall situation pastes filter model;
3rd sets up module, according to the interval two types T-S fuzzy time-delay systems model and the interval two patterns paste
Filter model sets up filtering error model;
Filtration module, for being filtered according to the filtering error model.
For prior art, filtering method, device and the electronic equipment that the present invention is provided have following beneficial effect:
Filtering method, device and the electronic equipment that the present invention is provided can preferably process the non-thread with parameter uncertainty
Sexual system, completes the design of filter parameter, filtering is more stablized.
To enable the above objects, features and advantages of the present invention to become apparent, preferred embodiment cited below particularly, and coordinate
Appended accompanying drawing, is described in detail below.
Brief description of the drawings
Technical scheme in order to illustrate more clearly the embodiments of the present invention, below will be attached to what is used needed for embodiment
Figure is briefly described, it will be appreciated that the following drawings illustrate only certain embodiments of the present invention, thus be not construed as it is right
The restriction of scope, for those of ordinary skill in the art, on the premise of not paying creative work, can also be according to this
A little accompanying drawings obtain other related accompanying drawings.
The structured flowchart of the electronic equipment that Fig. 1 is provided for present pre-ferred embodiments.
The flow chart of the filtering method that Fig. 2 is provided for present pre-ferred embodiments.
The Force principle figure of the spring-damp system that Fig. 3 is provided for present pre-ferred embodiments.
Fig. 4 be Fig. 3 in primary condition be x1=1,When replying state curve map.
Fig. 5 be Fig. 3 in primary condition be x2=-2,When replying state curve map.
Fig. 6 is error return curve figures of the Fig. 3 under zero initial condition.
The structured flowchart of the filter that Fig. 7 is provided for present pre-ferred embodiments.
Icon:10- electronic equipments;101- memories;102- storage controls;103- processors;104- Peripheral Interfaces;
105- display units;106- audio units;107- input-output units;200- filters;210- first sets up module;220-
Second sets up module;230- the 3rd sets up module;240- filtration modules.
Specific embodiment
Below in conjunction with accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is carried out clear, complete
Ground description, it is clear that described embodiment is only a part of embodiment of the invention, rather than whole embodiments.Generally exist
The component of the embodiment of the present invention described and illustrated in accompanying drawing can be arranged and designed with a variety of configurations herein.Cause
This, the detailed description of the embodiments of the invention to providing in the accompanying drawings is not intended to limit claimed invention below
Scope, but it is merely representative of selected embodiment of the invention.Based on embodiments of the invention, those skilled in the art are not doing
The every other embodiment obtained on the premise of going out creative work, belongs to the scope of protection of the invention.
It should be noted that:Similar label and letter represents similar terms in following accompanying drawing, therefore, once a certain Xiang Yi
It is defined in individual accompanying drawing, then it need not be further defined and explained in subsequent accompanying drawing.Meanwhile, of the invention
In description, term " first ", " second " etc. are only used for distinguishing description, and it is not intended that indicating or implying relative importance.
Fig. 1 is referred to, is the structured flowchart of the electronic equipment 10 that present pre-ferred embodiments are provided, the embodiment of the present invention is carried
The filter 200 of confession can be applied in the electronic equipment 10.The electronic equipment 10 may be, but not limited to, intelligent hand
Machine, PC (personal computer, PC), panel computer, personal digital assistant (personal digital
Assistant, PDA), mobile internet surfing equipment (mobile Internet device, MID) etc..The behaviour of the electronic equipment 10
Be may be, but not limited to, as system, Android (Android) system, IOS (iPhone operating system) system,
Windows phone systems, Windows systems etc..
In the embodiment of the present invention, the electronic equipment 10 also includes memory 101, storage control 102, processor
103rd, Peripheral Interface 104, display unit 105, audio unit 106 and input-output unit 107.
The memory 101, storage control 102, processor 103, Peripheral Interface 104, display unit 105, audio list
Unit 106 and input-output unit 107, each element is directly or indirectly electrically connected with each other, to realize the transmission of data
Or interaction.For example, these elements can be realized being electrically connected with by one or more communication bus or holding wire each other.It is described
During filter 200 can be stored in the memory 101 including at least one in the form of software or firmware (firmware) or
It is solidificated in the software function module in the operating system of the electronic equipment 10 (operating system, OS).The treatment
Device 103 is used to perform the executable module stored in memory 101, for example, the software function mould that the filter 200 includes
Block or computer program.
