CN106406092A - Robustness identification method to suit helicopter's self-adaptive flight control - Google Patents

Abstract

The invention provides a robustness identification method to suit helicopter's self-adaptive flight control. Through the determination of the noise boundary of the measured data, an indirect optimal boundary ellipsoid algorithm of a state space model with double iterative scheme is established for the feasible solution set of the model parameters described by the boundary ellipsoid and the ellipsoid center is used as the model parameter identification result to realize the real-time identification of a helicopter flight dynamic model. The identification method of the invention solves the shortcomings of the real-time identification technology of the helicopter flight dynamic model in the existing helicopter's self-adaptive flight control design method, and serves as a method for effectively eliminating the influence of the external disturbance such as measurement noise on the accuracy of the model identification and for significantly increasing the identification robustness of the dynamic model.

Description

A kind of robust identification method being applied to helicopter adaptive flight control system

Technical field

The present invention relates to helicopter flight kinetics and technical field of flight control, specifically one kind are applied to helicopter certainly Adapt to the robust identification method that flight controls.

Background technology

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, the method being also simultaneously presently most used is exactly to design a set of high-quality flight control System processed.Due to the non-linear of helicopter height and unsteady characteristic, the control effect of classical control method is often not ideal enough, And become the effective means solving this difficult problem based on the self-adaptation control method of modern control theory.

Two main issue 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, because its inherent character is extremely complex, shake Dynamic level and noise level height lead to measurement data seriously polluted, bring larger difficulty to its kinetic model of accurate recognition. The helicopter flight kinetic model identification technique of early stage with based on simple parameter identification method identification Decoupled Model, so And Decoupled Model is larger with helicopter real kinetic property difference, considerable influence is produced to the effect of controller design.Afterwards, The identification technique of fully-coupled model obtains large development, occurs in that the comprehensive discrimination method that Structure Identification and parameter identification combine, However, with respect to Decoupled Model, the complex characteristics of fully-coupled model also lead to various discrimination method precision obvious differences.From flight The authoritative expert U.S. NASA Ames research center flight mechanics of device model distinguish field controls team director Mark with flight The up-to-date monograph that B.Tischler publishes in AIAA publishing house《Aircraft and Rotorcraft System Identification:Engineering Methods with Flight Test Examples 2^ndEdition》Permissible Find out, the main flow discrimination method of international man the helo field flight dynamics model is still to be with classical identification theory at present Main, data affect using ignoring or be simply acted upon by the way of engineering correction for external interference such as measurement noises.

At present, in the helicopter self-adaptation control method of development, the real-time identification of helicopter flight kinetic model Mainly adopt least square method of recursion, noise is considered as white noise simultaneously, and mended by simple modifications are carried out to error variance Repay the estimation difference that noise causes.However, helicopter actual noise is complicated coloured noise, meanwhile, in non-principal passage, high The signal to noise ratio that noise level result in measurement data is very low.Thus simple engineering modification method not can solve complexity Noise produces the difficulty of considerable influence to Model Distinguish precision.To sum up, from existing helicopter flight kinetics both at home and abroad at present From the point of view of model real-time identification technology, not yet have during fundamentally solving practical flight and include measurement noise, dash forward including wind etc. External interference method that Model Distinguish precision is affected, and then cause necessarily to the design of helicopter adaptive control system Difficulty.

Content of the invention

The present invention is not enough in order to solve the problems, such as the on-line identification method robustness being currently based on least square method of recursion, carries Supply a kind of robust identification method being applied to helicopter adaptive flight control system, can effectively eliminate the external worlds such as measurement noise and disturb Move the impact to Model Distinguish precision, significantly improve the robustness that kinetic model recognizes.

