CN107294448B - A kind of asynchronous machine fuzzy discrete control method based on command filtering - Google Patents

A kind of asynchronous machine fuzzy discrete control method based on command filtering Download PDF

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CN107294448B
CN107294448B CN201710454917.2A CN201710454917A CN107294448B CN 107294448 B CN107294448 B CN 107294448B CN 201710454917 A CN201710454917 A CN 201710454917A CN 107294448 B CN107294448 B CN 107294448B
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command filtering
formula
kth
filtering device
indicate
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CN107294448A (en
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于金鹏
马玉梅
于海生
周真诚
牛浩
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Qingdao University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/06—Rotor flux based control involving the use of rotor position or rotor speed sensors
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/001—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control using fuzzy control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/0003—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
    • H02P21/0017—Model reference adaptation, e.g. MRAS or MRAC, useful for control or parameter estimation
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
    • H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P27/00—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage
    • H02P27/04—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage
    • H02P27/06—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters
    • H02P27/08—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters with pulse width modulation
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2203/00—Indexing scheme relating to controlling arrangements characterised by the means for detecting the position of the rotor
    • H02P2203/05—Determination of the rotor position by using two different methods and/or motor models
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
    • H02P2207/01—Asynchronous machines

Abstract

The asynchronous machine fuzzy discrete control method based on command filtering that the invention discloses a kind of.This method introduces command filtering technology for nonlinear problem present in Induction Motor-Driven and control system in traditional Backstepping design method, successfully overcomes and " calculates and explode " problem due to caused by continuous derivation in traditional Reverse Step Control；The method of the present invention approaches the nonlinear function in motor driven systems using fuzzy logic system, and command filtering technology is combined construction controller with adaptive approach；After adjusting by the method for the invention, motor operation can be rapidly achieved stable state, and simulation result shows that the method for the present invention can overcome the influence of parameter inaccuracy and be conducive to guarantee ideal control effect, realizes the quickly and stably response to revolving speed.

Description

A kind of asynchronous machine fuzzy discrete control method based on command filtering
Technical field
The invention belongs to asynchronous machine Position Tracking Control technical fields more particularly to a kind of based on the asynchronous of command filtering Motor fuzzy discrete control method.
Background technique
Asynchronous machine (induction motors, IMs) is a kind of alternating current generator, is also induction machine, mainly makees electronic Machine uses.Asynchronous motor is widely used in industrial and agricultural production, such as lathe, water pump, metallurgy, mining equiment and light industry machine Tool etc. all uses it as prime mover, and capacity is from several kilowatts to several megawatts.The household electrical appliance become increasingly popular, such as doing washing Machine, refrigerator, uses unidirectional asynchronous motor in air conditioner at fan, and capacity is from several watts to several kilowatts.In space flight, computer Etc. high-tech areas.Asynchronous machine can also be used as generator use, such as small hydropower station, wind-driven generator can also be used it is asynchronous Motor.Why asynchronous machine is used widely, and has the following advantages mainly due to it: structure is simple, reliable for operation, manufacture is held Easily, cheap, sturdy and durable, and have higher efficiency and fairly good working characteristics.
However since asynchronous machine mathematical model has the characteristics that nonlinearity, close coupling, multivariable, while vulnerable to electricity The influence of the uncertain factors such as machine Parameters variation and external loading disturbance, therefore, the high performance control of Yao Shixian asynchronous motor It is a challenging project.In recent years, the research of nonlinear control method achieves huge progress, such as sliding formwork control System, dynamic surface control, Hamilton control, Backstepping control and some other control methods.
Backstepping is that a kind of control has uncertain, nonlinear system, and especially those are unsatisfactory for specified criteria The method of system.Backstepping biggest advantage is high order system that can be original with the simplification of virtual controlling variable, thus final Output result can automatically be obtained by suitable Lyapunov equation.Adaptive backstepping control method will be complicated non-thread Property system decomposition at the subsystem of multiple simple low orders, gradually carry out controller design by introducing virtual controlling variable, most Control law and parameter update law are determined eventually, to realize effective control to system.However, to void in traditional Reverse Step Control Quasi- control function carries out continuous derivation, easily causes " calculating explosion " problem.Command filtering is introduced during controller design Technology can be with effective solution " calculating explosion " problem.In addition, fuzzy logic system is in terms of handling unknown nonlinear function Ability causes the extensive concern on the circle of control both at home and abroad, and for having nonlinearity and probabilistic complex control system In design.
