CN109039168A - The multiple dimensioned approximate explicit model forecast Control Algorithm of brshless DC motor - Google Patents
The multiple dimensioned approximate explicit model forecast Control Algorithm of brshless DC motor Download PDFInfo
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- CN109039168A CN109039168A CN201810771562.4A CN201810771562A CN109039168A CN 109039168 A CN109039168 A CN 109039168A CN 201810771562 A CN201810771562 A CN 201810771562A CN 109039168 A CN109039168 A CN 109039168A
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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
- H02P6/00—Arrangements for controlling synchronous motors or other dynamo-electric motors using electronic commutation dependent on the rotor position; Electronic commutators therefor
- H02P6/08—Arrangements for controlling the speed or torque of a single motor
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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
- H02P23/00—Arrangements or methods for the control of AC motors characterised by a control method other than vector control
- H02P23/0004—Control strategies in general, e.g. linear type, e.g. P, PI, PID, using robust control
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Abstract
The multiple dimensioned approximate explicit model forecast Control Algorithm of brshless DC motor, includes the following steps: that step 1) obtains Parametric optimization problem to Modeling of BLDCM Control System, that is, hereafter want approximate object；Step 2) piecewise linearity insertion tentatively obtains a kind of approximation control rule；Step 3) adaptive layered approximation to function, the form of conversion approximation control rule；Step 4) introduces center of gravity function and obtains the rule of the approximation control based on center of gravity function using barycentric interpolation；The multiple dimensioned approximate explicit model PREDICTIVE CONTROL of step 5) electric machine control system.The present invention improves the real-time of motor control, reduces the demand of controller memory capacity, saves in the line computation time, and possesses good control effect.
Description
Technical field
The present invention relates to a kind of optimal control methods of brushless motor.
Background technique
With the development of society, the effect of motor is increasingly prominent.Brshless DC motor is to pass through electronics in all kinds of motors
Device replaces a kind of motor of traditional mechanical switching, it is by the features such as torque is big, precision is high and work efficiency is high,
It is widely used in the fields such as computer, aviation, military affairs, industry and office automation.DC brushless motor can maintain brush
The advantageous characteristic of direct current generator, moreover it is possible to avoid brush bring a series of problems, including mechanical friction loss is big, noise is big and the longevity
It orders the disadvantages of short, therefore expands the application range of direct current generator to a certain extent.
For handling Multivariable Constrained optimal control problem, model predictive control method is a kind of very effective method,
It by years of researches and explores, achieves significant progress and be used widely.Model Predictive Control uses prediction mould
The new control strategy such as type, rolling optimization, feedback compensation and multi-step prediction, enables it effectively to inhibit to be to a certain extent
Influence of the inaccurate and external interference of system model for system control performance.But Model Predictive Control have the shortcomings that it is very big just
It is that Model Predictive Control is only applicable to slow procedure, has sizable limitation in the faster field of processing speed.It studies thus
Personnel propose explicit model PREDICTIVE CONTROL.
Explicit model PREDICTIVE CONTROL (Explicit Model Predictive Control) introduces multi-parametric programming reason
By carrying out convex division to the state region of system, and establish the optimal control law of the optimization problem on corresponding each Condition Areas
Explicit function relationship (being restrained for the Linear Control of state) between state；This method also has its limitation, it is only applicable to about
The system of beam, and complexity can be in exponential increase with the increase of problem scale, i.e., when input number increases or controls
Time domain processed just needs very big memory space when elongated, increases so that searching control law and handling the difficulty of problem.
Summary of the invention
The present invention proposes brshless DC motor to overcome the disadvantages mentioned above of the optimal control method of existing brushless motor
Multiple dimensioned approximate explicit model forecast Control Algorithm.
The method of the present invention, so that Condition Areas becomes the rectangle of rule, is obtained by carrying out gridding processing to state space
It is restrained to approximation control, by the way that maximum level status Condition Areas quantity is arranged, thus the convenient process searched online.
