CN106452250B - A kind of long model predictive control method of line inductance electromotor multistep - Google Patents
A kind of long model predictive control method of line inductance electromotor multistep Download PDFInfo
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- CN106452250B CN106452250B CN201610866309.8A CN201610866309A CN106452250B CN 106452250 B CN106452250 B CN 106452250B CN 201610866309 A CN201610866309 A CN 201610866309A CN 106452250 B CN106452250 B CN 106452250B
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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
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
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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
- H02P21/0003—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
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Abstract
The invention discloses a kind of long model predictive control methods of line inductance electromotor multistep, include the following steps：(1) state variable and angular speed of line inductance electromotor are acquired；(2) the motor input voltage vector optimal value under unconfined condition is solved；(3) whether judgement optimal value meets voltage constraints, if satisfied, then entering step (5), otherwise enters step (4)；(4) to meet voltage constraints as target update optimal value；(5) whether judgement optimal value meets restriction of current condition, if satisfied, then entering step (7), otherwise enters step (6)；(6) to meet restriction of current condition as target update optimal value；(7) duty ratio that three-phase bridge arm is calculated according to motor input voltage vector optimal value, is given inverter modulating motor working condition.The present invention applies to multistep long Model Predictive Control Algorithm in line inductance electromotor, improves the runnability of line inductance electromotor.
Description
Technical field
The invention belongs to line inductance electromotor control technology fields, more particularly, to a kind of line inductance electromotor multistep
Long model predictive control method.
Background technology
Line inductance electromotor can directly generate linear mechanical motion, not need intermediate transmission conversion equipment, therefore in work
The departments such as industry production, communications and transportation are widely used.Simultaneously as the advantages that operation noise is small, initial investment is small, economic and practical,
It is a kind of Urban Traffic Modes with good prospect in rail traffic that line inductance electromotor, which is widely used, in recent years.But
Since structure of the linear motion actuator is special, there are side-termind effects, are influenced on air-gap flux and magnetizing inductance very big.Compared to rotary inductive electricity
The mathematical model of machine, motor will become more complicated.
The current main control strategies of line inductance electromotor are divided into vector controlled and Direct Thrust Control two major classes.Due to side end
Effect leads to parameter of electric machine acute variation, and field orientation and thrust meter can be made not to calculate accurately really.Meanwhile current inner loop PI parameters
Adjust closely related with the parameter of electric machine, parameter acute variation can cause PI parameter tuning processes relatively complicated.Therefore, tradition is utilized
Control strategy control line inductance electromotor can not reach good control effect.
Model Predictive Control Algorithm can calculate optimal input voltage according to motor mathematical model, and can be good at
Restricted problem in processing control, the problems such as capable of effectively avoiding generating overcurrent and ovennodulation in motor operation course.
Meanwhile in order to adapt to line inductance electromotor Parameters variation, by introducing side-termind effect impact factor, Model Predictive Control is allowed
Algorithm can predict the influence of Parameters variation in advance, so that control effect is optimal.By the long prediction mode of multistep, in advance
Know the more Future Informations of line inductance electromotor so that controller can cope with the change of motor working condition in advance.
Invention content
For the disadvantages described above or Improvement requirement of the prior art, the present invention provides a kind of long moulds of line inductance electromotor multistep
Type forecast Control Algorithm solves optimal value by the long Model Predictive Control Algorithm of multistep, while utilizing voltage and electric current
Constraint, line inductance electromotor can be run in safe operating area.