Summary of the invention
It is an object of the invention to propose a kind of asynchronous machine fuzzy discrete control method based on command filtering, this method Nonlinear function unknown in Induction Motor-Driven system is approached using fuzzy logic system, and combines Backstepping construction adaptive Position Tracking Control device, to realize the efficient tracing control to asynchronous machine position.
To achieve the goals above, the present invention adopts the following technical scheme:
A kind of asynchronous machine fuzzy discrete control method based on command filtering, includes the following steps:
A establishes the Discrete Dynamic mathematical model of asynchronous machine
DefinitionΘ indicates that rotor Angle Position, ω indicate rotor angular speed, npIt is extremely right to indicate Number, J indicate rotary inertia, TLIndicate load torque, idAnd iqIndicate d-q axis stator current, udAnd uqIndicate d-q axis stator electricity Pressure, LmIndicate mutual inductance, RsIndicate stator resistance, LsIndicate stator inductance, RrIndicate rotor resistance, LrIndicate inductor rotor, ψdTable Show rotor flux；
For the Discrete Dynamic mathematical model for simplifying asynchronous machine, it is as follows to define new variable:
Then the Discrete Dynamic mathematical model of asynchronous machine indicates are as follows:
Wherein, ΔtFor the sampling period；
B designs a kind of asynchronous machine mould based on command filtering according to command filtering technology and adaptive Backstepping principle Discrete Control Method is pasted, above-mentioned model simplification is two independent subsystems, i.e., by state variable x1(k)、x2(k) it and controls defeated Enter uq(k) form subsystem and by state variable x4(k) and control inputs ud(k) subsystem formed；
Assuming that f (z (k)) is compacting ΩZIn be a continuous function, for arbitrary constant ε > 0, always there is one Fuzzy logic system WTS (z (k)) meets:In formula, input vectorQ is Indistinct Input dimension, RqFor real vector collection, W=[W1,...,Wl]T∈RlIt is fuzzy weight vector, mould Paste number of nodes l is positive integer, and l > 1, RlFor real vector collection, S (z (k))=[s1(z(k)),...,sl(z(k))]T∈RlFor Basis function vector usually chooses basic function si(z (k)) is following Gaussian function:
Wherein, μi=[μi1,...,μiq]TIt is the center of Gaussian function distribution curve, and ηiIt is then its width；
Definition command filter are as follows:
Wherein, ζ, ωnFor command filtering device parameter, xjc(k) and xjc(k+1) kth time of j-th of command filtering device and the output signal of kth+1 time sampling, z are respectively indicatedj,1(k), zj,2It (k) is the output signal of the kth of command filtering device time sampling, zj,1(k+1),zj,2It (k+1) is the kth+1 of command filtering device The output signal of secondary sampling, αjIt (k) is the input signal of the kth of j-th of command filtering device time sampling；If command filtering device Input signal αj(k) for all constant k >=0, so that | αj(k+1)-αj(k)|≤ρ1And αj(k+2)-2αj(k+1)+αj (k)|≤ρ2It sets up, wherein ρ1And ρ2It is normal number, αj(k+1) the input letter of kth+1 time sampling of command filtering device is indicated Number, αj(k+2) input signal of kth+2 times samplings of command filtering device is indicated；Z simultaneouslyj,1(0)=αj(0), zj,2(0)=0 it is The initial value of command filtering device；It can then obtain, to arbitrary constant λj> 0, there are ωn> 0 and ζ ∈ (0,1] so that | zj,1 (k)-αj(k)|≤λj；Δzj,1(k)=| zj,1(k+1)-zj,1(k) | it is bounded；
Define tracking error variable are as follows:
Define x1dIt (k) is desired position signal, x4dIt (k) is desired rotor flux signal, dummy pilot signal α1 (k)、α2(k)、α4It (k) is the input signal of command filtering device, x1c(k)、x2c(k)、x4c(k) believe for the output of command filtering device Number；
In control method each step can all choose a suitable Lyapunov function construct a virtual master function or True control law, control method specifically includes the following steps:
B.1 according to first EQUATION x in formula (2)1(k+1)=x1(k)+Δtx2(k), tracking error variable: e can be acquired1 (k+1)=x1(k)+Δtx2(k)-x1d(k+1), x1d(k+1) it is the desired locations signal of kth+1 time sampling, selects Lyapunov Function:To V1(k) ask difference that can obtain:
