CN108983750A - Multi-parameter stable region method for solving for the analysis of control system closed loop stability - Google Patents
Multi-parameter stable region method for solving for the analysis of control system closed loop stability Download PDFInfo
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Abstract
This exposure discloses the multi-parameter stable region method for solving for the analysis of control system closed loop stability, this method converts control system Handling Quality Requirements to the constraint condition that closed-loop pole is distributed in complex plane, using the stable region of super ellipsoids region description model multi-parameter.Firstly, calculating the stable region of single parameter respectively using protection mapping theory, the Bound constraints form about all model parameters is obtained；Secondly, being denoted as initial super ellipsoids according to the super ellipsoids of the boundary value building multi-parameter of multi-parameter tank constraint.The value of protection mapping is considered as optimization aim, model parameter is considered as optimized variable, and the pantograph ratio of multivariable stable region is determined by optimization problem of the building multivariable within super ellipsoids, finally determines the super ellipsoids stable region of multivariable.The present invention can quantitatively determine the variation range for meeting performance indicator model parameter, engineering application value with higher in the more situation of model parameter.
Description
Technical field
The present invention relates to becoming, closed loop stability analysis method more particularly to control system parameter in ginseng control system are more susceptible
Closed loop stability analysis is controlled under condition.
Background technique
The reliable flight control system of the development need of modern advanced aircraft plays its superior new energy.Advanced flight
The kinetic characteristics of device are not quite similar compared with conventional lighter-than-air vehicles, wherein hypersonic aircraft is using fuselage/propelling integrated
Configuration leads to there is close coupling between multisystem.Its Design of Flight Control needs to consider factors, including flight envelope across
Spend big, coupling between multisystem etc..
When carrying out Design of Flight Control, under the premise of guaranteeing system closed-loop stabilization, it is also necessary to flight control
System processed has stronger robustness, including the compacting to structural uncertainty (parameter uncertainty) and unstructured uncertainty
Ability.Wherein, unstructured uncertainty can not be analyzed using analytic method, it is also difficult to be modeled using mathematical measure；Knot
Structure uncertainty refers to controlled system, and there are Parameter Perturbations.It is compared to unstructured uncertainty, structural uncertainty is for control
It can be completely eliminated using certain means design control law for system design processed, such as self adaptive control, Huo Zhezeng
Beneficial scheduling controlling etc..Although considering the influence of Parameter Perturbation in controller design, Parameters variation can in practical application
Can with assume and mismatch.Therefore, for the system of parameter uncertainty, the boundary of parameter how is found, it is ensured that it is on boundary
When interior variation, the problem of being able to satisfy control performance requirement, become urgent need to resolve in engineer application.
Protection mapping theory is proved to be a kind of method for solving parameter uncertainty stability boundaris.Although theoretically protecting
Mapping can handle the change moduli type of Arbitrary Dimensions.But presently disclosed document only has one-parameter and two-parameter stability boundaris
Derivation algorithm.
Summary of the invention
Goal of the invention: in order to overcome the deficiencies in the prior art, this exposure provides a kind of control system closed-loop stabilization
Property analysis multi-parameter stable region method for solving.Under the conditions of multi-parameter becomes and joins or under the conditions of Parameter uncertainties, it can quantify
It is calculated under the premise of ensuring that closed-loop system meets performance, changeable parameters range, there is preferable engineering application value.
Technical solution: to achieve the above object, the technical solution adopted by the present invention are as follows: one kind is steady for control system closed loop
The multi-parameter stable region method for solving of qualitative analysis, which is characterized in that method includes the following steps:
Step 1): the protection according to the building of Performance of Closed Loop System index about control system multi-parameter closed-loop system maps,
The protection mapping is used as closed-loop characteristic constraint condition, while obtaining the original model parameter for meeting closed-loop characteristic constraint condition；
Step 2): based on protection mapping theory, the stable region of single parameter is calculated, other single ginsengs in calculating process
Number is initial value；
Step 3): according to the calculated result of step 2), the stable region of all single parameters is obtained, minimum case is calculated
Constraint, the minimum Bound constraints include multi-parameter stable region；
Step 4): the multivariable Bound constraints condition obtained according to step 3) constructs the hyperelliptic constraint of multivariable；
Step 5): it regard the constraint of hyperelliptic obtained in step 4) as primary condition, is asked by constructing constrained optimization problem
Constriction coefficient is solved, the multi-parameter super ellipsoids stable region for meeting closed-loop characteristic constraint condition is calculated.