When being controlled using explicit model PREDICTIVE CONTROL, online progress solving optimization problem is not had to, off-line calculation is good
The control law of each Condition Areas, finds the subregion where current system conditions online, just can determine that the optimal of parameter current
Control amount.But when inputting number increase or elongated control time domain, complexity can be exponentially increased, so that online search control
Rule difficulty becomes larger.For the disadvantage, the present invention provides a kind of new multiple dimensioned approximation method, by seeking the thinking of approximate solution,
State space carries out the gridding processing of rule, convenient to search control rate online, can also change state by setting level
Divide domain number.
On multiple dimensioned approximate explicit prediction model control method algorithm based on explicit model forecast Control Algorithm, introduce
Piecewise linearity insertion and adaptive layered function approximation method, and combine barycentric coodinates and barycentric interpolation method.Pass through segmentation
Linear interpolation carries out lattice to subspace method, describes mesh point with basic function, the in due course described point of use has just started first big
The division subspace of cause, with layering basic function again to those there are no the region of enough approximations carry out it is subdivided, it is continuous in this way
Constantly divide layer by layer, until all regions are all by approximation, finally obtain one based on layering detail index it is close
Like control law.In order to facilitate processing higher-dimension problem, and adaptive layered approximation to function method is introduced, approximate control law is suitably become
Shape obtains another form of approximation control rule, is finally introducing the method for center of gravity function and center of gravity function interpolation for pairing approximation control
Make the feasibility of rule and the proof of stability.
To be more clear the object, technical solutions and advantages of the present invention, below just to technical solution of the present invention make into
The description of one step.The multiple dimensioned approximate explicit model forecast Control Algorithm of brshless DC motor, includes the following steps:
Step 1) establishes brushless DC motor system model；
The voltage equation of each phase winding of stator are as follows:
Wherein RsIt is the stator resistance of every phase；Ia,Ib,IcIt is stator phase currents；P is differential calculation symbol；Ea,Eb,EcIt is
The induced electromotive force of motor；Vas、Vbs、VcsIt is the voltage input of each phase；L is each phase winding mutual inductance.
It is expressed as the form of state equation after the equation of motion is linearized are as follows:
Wherein x=[Ia Ib Ic w θ]T, u three-phase input voltage, u=[ua ub uc Tl]T, parameter A, B are state equation
Coefficient, Ia、Ib、IcIt is stator phase currents, w is rotor velocity, and θ is rotor-position as state vector.
The quadratic performance index for designing control system is as follows:
J*(x, u)=x ' Qx+u ' Ru+ (y-yref)′Qy(y-yref) (3)
Wherein Q is state weight matrix, and R is weighted input matrix, QyIt is SOT state of termination weight, u is input vector, and x is
State vector, Ia,Ib,IcFor stator phase currents；Based on the above performance indicator and system state space expression formula, at it
Reason and calculating；Then by brushless DC motor control system performance index function J*It is converted, converts thereof into a parameter
Optimization problem u*(x), this Parametric optimization problem is exactly the object of last desired approximation.
After obtaining electric machine control system performance index function J, using piecewise linearity insertion by electric machine control system index
The corresponding polyhedral subspace method of function J is divided, and introduces adaptive layered function, to the approximation control obtained
Rule has carried out deformation appropriate, here it is having carried out the division of height rule to control law corresponding to Condition Areas, while again
Approximation has been carried out, and has met system feasibility and stability.
The processing of step 2) piecewise linear interpolation；
The cell cube Ω tieed up with dd=[0,1]dInstead of subspace method χ, function u (x): R is consideredd→ R, x=
(x1,...,xd), use ΩdIn point come to cell cube carry out lattice.It allows l as level of discretization, uses hl=2-lTo indicate
Sizing grid.This d rectangular mesh tieed up is set to Ωl。ΩlOn mesh point be represented as
Here i indicates Ω with multiple indexeslOn point coordinate.