To achieve the above object, the present invention provides a kind of long model predictive control method of line inductance electromotor multistep, packets
Include following steps：
A kind of long model predictive control method of line inductance electromotor multistep, which is characterized in that include the following steps：
A kind of long model predictive control method of line inductance electromotor multistep, which is characterized in that include the following steps：
(1) it samples：Acquire the state variable [i of k moment line inductance electromotorsα1,iβ1,ψα2,ψβ2] and angular velocity omega2,
iα1,iβ1The respectively α of electric motor primary electric current, beta -axis component, ψα2,ψβ2The respectively α of motor secondary magnetic linkage, beta -axis component；
(2) the motor input voltage vector optimal value under unconfined condition is solved：The data information that the k moment acquires substitutes into most
Motor input voltage vector optimal value is solved in figure of merit calculating formula, the optimal value calculating formula is expressed as：
Wherein,
Subscript T representing matrix transposition；
P is prediction step；
For motor input voltage vector optimal value；
uα1(k),uβ1(k)The respectively α, beta -axis component of input voltage vector；
I is second order unit matrix, and O is second order null matrix；
Weight coefficient Γy=diag (Γy,1,Γy,2,...,Γy,p), Γu=diag (Γu,1,Γu,2,...,Γu,p),
Diag () is diagonal matrix, current reference value
ω2Represent secondary angular speed；uα1(k)And uβ1(k)Represent motor input voltage vector α, beta -axis component；iα1(k)And iβ1(k)
Represent electric motor primary electric current α, beta -axis component；R1And R2Respectively represent the primary and secondary resistance of motor；ψα1(k)And ψβ1(k)Represent motor
α, the beta -axis component of grade magnetic linkage；Ll1And Ll2Represent the primary and secondary leakage inductance of motor；D is electric motor primary length；v
For motor linear velocity；LmFor motor mutual inductance；Lr=Ll2+Lm[1-f(Q)]；Ls=Ll1+Lm[1-f(Q)]；
L'm=Lm[1-f(Q)]；TsFor the sampling period；
(3) whether judgement motor input voltage vector optimal value meets voltage constraints, if satisfied, then entering step
(5), it otherwise enters step (4), the voltage constraints is expressed as：
(uα1(k))2+(uβ1(k))2≤R2
Wherein：VdcFor DC bus-bar voltage；
(4) to meet voltage constraints as target update motor input voltage vector optimal value：
The motor input voltage vector time figure of merit is sought first：
Wherein：WithMeet the motor input voltage vector time figure of merit of voltage constraints after respectively updating
α, beta -axis component,WithRespectively update α, the beta -axis component of front motor input voltage vector optimal value；
Then using the updated secondary figure of merit as new optimal value, i.e.,
(5) whether judgement motor input voltage vector optimal value meets restriction of current condition, if satisfied, then entering step
(7), it otherwise enters step (6), the restriction of current condition is expressed as：
(uα1(k)+ox)2+(uβ1(k)+oy)2≤r2
Wherein： ImaxElectric current maximum limit amplitude.
(6) to meet restriction of current condition as target update motor input voltage vector optimal value：
The motor input voltage vector time figure of merit is calculated first：
Wherein：WithMeet the motor input voltage vector time figure of merit of restriction of current condition after respectively updating
α, beta -axis component,WithRespectively update α, the beta -axis component of front motor input voltage vector optimal value；
Then using the motor input voltage vector time figure of merit as new optimal value, i.e.,
Finally judge whether motor input voltage vector optimal value meets voltage constraints, (7) entered step if meeting,
Otherwise it enters step (4)：
(7) duty ratio that three-phase bridge arm is calculated according to motor input voltage vector optimal value is given inverter modulation
Control electric machine operation state.
Further, according to the optimal value for meeting constraints is iteratively solved out before, using simplified modulation strategy to inverse
Become device to be modulated, the specific implementation process is as follows：
According to motor input voltage vector optimal value, judges affiliated sector, utilize the corresponding duty ratio calculation formula in sector
Calculate the duty ratio of three-phase bridge arm；The sector and the correspondence of duty ratio calculation formula are as shown in the table：
Wherein：M is amplitude modulation ratio；||V*| | it is long for the mould of motor input voltage vector optimal value；Withα, beta -axis component for motor input voltage vector optimal value.
In general, through the invention it is contemplated above technical scheme is compared with the prior art, have below beneficial to effect
Fruit：
1, the long Model Predictive Control Algorithm of multistep is taken, line inductance electromotor future possible operating condition, thing can be predicted
Corresponding response is first made, so as to improve line inductance electromotor runnability；
2, voltage and restriction of current are taken, can ensure that motor operates in safety zone always, do not occur overcurrent and
Ovennodulation problem enables to the optimal value sought out to meet constraints according to the iterative algorithm proposed；
3, in order to allow the optimal value solved to disclosure satisfy that voltage and restriction of current, the present invention proposes a kind of optimization side
Method can be to avoid complicated coordinate transform and triangle letter in modulated process by simplifying to Space Vector Modulation Strategy
Number calculates, and simplifies the execution calculation amount of algorithm, can ensure that solving optimal value finally meets constraints.