Further, control system multi-parameter closed-loop system includes: in the step 1)
Wherein:
x∈RnIndicate system mode；The dimension of n expression state；Indicate system mode to the derivative of time；y∈RkIt indicates
System output；K indicates the dimension of system output；Indicate model parameter；npIndicate the dimension of model parameter, wherein model
Parameter includes system open loop system model parameter and closed loop controller parameter；A (p), C (p) respectively indicate the state of closed-loop system
Matrix and output matrix；Here RnIt is the n dimensional linear space of real number field, R2That is 2 dimensional linear spaces of real number field.
According to the requirement of control system flight quality, the constraint condition of Distribution of Closed Loop Poles, the closed-loop pole point are constructed
The constraint condition of cloth be state matrix A (p) characteristic value complex plane position constraint, including attenuation coefficient σ, dampingratioζ and from
Right frequencies omega, the set that the constraint condition is met in complex plane are denoted as Ω；According to protection mapping theory building about the constraint item
The protection of part maps νΩ:
vΩ(p)=vσ[A(p)]vζ[A(p)]vω[A(p)] (13)
Wherein:
vσ[A (p)] be respectively protection constrain about attenuation coefficient σ map, vζ[A (p)] is to constrain about dampingratioζ
Protection mapping, vω[A (p)] is the protection mapping constrained about natural frequency ω；Original model parameter vector p is calculated0,
Original model parameter vector p0Under the conditions of, the pole of the closed-loop system and the state matrix A (p0) characteristic value be located at constraint
In the set omega that condition determines.
Further, the stable region that single parameter is calculated in the step 2) includes the following steps:
2.1) the original model parameter vector p for meeting Performance of Closed Loop System is obtained according to model parameter vectors0；I is enabled to indicate
The serial number of element, p in model parameter vectorsiIndicate i-th of element；eiIndicate that when i-th of element be 1, when other elements are zero
Unit vector；I=1 is enabled, element sequence is initialized；
2.2) according to protection mapping theory, i-th of model parameter, which is calculated, can satisfy the variation of closed-loop characteristic constraint
Section isWherein, Δp iIndicate the lower bound of i-th of model parameter variation,Indicate i-th of model parameter variation
The upper bound；I-th of model parameter meets in the constant interval:
Wherein, Δ p indicates the variable quantity of model parameter；And on the boundary of the constant intervalInterior satisfaction:
2.3) the constant interval Δ P that i-th of model parameter meets closed-loop characteristic constraint is obtained by step 2.2)i, judge i
With the dimension n of model parameterpRelationship:
If i is less than np, then i=i+1 is enabled, is gone to step 2.2)；
Otherwise terminate, obtain the constant interval Δ P that all model parameters meet closed-loop characteristici, i=1,2 ..., np。
Further, it includes following step that the minimum Bound constraints including multi-parameter stable region are calculated in the step 3)
It is rapid:
3.1) it enables i indicate the serial number of element in model parameter vectors, and enables i=1；
3.2) i-th of model parameter according to obtained in step 2.2) meets the constant interval of closed-loop characteristic constraintCalculate the maximum symmetrical variation range of i-th of model parameter(it is symmetrical changing value here,
It is defined as that the smallest value in increase or reduction amount absolute value.Area is carried out using the p and constant interval before of small letter
Point), the Bound constraints boundary of referred to as i-th model parameter；I-th of model parameter meets in the constant interval:
3.3) Bound constraints of i-th of model parameter are obtainedWherein,It indicates in original model parameter vector
I-th of element；
Judge the dimension n of i and model parameterpRelationship:
If i is less than np, i=i+1 is enabled, is gone to step 3.2)；
Otherwise terminate, obtain the Bound constraints boundary of all parameters, each restrained boundary square is Bound constraints vector Δ pb,
Further, the hyperelliptic constraint of building multi-parameter specifically includes in step 4): original model parameter vector p0If
Model parameterMeet:
(p-p0)TS(p-p0) < 1 (18)
Wherein,
If matrixFor diagonal matrix, then it is original model parameter vector p that model parameter vectors, which meet center,0, condition
It is constrained for the super ellipsoids of S；The collection of all model parameter vectors for meeting formula (7) is combined into super ellipsoids region, is denoted as Sp(p0,S)；
Bound constraints vector Δ pbConstruct initial super ellipsoids constraint condition S0Meet:
S0=diag (1/ Δ pb)
Wherein,It indicates to vector Δ pbIn each element ask reciprocal；Matrix S0
(1/ Δ p) is indicated with 1/ Δ p of vector=diagbMiddle element is the diagonal matrix of diagonal element.