It selects one-dimensional cap function phi (x) and converts and derive to describe mesh point, φ (x) is converted to a segmentation
D Wiki function:
Basic function φl,i(x) it is used to the space of building segmentation d dimension functionThis segmentation d dimension function is:
Each multi-variable functionIt can be expressed as unique φl,i(x) weighted sum:
It can be described as being segmented d dimensional linear functionD dimension hierarchical function space sum, then it is each is changeable
Flow functionWrite as a weighted sum:
Here wk,iReferred to as it is layered detail index.By defining Ψk,i=φk,i(x), i ∈ Ik, and write as:
The approximation control rule based on layering detail index is obtained.It is to sum up exactly using above-mentioned mathematical method, first
In due course described point is carried out, rough subspace is divided, it is then still subdivided without the region progress of enough approximations to those again,
It continuously divides layer by layer in this way, until all regions are all by approximation.
Step 3) quotes adaptive layered approximation to function method, and approximate control law is become another form；
Introduce adaptive layered approximation to function method.Consider function u (x) ∈ R, x:=(x1,...,xd)∈Ωd, set first
One rough primary grid coefficient l0>=0, for l0Mesh point, store relevant functional value u (xl0), then mesh point obtains
Continuous processing has been arrived until desired horizontal lmax.In each step, those parts for being unsatisfactory for particular requirement will be obtained more
Fine processing.For the mesh point in k level newly obtained, functional value is not u (xk), but in horizontal k-1
The difference of functional value is:
This difference can be stored, wk,iReferred to as it is layered detail.It can be nearly by adaptive layered approximation to function method
It is indicated depending on control law are as follows:
Λ is the set of relevant level index.By the property of hereinbefore involved basic function, this is approximately to connect
Continuous.
Step 4) introduce the method for center of gravity function and barycentric interpolation for pairing approximation control law feasibility and stability into
Line justification；
3.1 for setHere conv (R) is convex set, and extr (R) is pole, introduces barycentric coodinates function fv
(x), wherein x ∈ S, v ∈ extr (S),
fv(x) >=0 positive value (12)
A function is inserted on a grid, according to the property of barycentric coodinates function, the functional value only on vertex is used
To carry out interpolation arithmetic.What adaptive layered approximation to function method obtained is some hypermatrix, these hypermatrix are by interpolation operation
It limits.Because hypermatrix is convex polytope, approximation control rule ensures that feasibility, stability and performance range.
3.2, by approximate closed-loop systemLiapunov function can come verify these regions
Row, stability and performance range.Approximation control rule has been obtained in hierarchical function in step 2 described above, then right
Each hypermatrix region R ∈ Rh,It can be write as the form obtained with center of gravity function interpolation:
For problemAnd if only ifTo be with all v ∈ extr (R) it is feasible, that
Approximation control ruleIt is exactly a feasible solution of optimal problem (2-1).
If be defined onGravity's center control rule aboveAll be to all v ∈ extr (R) it is feasible, then:
For set R*:={ x ∈ R:R ∈ Rh, err (R) >=0 }, approximate functionIt is a Liapunov letter
Number.If R*This region is constrained, then from(R*Boundary) and Jmin(OnMinimum value)
Find out setIt is restrained in approximation controlUnder it is constant, so control law is stable.
The multiple dimensioned approximate explicit model PREDICTIVE CONTROL of step 5) electric machine control system；
The multiple dimensioned explicit model PREDICTIVE CONTROL course of work of electric machine control system is divided into two parts；When off-line calculation, press
According to brshless DC motor Control performance standard, using above-mentioned steps 1)-step 4) establish electric machine control system state region it is convex
It divides, is drawn the corresponding polyhedral subspace method of electric machine control system target function J using piecewise linearity insertion
Point, and adaptive layered function is introduced again, deformation appropriate has been carried out to the approximation control rule obtained；
In line computation, by measuring stator phase currents Ia, Ib, Ic, angle speed w and electric degree angle θ when motor operation etc.