Processor 103 is probably a kind of IC chip, the disposal ability with signal.Above-mentioned processor 103 can
Being general processor, including central processing unit (Central Processing Unit, abbreviation CPU), network processing unit
(Network Processor, abbreviation NP) etc.;Can also be digital signal processor (DSP), application specific integrated circuit (ASIC),
It is ready-made programmable gate array (FPGA) or other PLDs, discrete gate or transistor logic, discrete hard
Part component.Can realize or perform disclosed each method in the embodiment of the present invention, step and logic diagram.General processor
Can be microprocessor or the processor 103 can also be any conventional processor etc..
Various input/output devices are coupled to processor 103 and memory 101 by the Peripheral Interface 104.At some
In embodiment, Peripheral Interface 104, processor 103 and storage control 102 can be realized in one single chip.Other one
In a little examples, they can be realized by independent chip respectively.
Display unit 105 provides (such as user's operation of an interactive interface between the electronic equipment 1010 and user
Interface) or referred to user for display image data.In the present embodiment, the display unit 105 can be liquid crystal display
Device or touch control display.If touch control display, it can be the capacitance type touch control screen or electricity for supporting single-point and multi-point touch operation
Resistive touch screen etc..Support that single-point and multi-point touch operation refer to that touch control display can be sensed from one on the touch control display
The touch control operation produced simultaneously at individual or multiple positions, and transfer to processor to be calculated and located the touch control operation for sensing
Reason.
Audio unit 106 provides a user with COBBAIF, and it may include one or more microphones, one or more raises
Sound device and voicefrequency circuit.
Input-output unit 107 is used to be supplied to user input data to realize interacting for user and the electronic equipment 10.
The input-output unit 107 may be, but not limited to, mouse and keyboard etc..
Fig. 2 is referred to, is the flow of the filtering method for being applied to filter 200 that present pre-ferred embodiments are provided
Figure, will be described in detail to the idiographic flow described in Fig. 2 below.
Step S101, sets up global interval two types T-S fuzzy time-delay systems models.
In the present embodiment, global interval two types T-S fuzzy time-delay systems models fαFor:
Wherein, i=1,2 ... p, α=1,2 ... r, x (t) ∈ RnIt is state vector, z (t) ∈ RvIt is controlled output, y (t)
∈RmIt is measurement output, w ∈ RqIt is disturbance input, Ai,Adi,D1i,Ci,Cdi,D2i,Ei,EdiAnd D3iIt is known sytem matrix, d
T () is Time-varying time-delays, d (t) meets:
H and μ are two scalars,
ai(x (t)) ∈ [0,1] andIt is two nonlinear functions and meets
Specifically, when global interval two types T-S fuzzy time-delay systems models are set up, following rule is considered first,
If f1(x (t)) isAnd fr(x (t)) isThen:
WhereinIt is on function fαThe interval type-2 fuzzy sets of (x (t)) are closed, i=1,2 ... p, α=1,2 ... r, x
(t)∈RnIt is state vector, z (t) ∈ RvIt is controlled output, y (t) ∈ RmIt is measurement output, w ∈ RqIt is disturbance input, Ai,Adi,
D1i,Ci,Cdi,D2i,Ei,EdiAnd D3iIt is known sytem matrix.D (t) is Time-varying time-delays, and d (t) meets:
Wherein h and μ are two scalars.
The intensity of activation of the i-th rule is defined as Interval Set:
Wherein
WithUpper and lower degree of membership is represented respectively.
Then, the interval two types T-S fuzzy time-delay systems models of the overall situation be can obtain:
Wherein, a i(x
(t)) ∈ [0,1] andIt is two nonlinear functions and meets
Step S102, sets up global interval two pattern paste filter model.
In the present embodiment, global interval two pattern paste filter model gβFor:
Wherein, j=1,2 ... p, β=1,2 ... r, Afj, BfjAnd CfjIt is filtering parameter, β j(x(t))∈[0,1]
WithIt is two nonlinear functions and meets
Specifically, the unmatched interval two types fuzzy filter of premise membership function is defined, filter system rule:If
g1(x (t)) isAnd gl(x (t)) isThen:
WhereinIt is on function gβThe interval type-2 fuzzy sets of (x (t)) are closed, j=1,2 ... p, β=1,2 ... r, Afj,
BfjAnd CfjIt is filter parameter.The intensity of activation of j-th strip rule is defined as Interval Set:
Wherein
WithUpper and lower degree of membership is represented respectively.