Further, the step 5) includes the following steps:
(5.1) with initial super ellipsoids constraint condition S0It constructs and is constrained about the super ellipsoids of model parameter:
(p-p0)TS0(p-p0) < 1 (19)
The super ellipsoids region for obtaining meeting the model parameter feasible solution of constraint condition (8) is Sp(p0,S0)；
Constriction coefficient r is defined, the value range of constriction coefficient indicates initial super ellipsoids region S between 0 to 1p(p0,S0)
Contraction situation；
The variation delta p=p-p of Definition Model parameter0For design variable, formula (9) is performance indicator:
JΩ(Δp,p0)=vσ(p0)=vσ(p0+ Δ p)=vζ(p0)·vζ(p0+Δp)+vωp0)·vωp0+Δp)； (20)
(5.2) constriction coefficient calculates initialization:
rl,ruRespectively indicate the bound of shrinkage ratio, irIndicate constriction coefficient i-thrSecondary iteration；
Enable ir=1, initialize constriction coefficient:
Wherein,Respectively indicate i-thrWhen secondary iteration, constriction coefficient, the upper bound of constriction coefficient and constriction coefficient
Lower bound；
(5.3) according to current contraction coefficientConstruct super ellipsoids constraint:
The set of feasible solution for meeting constraint condition (10) is combined into super ellipsoids region:
(5.4) optimal solution and performance indicator of nonlinear optimal problem under constraint condition are solved:
With performance indicator (9) for optimization aim, the nonlinear optimal problem under constraint condition (10) is constructed:
Constrained nonlinear systems problem (11) is solved using optimization algorithm, obtains optimal solution Δ poptAnd optimality
It can index JΩ,opt；Here optimization algorithm can be existing any one, including Non-Linear Programming, SQP, genetic algorithm, grain
Swarm optimization etc.；
(5.5) according to optimal performance index JΩ,optPolarity, obtain constriction coefficient in constriction coefficient or next iteration
More new strategy；
Defining the convergence precision in numerical value calculating is ε；
(5.5.1) is if 0≤JΩ,opt≤ ε, iteration ends, constriction coefficient are
(5.5.2) is if JΩ,opt> ε；
1) work as irWhen=1, iteration ends, constriction coefficient r=1；
2) work as irWhen ≠ 1, lower bound and the upper bound of constriction coefficient are updated, and use golden section criterion, according to updated
Constriction coefficient lower bound and the upper bound calculate the constriction coefficient in next iteration:
Update the number of iterations ir=ir+ 1, go to step (5.3)；
(5.5.3) is if JΩ,opt< 0 updates lower bound and the upper bound of constriction coefficient, and using golden section criterion according to new
Bound afterwards calculates constriction coefficient in next iteration:
Update the number of iterations ir=ir+ 1, go to step (5.3)；
(5.6) it according to obtained constriction coefficient r, is calculated and meets Performance of Closed Loop System constraint condition Ω lower die shape parameter
The super ellipsoids stable region of variable quantity is SΔp(p0,S0/r)。
The utility model has the advantages that this exposure compared with prior art, has the advantages that
The present invention is closed using the function between protection mapping theory building model parameter and the constraint of closed-loop system pole distribution
System, by protecting the polarity of mapping function value to judge to determine whether the Distribution of Closed Loop Poles under model parameter meets constraint condition,
And then determine the parametric stability region for meeting constraint.