Physical quantity, then the state that motor is presently in is found out by given parameters, and be in by determining current time system of tabling look-up
Which subregion of state, and according to the optimum control amount at the optimal control law calculating current time on the subregion.Work as electrical power
After normal work, in a swing circle, stator three-phase symmetric winding generates six stator composite magnetic powers in space.When turn
It is sub to turn over 60 every time。When electric degree angle, stator three-phase symmetric winding is primary with regard to commutation, and corresponding stator composite magnetic power can also jump one
It is secondary.Each stator winding conduction duration is 120 °, and each stator composite magnetic power will continue 60 °, i.e. 1/6 swing circle.
Therefore driving motor rotor ceaselessly rotates under the stator composite magnetic power continuously jumped at this six, and obtained by inquiry
Stablize in the normal range when control law makes torque work.
The invention has the following advantages that
1. the present invention solves the problems, such as that original motor explicit model forecast Control Algorithm complexity is too high, by obtaining electricity
Machine explicit model approximation control rule, and original memory module is changed in the storage of Condition Areas, it uses very regular
Coarse gridding, bring great convenience to online search procedure.
2. this method is applied in brshless DC motor control problem by the present invention, the real-time of motor control is substantially increased
Property, reduce the demand of controller memory capacity, save in the line computation time, and possesses good control effect.
3. the present invention is directed to the actual requirement of electric machine control system, using multiple dimensioned thought, by for motor control
Performance, control complexity, the compromise between realtime control and controller capacity, meet various controls require with
Performance constraints.
Detailed description of the invention
Fig. 1 is brshless DC motor hardware
Fig. 2 is brshless DC motor schematic diagram
Fig. 3 is one-dimensional cap functional arrangement
Fig. 4 is multiple dimensioned approximate overview flow chart
Fig. 5 is the Condition Areas that accurate EMPC is obtained under primary condition
Fig. 6 is the state change curve under primary condition
Fig. 7 is the Condition Areas that precisely EMPC is obtained after modification is set
Fig. 8 is the state change curve obtained after modification is set
Fig. 9 is the Condition Areas that the multiple dimensioned approximation method that maximum level is 6 obtains
Figure 10 is the Condition Areas that the multiple dimensioned approximation method that maximum level is 9 obtains
Specific embodiment
The present invention will be further described below with reference to the accompanying drawings:
Multiple dimensioned approximate explicit model of the invention predicts disk drive optimal control method, is as shown in Figure 1 application pair
As for brshless DC motor hardware chart, Fig. 2 is brshless DC motor schematic diagram, while specifically includes the following steps:
Step 1) establishes brushless DC motor system model；
The voltage equation of each phase winding of stator are as follows:
Wherein RsIt is the stator resistance of every phase；Ia,Ib,IcIt is stator phase currents；P is differential calculation symbol；Ea,Eb,EcIt is
The induced electromotive force of motor；Vas、Vbs、VcsIt is the voltage input of each phase；L is each phase winding mutual inductance.
It is expressed as the form of state equation after the equation of motion is linearized are as follows:
Wherein x=[Ia Ib Ic w θ]T, u three-phase input voltage, u=[ua ub uc Tl]T, parameter A, B are state equation
Coefficient, Ia、Ib、IcIt is stator phase currents, w is rotor velocity, and θ is rotor-position as state vector.
The quadratic performance index for designing control system is as follows:
J*(x, u)=x ' Qx+u ' Ru+ (y-yref)′Qy(y-yref) (3)
Wherein Q is state weight matrix, and R is weighted input matrix, QyIt is SOT state of termination weight, u is input vector, and x is
State vector, Ia,Ib,IcFor stator phase currents；Based on the above performance indicator and system state space expression formula, at it
Reason and calculating；Then by brushless DC motor control system performance index function J*It is converted, converts thereof into a parameter
Optimization problem u*(x), this Parametric optimization problem is exactly the object of last desired approximation.