Then, can obtain the interval two pattern paste filter model of the overall situation:
Wherein
β j(x (t)) ∈ [0,1] andIt is two nonlinear functions and meets
Step S103, sets up filtering error model, and be filtered according to the filtering error model.
In the present embodiment, filtering error model is:
Wherein,
Specifically, after formula (3) and (5) are obtained, the filtering error model can be obtained by formula (3) and (5) computing.
After obtaining the filtering error model, it is filtered according to the filtering error model.
For example, as shown in figure 3, be the Force principle figure of spring-damp system, can be obtained by Newton's laws of motion:
Wherein m is mass of object, FfAnd FsThe respectively elastic force of object friction and spring, u (t) is horizontal direction
With joint efforts, x represents displacement.Due toWhereinIt is constant with a.Then above formula can be represented
For:
DefinitionMake x1(t) ∈ [- 2,2], m=1kg, c=
2Nm/s, a=0.3m-1.Assuming thatThen whenWhen,Taking maximum is
WhenWhen,Taking minimum value isDue toIt is uncertain parameter, the pattern paste for existing
Filtering method can not be employed.In the embodiment of the present invention, original nonlinear system can approximately be converted into the complete of formula (3)
The interval two types T-S fuzzy time-delay systems models of office.
Wherein relevant parameter is:
C1=[0.1 0.1], C2=[0.1 0.1], Cd1=[- 0.8 0.6], Cd2=[-
0.2 1], D21=-0.7, D22=0.2, E1=[1 0], E2=[1 0], Ed1=[0.1 0], Ed2=[0 0.2], D31=0, D32
=0.
Due to uncertain parameterThe difference of value, the upper and lower membership function of global interval two patterns paste filter model is such as
Under:
Next, providing L2-L∞The parameter designing of the wave filter under performance indications.Make Φ=I, Ψ1=Ψ2=0, Ψ3=
γ2I.When taking α=1, β=10, h=0.5, μ=0.2 obtains the L of minimum2-L∞Performance indications γ=1.0302, and try to achieve filtering
Device gain matrix is:
Cf1=[- 0.0009 0.0270],
Cf2=[- 0.0009 0.0271].
In primary condition x1=1, x2=-2,Replying state curve such as Fig. 4, Fig. 5.
If disturbance isUnder zero initial condition, the error return curve of system is Fig. 6.
Figures 4-6 it can be seen that spring-damp system of the filtering method provided in an embodiment of the present invention to Parameter uncertainties
It is effective.
To sum up, filtering method provided in an embodiment of the present invention, using interval two types T-S fuzzy models, is preferably processed
Nonlinear system with parameter uncertainty, completes the design of filter parameter, filtering is more stablized.
Fig. 7 is referred to, is the structured flowchart of the filter 200 that present pre-ferred embodiments are provided, the filter
200 include first sets up module 210, second sets up module the 220, the 3rd and set up module 230 and filtration module 240.
First sets up module 210 for setting up the interval two types T-S fuzzy time-delay systems models of the overall situation.
Specifically, filter 200 sets up module 210 for setting up the interval two types T-S moulds of the overall situation by described first
Paste time lag system model fα
Wherein, i=1,2 ... p, α=1,2 ... r, x (t) ∈ RnIt is state vector, z (t) ∈ RvIt is controlled output, y (t)
∈RmIt is measurement output, w ∈ RqIt is disturbance input, Ai,Adi,D1i,Ci,Cdi,D2i,Ei,EdiAnd D3iIt is known sytem matrix, d
T () is Time-varying time-delays, d (t) meets:
H and μ are two scalars, a i(x (t)) ∈ [0,1] andIt is two nonlinear functions and meets
It should be understood that described first sets up module 210 and can be used for performing above-mentioned step S101.
Second sets up module 220 pastes filter model for setting up interval two pattern of the overall situation.
Specifically, filter 200 sets up module 220 by described second pastes filter for setting up interval two pattern of the overall situation
Ripple device model gβ
Wherein, j=1,2 ... p, β=1,2 ... r, Afj, BfjAnd CfjIt is filtering parameter, β j(x(t))∈[0,1]
WithIt is two nonlinear functions and meets
It should be understood that described second sets up module 220 and can be used for performing above-mentioned step S102.
3rd sets up module 230 for according to the interval two types T-S fuzzy time-delay systems model and described interval two
Pattern paste filter model sets up filtering error model.