It is compared to the algorithm of existing one-parameter and the solution of two-parameter stable region, the present invention can handle under multiparameter case
System stable region, extend the scope of application of the prior art, in addition, the present invention by building multivariable super ellipsoids stablize
Domain has quantitatively determined multi-parameter collaborative variation situation stability range, and controller parameter determining for model stability boundary selects
It selects and quantitatively provides inhibited stably.Term of reference is provided not only for control parameter tune ginseng, and for model parameter
The determination of stability range provides theory support.
Detailed description of the invention
Fig. 1 is multivariable stable region method for solving flow chart
Fig. 2 is the constraint of complex plane inpolar under attenuation coefficient, damping ratio and natural frequency constraint condition
Fig. 3 is constriction coefficient derivation algorithm flow chart
Fig. 4 is two-parameter oval stable region solution procedure and result signal
Specific embodiment
The present invention will be further explained with reference to the accompanying drawing.
Needle of the present invention is in the characteristic of control system multivariable collaborative variation, it is proposed that a kind of new is used for control system closed loop
The multi-parameter stable region method for solving of stability analysis.By constructing hyperelliptic constraint condition about multi-parameter, and this about
Nonlinear optimal problem under the conditions of beam, the hyperelliptic for solving the multi-parameter collaborative variation for obtaining meeting closed-loop characteristic index are stablized
Domain.
The present invention is further described in detail below with reference to the accompanying drawings and embodiments.It should be appreciated that described herein
The specific embodiments are only for explaining the present invention, is not intended to limit the present invention.In addition, each implementation of invention described below
Involved technical characteristic can be combined with each other as long as they do not conflict with each other in mode.
Embodiment: as shown in Figure 1, the stable region of controller parameter solves
Step 1: it is mapped and is made about the protection of control system multi-parameter closed-loop system according to the building of Performance of Closed Loop System index
For closed-loop characteristic constraint condition, and obtain the original model parameter for meeting closed-loop characteristic constraint:
Consider controlled device state equation are as follows:
Wherein,Indicate system mode,System mode is indicated to the derivative of time, A is the state square of open cycle system
Battle array, b are the control matrix of open cycle system.
Design full state feedback controller u=-Kx meets closed loop feedback system
Wherein, Ac(K)=A-bK indicates closed loop states matrix, σ [Ac(K)],ζ[Ac(K)],ω[Ac(K)] it respectively indicates and closes
The attenuation coefficient of all characteristic values of ring status matrix, damping ratio and natural frequency, meet the feature distribution of constraint condition (24) in
In the region Ω in complex plane as shown in Fig. 2.The abscissa of Fig. 2 indicates that real axis, ordinate indicate the imaginary axis.
For an eigenvalue λ=x+iy, wherein i indicates imaginary unit, attenuation coefficient, the meter of damping ratio and natural frequency
It is as follows to calculate formula:
σ (λ)=x
According to protection mapping theory, obtain about control parameter K and attenuation coefficient, damping ratio and the relevant guarantor of natural frequency
Shield mapping are as follows:
vΩ(K)=νσ[Ac(K)]νζ[Ac(K)]νω[Ac(K)]
DefinitionIndicate model parameter；Definition calculates and obtains the controller parameter for meeting constraint condition (24)
Are as follows:
Step 2: based on protection mapping theory, the stable region of single parameter is calculated separately, guarantees it in calculating process
His parameter is initial value；The controller parameter p for meeting Performance of Closed Loop System constraint that step 1 is calculated0As initial
Point respectively obtains the variation range of control parameter using protection mapping theory are as follows:
Step 3: according to the calculated result of step 2, the stable region Δ P of all parameters is obtained1,ΔP2, packet is calculated
The minimum Bound constraints of the stable region containing multi-parameter:
Step 4: the multivariable Bound constraints condition obtained according to step 3 constructs the hyperelliptic constraint condition of multivariable:
(p-p0)TS0(p-p0) < 1 (25)
Wherein, S0=diag (1/ Δ pb),It indicates to vector Δ pbIn each element ask down
Number；Matrix S0(1/ Δ p) is indicated with 1/ Δ p of vector=diagbMiddle element is the diagonal matrix of diagonal element.