After obtaining electric machine control system performance index function J, using piecewise linearity insertion by electric machine control system index
The corresponding polyhedral subspace method of function J is divided, and introduces adaptive layered function, to the approximation control obtained
Rule has carried out deformation appropriate, here it is having carried out the division of height rule to control law corresponding to Condition Areas, while again
Approximation has been carried out, and has met system feasibility and stability.
The processing of step 2) piecewise linear interpolation；
The cell cube Ω tieed up with dd=[0,1]dInstead of subspace method χ, function u (x): R is consideredd→ R, x=
(x1,...,xd), use ΩdIn point come to cell cube carry out lattice.It allows l as level of discretization, uses hl=2-lTo indicate
Sizing grid.This d rectangular mesh tieed up is set to Ωl。ΩlOn mesh point be represented as
Here i indicates Ω with multiple indexeslOn point coordinate.
It selects one-dimensional cap function phi (x) and converts and derive to describe mesh point, cap function is as shown in figure 3, φ (x)
It is converted to the d Wiki function of a segmentation:
Basic function φl,i(x) it is used to the space of building segmentation d dimension functionThis segmentation d dimension function is:
Each multi-variable functionIt can be expressed as unique φl,i(x) weighted sum:
It can be described as being segmented d dimensional linear functionD dimension hierarchical function space sum, then it is each is changeable
Flow functionWrite as a weighted sum:
Here wk,iReferred to as it is layered detail index.By defining Ψk,i=φk,i(x), i ∈ Ik, and write as:
The approximation control rule based on layering detail index is obtained.It is to sum up exactly using above-mentioned mathematical method, first
In due course described point is carried out, rough subspace is divided, it is then still subdivided without the region progress of enough approximations to those again,
It continuously divides layer by layer in this way, until all regions are all by approximation.
Step 3) quotes adaptive layered approximation to function method, and approximate control law is become another form；
Introduce adaptive layered approximation to function method.Consider function u (x) ∈ R, x:=(x1,...,xd)∈Ωd, set first
One rough primary grid coefficient l0>=0, for l0Mesh point, store relevant functional value u (xl0), then mesh point obtains
Continuous processing has been arrived until desired horizontal lmax.In each step, those parts for being unsatisfactory for particular requirement will be obtained more
Fine processing.For the mesh point in k level newly obtained, functional value is not u (xk), but in horizontal k-1
The difference of functional value is:
This difference can be stored, wk,iReferred to as it is layered detail.It can be nearly by adaptive layered approximation to function method
It is indicated depending on control law are as follows:
Λ is the set of relevant level index.By the property of hereinbefore involved basic function, this is approximately to connect
Continuous.
Step 4) introduce the method for center of gravity function and barycentric interpolation for pairing approximation control law feasibility and stability into
Line justification；
3.1, for setHere conv (R) is convex set, and extr (R) is pole, introduces barycentric coodinates function fv
(x), wherein x ∈ S, v ∈ extr (S),
fv(x) >=0 positive value (12)
A function is inserted on a grid, according to the property of barycentric coodinates function, the functional value only on vertex is used
To carry out interpolation arithmetic.What adaptive layered approximation to function method obtained is some hypermatrix, these hypermatrix are by interpolation operation
It limits.Because hypermatrix is convex polytope, approximation control rule ensures that feasibility, stability and performance range.
3.2, by approximate closed-loop systemLiapunov function verify the feasible of these regions
Property, stability and performance range.Approximation control rule has been obtained in hierarchical function in step 2 described above, then to every
One hypermatrix region R ∈ Rh,It can be write as the form obtained with center of gravity function interpolation:
For problemAnd if only ifTo be with all v ∈ extr (R) it is feasible, that
Approximation control ruleIt is exactly a feasible solution of optimal problem (2-1).