The present invention comprises the following steps：

The first step, the state-space model of initialization helicopter floating state, as shown in formula (1), calculate floating state 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 to manipulate matrix, and y is helicopter observation vector, C It is respectively observing matrix with D and manipulate the influence matrix to observation vector；

Second step, from the beginning of connecting and flying after control, the parameter value being obtained using the first step as model parameter initial value, based on quadravalence Runge-Kutta method carries out single step solution to the helicopter flight dynamics state space equation shown in formula (1), that is, obtain t Condition responsive and observation vector x (t) and y (t), simultaneously each airborne sensor record helicopter actual observation vector y_m (t), computation model estimation difference；

3rd step, actual observation vector is carried out low-pass filtering treatment by the wave filter shown in formula (3), and records filtering Actual observation vector y afterwards_mfT (), calculates the noise in time window width for L for N number of observed quantity respectively according to formula (4) and formula (5) The average of sequence and variance, and using this variance as noise margin σ (t) of the N number of observed quantity of current time, expression such as formula (6) shown in.Meanwhile, set up the mould as shown in formula (7) on the basis of the state-space model of straight helicopter floating state Shape parameter sensitivity equation, and it is equally based on fourth-order Runge-Kutta method solution helicopter condition responsive vector to each model ginseng The sensitivity of number

σ (t)=[Var (n₁),Var(n₂),…,Var(n_N)]^T(6),

Wherein, T is the time constant of first-order filtering function, and s is multifrequency variable,For the noise average of i-th observed quantity, Var(n_i) be i-th observed quantity noise variance.

4th step, is estimated to model parameter deviation based on Optimal Boundary ellipsoid method, first, Definition Model parameter error Vector is Δ θ, and arranges its initial value for 0I, and wherein, I is unit matrix, respectively according to output in the middle of formula (8) and formula (9) calculating VectorWith middle regression matrix

Secondly, three coefficient C for optimizing border ellipsoid are calculated according to formula (10) (12)₁、C₂And C₃, recycle formula (13) it is calculated Optimal Boundary ellipsoid weight coefficient λ (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 is regression matrixLine number, e (t)=y (t)-y_mfT () calculates for model Response and the response of actual measurement between error, P is covariance matrix, and κ is spheroid-like parameter, covariance matrix P and Spheroid-like parameter κ takes initial value to be P (0)=10- in first time calculates⁶I and κ (0)=1, I is unit matrix；

5th step, sets up the iterative algorithm shown in formula (14) formula (16), and using the Optimal Boundary obtaining in the 4th step The identification result of ellipsoid weight coefficient corrected parameter, obtains the optimal feasible solution collection of parameter to be identified, and is made with ellipsoid central point For 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, the identification result according to "current" model parameter estimation deviation utilizes formula (17) correction model parameter and updates A and B matrix in formula (1), returns to second step using the state-space model of the helicopter floating state after updating and proceeds Identification calculates.

θ_i=θ_i-1+Δθ (17)

Wherein, θ_iFor the model parameter vector after updating, θ_i-1For update before a upper iterative process model parameter to Amount.

In the first step, based on Nonlinear Mechanism modeling, then calculated in the model shown in formula (1) by trim and line The value of parameters.

In the first step, by once single floating state frequency sweep flight test, calculate formula (1) using method of least square The value of middle parameters.

Described method of least square comprises the following steps that, first, helicopter is carried out trim in floating state by test pilot, so Apply successively afterwards always away from, longitudinal feathering, horizontal feathering and tail-rotor always away from sine sweep pumping signal, every group of manipulation Continue 10 30 seconds, the test flight data obtaining is filtered, sensing station corrects data consistency checks, afterwards The value of parameters in formula (1) can be estimated according to the standard least-squares shown in formula (2),

θ=(X^TX)^-1X^TY (2),

Wherein, θ is parameter to be identified, is made up 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 up of the x vector in formula (1).

The present invention has the beneficial effects that：

1) border ellipsoid method is solved as middle identified parameters using parameter estimation bias vector and be not used to differential system A difficult problem it is achieved that border ellipsoid method helicopter flight kinetic model identification in application.

2) effectively improve the effect of optimization of border ellipsoid by real-time estimation noise margin, enhance parameter identification precision.

3) existing recursive least-squares method needs to know the concrete statistical property of noise, due to the statistics of actual noise Characteristic cannot obtain the reduction leading to method precision especially robustness.And the parameter that the present invention is weighted with border ellipsoidal parameter is passed Pushing away identification algorithm only needs to consider noise margin, so the Model Distinguish being applied under various non-ideal noise jamming environment, phase The precision of parameter identification can be improved than existing method, and robustness then more significantly improves.

Brief description

Fig. 1 is the robust identification method implementing procedure of the present invention.

Fig. 2 is helicopter flight kinetic model initialization flow process.

Fig. 3 is the checking of the inventive method identification result in embodiment.