Step 5: hyperelliptic constraint will be obtained in step 4 as primary condition, by non-linear under building constraint condition
The multi-parameter super ellipsoids stable region for meeting closed-loop characteristic constraint condition is calculated in optimization problem solving constriction coefficient, specific to flow
Journey is referring to attached drawing 3.
Remember rl,ruRespectively indicate the bound of shrinkage ratio, irIndicate constriction coefficient i-thrSecondary the number of iterations.
Enable ir=1, initialize constriction coefficient
WhereinRespectively indicate i-thrIteration, constriction coefficient, the lower bound of constriction coefficient and the upper bound.
According to current constriction coefficientConstruct the nonlinear optimal problem under constraint condition (10):
Constrained nonlinear systems problem (26) is solved using SQP optimization algorithm, obtains optimal solution Δ poptAnd it is optimal
Performance indicator JΩ,opt。
Judge more new strategy according to the polarity of optimal index and obtain final constriction coefficient r=0.61 with it is two-parameter steady
Localization, as shown in Fig. 4.
When controller parameter K variation, and meet:
Then closed-loop system still meets performance indicator requirement.
The above is only a preferred embodiment of the present invention, it should be pointed out that: for the ordinary skill people of the art
For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also answered
It is considered as protection scope of the present invention.
Claims (6)
1. the multi-parameter stable region method for solving for the analysis of control system closed loop stability, which is characterized in that this method includes
Following steps:
Step 1): the protection according to the building of Performance of Closed Loop System index about control system multi-parameter closed-loop system maps, described
Protection mapping is used as closed-loop characteristic constraint condition, while obtaining the original model parameter for meeting closed-loop characteristic constraint condition；
Step 2): based on protection mapping theory, the stable region of single parameter is calculated, other single parameters are equal in calculating process
For initial value；
Step 3): according to the calculated result of step 2), the stable region of all single parameters is obtained, minimum case is calculated about
Beam, the minimum Bound constraints include multi-parameter stable region；
Step 4): the multivariable Bound constraints condition obtained according to step 3) constructs the hyperelliptic constraint of multivariable；
Step 5): it regard the constraint of hyperelliptic obtained in step 4) as primary condition, is received by building constrained optimization problem solving
The multi-parameter super ellipsoids stable region for meeting closed-loop characteristic constraint condition is calculated in contracting coefficient.
2. the multi-parameter stable region method for solving according to claim 1 for the analysis of control system closed loop stability,
It is characterized in that, control system multi-parameter closed-loop system includes: in the step 1)
Wherein:
x∈RnIndicate system mode；The dimension of n expression state；Indicate system mode to the derivative of time；y∈RkExpression system
Output；K indicates the dimension of system output；Indicate model parameter；npIndicate the dimension of model parameter, wherein model parameter
Including system open loop system model parameter and closed loop controller parameter；A (p), C (p) respectively indicate the state matrix of closed-loop system
And output matrix；
The constraint condition of Distribution of Closed Loop Poles is constructed, the constraint condition of the Distribution of Closed Loop Poles is state matrix A (p) characteristic value
Meet the constraint condition in the position constraint of complex plane, including attenuation coefficient σ, dampingratioζ and natural frequency ω, complex plane
Set is denoted as Ω；Protection according to the building of protection mapping theory about the constraint condition maps νΩ:
νΩ(p)=νσ[A(p)]vζ[A(p)]vω[A(p)] (2)
Wherein:
vσ[A (p)] be respectively protection constrain about attenuation coefficient σ map, νζ[A (p)] is the protection constrained about dampingratioζ
Mapping, vω[A (p)] is the protection mapping constrained about natural frequency ω；Original model parameter vector p is calculated0, initial
Model parameter vectors p0Under the conditions of, the pole of the closed-loop system and the state matrix A (p0) characteristic value be located at constraint condition
In determining set omega.