If be defined onGravity's center control rule aboveAll be to all v ∈ extr (R) it is feasible, then:
For set R*:={ x ∈ R:R ∈ Rh, err (R) >=0 }, approximate functionIt is a Liapunov letter
Number.If R*This region is constrained, then from(R*Boundary) and Jmin(OnMinimum value)
Find out setIt is restrained in approximation controlUnder it is constant, so control law is stable.Entirely
Process is as shown in Figure 4.
The multiple dimensioned approximate explicit model PREDICTIVE CONTROL of step 5) electric machine control system；
The multiple dimensioned explicit model PREDICTIVE CONTROL course of work of electric machine control system is divided into two parts；When off-line calculation, press
According to brshless DC motor Control performance standard, using above-mentioned steps 1)-step 4) establish electric machine control system state region it is convex
It divides, is drawn the corresponding polyhedral subspace method of electric machine control system target function J using piecewise linearity insertion
Point, and adaptive layered function is introduced again, deformation appropriate has been carried out to the approximation control rule obtained；
In line computation, by measuring stator phase currents Ia, Ib, Ic, angle speed w and electric degree angle θ when motor operation etc.
Physical quantity, then the state that motor is presently in is found out by given parameters, and be in by determining current time system of tabling look-up
Which subregion of state, and according to the optimum control amount at the optimal control law calculating current time on the subregion.Work as electrical power
After normal work, in a swing circle, stator three-phase symmetric winding generates six stator composite magnetic powers in space.When turn
It is sub to turn over 60 every time.When electric degree angle, stator three-phase symmetric winding is primary with regard to commutation, and corresponding stator composite magnetic power can also jump one
It is secondary.Each stator winding conduction duration is 120., each stator composite magnetic power will continue 60., i.e. 1/6 swing circle.
Therefore driving motor rotor ceaselessly rotates under the stator composite magnetic power continuously jumped at this six, and obtained by inquiry
Stablize in the normal range when control law makes torque work.
Analysis of cases
The present invention presents the pre- observing and controlling of multiple dimensioned explicit model by carrying out emulation experiment by object of brshless DC motor
Method processed specifically shows in motor control, by contrast and experiment, embodies superior function of the invention.
It is calculated with accurate EMPC, prediction time domain is 2, in the case that stator A phase current is constrained to as [- 2,2], system
The Condition Areas that off-line calculation obtains is as shown in figure 5, wherein one be obtained 1260 Condition Areas.It is illustrated in figure 6 initial
State is x0=[0.2；0.2；0.002] state change curve.As seen from the figure, system mode value becomes in setting restriction range
Change, control effect is clearly.When being calculated with multiple dimensioned approximation method, prediction time domain is 2, and maximum level is set as 6, xmin=
[-2；-2；0], xmax=[2；2；6.2832], the Condition Areas finally obtained is as shown in fig. 7, one has been obtained 120 states point
Area is fewer than the number of partitions that accurately EMPC is obtained.
Modification setting on the original basis is counted with accurate EMPC again when phase current constraint is changed to [- 2,0.6]
It calculates, other conditions are constant, and the Condition Areas that system-computed obtains is as shown in figure 8, one has been obtained 1159 Condition Areas.Such as figure
9 show original state as x0=[0.2；0.2；0.002] state change curve.Multiple dimensioned approximation method is used instead to be calculated
When, other conditions remain unchanged, and after the maximum level of Multi-Scale Calculation is set as 9, have obtained 452 Condition Areas, specifically such as
Shown in Figure 10.By comparison it can be concluded that, can be by the way that maximum number of levels be arranged come the quantity of restrained condition subregion, for accurate
Degree requires not being extra high system, and the quantity that reasonable maximum number of levels reduces Condition Areas can be set, additionally, due to
The gridding that multiple dimensioned approximate algorithm carries out rule to state space is handled, and substantially increases the efficiency of inquiry.