Choose virtual master function:
Then obtain:
B.2 according to second EQUATION x in formula (2)2(k+1)=x2(k)+a1Δtx3(k)x4(k)+a2ΔtTL, can acquire Error variance: e2(k+1)=x2(k)+a1Δtx3(k)x4(k)+a2ΔtTL-x1c(k+1), x1c(k+1) command filtering device is indicated + 1 sampled output signal of kth selects Lyapunov function:Then to V2(k) ask difference that can obtain:
Load torque T in systems in practiceLIt is bounded, defines TLIt is unknown normal number and the upper limit is d, i.e., | TL|≤ D, wherein d >=0；Choose virtual master function:
Then Δ V2(k) it may be expressed as:
B.3 according to third equation in formula (2):
Error variance can be acquired: x2c(k+1)+1 sampled output signal of kth of command filtering device, selection are indicated Lyapunov function:
To V3(k) ask difference that can obtain:
Wherein:
z3(k)=[x2(k),x3(k),x4(k),x5(k),x2c(k+1)]T；By almighty approaching theorem, for it is arbitrarily small just Number ε3, choose fuzzy logic system W3 TS3(z3(k)), so that f3(z3(k))=W3 TS3(z3(k))+τ3, wherein τ3Expression approaches Error, and meet inequality | τ3|≤ε3, | | W3| | it is vector W3Norm, thus:
Choose control law uq(k) and adaptive lawAre as follows:
Wherein, γ3And δ3It is normal number；Definition | | W3| |=η3And η3> 0, defined variable η3Evaluated error beFor the estimated value of variable η 3；Formula (11) are substituted into formula (10) to obtain:
B.4 according to the 4th EQUATION x in formula (2)4(k+1)=(1+c1Δt)x4(k)+b4Δtx5(k), error can be acquired Variable: e4(k+1)=(1+c1Δt)x4(k)+b4Δtx5(k)-x4d(k+1), x4dIt (k+1) is the desired locations of kth+1 time sampling Signal；Select Lyapunov function:To V4(k) ask difference that can obtain:
Choose virtual master function:
Then obtain:
B.5 according to the 5th equation in formula (2):
Error dynamics equation can be obtained: x4c(k+1)+1 sampled output signal of kth for indicating command filtering device, selects Lyapunov letter Number:Wherein, P is constant and P > 0；To V5(k) ask difference that can obtain:
Wherein, z5(k)=[x2(k),x3(k),x4(k),x5(k),x4c(k+1)]T, fuzzy logic system Nonlinear Function Approximation is utilized again f5(z5(k)) arbitrarily small positive number ε, is given5, there are fuzzy logic system W5 TS5(z5(k))；Enable f5(z5(k))=W5 TS5(z5 (k))+τ5, wherein τ5Indicate approximate error, and meet | τ5|≤ε5, | | W5| | it is vector W5Norm, thus:
Choose control law ud(k) and adaptive lawAre as follows:
Wherein, γ5And δ5For normal number, define | | W5| |=η5And η5> 0, defined variable η5Evaluated error beFor the estimated values of variable η 5, formula (19) are substituted into formula (18) and are obtained:
To have:
C carries out stability analysis to the asynchronous machine fuzzy controller of foundation, selects Lyapunov function:
Ask difference that can obtain V:
Wherein,Indicate the evaluated error of kth+1 time sampling；
According toIt can be obtained with formula (12):
By | | S3(z3(k))||2< 1 can be obtained:
From Young inequality:
Above-mentioned two inequality below formula (25), which is substituted into formula (25), to be obtained:
It can similarly obtain:
DefinitionM is any positive number, because | xjc(k)-αj(k)|≤λj, j=1,2,4, by formula (22), Formula (26) and formula (27) substitute into formula (24) and can obtain:
Wherein,
Select suitable parameter P and sampling period Δt, make its satisfactionWith
If selection parameter meetsSo As long asWithIt sets up, then can obtain Δ V (k)≤0；Further may be used Know for arbitrarily small positive number σ,It sets up.The present invention can guarantee that the tracking error of position can be received It holds back in a sufficiently small neighborhood of origin, realizes to the efficient tracing control in the position of asynchronous machine.
The present invention has the advantage that
(1) the method for the present invention is directed to discrete-time system, with higher compared to the control method of continuous time system Stability and realizability.
(2) the method for the present invention combines command filtering technology and fuzzy self-adaption method, efficiently solves in parameter In the case where not knowing and thering is load torque to disturb the problem of the Position Tracking Control of asynchronous machine.