Description of the drawings
Fig. 1 is line inductance electromotor structure principle chart；
Fig. 2 is voltage limit constraint；
Fig. 3 is voltage and current limit restraint；
Fig. 4 is iterative algorithm flow chart；
Fig. 5 is simplified modulation strategy schematic diagram.
Specific implementation mode
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to the accompanying drawings and embodiments, right
The present invention is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, and
It is not used in the restriction present invention.As long as in addition, technical characteristic involved in the various embodiments of the present invention described below
It does not constitute a conflict with each other and can be combined with each other.
One, line inductance electromotor mathematical model under α β coordinate systems is established.
In order to compensate for the side-termind effect that line inductance electromotor operational process generates, side-termind effect impact factor is introduced：
Wherein：D is electric motor primary length；V is motor linear velocity；R2For motor secondary resistance；Ll2For motor secondary inductance；
LmFor motor mutual inductance.
According to Fig. 1 line inductance electromotor structure principle charts, can obtain electric moter voltage equation is：
Motor flux linkage equations are：
Wherein：ω2Represent secondary angular speed；uα1And uβ1Represent motor input voltage vector α, beta -axis component；iα1And iβ1Generation
Table electric motor primary electric current α, beta -axis component；R1And R2Respectively represent the primary and secondary resistance of motor；ψα1And ψβ1Represent motor secondary magnetic linkage
α, beta -axis component；Ll1And Ll2Represent the primary and secondary leakage inductance of motor；
Choose state variable [iα1,iβ1,ψα2,ψβ2], it can be obtained in conjunction with electric moter voltage and flux linkage equations：
Wherein：P represents differential operator；Lr=Ll2+Lm[1-f(Q)]；Ls=Ll1+Lm[1-f(Q)]；L'm=Lm[1-f
(Q)]。
Using single order Euler's discrete method, formula (4) progress discretization can be obtained：
Wherein：TsFor the sampling period.
Two, the long Model Predictive Control Algorithm of line inductance electromotor multistep derives
K+p moment α β shaft currents are predicted to obtain using formula (5) at the k moment：
x(k+p|k)=Apx(k)+[Ap-1Bu(k)+....+Bu(k+p-1)]+[Ap-1Cψ(k)+....+Cψ(k+p-1)]+[Ap-1Dd(k)
+....+Dd(k+p-1)] (6)
It is assumed that magnetic linkage and counter electromotive force remain unchanged in predetermined period, i.e.,Convolution (6),
Can obtain line inductance electromotor mathematical prediction model is：
X(k+1|k)=Sxx(k)+SuU(k)+Sψψ(k)+Sdd(k) (7)
Wherein：
Defining input voltage variation is：
Wherein：I is second order unit matrix.
Object function can be expressed as：
J=| | Γy(X(k+1|k)-R(k+1))||2+||ΓuΔU(k)||2 (9)
Wherein：Weight coefficient Γy=diag (Γy,1,Γy,2,...,Γy,p), Γu=diag (Γu,1,Γu,2,...,
Γu,p)；Current reference value
Define auxiliary variable：
The minimum for solving object function is the optimal value of control input, therefore optimal Solve problems can indicate
For：
Since minimum value first derivative is equal to 0, second dervative is more than 0, can obtain according to this：
In system, the optimal value expression finally solved under unconfined condition is first element interaction：
Wherein：O is second order null matrix.
Three, consider voltage and current constrained optimum value solution procedure
The optimal value that formula (13) is solved may be unsatisfactory for line inductance electromotor voltage and restriction of current condition.If examining
Consider voltage and current constraint to go to solve optimal value, calculating process can become more complicated, be unfavorable for realizing in microprocessor.For
Approximate solution constraints optimal value problem, the present invention take iteration thought using the unconfined condition optimal value solved,
The optimal value for meeting constraints is allowed to be sufficiently close together the optimal value under unconfined condition.
Inverter output voltage limitation is that line inductance electromotor voltage is caused to constrain main cause, as shown in Fig. 2, positive six side
Shape is inverter maximum output voltage, solves for convenience, represents voltage constraints using its inscribed circle, can obtain：
(uα1(k))2+(uβ1(k))2≤R2 (14)
Wherein：VdcFor DC bus-bar voltage.
It is the reason of leading to restriction of current, for unified voltage constraint and electric current that line inductance electromotor maximum, which bears electric current,
Constraint, restriction of current expression formula, which is converted to voltage expression, using formula (5) to obtain：
Wherein：ImaxElectric current is maximum
Amplitude limit value.
