CN106406092B - A kind of robust identification method suitable for helicopter adaptive flight control system - Google Patents
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Abstract
The present invention provides a kind of robust identification methods suitable for helicopter adaptive flight control system, by the noise margin for determining measurement data, establish the indirect Optimal Boundary ellipsoid algorithm of state-space model with double iterative format, obtain the model parameter set of feasible solution described with boundary ellipsoid, and using ellipsoid center as results of model parameter identification, the real-time identification of helicopter flight kinetic model is realized.The present invention solves in current helicopter design method of adaptive control, the dissatisfactory deficiency of helicopter flight kinetic model real-time identification technology robustness proposes a kind of real-time identification method that can be effectively eliminated the influence measured the external disturbances such as noise to Model Distinguish precision, significantly improve kinetic model identification robustness.
Description
Technical field
It is specifically a kind of to be suitable for helicopter certainly the present invention relates to helicopter flight dynamics and technical field of flight control
Adapt to the robust identification method of flight control.
Background technique
Helicopter has hovering, VTOL and low-speed maneuver ability, becomes indispensable important aircraft.However,
The intrinsic close coupling of helicopter and unstability also result in helicopter flight inferior quality, not steerable.In order to fundamentally
Solve this problem, most efficient method, at the same be also presently most used method be exactly to design the flight control of a set of high quality
System processed.Due to the non-linear and unsteady characteristic of helicopter height, the control effect of classic control method is often not ideal enough,
And the self-adaptation control method based on modern control theory becomes the effective means for solving this problem.
Two main issues of self-adaptation control method are exactly the reality of ADAPTIVE CONTROL design and control object
When identification technique.For the real-time identification technology of helicopter flight kinetic model, since its inherent characteristic is extremely complex, vibration
Dynamic horizontal and noise level height causes measurement data seriously polluted, and to accurate recognition, its kinetic model brings larger difficulty.
The helicopter flight kinetic model identification technique of early stage is based on the simple parameter identification method identification Decoupled Model of use, so
And Decoupled Model and helicopter real kinetic property difference are larger, produce bigger effect to the effect of controller design.Later,
The identification technique of fully-coupled model obtains large development, the synthesis discrimination method of Structure Identification and parameter identification combination occurs,
However, the complex characteristics of fully-coupled model also cause various discrimination method precision differences obvious relative to Decoupled Model.From flight
The authoritative expert U.S. NASA Ames research center flight mechanics and flight control team director Mark of device model distinguish field
Newest monograph " the Aircraft and Rotorcraft System that B.Tischler is published in AIAA publishing house
Identification:Engineering Methods with Flight Test Examples 2ndEdition " it can be with
Find out, the mainstream discrimination method of world man the helo field flight dynamics model is still to be with classical identification theory at present
It leads, the influence use for external interferences such as measurement noises to data is ignored or the simple modified mode of engineering is pocessed.
Currently, in the helicopter self-adaptation control method developed, the real-time identification of helicopter flight kinetic model
Least square method of recursion is mainly used, while noise is considered as white noise, and by carrying out simple modifications to error variance to mend
Repay evaluated error caused by noise.However, helicopter actual noise is complicated coloured noise, meanwhile, it is high in non-principal channel
The signal-to-noise ratio that noise level results in measurement data is very low.To which simple engineering modification method not can solve complexity
The difficulty that noise produces bigger effect Model Distinguish precision.To sum up, from current existing helicopter flight dynamics both at home and abroad
From the point of view of model real-time identification technology, there has been no fundamentally solve practical flight in the process including measuring noise, including wind etc. of dashing forward
External interference method that Model Distinguish precision is influenced, and then caused centainly to the design of helicopter adaptive control system
Difficulty.
Summary of the invention
The present invention is insufficient in order to solve the problems, such as the on-line identification method robustness for being currently based on least square method of recursion, mentions
A kind of robust identification method suitable for helicopter adaptive flight control system has been supplied, the external worlds such as measurement noise can be effectively eliminated and disturbed
The dynamic influence to Model Distinguish precision, the robustness for significantly improving kinetic model identification.