(3) the method for the present invention uses command filtering technology, efficiently avoids in traditional Backstepping to virtual function Continuous derivation, to overcome " calculating explosion " problem of traditional Backstepping design；Department of electrical engineering is approached using fuzzy logic system Unknown nonlinear terms in system, while so that tracking error is converged to one of origin using adaptive fuzzy contragradience law technology In sufficiently small neighborhood, efficiently solves the problems, such as the nonlinear Control of asynchronous machine, more accurate control may finally be reached Precision processed.
(4) the method for the present invention does not need the difference according to asynchronous machine and modifies the parameter of controller, can be real in principle Now to the stability contorting of the asynchronous machines of all models and power, the measurement to non-synchronous motor parameter is reduced in control process, Conducive to the quick response for realizing that Rotational Speed of Asynchronous Motor is adjusted.
(5) the method for the present invention robustness is good, has stronger anti-disturbance ability, realizes ideal control effect.
Detailed description of the invention
Fig. 1 is asynchronous machine fuzzy discrete controller, coordinate transform and SVPWM inversion based on command filtering in the present invention The schematic diagram of the composite controlled object of device composition；
Fig. 2 be the present invention in based on command filtering asynchronous machine fuzzy discrete control method control after rotor angle location and The tracking analogous diagram of rotor angle location setting value；
Fig. 3 is rotor flux after the asynchronous machine fuzzy discrete control method control in the present invention based on command filtering and turns The tracking analogous diagram of sub- magnetic linkage setting value；
Fig. 4 be the present invention in based on command filtering asynchronous machine fuzzy discrete control method control after rotor angle location and The tracking error analogous diagram of rotor angle location setting value；
Fig. 5 is q axis stator voltage after the asynchronous machine fuzzy discrete control method in the present invention based on command filtering controls Analogous diagram；
Fig. 6 is d axis stator voltage after the asynchronous machine fuzzy discrete control method in the present invention based on command filtering controls Analogous diagram.
Specific embodiment
Basic thought of the invention are as follows: the discrete model of asynchronous machine is obtained using Euler's method, while being patrolled using fuzzy The nonlinearity function in system approximation system, and combining adaptive and contragradience technical construction controller are collected, by command filtering Technology is introduced into the selection of recursive process Lyapunov function and the construction of intermediate virtual control signal, and recursion is controlled Rule, while corresponding adaptive law is designed to adjust unknown parameter；Command filtering technology is introduced, in the feelings without calculus of differences Under condition, can produce the differential signal of filtering signal, reduce calculation amount, solve traditional Backstepping to virtual master function into Problem " is calculated and exploded " caused by the continuous derivation of row；The introducing of dynamic surface technology greatlies simplify design process, in addition, for control The selection of preset parameter opens a kind of new thinking in device, substantially increases design efficiency, improves systematic steady state performance.
Specifically, with reference to the accompanying drawing and specific embodiment invention is further described in detail:
As shown in connection with fig. 1, a kind of asynchronous machine fuzzy discrete control method based on command filtering, the component packet used Include asynchronous machine fuzzy discrete controller 1, coordinate transformation unit 2, SVPWM inverter 3 and Rotating speed measring based on command filtering Unit 4 and current detecting unit 5.Wherein, rotation speed detection unit 4 and current detecting unit 5 are mainly for detection of asynchronous machine Current value and revolving speed correlated variables, by the electric current and speed variable of actual measurement as input, by based on command filtering Asynchronous machine fuzzy discrete controller 1 carries out voltage control, is ultimately converted to the revolving speed of three-phase electric control asynchronous machine.In order to set A significantly more efficient controller is counted, it is very necessary for establishing the Discrete Dynamic mathematical model of asynchronous machine.