3. the multi-parameter stable region method for solving according to claim 2 for the analysis of control system closed loop stability,
It is characterized in that, the stable region that single parameter is calculated in the step 2) includes the following steps:
2.1) the original model parameter vector p for meeting Performance of Closed Loop System is obtained according to model parameter vectors0；I is enabled to indicate model ginseng
The serial number of element, p in number vectoriIndicate i-th of element；eiIndicate that when i-th of element be 1, Unit Vector when other elements are zero
Amount；I=1 is enabled, element sequence is initialized；
2.2) according to protection mapping theory, i-th of model parameter, which is calculated, can satisfy the constant interval of closed-loop characteristic constraint
ForWherein, Δp iIndicate the lower bound of i-th of model parameter variation,Indicate i-th of model parameter variation
The upper bound；I-th of model parameter meets in the constant interval:
Wherein, Δ p indicates the variable quantity of model parameter；And on the boundary of the constant intervalInterior satisfaction:
2.3) the constant interval Δ P that i-th of model parameter meets closed-loop characteristic constraint is obtained by step 2.2)i, judge i and mould
The dimension n of shape parameterpRelationship:
If i is less than np, then i=i+1 is enabled, is gone to step 2.2)；
Otherwise terminate, obtain the constant interval Δ P that all model parameters meet closed-loop characteristici, i=1,2 ..., np。
4. the multi-parameter stable region method for solving according to claim 3 for the analysis of control system closed loop stability,
It is characterized in that, the minimum Bound constraints including multi-parameter stable region is calculated in the step 3) and include the following steps:
3.1) i is enabled to indicate the serial number of element in model parameter vectors, and enable i=1；
3.2) i-th of model parameter according to obtained in step 2.2) meets the constant interval of closed-loop characteristic constraint
Calculate the maximum symmetrical variation range of i-th of model parameterThe Bound constraints side of referred to as i-th model parameter
Boundary；I-th of model parameter meets in the constant interval:
3.3) Bound constraints of i-th of model parameter are obtainedWherein,It indicates i-th in original model parameter vector
A element；
Judge the dimension n of i and model parameterpRelationship:
If i is less than np, i=i+1 is enabled, is gone to step 3.2)；
Otherwise terminate, obtain the Bound constraints boundary of all parameters, each restrained boundary square is Bound constraints vector Δ pb,
5. the multi-parameter stable region method for solving according to claim 1 for the analysis of control system closed loop stability,
It is characterized in that, the hyperelliptic constraint of building multi-parameter specifically includes in step 4): original model parameter vector p0If model parameterMeet:
(p-p0)TS(p-p0) < 1 (7)
Wherein,
If matrixFor diagonal matrix, then it is original model parameter vector p that model parameter vectors, which meet center,0, condition be S
Super ellipsoids constraint；The collection of all model parameter vectors for meeting formula (7) is combined into super ellipsoids region, is denoted as Sp(p0,S)；Bound constraints
Vector Δ pbConstruct initial super ellipsoids constraint condition S0Meet:
S0=diag (1/ Δ pb)
Wherein,It indicates to vector Δ pbIn each element ask reciprocal；Matrix S0=diag
(1/ Δ p) is indicated with 1/ Δ p of vectorbMiddle element is the diagonal matrix of diagonal element.