Arrangement formula (15) can obtain：
(uα1(k)+ox)2+(uβ1(k)+oy)2≤r2 (16)
Wherein：
From formula (16) and formula (14) it is found that voltage constraint and restriction of current are circle, two circle common portions are to meet
The region of constraints, as shown in Figure 3.Therefore optimal value has to fall can meet constraints in the region.And formula
(13) optimal value solved, it is difficult to fall in the public domain.Therefore, meet constraints most to be found using formula (13)
The figure of merit, the present invention propose a kind of iterative algorithm, the optimal value finally solved are enabled to meet constraints.
It is assumed that the optimal value solved is discontented with afc voltage constraints, defines any point in circle (including boundary) and arrive optimal value
Between the minimum new optimal value solution of distance, then the new optimal value solution can be solved being：
Wherein：WithRespectively optimal value α beta -axis components；WithRespectively meet voltage constraints
Optimal value α beta -axis components.
Similarly, it can solve when being unsatisfactory for restriction of current condition, optimal value expression is：
Wherein：WithRespectively meet the optimal value α beta -axis components of restriction of current condition.
It is iterated judgement by recycling formula (17) and (18), until finally meeting constraints.Iteration is calculated
Method flow is as shown in Figure 4.
Four, simplify modulation strategy
Traditional Space Vector Modulation strategy needs to calculate trigonometric function, needs certain calculation amount.In order to avoid triangle letter
Several calculating, the present invention propose that a kind of modulation strategy of simplification, concrete methods of realizing are as follows：
It is assumed that the optimal value that iterative algorithm solves before is fallen in the first sector, optimal value place can be solved and cross origin
The intersection point of straight line and the first sector borders is defined as time figure of merit, can be obtained according to Fig. 5 and similar triangles theorem：
Wherein：Modulation ratios of the d between the first sector neighbouring vectors.
It is 0 that front, which derives and enables to secondary angular error between the figure of merit and optimal value, in order to enable amplitude and optimal value
Unanimously, defining amplitude modulation ratio is：
Wherein：||V*| | it is long for optimal value mould；| | V'| | it is long for time figure of merit mould.
It since the secondary figure of merit is fallen always on regular hexagon boundary, is calculated to simplify, voltage limit can be justified half
The mould of the diameter approximate substitution time figure of merit is long, then formula can be reduced to：
Wherein：R is voltage limit radius of circle.
The voltage vector of final modulation output expresses formula and is：
Vin=m (1-d) V1+mdV2 (22)
Wherein：V1And V2For the two adjacent voltage vectors in the first sector.
Using analysis method before, other sectors can be obtained similar to conclusion, formula (22) voltage vector expression formula is turned
The three-phase bridge arm duty ratio form of expression is shifted to, as shown in the table：
Withα, beta -axis component for motor input voltage vector optimal value.
According to upper table it is found that optimal value by solving, can directly determine three-phase bridge arm duty ratio, not need complexity
Coordinate transform and trigonometric function calculate, it is many to realize that process simplifies compared with Space Vector Modulation Strategy.
As it will be easily appreciated by one skilled in the art that the foregoing is merely illustrative of the preferred embodiments of the present invention, not to
The limitation present invention, all within the spirits and principles of the present invention made by all any modification, equivalent and improvement etc., should all include
Within protection scope of the present invention.