Asynchronous machine fuzzy discrete control method in the present invention based on command filtering, includes the following steps:
A establishes the Discrete Dynamic mathematical model of asynchronous machine
DefinitionΘ indicates that rotor Angle Position, ω indicate rotor angular speed, npIndicate number of pole-pairs, J indicates rotary inertia, TLIndicate load torque, idAnd iqIndicate d-q axis stator current, udAnd uqIndicate d-q axis stator voltage, Lm Indicate mutual inductance, RsIndicate stator resistance, LsIndicate stator inductance, RrIndicate rotor resistance, LrIndicate inductor rotor, ψdIndicate rotor Magnetic linkage；
For the Discrete Dynamic mathematical model for simplifying asynchronous machine, it is as follows to define new variable:
Then the Discrete Dynamic mathematical model of asynchronous machine indicates are as follows:
Wherein, ΔtFor the sampling period；
B designs a kind of asynchronous machine mould based on command filtering according to command filtering technology and adaptive Backstepping principle Discrete Control Method is pasted, above-mentioned model simplification is two independent subsystems, i.e., by state variable x1(k)、x2(k) it and controls defeated Enter uq(k) form subsystem and by state variable x4(k) and control inputs ud(k) subsystem formed；
Assuming that f (z (k)) is compacting ΩZIn be a continuous function, for arbitrary constant ε > 0, always there is one Fuzzy logic system WTS (z (k)) meets:In formula, input vectorq It is Indistinct Input dimension, RqFor real vector collection, W=[W1,...,Wl]T∈RlIt is fuzzy weight vector, fuzzy number of nodes l is positive whole Number, and l > 1, RlFor real vector collection, S (z (k))=[s1(z(k)),...,sl(z(k))]T∈RlFor basis function vector, usually Choose basic function si(z (k)) is following Gaussian function:
Wherein, μi=[μi1,...,μiq]TIt is the center of Gaussian function distribution curve, and ηiIt is then its width；
Definition command filter are as follows:
Wherein, ζ, ωnFor command filtering device parameter, xjc(k) and xjc(k+1) kth time of j-th of command filtering device and the output signal of kth+1 time sampling, z are respectively indicatedj,1(k), zj,2It (k) is the output signal of the kth of command filtering device time sampling, zj,1(k+1),zj,2It (k+1) is the kth+1 of command filtering device The output signal of secondary sampling, αjIt (k) is the input signal of the kth of j-th of command filtering device time sampling.If command filtering device Input signal αj(k) for all constant k >=0, so that | αj(k+1)-αj(k)|≤ρ1And | αj(k+2)-2αj(k+1)+αj (k)|≤ρ2It sets up, wherein ρ1And ρ2It is normal number, αj(k+1) the input letter of kth+1 time sampling of command filtering device is indicated Number, αj(k+2) input signal of kth+2 times samplings of command filtering device is indicated；Z simultaneouslyj,1(0)=αj(0), zj,2(0)=0 it is The initial value of command filtering device；It can then obtain, to arbitrary constant λj> 0, there are ωn> 0 and ζ ∈ (0,1] so that | zj,1 (k)-αj(k)|≤λj；Δzj,1(k)=| zj,1(k+1)-zj,1(k) | it is bounded；
Define tracking error variable are as follows:
Define x1dIt (k) is desired position signal, x4dIt (k) is desired rotor flux signal, dummy pilot signal α1 (k)、α2(k)、α4It (k) is the input signal of command filtering device, x1c(k)、x2c(k)、x4c(k) believe for the output of command filtering device Number；
In control method each step can all choose a suitable Lyapunov function construct a virtual master function or True control law, control method specifically includes the following steps:
B.1 according to first EQUATION x in formula (2)1(k+1)=x1(k)+Δtx2(k), tracking error variable: e can be acquired1 (k+1)=x1(k)+Δtx2(k)-x1d(k+1), x1d(k+1) it is the desired locations signal of kth+1 time sampling, selects Lyapunov Function:To V1(k) ask difference that can obtain:
Choose virtual master function:
Then obtain:
B.2 according to second EQUATION x in formula (2)2(k+1)=x2(k)+a1Δtx3(k)x4(k)+a2ΔtTL, can acquire Error variance: e2(k+1)=x2(k)+a1Δtx3(k)x4(k)+a2ΔtTL-x1c(k+1), x1c(k+1) command filtering device is indicated + 1 sampled output signal of kth selects Lyapunov function:Then to V2(k) ask difference that can obtain:
Load torque T in systems in practiceLIt is bounded, defines TLIt is unknown normal number and the upper limit is d, i.e., | TL|≤ D, wherein d >=0；Choose virtual master function:
Then Δ V2(k) it may be expressed as:
B.3 according to third equation in formula (2):
Error variance can be acquired: x2c(k+1)+1 sampled output signal of kth of command filtering device, selection are indicated Lyapunov function:
To V3(k) ask difference that can obtain:
Wherein:
z3(k)=[x2(k),x3(k),x4(k),x5(k),x2c(k+1)]T；By almighty approaching theorem, for it is arbitrarily small just Number ε3, choose fuzzy logic system W3 TS3(z3(k)), so that f3(z3(k))=W3 TS3(z3(k))+τ3, wherein τ3Expression approaches Error,
And meet inequality | τ3|≤ε3, | | W3| | it is vector W3Norm, thus:
Choose control law uq(k) and adaptive lawAre as follows:
Wherein, γ3And δ3It is normal number；Definition | | W3| |=η3And η3> 0, defined variable η3Evaluated error beFor variable η3Estimated value；Formula (11) are substituted into formula (10) to obtain:
B.4 according to the 4th EQUATION x in formula (2)4(k+1)=(1+c1Δt)x4(k)+b4Δtx5(k), error can be acquired Variable: e4(k+1)=(1+c1Δt)x4(k)+b4Δtx5(k)-x4d(k+1), x4dIt (k+1) is the desired locations of kth+1 time sampling Signal；Select Lyapunov function:To V4(k) ask difference that can obtain:
Choose virtual master function:
Then obtain:
B.5 according to the 5th equation in formula (2):
Error dynamics equation can be obtained: x4c(k+1)+1 sampled output signal of kth for indicating command filtering device, selects Lyapunov letter Number:Wherein, P is constant and P > 0；To V5(k) ask difference that can obtain:
Wherein,
z5(k)=[x2(k),x3(k),x4(k),x5(k),x4c(k+1)]T, approached again using fuzzy logic system non- Linear function f5(z5(k)) arbitrarily small positive number ε, is given5, there are fuzzy logic system W5 TS5(z5(k))；Enable f5(z5(k))= W5 TS5(z5(k))+τ5, wherein τ5Indicate approximate error, and meet | τ5|≤ε5, | | W5| | it is vector W5Norm, thus:
Choose control law ud(k) and adaptive lawAre as follows:
Wherein, γ5And δ5For normal number, define | | W5| |=η5And η5> 0, defined variable η5Evaluated error beFor the estimated values of variable η 5, formula (19) are substituted into formula (18) and are obtained:
To have:
C carries out stability analysis to the asynchronous machine fuzzy controller of foundation, selects Lyapunov function:
Ask difference that can obtain V:
Wherein,Indicate the evaluated error of kth+1 time sampling.
According toIt can be obtained with formula (12):
By | | S3(z3(k))||2< 1 can be obtained:
From Young inequality:
Above-mentioned two inequality below formula (25), which is substituted into formula (25), to be obtained:
It can similarly obtain:
DefinitionM is any positive number, because | xjc(k)-αj(k)|≤λj, j=1,2,4, by formula (22), public affairs Formula (26) and formula (27) substitute into formula (24) and can obtain:
Wherein,
Select suitable parameter P and sampling period Δt, make its satisfactionWith
If selection parameter meetsSo As long asWithIt sets up, then can obtain Δ V (k)≤0；Further may be used Know for arbitrarily small positive number σ,It sets up.The present invention can guarantee that the tracking error of position can be received It holds back in a sufficiently small neighborhood of origin, realizes to the efficient tracing control in the position of asynchronous machine.
By analyzing to obtain in control law u aboveqAnd udUnder the action of, the tracking error of system converge to origin one fills In neighborhood under point, and guarantee other signal boundeds.
The asynchronous machine fuzzy discrete controller based on command filtering established is emulated under virtual environment, is tested Demonstrate,prove the feasibility of the asynchronous machine fuzzy discrete control method based on command filtering proposed:
Motor and load parameter are as follows:
J=0.0586Kgm2, Rs=0.1 Ω, Rr=0.15 Ω, Ls=Lr=0.0699H, Lm=0.068H, np=1.
Select control law parameter are as follows:
δ3=0.87, δ5=0.0021, γ3=0.98, γ5=0.25, ζ=0.9, ωn=200.