To sum up it is a series of comparison and analysis shows, the control for brushless DC motor system, the pre- observing and controlling of explicit model
It makes multiple dimensioned approximation method and is better than explicit model forecast Control Algorithm.
Content described in this specification embodiment is only enumerating to the way of realization of inventive concept, protection of the invention
Range should not be construed as being limited to the specific forms stated in the embodiments, and protection scope of the present invention is also and in art technology
Personnel conceive according to the present invention it is conceivable that equivalent technologies mean.
Claims (1)
1. a kind of multiple dimensioned approximate explicit model forecast Control Algorithm of brshless DC motor comprising the steps of:
Step 1) establishes brushless DC motor system model；
The voltage equation of each phase winding of stator are as follows:
Wherein RsIt is the stator resistance of every phase；Ia,Ib,IcIt is stator phase currents；P is differential calculation symbol；Ea,Eb,EcIt is motor
Induced electromotive force；Vas、Vbs、VcsIt is the voltage input of each phase；L is each phase winding mutual inductance；
It is expressed as the form of state equation after the equation of motion is linearized are as follows:
Wherein x=[Ia Ib Ic w θ]T, u three-phase input voltage, u=[ua ub uc Tl]T, parameter A, B are for state equation
Number, Ia、Ib、IcIt is stator phase currents, w is rotor velocity, and θ is rotor-position as state vector；
The quadratic performance index for designing control system is as follows:
J*(x, u)=x ' Qx+u ' Ru+ (y-yref)′Qy(y-yref) (3)
Wherein Q is state weight matrix, and R is weighted input matrix, QySOT state of termination weight, u is input vector, x be state to
Amount, Ia,Ib,IcFor stator phase currents；Based on the above performance indicator and system state space expression formula, it is handled and is counted
It calculates；Then by brushless DC motor control system performance index function J*It is converted, converts thereof into a parameter optimization and ask
Topic, this Parametric optimization problem is exactly the object of last desired approximation；
After obtaining electric machine control system performance index function J, using piecewise linearity insertion by electric machine control system target function J
Corresponding polyhedral subspace method is divided, and introduces adaptive layered function, to the approximation control obtained restrain into
It has gone deformation appropriate, here it is having carried out the division of height rule to control law corresponding to Condition Areas, while having carried out again
Approximation, and meet system feasibility and stability；
The processing of step 2) piecewise linear interpolation；
The cell cube Ω tieed up with dd=[0,1]dInstead of subspace method χ, function u (x): R is consideredd→ R, x=(x1,...,
xd), use ΩdIn point come to cell cube carry out lattice；It allows l as level of discretization, uses hl=2-lTo indicate that grid is big
It is small；This d rectangular mesh tieed up is set to Ωl；ΩlOn mesh point be represented as:
Here i indicates Ω with multiple indexeslOn point coordinate；
It selects one-dimensional cap function phi (x) and converts and derive to describe mesh point, φ (x) is converted to the d dimension of a segmentation
Basic function:
Basic function φl,i(x) it is used to the SPACE V of building segmentation d dimension functionl d, this segmentation d dimension function is:
Vl d:=span { φl,i: 0≤i≤2l} (6)
Each multi-variable function ul(x)∈Vl dIt can be expressed as unique φl,i(x) weighted sum:
Vl dIt can be described as being segmented d dimensional linear functionD dimension hierarchical function space sum, then by each multivariable letter
Number ul(x)∈Vl dWrite as a weighted sum:
Here wk,iReferred to as it is layered detail index；By defining ψk,i=φk,i(x), i ∈ Ik, and write as:
The approximation control rule based on layering detail index is obtained；It is to sum up exactly first to be carried out using above-mentioned mathematical method
In due course described point divides rough subspace, then still subdivided without the region progress of enough approximations to those again, in this way
It continuously divides layer by layer, until all regions are all by approximation；
Step 3) quotes adaptive layered approximation to function method, and approximate control law is become another form；