Fig. 4 is the identification effect contrast of the inventive method and least square method of recursion under the conditions of high s/n ratio in embodiment.

Fig. 5 is that under Low SNR in embodiment, the inventive method and the identification effect of least square method of recursion contrast.

Specific embodiment

The present invention will be further described with reference to the accompanying drawings and detailed description.

The invention provides a kind of robust identification method being applied to helicopter adaptive flight control system, flow process such as Fig. 1 institute Show, specifically include following step：

The first step, as shown in Fig. 2 carrying 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 the speed under body shafting, angle speed Degree and attitude angle, A is matrix stability, and B is to manipulate matrix, and y is helicopter observation vector, such as air speed, attitude angle, angular velocity, Acceleration etc., C and D is respectively observing matrix and manipulates the influence matrix to observation vector.Ordinary circumstance, D is null matrix, C is directly determined by the transformational relation of selected observed quantity and helicopter state variable.That need to carry out initial work is exactly mainly A With two matrixes of B.Because for helicopter, it flies always from the beginning of hovering of taking off vertically every time, so to flying power The initialization learning model only needs to carry out for floating state.Additionally, for same helicopter, although may fly every time Take-off weight otherwise varied, but under same state of flight for the dimensionless group impact in A and B matrix less, so Only 1 initialization need to be carried out to calculate.After the completion of initialization, floating state model parameter will be obtained and recorded model data In storehouse, each flight afterwards can be introduced directly into model data and can complete initial work, need not recalculate.

The helicopter state space equation of initialization floating state has two kinds of approach, and one kind is to be built based on Nonlinear Mechanism Mould, then obtains the model shown in formula (1) by trim and line.Another approach is also the side that the present invention adopts and recommends Method, that is, passed through once individually floating state frequency sweep flight test, obtained in A and B matrix in formula (1) using method of least square Model parameter, idiographic flow is as shown in Figure 2.First, helicopter is carried out trim in floating state by test pilot, then applies successively Always away from, longitudinal feathering, horizontal feathering and tail-rotor always away from sine sweep pumping signal, every group of manipulation continue 10 30 Second.The test flight data obtaining is filtered, sensing station corrects data consistency checks it is ensured that data is credible. Model parameter can be estimated according to the standard least-squares as shown in formula (2) afterwards.Wherein, θ is parameter to be identified, by matrix In A and B parameter composition, Y is output vector, by formula (1) y vector form, X is regression matrix, from the x in formula (1) to Amount composition.

θ=(X^TX)^-1X^TY (2).

Second step, from the beginning of connecting and flying after control, enters model real-time identification link, the i.e. main part of the present invention.First Single step solution is carried out to the helicopter flight dynamics state space equation shown in formula (1) based on fourth-order Runge-Kutta method, obtains final product To condition responsive and observation vector x (t) and the y (t) of t, each airborne sensor records that helicopter is actual to be seen simultaneously Direction finding amount y_m(t).

3rd step, actual observation vector is carried out low-pass filtering treatment by the wave filter shown in formula (3), and records filtering Actual observation vector y afterwards_mf(t).The noise in time window width for L for N number of observed quantity is calculated respectively according to formula (4) and formula (5) The average of sequence and variance, and using this variance as noise margin σ (t) of the N number of observed quantity of current time, expression such as formula (6) shown in.Meanwhile, the model parameter set up as shown in formula (7) on the basis of helicopter state-space model (1) is sensitive Degree equation, and it is equally based on the sensitivity to each model parameter for the fourth-order Runge-Kutta method solution helicopter condition responsive vector

σ (t)=[Var (n₁),Var(n₂),…,Var(n_N)]^T(6),

Wherein, T is the time constant of first-order filtering function, and s is multifrequency variable,For the noise average of i-th observed quantity, Var(n_i) be i-th observed quantity noise variance.

4th step, is estimated to model parameter deviation based on Optimal Boundary ellipsoid method.First, Definition Model parameter error Vector is Δ θ, and arranges its initial value for 0I, and wherein, I is unit matrix.Respectively middle output is calculated according to formula (8) and formula (9) VectorWith middle regression matrix

Secondly, three coefficients for optimizing border ellipsoid are calculated according to formula (10) (12).Wherein, tr representing matrix Mark, m is regression matrixLine number, e (t)=y (t)-y_mfT () responds and the response of actual measurement between for what model calculated Error, covariance matrix P and spheroid-like parameter κ desirable initial value in first time calculates is P (0)=10^-6I and κ (0)=1, I is unit matrix, and hereafter this two parameters are all obtained by iterative calculation, and specific algorithm is introduced in the 5th step of the present invention. It is calculated Optimal Boundary ellipsoid weight coefficient λ (t) using formula (13).