Desired position signal are as follows: x1d(k)=2cos (ΔtK pi/2), it is expected that rotor flux signal are as follows: x4d(k)=1；It adopts The sample period: Δt=0.0025s, load torque are as follows:
Select fuzzy membership function are as follows:
Emulation is carried out under the premise of system parameter and unknown nonlinear function, corresponding simulation result such as attached drawing 2- Shown in 6.Wherein, Fig. 2 and Fig. 3 is respectively rotor angle position after the asynchronous machine fuzzy discrete control method control based on command filtering The tracking analogous diagram with rotor angle location setting value and rotor flux and rotor flux setting value is set, is shown by simulation result Effect is ideal, and tracking effect is ideal, fast response time；Fig. 4 is the asynchronous machine fuzzy discrete control method based on command filtering The tracking error analogous diagram of rotor angle location and rotor angle location setting value after control；Fig. 5 and Fig. 6 is respectively to be based on command filtering Asynchronous machine fuzzy discrete controller control asynchronous machine q axis stator and asynchronous machine d axis stator voltage analogous diagram, lead to It crosses simulation result and shows that effect is ideal, fluctuates small, fast response time.Analog signal clearly illustrates, proposed by the present invention to be based on The asynchronous machine fuzzy discrete control method of command filtering, can efficiently track reference signal.
Certainly, described above is only that presently preferred embodiments of the present invention is answered the present invention is not limited to enumerate above-described embodiment When explanation, anyone skilled in the art is all equivalent substitutes for being made, bright under the introduction of this specification Aobvious variant, all falls within the essential scope of this specification, ought to be by protection of the invention.

Claims (1)

1. a kind of asynchronous machine fuzzy discrete control method based on command filtering, which comprises the steps of:
A establishes the Discrete Dynamic mathematical model of asynchronous machine
DefinitionΘ indicates that rotor Angle Position, ω indicate rotor angular speed, npIndicate number of pole-pairs, J table Show rotary inertia, TLIndicate load torque, idAnd iqIndicate d-q axis stator current, udAnd uqIndicate d-q axis stator voltage, LmTable Show mutual inductance, RsIndicate stator resistance, LsIndicate stator inductance, RrIndicate rotor resistance, LrIndicate inductor rotor, ψdIndicate rotor magnetic Chain；
For the Discrete Dynamic mathematical model for simplifying asynchronous machine, it is as follows to define new variable:
Then the Discrete Dynamic mathematical model of asynchronous machine indicates are as follows:
Wherein, ΔtFor the sampling period；
B according to command filtering technology and adaptive Backstepping principle, design a kind of asynchronous machine based on command filtering obscure from Control method is dissipated, above-mentioned model simplification is two independent subsystems, i.e., by state variable x1(k)、x2(k) and control inputs uq (k) form subsystem and by state variable x4(k) and control inputs ud(k) subsystem formed；
Assuming that f (z (k)) is compacting ΩZIn be a continuous function, for arbitrary constant ε > 0, always there is one fuzzy to patrol Collect system WTS (z (k)) meets:In formula, input vectorQ is Indistinct Input dimension, RqFor real vector collection, W=[W1,...,Wl]T∈RlIt is fuzzy weight vector, fuzzy number of nodes l is positive whole Number, and l > 1, RlFor real vector collection, S (z (k))=[s1(z(k)),...,sl(z(k))]T∈RlFor basis function vector, usually Choose basic function si(z (k)) is following Gaussian function:
Wherein, μi=[μi1,...,μiq]TIt is the center of Gaussian function distribution curve, and ηiIt is then its width；
Definition command filter are as follows:
Wherein, ζ, ωnFor command filtering device parameter, xjc(k) and xjc(k+1) kth time of j-th of command filtering device and the output signal of kth+1 time sampling, z are respectively indicatedj,1(k), zj,2It (k) is the output signal of the kth of command filtering device time sampling, zj,1(k+1),zj,2It (k+1) is the kth+1 of command filtering device The output signal of secondary sampling, αjIt (k) is the input signal of the kth of j-th of command filtering device time sampling；If command filtering device Input signal αj(k) for all constant k >=0, so that | αj(k+1)-αj(k)|≤ρ1And αj(k+2)-2αj(k+1)+αj (k)|≤ρ2It sets up, wherein ρ1And ρ2It is normal number, αj(k+1) the input letter of kth+1 time sampling of command filtering device is indicated Number, αj(k+2) input signal of kth+2 times samplings of command filtering device is indicated；Z simultaneouslyj,1(0)=αj(0), zj,2(0)=0 it is The initial value of command filtering device；It can then obtain, to arbitrary constant λj> 0, there are ωn> 0 and ζ ∈ (0,1] so that | zj,1 (k)-αj(k)|≤λj；Δzj,1(k)=| zj,1(k+1)-zj,1(k) | it is bounded；