The present invention the following steps are included:
The state-space model of the first step, initialization helicopter floating state calculates floating state as shown in formula (1)
The value of parameters in lower helicopter state-space model,
In formula, x is helicopter state vector, and A is matrix stability, and B is manipulation matrix, and y is helicopter observation vector, C
It is respectively the influence matrix of observing matrix and manipulation to observation vector with D;
Since second step, using the parameter value that the first step obtains as model parameter initial value, be based on quadravalence connecting and flying after control
Runge-Kutta method carries out single step solution to helicopter flight dynamics state space equation shown in formula (1) to get t moment is arrived
Condition responsive and observation vector x (t) and y (t), while each airborne sensor records helicopter actual observation vector ym
(t), computation model evaluated error;
Actual observation vector is carried out low-pass filtering treatment by filter shown in formula (3), and records filtering by third step
Actual observation vector y afterwardsmf(t), N number of observed quantity is calculated separately in the noise that time window width is L according to formula (4) and formula (5)
The mean value and variance of sequence, and using this variance as the noise margin σ (t) of current time N number of observed quantity, expression such as formula
(6) shown in.At the same time, the mould as shown in formula (7) is established on the basis of the state-space model of straight helicopter floating state
Shape parameter sensitivity equation, and helicopter condition responsive vector is equally solved based on fourth-order Runge-Kutta method, each model is joined
Several sensitivity
σ (t)=[Var (n1), Var (n2) ..., Var (nN)]T(6),
Wherein, T is the time constant of first-order filtering function, and s is multifrequency variable,For the noise mean value of i-th of observed quantity,
Var(ni) be i-th of observed quantity noise variance.
4th step is estimated model parameter deviation based on Optimal Boundary ellipsoid method, firstly, Definition Model parameter error
Vector is Δ θ, and it is 0I that its initial value, which is arranged, wherein I is unit matrix, calculates intermediate output according to formula (8) and formula (9) respectively
VectorWith intermediate regression matrix
Secondly, calculating three coefficient C for optimizing boundary ellipsoid according to formula (10)-(12)1、C2And C0, recycle formula
(13) Optimal Boundary ellipsoid weighting coefficient λ (t) is calculated,
C2=[m-1] tr [σ (t) σ (t)T]·[x(t)TP(t-1)x(t)]2(10),
C1=[[2m-1] tr [σ (t) σ (t)T]+tr[e(t)e(t)T]-κ(t-1)x(t)TP(t-1)x(t)]·x(t)TP
(t-1) (11) x (t),
C0=m [tr [σ (t) σ (t)T]-tr[e(t)e(t)T]]-κ(t-1)x(t)TP (t-1) x (t) (12),
Wherein, the mark of tr representing matrix, m are regression matrixLine number, e (t)=y (t)-ymf(t) in formula (1)
The error of observation vector and actual observation vector, P are covariance matrix, and κ is spheroid-like parameter, covariance matrix P and ellipsoid
It is P (0)=10 that form parameter κ takes initial value in first time calculates-6I and κ (0)=1, I is unit matrix;
5th step establishes iterative algorithm shown in formula (14)-formula (16), and ellipse using Optimal Boundary obtained in the 4th step
The identification result of ball weighting coefficient corrected parameter, obtains the optimal feasible solution collection of parameter to be identified, and using ellipsoid central point as
The identification result of model parameter estimation deviation delta θ,
Δ θ (t)=Δ θ (t-1)+λ (t) P (t) x (t) e (t)T(14),
6th step using formula (17) correction model parameter and is updated according to the identification result of "current" model parameter Estimation deviation
A and B matrix in formula (1) returns to second step using the state-space model of updated helicopter floating state and continues
Identification calculates.
θi=θi-1+Δθ (17)
Wherein, θiFor updated model parameter vector, θi-1For update before a upper iterative process model parameter to
Amount.
It in the first step, is modeled based on Nonlinear Mechanism, then by being calculated in model shown in formula (1) with gentle line
The value of parameters.
In the first step, by primary individually floating state frequency sweep flight test, formula (1) is calculated using least square method
The value of middle parameters.
Specific step is as follows for the least square method, firstly, helicopter is carried out trim in floating state by Aviatrix, so
Successively apply afterwards always away from, longitudinal feathering, lateral feathering and tail-rotor always away from sine sweep pumping signal, every group of manipulation
Continue 10-30 seconds, obtained test flight data is filtered, sensor position correction and data consistency checks, later
Can the standard least-squares according to shown in formula (2) estimate the values of parameters in formula (1),
θ=(XTX)-1XTY (2),
Wherein, θ is parameter to be identified, is made of the parameter in matrix A and matrix B in formula (1), Y is output vector, by formula
(1) the y vector composition in, X is regression matrix, is made of the x vector in formula (1).
The beneficial effects of the invention are that:
1) it solves boundary ellipsoid method using parameter Estimation bias vector as intermediate identified parameters and is not used to differential system
Problem, realize boundary ellipsoid method helicopter flight kinetic model identification in application.