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 sets up the iterative algorithm shown in formula (14) formula (16), and obtains using in the 4th step The identification result of excellent border ellipsoid weight coefficient corrected parameter, obtains the optimal feasible solution collection of parameter to be identified, and with ellipsoid Heart point is 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, the identification result according to "current" model parameter estimation deviation utilizes formula (17) correction model parameter and updates A and B matrix in formula (1).Use because the real-time identification algorithm of the present invention is mainly directed towards flight control system, as long as so flying Row control system is not turned off, then this identification flow process continuously carries out, that is, after completing the 6th step, using the state space side after updating Journey (1), and return to second step proceed identification calculate.

θ_i=θ_i-1+Δθ (17)

Wherein, θ_iFor the model parameter vector after updating, θ_i-1For update before a upper iterative process model parameter to Amount.

A kind of specific embodiment of the present invention is as follows：

In the present embodiment, the helicopter flight kinetic model robust identification method of the present invention is used for actual helicopter Online real-time identification, use certain 2 tonnes light helicopter as identification objects, carried out about 30 seconds about fly Row test, and Model Distinguish is completed based on real-time flight test data, Fig. 3 illustrates the identification effect of the inventive method, can To find out, identification precision is that comparison is high.In order to show the superiority of the present invention, employ least square method of recursion simultaneously and also enter Go real-time identification, and contrasted with the identification effect of the inventive method.As can be seen from Figure 4 and Figure 5, in signal to noise ratio relatively Under conditions of height (Fig. 4), the inventive method is more slightly higher than least square method of recursion precision, but improves in noise level, and signal to noise ratio is relatively In the case of low (Fig. 5), the precision of least square method of recursion is remarkably decreased, and the precision of the inventive method remains in that preferably, There is higher robustness.

Concrete application approach of the present invention is a lot, the above be only the preferred embodiment of the present invention it is noted that for For those skilled in the art, under the premise without departing from the principles of the invention, some improvement can also be made, this A little improvement also should be regarded as protection scope of the present invention.

Claims (4)

1. a kind of robust identification method being applied to helicopter adaptive flight control system is it is characterised in that comprise the following steps：

The first step, the state-space model of initialization helicopter floating state, as shown in formula (1), calculate straight under floating state Rise the value of parameters in machine state-space model,

$\left\{\begin{array}{c}\stackrel{\·}{x}=Ax+Bu\\ y=Cx+Du\end{array}\right.---\left(1\right),$

In formula, x is helicopter state vector, and A is matrix stability, and B is to manipulate matrix, and y is helicopter observation vector, C and D divides Wei not the observing matrix and manipulation influence matrix to observation vector；

Second step, flies to start after control from connecting, the parameter value obtaining using the first step is as model parameter initial value, imperial based on quadravalence Ge-Ku Tafa carries out single step solution to the helicopter flight dynamics state space equation shown in formula (1), that is, obtain t Condition responsive and observation vector x (t) and y (t), simultaneously each airborne sensor record helicopter actual observation vector y_m (t), computation model estimation difference；

3rd step, actual observation vector is carried out low-pass filtering treatment by the wave filter shown in formula (3), and records filtered Actual observation vector y_mfT (), calculates the noise sequence in time window width for L for N number of observed quantity respectively according to formula (4) and formula (5) Average and variance, and using this variance as noise margin σ (t) of the N number of observed quantity of current time, expression such as formula (6) Shown, meanwhile, set up the model ginseng as shown in formula (7) on the basis of the state-space model of straight helicopter floating state Number sensitivity equation, and it is equally based on fourth-order Runge-Kutta method solution helicopter condition responsive vector to each model parameter Sensitivity

${\stackrel{\‾}{n}}_i=\frac{1}{L}\underset{\mathrm{\τ}=t-L+1}{\overset{t}{\Σ}}\[y_m^i\left(\mathrm{\τ}\right)-y_{mf}^i\left(\mathrm{\τ}\right)\],i=1,2,...,N---\left(4\right),$