Introduce adaptive layered approximation to function method；Consider function u (x) ∈ R, x:=(x1,...,xd)∈Ωd, one is set first
Rough primary grid coefficient l0>=0, for l0Mesh point, store relevant functional valueThen mesh point obtains
Continuous processing is until desired horizontal lmax；In each step, those parts for being unsatisfactory for particular requirement will obtain more fine
Processing；For the mesh point in k level newly obtained, functional value is not u (xk), but it is in the function of horizontal k-1
The difference of value is:
This difference can be stored, wk,iReferred to as it is layered detail；Myopia can be controlled by adaptive layered approximation to function method
System rule indicates are as follows:
Λ is the set of relevant level index；By the property of hereinbefore involved basic function, this is approximately continuous；
Step 4) introduces feasibility and stability of the method for center of gravity function and barycentric interpolation for pairing approximation control law and is demonstrate,proved
It is bright；
3.1, for setHere conv (R) is convex set, and extr (R) is pole, introduces barycentric coodinates function fv(x),
Wherein x ∈ S, v ∈ extr (S),
fv(x) >=0 positive value (12)
A function is inserted on a grid, according to the property of barycentric coodinates function, only the functional value on vertex be used into
Row interpolation operation；What adaptive layered approximation to function method obtained is some hypermatrix, these hypermatrix are limited by interpolation operation
's；Because hypermatrix is convex polytope, approximation control rule ensures that feasibility, stability and performance range；
3.2, by approximate closed-loop systemLiapunov function verify the feasibility in these regions,
Stability and performance range；Approximation control rule has been obtained in hierarchical function in step 2 described above, then to each
Hypermatrix region R ∈ Rh,It can be write as the form obtained with center of gravity function interpolation:
For problemAnd if only ifTo being feasible with all v ∈ extr (R), then closely
Like control lawIt is exactly a feasible solution of optimal problem (2-1)；
If be defined onGravity's center control rule aboveAll be to all v ∈ extr (R) it is feasible, then:
For set R*:={ x ∈ R:R ∈ Rh, err (R) >=0 }, approximate functionIt is a liapunov function；Such as
Fruit R*This region is constrained, then from(R*Boundary) and Jmin(OnMinimum value) can find out
SetIt is restrained in approximation controlUnder it is constant, so control law is stable；
The multiple dimensioned approximate explicit model PREDICTIVE CONTROL of step 5) electric machine control system；
The multiple dimensioned explicit model PREDICTIVE CONTROL course of work of electric machine control system is divided into two parts；When off-line calculation, according to nothing
Brushless motor Control performance standard, using above-mentioned steps 1)-step 4) establishes convex stroke of state region of electric machine control system
Point, the corresponding polyhedral subspace method of electric machine control system target function J is divided using piecewise linearity insertion,
And adaptive layered function is introduced again, deformation appropriate has been carried out to the approximation control rule obtained；
In line computation, by measuring stator phase currents Ia, Ib, Ic, the physics such as angle speed w and electric degree angle θ when motor operation
Amount, then the state that motor is presently in is found out by given parameters, and state is in by determining current time system of tabling look-up
Which subregion, and according on the subregion optimal control law calculate current time optimum control amount；When electrical power is normal
After work,
In a swing circle, stator three-phase symmetric winding generates six stator composite magnetic powers in space；When rotor is each
When turning over 60 ° of electric degree angles, stator three-phase symmetric winding is primary with regard to commutation, and corresponding stator composite magnetic power can also jump once；Often
A stator winding conduction duration is 120 °, and each stator composite magnetic power will continue 60 °, i.e. 1/6 swing circle；Therefore exist
Driving motor rotor ceaselessly rotates under this six stator composite magnetic powers continuously jumped, and the control law obtained by inquiry
So that stablizing in the normal range when torque works.
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