2) effect of optimization that boundary ellipsoid is effectively improved by real-time estimation noise margin, enhances parameter identification precision.
3) existing recursive least-squares method needs to know the specific statistical property of noise, due to the statistics of actual noise
Characteristic can not obtain the reduction for leading to method precision especially robustness.And the present invention is passed with the parameter that boundary ellipsoidal parameter weights
It pushes away identification algorithm only to need to consider noise margin, so being suitable for the Model Distinguish under various non-ideal noise jamming environment, phase
Than the precision that existing method can be improved parameter identification, and robustness then more significantly improves.
Detailed description of the invention
Fig. 1 is robust identification method implementing procedure of the invention.
Fig. 2 is helicopter flight kinetic model initialization process.
Fig. 3 is the verifying of the method for the present invention identification result in embodiment.
Fig. 4 is that the identification effect of the method for the present invention and least square method of recursion compares under the conditions of high s/n ratio in embodiment.
Fig. 5 is that the identification effect of the method for the present invention and least square method of recursion compares under Low SNR in embodiment.
Specific embodiment
The present invention will be further described with reference to the accompanying drawings and detailed description.
The present invention provides a kind of robust identification method suitable for helicopter adaptive flight control system, process such as Fig. 1 institutes
Show, specifically include following steps:
The first step, as shown in Fig. 2, carry out flight dynamics model initialization for object helicopter, i.e. initialization hovering
The state-space model of state, as shown in formula (1).Wherein, x is helicopter state vector, including speed, the angle speed under body shafting
Degree and attitude angle, A are matrix stability, and B is manipulation matrix, and y is helicopter observation vector, as air speed, attitude angle, angular speed,
Acceleration etc., C and D are respectively the influence matrix of observing matrix and manipulation to observation vector.Ordinary circumstance, D are null matrix,
C is directly determined by the transformational relation of selected observed quantity and helicopter state variable.Need to carry out initial work is exactly mainly A
With two matrixes of B.Due to being flown every time always since taking off vertically to hovering, so to flying power for helicopter
The initialization for learning model only needs to carry out for floating state.In addition, for same helicopter, although may fly every time
Take-off weight different from, but under same state of flight in A and B matrix dimensionless group influence less, so
1 initialization calculating need to only be carried out.After the completion of initialization, floating state model parameter will be obtained, model data is recorded
In library, each flight later can be introduced directly into model data and initial work can be completed, without recalculating.
There are two types of approach for the helicopter state space equation of initialization floating state, and one is built based on Nonlinear Mechanism
Mould, then by obtaining model shown in formula (1) with gentle line.Another approach is also the side that the present invention uses and recommends
Method is obtained in formula (1) in A and B matrix that is, by primary individually floating state frequency sweep flight test using least square method
Model parameter, detailed process are as shown in Figure 2.Firstly, helicopter is carried out trim in floating state by Aviatrix, then successively apply
Always away from, longitudinal feathering, lateral feathering and tail-rotor always away from sine sweep pumping signal, every group of manipulation continue 10-30
Second.Obtained test flight data is filtered, sensor position corrects and data consistency checks, it is ensured that data are credible.
Model parameter can be estimated according to the standard least-squares as shown in formula (2) later.Wherein, θ is parameter to be identified, by matrix
In A and B parameter composition, Y is output vector, is made of the y vector in formula (1), and X is regression matrix, from the x in formula (1) to
Amount composition.
θ=(XTX)-1XTY (2)。
Second step, since connecting and flying after control, into model real-time identification link, i.e., main part of the invention.First
Based on fourth-order Runge-Kutta method to helicopter flight dynamics state space equation shown in formula (1) carry out single step solve to get
To the condition responsive and observation vector x (t) and y (t) of t moment, while each airborne sensor records the practical sight of helicopter
Direction finding amount ym(t)。
Actual observation vector is carried out low-pass filtering treatment by filter shown in formula (3), and records filtering by third step
Actual observation vector y afterwardsmf(t).N number of observed quantity is calculated separately in the noise that time window width is L according to formula (4) and formula (5)
The mean value and variance of sequence, and using this variance as the noise margin σ (t) of current time N number of observed quantity, expression such as formula
(6) shown in.At the same time, it is established on the basis of helicopter state-space model (1) as model parameter shown in formula (7) is sensitive
Equation is spent, and sensitivity of the helicopter condition responsive vector to each model parameter is equally solved based on fourth-order Runge-Kutta method
σ (t)=[Var (n1),Var(n2),…,Var(nN)]T(6),
Wherein, T is the time constant of first-order filtering function, and s is multifrequency variable,For the noise mean value of i-th of observed quantity,
Var(ni) be i-th of observed quantity noise variance.