$Var\left(n_i\right)=\frac{1}{L}\underset{\mathrm{\τ}=i-L+1}{\overset{t}{\Σ}}{\[y_m^i\left(\mathrm{\τ}\right)-y_{mf}^i\left(\mathrm{\τ}\right)-{\stackrel{\‾}{n}}_i\]}^2,i=1,2,...,N---\left(5\right),$

σ (t)=[Var (n₁),Var(n₂),…,Var(n_N)]^T(6),

$\frac{d}{dt}\left(\frac{\∂x}{\∂\mathrm{\θ}}\right)=A\frac{\∂x}{\∂\mathrm{\θ}}+\frac{\∂A}{\∂\mathrm{\θ}}x+\frac{\∂B}{\∂\mathrm{\θ}}u---\left(7\right),$

Wherein, T is the time constant of first-order filtering function, and s is multifrequency variable,For the noise average of i-th observed quantity, Var (n_i) be i-th observed quantity noise variance；

4th step, is estimated to model parameter deviation based on Optimal Boundary ellipsoid method, first, Definition Model parameter error vector For Δ θ, and to arrange its initial value be 0I, and wherein, I is unit matrix, calculates centre output vector according to formula (8) and formula (9) respectivelyWith middle regression matrix

$\tilde{y}\left(t\right)=y\left(t\right)-Cx\left(t\right)---\left(8\right),$

$\tilde{x}\left(t\right)=C\frac{\∂x}{\∂\mathrm{\θ}}\left(t\right)---\left(9\right),$

Secondly, three coefficient C for optimizing border ellipsoid are calculated according to formula (10) (12)₁、C₂And C₃, recycle formula (13) It is calculated Optimal Boundary ellipsoid weight coefficient λ (t),

$\mathrm{\λ}\left(t\right)=\frac{-C_1+\sqrt{{C_1}^2-4C_2{C}_0}}{2C_2}---\left(13\right),$

Wherein, the mark of tr representing matrix, m is regression matrixLine number, e (t)=y (t)-y_mfT response that () calculates for model The error and response of actual measurement between, P is covariance matrix, and κ is spheroid-like parameter, covariance matrix P and elliposoidal Shape parameter κ takes initial value to be P (0)=10 in first time calculates^-6I and κ (0)=1, I is unit matrix；

5th step, sets up the iterative algorithm shown in formula (14) formula (16), and using the Optimal Boundary ellipsoid obtaining in the 4th step The identification result of weight 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),

$P\left(t\right)=P(t-1)-\frac{\mathrm{\λ}\left(t\right)P(t-1)x\left(t\right)x{\left(t\right)}^{T}P(t-1)}{1+\mathrm{\λ}\left(t\right)x{\left(t\right)}^{T}P(t-1)x\left(t\right)}---\left(15\right),$

6th step, the identification result according to "current" model parameter estimation deviation utilizes formula (17) correction model parameter newer (1) A the and B matrix in, returns to second step using the state-space model of the helicopter floating state after updating and proceeds to distinguish Know and calculate；

θ_i=θ_i-1+Δθ (17)

Wherein, θ_iFor the model parameter vector after updating, θ_i-1Model parameter vector for the upper iterative process before updating.

2. the robust identification method being applied to helicopter adaptive flight control system according to claim 1 it is characterised in that： In the described first step, based on Nonlinear Mechanism modeling, then calculated each in the model shown in formula (1) by trim and line The value of individual parameter.

3. the robust identification method being applied to helicopter adaptive flight control system according to claim 1 it is characterised in that： In the described first step, by once single floating state frequency sweep flight test, calculated in formula (1) using method of least square The value of parameters.

4. the robust identification method being applied to helicopter adaptive flight control system according to claim 3 it is characterised in that： Described method of least square comprises the following steps that, first, helicopter is carried out trim in floating state by test pilot, then applies successively Add up away from, longitudinal feathering, horizontal feathering and tail-rotor always away from sine sweep pumping signal, every group of manipulation continue 10 30 seconds, the test flight data obtaining is filtered, sensing station corrects data consistency checks, afterwards can be according to formula (2) standard least-squares shown in estimate the value of parameters in formula (1),

θ=(X^TX)^-1X^TY (2),

Wherein, θ is parameter to be identified, is made up 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, by formula (1) x vector form.