Specifically, filter 200 sets up module 230 for according to the global interval two types T- by the described 3rd
S fuzzy time-delay systems models fαAnd the global interval two pattern paste filter model gβSet up filtering error model
Wherein,
It should be understood that the described 3rd sets up module 230 and can be used for performing in above-mentioned step S103 according to the area
Between two type T-S fuzzy time-delay systems models and interval two pattern paste filter model set up filtering error model this mistake
Journey.
Filtration module 240 is used to be filtered according to filtering error model.
After setting up filtering error model, the filtration module 240 of filter 200 is filtered according to the filtering error model
Ripple.
It should be understood that the filtration module 240 can be used in the above-mentioned step S103 of execution according to filtering error mould
Type is filtered this process.
To sum up, filter provided in an embodiment of the present invention 200, using interval two types T-S fuzzy models, is preferably processed
Nonlinear system with parameter uncertainty, completes the design of filter parameter, filtering is more stablized.
In several embodiments provided herein, it should be understood that disclosed apparatus and method, it is also possible to pass through
Other modes are realized.Device embodiment described above is only schematical, for example, flow chart and block diagram in accompanying drawing
Show the device of multiple embodiments of the invention, the architectural framework in the cards of method and computer program product,
Function and operation.At this point, each square frame in flow chart or block diagram can represent one the one of module, program segment or code
Part a, part for the module, program segment or code is used to realize holding for the logic function for specifying comprising one or more
Row instruction.It should also be noted that at some as in the implementation replaced, the function of being marked in square frame can also be being different from
The order marked in accompanying drawing occurs.For example, two continuous square frames can essentially be performed substantially in parallel, they are sometimes
Can perform in the opposite order, this is depending on involved function.It is also noted that every in block diagram and/or flow chart
The combination of the square frame in individual square frame and block diagram and/or flow chart, can use the function or the special base of action for performing regulation
Realized in the system of hardware, or can be realized with the combination of computer instruction with specialized hardware.
In addition, each functional module in each embodiment of the invention can integrate to form an independent portion
Divide, or modules individualism, it is also possible to which two or more modules are integrated to form an independent part.
If the function is to realize in the form of software function module and as independent production marketing or when using, can be with
Storage is in a computer read/write memory medium.Based on such understanding, technical scheme is substantially in other words
The part contributed to prior art or the part of the technical scheme can be embodied in the form of software product, the meter
Calculation machine software product is stored in a storage medium, including some instructions are used to so that a computer equipment (can be individual
People's computer, server, or network equipment etc.) perform all or part of step of each embodiment methods described of the invention.
And foregoing storage medium includes:USB flash disk, mobile hard disk, read-only storage (ROM, Read-Only Memory), arbitrary access are deposited
Reservoir (RAM, Random Access Memory), magnetic disc or CD etc. are various can be with the medium of store program codes.Need
Illustrate, herein, such as first and second or the like relational terms be used merely to by an entity or operation with
Another entity or operation make a distinction, and not necessarily require or imply these entities or there is any this reality between operating
The relation or order on border.And, term " including ", "comprising" or its any other variant be intended to the bag of nonexcludability
Contain, so that process, method, article or equipment including a series of key elements are not only including those key elements, but also including
Other key elements being not expressly set out, or it is this process, method, article or the intrinsic key element of equipment also to include.
In the absence of more restrictions, the key element limited by sentence "including a ...", it is not excluded that including the key element
Process, method, article or equipment in also there is other identical element.
The preferred embodiments of the present invention are the foregoing is only, is not intended to limit the invention, for the skill of this area
For art personnel, the present invention can have various modifications and variations.It is all within the spirit and principles in the present invention, made any repair
Change, equivalent, improvement etc., should be included within the scope of the present invention.It should be noted that:Similar label and letter exists
Similar terms is represented in following accompanying drawing, therefore, once being defined in a certain Xiang Yi accompanying drawing, then it is not required in subsequent accompanying drawing
It is further defined and is explained.
The above, specific embodiment only of the invention, but protection scope of the present invention is not limited thereto, and it is any
Those familiar with the art the invention discloses technical scope in, change or replacement can be readily occurred in, should all contain
Cover within protection scope of the present invention.Therefore, protection scope of the present invention described should be defined by scope of the claims.