Claims (2)
1. a kind of long model predictive control method of line inductance electromotor multistep, which is characterized in that include the following steps：
(1) it samples：Acquire the state variable [i of k moment line inductance electromotorsα1,iβ1,ψα2,ψβ2] and angular velocity omega2, iα1,iβ1
The respectively α of electric motor primary electric current, beta -axis component, ψα2,ψβ2The respectively α of motor secondary magnetic linkage, beta -axis component；
(2) the motor input voltage vector optimal value under unconfined condition is solved：The data information that the k moment acquires substitutes into optimal value
Motor input voltage vector optimal value is solved in calculating formula, the optimal value calculating formula is expressed as：
Wherein,
Subscript T representing matrix transposition；
P is prediction step；
For motor input voltage vector optimal value；
uα1(k),uβ1(k)The respectively α, beta -axis component of input voltage vector；
I is second order unit matrix, and O is second order null matrix；
Weight coefficient Γy=diag (Γy,1,Γy,2,...,Γy,p), Γu=diag (Γu,1,Γu,2,...,Γu,p), diag ()
For diagonal matrix, current reference value
ω2Represent secondary angular speed；uα1(k)And uβ1(k)Represent motor input voltage vector α, beta -axis component；iα1(k)And iβ1(k)It represents
Electric motor primary electric current α, beta -axis component；R1And R2Respectively represent the primary and secondary resistance of motor；ψα1(k)And ψβ1(k)Represent motor secondary magnetic
α, the beta -axis component of chain；Ll1And Ll2Represent the primary and secondary leakage inductance of motor；D is electric motor primary length；V is electricity
Machine linear velocity；LmFor motor mutual inductance；Lr=Ll2+Lm[1-f(Q)]；Ls=Ll1+Lm[1-f(Q)]；L'm=
Lm[1-f(Q)]；TsFor the sampling period；u(k-1)For k-1 moment motor input voltage vectors；
(3) whether judgement motor input voltage vector optimal value meets voltage constraints, if satisfied, (5) are then entered step, it is no
It then enters step (4), the voltage constraints is expressed as：
(uα1(k))2+(uβ1(k))2≤R2
Wherein：VdcFor DC bus-bar voltage；
(4) to meet voltage constraints as target update motor input voltage vector optimal value：
The motor input voltage vector time figure of merit is sought first：
Wherein：WithMeet α, β of the motor input voltage vector time figure of merit of voltage constraints after respectively updating
Axis component,WithRespectively update α, the beta -axis component of front motor input voltage vector optimal value；
Then using the updated secondary figure of merit as new optimal value, i.e.,
(5) whether judgement motor input voltage vector optimal value meets restriction of current condition, if satisfied, (7) are then entered step, it is no
It then enters step (6), the restriction of current condition is expressed as：
(uα1(k)+ox)2+(uβ1(k)+oy)2≤r2
Wherein： ImaxElectric current maximum limit amplitude；
(6) to meet restriction of current condition as target update motor input voltage vector optimal value：
The motor input voltage vector time figure of merit is calculated first：
Wherein：WithMeet α, β of the motor input voltage vector time figure of merit of restriction of current condition after respectively updating
Axis component,WithRespectively update α, the beta -axis component of front motor input voltage vector optimal value；
Then using the motor input voltage vector time figure of merit as new optimal value, i.e.,
Finally judge whether motor input voltage vector optimal value meets voltage constraints, enters step (7) if meeting, otherwise
It enters step (4)：
(7) duty ratio that three-phase bridge arm is calculated according to motor input voltage vector optimal value, is given inverter modulation control
Electric machine operation state.
2. according to the method described in claim 1, it is characterized in that, the specific implementation of the step (7) is：According to before
The optimal value for meeting constraints is iteratively solved out, is modulated to inverter using modulation strategy is simplified, implements process
It is as follows：
According to motor input voltage vector optimal value, affiliated sector is judged, the corresponding duty ratio calculation formula in sector is utilized to calculate
The duty ratio of three-phase bridge arm；The sector and the correspondence of duty ratio calculation formula are as shown in the table：
Wherein：M is amplitude modulation ratio；||V*| | it is long for the mould of motor input voltage vector optimal value；WithFor
α, the beta -axis component of motor input voltage vector optimal value.
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| CN108964549B (en) * | 2018-07-04 | 2020-01-03 | 华中科技大学 | Thrust control method for linear induction motor without weight coefficient model prediction |
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| CN109921706B (en) * | 2019-01-18 | 2021-01-19 | 华中科技大学 | Control method and system for predicting thrust of linear induction motor containing current constraint model |
| CN109728757B (en) * | 2019-02-28 | 2020-11-24 | 华中科技大学 | Method and system for controlling prediction thrust of linear induction motor by using arbitrary double-vector model |
| CN111769770B (en) | 2020-01-17 | 2022-03-18 | 华中科技大学 | Linear induction motor multi-step finite set model prediction control method and system |
| CN112398401B (en) * | 2020-10-29 | 2022-03-29 | 上海大学 | Low switching frequency multi-step model prediction control method based on parameter mismatch |
| CN112234899B (en) * | 2020-10-29 | 2021-12-24 | 河北工业大学 | Method and system for setting prediction step length of permanent magnet synchronous motor model |
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