6. the multi-parameter stable region method for solving according to claim 5 for the analysis of control system closed loop stability,
It is characterized in that, the step 5) includes the following steps:
(5.1) with initial super ellipsoids constraint condition S0It constructs and is constrained about the super ellipsoids of model parameter:
(p-p0)TS0(p-p0) < 1 (8)
The super ellipsoids region for obtaining meeting the model parameter feasible solution of constraint condition (8) is Sp(p0,S0)；
Constriction coefficient r is defined, the value range of constriction coefficient indicates initial super ellipsoids region S between 0 to 1p(p0,S0) receipts
Contracting situation；
The variation delta p=p-p of Definition Model parameter0For design variable, formula (9) is performance indicator:
JΩ(Δp,p0)=vσ(p0)·νσ(p0+Δp)+νζ(p0)·νζ(p0+Δp)+νω(p0)·νω(p0+Δp)； (9)
(5.2) constriction coefficient calculates initialization:
rl,ruRespectively indicate the bound of shrinkage ratio, irIndicate constriction coefficient i-thrSecondary iteration；
Enable ir=1, initialize constriction coefficient:
Wherein,Respectively indicate i-thrWhen secondary iteration, constriction coefficient, the upper bound of constriction coefficient and constriction coefficient lower bound；
(5.3) according to current contraction coefficientConstruct super ellipsoids constraint:
The set of feasible solution for meeting constraint condition (10) is combined into super ellipsoids region:
(5.4) optimal solution and performance indicator of nonlinear optimal problem under constraint condition are solved:
With performance indicator (9) for optimization aim, the nonlinear optimal problem under constraint condition (10) is constructed:
Constrained nonlinear systems problem (11) is solved using optimization algorithm, obtains optimal solution Δ poptAnd optimal performance refers to
Mark JΩ,opt；
(5.5) according to optimal performance index JΩ,optPolarity, obtain the update of constriction coefficient in constriction coefficient or next iteration
Strategy；
Defining the convergence precision in numerical value calculating is ε；
(5.5.1) is if 0≤JΩ,opt≤ ε, iteration ends, constriction coefficient are
(5.5.2) is if JΩ,opt> ε；
1) work as irWhen=1, iteration ends, constriction coefficient r=1；
2) work as irWhen ≠ 1, lower bound and the upper bound of constriction coefficient are updated, and use golden section criterion, is according to updated contraction
Number lower bound and the upper bound calculate the constriction coefficient in next iteration:
Update the number of iterations ir=ir+ 1, go to step (5.3)；
(5.5.3) is if JΩ,opt< 0, updates lower bound and the upper bound of constriction coefficient, and using golden section criterion according to after newly
Bound calculates constriction coefficient in next iteration:
Update the number of iterations ir=ir+ 1, go to step (5.3)；
(5.6) it according to obtained constriction coefficient r, is calculated and meets Performance of Closed Loop System constraint condition Ω drag Parameters variation
The super ellipsoids stable region of amount is SΔp(p0,S0/r)。
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| CN109738707A (en) * | 2019-01-31 | 2019-05-10 | 张欣 | A kind of the broad sense stability criteria and application method of power electronic system |
| CN111814267A (en) * | 2020-06-10 | 2020-10-23 | 东南大学 | Improved tolerance modeling method based on Bezier parameter space envelope |
| CN112486100A (en) * | 2020-12-11 | 2021-03-12 | 华中科技大学 | Method for solving control parameter stability domain of alternating current servo system |
| CN113486605A (en) * | 2021-06-22 | 2021-10-08 | 南京航空航天大学 | Aircraft model parameter design method considering flight quality |
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| US8407171B2 (en) * | 2010-02-01 | 2013-03-26 | Seiko Epson Corporation | Method for constraint optimization under box constraints |
| CN103713517B (en) * | 2013-12-20 | 2016-08-24 | 南京航空航天大学 | A kind of flight control system self adaptation parameter adjustment method |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN109738707A (en) * | 2019-01-31 | 2019-05-10 | 张欣 | A kind of the broad sense stability criteria and application method of power electronic system |
| CN111814267A (en) * | 2020-06-10 | 2020-10-23 | 东南大学 | Improved tolerance modeling method based on Bezier parameter space envelope |
| CN112486100A (en) * | 2020-12-11 | 2021-03-12 | 华中科技大学 | Method for solving control parameter stability domain of alternating current servo system |
| CN112486100B (en) * | 2020-12-11 | 2022-02-22 | 华中科技大学 | Method for solving control parameter stability domain of alternating current servo system |
| CN113486605A (en) * | 2021-06-22 | 2021-10-08 | 南京航空航天大学 | Aircraft model parameter design method considering flight quality |
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