Define tracking error variable are as follows:
Define x1dIt (k) is desired position signal, x4dIt (k) is desired rotor flux signal, dummy pilot signal α1(k)、α2 (k)、α4It (k) is the input signal of command filtering device, x1c(k)、x2c(k)、x4cIt (k) is the output signal of command filtering device；
Each step can all choose a suitable Lyapunov function and construct a virtual master function or true in control method Control law, control method specifically includes the following steps:
B.1 according to first EQUATION x in formula (2)1(k+1)=x1(k)+Δtx2(k), tracking error variable: e can be acquired1(k+ 1)=x1(k)+Δtx2(k)-x1d(k+1), x1d(k+1) it is the desired locations signal of kth+1 time sampling, selects Lyapunov letter Number:To V1(k) ask difference that can obtain:
Choose virtual master function:
Then obtain:
B.2 according to second EQUATION x in formula (2)2(k+1)=x2(k)+a1Δtx3(k)x4(k)+a2ΔtTL, error can be acquired Variable: e2(k+1)=x2(k)+a1Δtx3(k)x4(k)+a2ΔtTL-x1c(k+1), x1c(k+1) indicate command filtering device kth+ 1 sampled output signal selects Lyapunov function:Then to V2(k) ask difference that can obtain:
Load torque T in systems in practiceLIt is bounded, defines TLIt is unknown normal number and the upper limit is d, i.e., | TL|≤d, Middle d >=0；Choose virtual master function:
Then Δ V2(k) it may be expressed as:
B.3 according to third equation in formula (2):
Error variance can be acquired: x2c(k+1)+1 sampled output signal of kth of command filtering device, selection are indicated Lyapunov function:
To V3(k) ask difference that can obtain:
Wherein:
z3(k)=[x2(k),x3(k),x4(k),x5(k),x2c(k+1)]T；By almighty approaching theorem, for arbitrarily small positive number ε3, choose fuzzy logic systemSo thatWherein, τ3Expression approaches mistake Difference, and meet inequality | τ3|≤ε3, | | W3| | it is vector W3Norm, thus:
Choose control law uq(k) and adaptive lawAre as follows:
Wherein, γ3And δ3It is normal number；Definition | | W3| |=η3And η3> 0, defined variable η3Evaluated error be For variable η3Estimated value；Formula (11) are substituted into formula (10) to obtain:
B.4 according to the 4th EQUATION x in formula (2)4(k+1)=(1+c1Δt)x4(k)+b4Δtx5(k), error variance can be acquired: e4(k+1)=(1+c1Δt)x4(k)+b4Δtx5(k)-x4d(k+1), x4dIt (k+1) is the desired locations signal of kth+1 time sampling； Select Lyapunov function:To V4(k) ask difference that can obtain:
Choose virtual master function:
Then obtain:
B.5 according to the 5th equation in formula (2):
Error dynamics equation can be obtained:+ b5Δtud(k)-x4c(k+1), x4c(k+1)+1 sampled output signal of kth for indicating command filtering device, selects Lyapunov letter Number:Wherein, P is constant and P > 0；To V5(k) ask difference that can obtain:
Wherein,z5(k) =[x2(k),x3(k),x4(k),x5(k),x4c(k+1)]T, fuzzy logic system Nonlinear Function Approximation f is utilized again5(z5 (k)) arbitrarily small positive number ε, is given5, there are fuzzy logic systemsIt enablesIts In, τ5Indicate approximate error, and meet | τ5|≤ε5, | | W5| | it is vector W5Norm, thus:
Choose control law ud(k) and adaptive lawAre as follows:
Wherein, γ5And δ5For normal number, define | | W5| |=η5And η5> 0, defined variable η5Evaluated error be For variable η5Estimated value, formula (19) are substituted into formula (18):
To have:
C carries out stability analysis to the asynchronous machine fuzzy controller of foundation, selects Lyapunov function:
Ask difference that can obtain V:
Wherein,Indicate the evaluated error of kth+1 time sampling；
According toIt can be obtained with formula (12):
By | | S3(z3(k))||2< 1 can be obtained:
From Young inequality:
Above-mentioned two inequality below formula (25), which is substituted into formula (25), to be obtained:
It can similarly obtain:
DefinitionM is any positive number, because | xjc(k)-αj(k)|≤λj, j=1,2,4, by formula (22), formula (26) it can be obtained with formula (27) substitution formula (24):
Wherein,
Select suitable parameter P and sampling period Δt, make its satisfactionWith
If selection parameter meetsW=3,5, as long as thenWithIt sets up, then can obtain Δ V (k)≤0；It is further known that right In arbitrarily small positive number σ,It sets up.
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