4th step estimates model parameter deviation based on Optimal Boundary ellipsoid method.Firstly, Definition Model parameter error
Vector is Δ θ, and it is 0I that its initial value, which is arranged, wherein I is unit matrix.Intermediate output is calculated according to formula (8) and formula (9) respectively
VectorWith intermediate regression matrix
Secondly, calculating three coefficients for optimizing boundary ellipsoid according to formula (10)-(12).Wherein, tr representing matrix
Mark, m are regression matrixLine number, e (t)=y (t)-ymfIt (t) is the observation vector and actual observation vector in formula (1)
It is P (0)=10 that error, covariance matrix P and spheroid-like parameter κ can use initial value in first time calculates-6I and κ (0)=1, I
For unit matrix, hereafter the two parameters all pass through iterative calculation and obtain, and specific algorithm is introduced in the 5th step of the invention.Benefit
Optimal Boundary ellipsoid weighting coefficient λ (t) is calculated with formula (13).
C2=[m-1] tr [σ (t) σ (t)T]·[x(t)TP(t-1)x(t)]2(10),
C1=[[2m-1] tr [σ (t) σ (t)T]+tr[e(t)e(t)T]-κ(t-1)x(t)TP(t-1)x(t)]·x(t)TP
(t-1) (11) x (t),
C0=m [tr [σ (t) σ (t)T]-tr[e(t)e(t)T]]-κ(t-1)x(t)TP (t-1) x (t) (12),
5th step, the present invention establish iterative algorithm shown in formula (14)-formula (16), and utilize optimal obtained in the 4th step
The identification result of boundary ellipsoid weighting coefficient corrected parameter, obtains the optimal feasible solution collection of parameter to be identified, and with ellipsoid center
Identification result of the point as model parameter estimation deviation delta θ.
Δ θ (t)=Δ θ (t-1)+λ (t) P (t) x (t) e (t)T(14),
6th step using formula (17) correction model parameter and is updated according to the identification result of "current" model parameter Estimation deviation
A and B matrix in formula (1).It is used since real-time identification algorithm of the invention is mainly directed towards flight control system, as long as so flying
Row control system is not turned off, then the identification process continuously carries out, i.e., after the 6th step of completion, uses updated state space side
Journey (1), and return to second step and continue identification calculating.
θi=θi-1+Δθ (17)
Wherein, θiFor updated model parameter vector, θi-1For update before a upper iterative process model parameter to
Amount.
A kind of specific embodiment of the invention is as follows:
In the present embodiment, helicopter flight kinetic model robust identification method of the invention is used for practical helicopter
Online real-time identification carried out about 30 seconds or so flying using certain 2 tonnes light helicopter as identification objects
Row test, and Model Distinguish is completed based on real-time flight test data, Fig. 3 illustrates the identification effect of the method for the present invention, can
To find out, identification precision is relatively high.In order to show superiority of the invention, at the same use least square method of recursion also into
It has gone real-time identification, and has been compared with the identification effect of the method for the present invention.As can be seen from Figure 4 and Figure 5, compare in noise
Under conditions of height (Fig. 4), the method for the present invention is more slightly higher than least square method of recursion precision, but improves in noise level, and noise compares
In the case where low (Fig. 5), the precision of least square method of recursion is remarkably decreased, and the precision of the method for the present invention still maintains preferably,
Robustness with higher.
There are many concrete application approach of the present invention, the above is only a preferred embodiment of the present invention, it is noted that for
For those skilled in the art, without departing from the principle of the present invention, it can also make several improvements, this
A little improve also should be regarded as protection scope of the present invention.