Claims (10)
1. a kind of filtering method, it is characterised in that methods described includes:
Set up global interval two types T-S fuzzy time-delay systems models;
Set up global interval two pattern paste filter model;
Filtering is set up according to the interval two types T-S fuzzy time-delay systems model and the interval two patterns paste filter model
Error model, and be filtered according to the filtering error model.
2. filtering method according to claim 1, it is characterised in that when the global interval two types T-S of the foundation is fuzzy
Stagnant system model includes:
Set up global interval two types T-S fuzzy time-delay systems models fα
Wherein, i=1,2 ... p, α=1,2 ... r, x (t) ∈ RnIt is state vector, z (t) ∈ RvIt is controlled output, y (t) ∈ Rm
It is measurement output, w ∈ RqIt is disturbance input, Ai,Adi,D1i,Ci,Cdi,D2i,Ei,EdiAnd D3iIt is known sytem matrix, d (t)
It is Time-varying time-delays, d (t) meets:
H and μ are two scalars, a i(x (t)) ∈ [0,1] andIt is two nonlinear functions and meets
3. filtering method according to claim 2, it is characterised in that the global interval two types fuzzy filter of the foundation
Model includes:
Set up global interval two pattern paste filter model gβ
Wherein, j=1,2 ... p, β=1,2 ... r, Afj, BfjAnd CfjIt is filtering parameter, β j(x(t))∈[0,1]
WithIt is two nonlinear functions and meets
4. filtering method according to claim 3, it is characterised in that described that time lag is obscured according to the interval two types T-S
System model and the interval two patterns paste filter model are set up filtering error model and are included:
According to the global interval two types T-S fuzzy time-delay systems models fαAnd the global interval two types fuzzy filter
Device model gβSet up filtering error model
Wherein,
5. a kind of filter, it is characterised in that the filter includes:
First sets up module, the interval two types T-S fuzzy time-delay systems models for setting up the overall situation;
Second sets up module, and interval two pattern for setting up the overall situation pastes filter model;
3rd sets up module, for according to the interval two types T-S fuzzy time-delay systems model and the interval two patterns paste
Filter model sets up filtering error model;
Filtration module, for being filtered according to the filtering error model.
6. filter according to claim 5, it is characterised in that described first sets up module for setting up the area of the overall situation
Between two type T-S fuzzy time-delay systems models fα
Wherein, i=1,2 ... p, α=1,2 ... r, x (t) ∈ RnIt is state vector, z (t) ∈ RvIt is controlled output, y (t) ∈ Rm
It is measurement output, w ∈ RqIt is disturbance input, Ai,Adi,D1i,Ci,Cdi,D2i,Ei,EdiAnd D3iIt is known sytem matrix, d (t)
It is Time-varying time-delays, d (t) meets:
H and μ are two scalars, a i
(x (t)) ∈ [0,1] andIt is two nonlinear functions and meets
7. filter according to claim 6, it is characterised in that described second sets up module for setting up the area of the overall situation
Between two patterns paste filter model gβ
Wherein, j=1,2 ... p, β=1,2 ... r, Afj, BfjAnd CfjIt is filtering parameter, β j(x(t))∈[0,1]
WithIt is two nonlinear functions and meets
8. filter according to claim 7, it is characterised in that the described 3rd sets up module for according to the overall situation
Interval two types T-S fuzzy time-delay systems models fαAnd the global interval two pattern paste filter model gβSet up filtering
Error model
Wherein,
9. a kind of electronic equipment, it is characterised in that the electronic equipment includes:
Memory;
Processor;And
Filter, the filter is installed in the memory and including one or more by the computing device
Software function module, the filter includes:
First sets up module, the interval two types T-S fuzzy time-delay systems models for setting up the overall situation;
Second sets up module, and interval two pattern for setting up the overall situation pastes filter model;
3rd sets up module, according to the interval two types T-S fuzzy time-delay systems model and the interval two types fuzzy filter
Device model sets up filtering error model;
Filtration module, for being filtered according to the filtering error model.
10. electronic equipment according to claim 9, it is characterised in that the electronic equipment is PC.
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Cited By (3)
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CN108803378A (en) * | 2018-08-08 | 2018-11-13 | 四川大学 | Data processing method, device, flight simulator and storage medium |
CN109558594A (en) * | 2018-12-03 | 2019-04-02 | 深圳大学 | Interactive T-S fuzzy semantics model estimation method, system and computer readable storage medium |
CN110275439A (en) * | 2019-06-28 | 2019-09-24 | 四川大学 | The control method of self-balancing trolley, the design method of controller and device |
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