Claims (4)
1. a kind of robust identification method suitable for helicopter adaptive flight control system, it is characterised in that the following steps are included:
The first step initializes the state-space model of helicopter floating state, as shown in formula (1), calculates straight under floating state
The value of parameters in machine state-space model is risen,
In formula, x is helicopter state vector, and A is matrix stability, and B is manipulation matrix, and y is helicopter observation vector, and C and D divide
Not Wei observing matrix and manipulation to the influence matrix of observation vector;
Second step, since connecting and flying after control, using the parameter value that the first step obtains as model parameter initial value, based on quadravalence dragon
Ge-Ku Tafa carries out single step solution to helicopter flight dynamics state space equation shown in formula (1) to get t moment is arrived
Condition responsive and observation vector x (t) and y (t), while each airborne sensor records helicopter actual observation vector ym
(t), computation model evaluated error;
Actual observation vector is carried out low-pass filtering treatment by filter shown in formula (3), and recorded filtered by third step
Actual observation vector ymf(t), N number of observed quantity is calculated separately in the noise sequence that time window width is L according to formula (4) and formula (5)
Mean value and variance, and using this variance as the noise margin σ (t) of current time N number of observed quantity, expression such as formula (6)
It is shown, at the same time, the model parameter as shown in formula (7) is established on the basis of the state-space model of helicopter floating state
Sensitivity equation, and spirit of the helicopter condition responsive vector to each model parameter is equally solved based on fourth-order Runge-Kutta method
Sensitivity
σ (t)=[Var (n1),Var(n2),…,Var(nN)]T(6),
Wherein, θ be parameter to be identified, be made of the parameter in matrix A and matrix B in formula (1), T for first-order filtering function when
Between constant, s be multifrequency variable,For the noise mean value of i-th of observed quantity, Var (ni) be i-th of observed quantity noise variance;
4th step estimates model parameter deviation based on Optimal Boundary ellipsoid method, firstly, Definition Model parameter error vector
For Δ θ, and it is 0I that its initial value, which is arranged, wherein I is unit matrix, calculates centre output vector according to formula (8) and formula (9) respectivelyWith intermediate regression matrix
Secondly, calculating three coefficient C for optimizing boundary ellipsoid according to formula (10)-(12)1、C2And C0, recycle formula (13)
Optimal Boundary ellipsoid weighting coefficient λ (t) is calculated,
C2=[m-1] tr [σ (t) σ (t)T]·[x(t)TP(t-1)x(t)]2(10),
C1=[[2m-1] tr [σ (t) σ (t)T]+tr[e(t)e(t)T]-κ(t-1)x(t)TP(t-1)x(t)]·x(t)TP(t-
1) (11) x (t),
C0=m [tr [σ (t) σ (t)T]-tr[e(t)e(t)T]]-κ(t-1)x(t)TP (t-1) x (t) (12),
Wherein, the mark of tr representing matrix, m are regression matrixLine number, e (t)=y (t)-ymfIt (t) is the observation in formula (1)
The error of vector and actual observation vector, P are covariance matrix, and κ is spheroid-like parameter, covariance matrix P and spheroid-like
It is P (0)=10 that parameter κ takes initial value in first time calculates-6I and κ (0)=1, I is unit matrix;
5th step establishes iterative algorithm shown in formula (14)-formula (16), and utilizes Optimal Boundary ellipsoid obtained in the 4th step
The identification result of weighting coefficient corrected parameter obtains the optimal feasible solution collection of parameter to be identified, and using ellipsoid central point as mould
The identification result of shape parameter estimated bias Δ θ,
Δ θ (t)=Δ θ (t-1)+λ (t) P (t) x (t) e (t)T(14),
6th step utilizes formula (17) correction model parameter and newer according to the identification result of "current" model parameter Estimation deviation
(1) A the and B matrix in returns to second step using the state-space model of updated helicopter floating state and continues to distinguish
Know and calculates;
θi=θi-1+Δθ (17)
Wherein, θiFor updated model parameter vector, θi-1For the model parameter vector of the upper iterative process before update.
2. the robust identification method according to claim 1 suitable for helicopter adaptive flight control system, it is characterised in that:
It in the first step, is modeled based on Nonlinear Mechanism, then by going out in model shown in formula (1) with gentle linearization calculation
The value of parameters.
3. the robust identification method according to claim 1 suitable for helicopter adaptive flight control system, it is characterised in that:
In the first step, by primary individually floating state frequency sweep flight test, calculated in formula (1) using least square method
The value of parameters.
4. the robust identification method according to claim 3 suitable for helicopter adaptive flight control system, it is characterised in that:
Specific step is as follows for the least square method, firstly, helicopter is carried out trim in floating state by Aviatrix, then successively applies
Add up away from, longitudinal feathering, lateral feathering and tail-rotor always away from sine sweep pumping signal, every group of manipulation continue 10-
30 seconds, obtained test flight data is filtered, sensor position correction and data consistency checks, later can be according to formula
(2) standard least-squares shown in estimate the value of parameters in formula (1),
θ=(XTX)-1XTY (2),
Wherein, θ is parameter to be identified, is made of the parameter in matrix A and matrix B in formula (1), Y is output vector, by formula (1)
In y vector composition, X is regression matrix, is made of the x vector in formula (1).
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