CN104281155A - Three-dimensional flight path tracking method for unmanned airship - Google Patents

Abstract

The invention discloses a three-dimensional flight path tracking method for an unmanned airship. The three-dimensional flight path tracking method comprises the steps of firstly, calculating an error amount by use of a given instruction flight path and an actual flight path, secondly, designing a flight path control law by use of a sliding mode control method and then calculating a flight path control quantity; in order to effectively suppress buffeting caused by sliding mode control, designing a neural network sliding mode control law by taking a sliding mode surface and the change rate as the input variables of a neural network and taking a control gain as the output variable of the neural network; adjusting the control gain on line by virtue of the self-learning function of the neural network. According to the three-dimensional flight path tracking method for the unmanned airship, the mathematical model of the space motion of the unmanned airship is established aiming at the flight path tracking problem of the unmanned airship; with the model as a control object, the flight path control law is designed by use of the sliding mode control method; in order to suppress buffeting, the neural network sliding mode control law is designed by taking the sliding mode surface and the change rate as the input variables of the neural network and taking the control gain as the output variable of the neural network, and the control gain is adjusted on line by virtue of the self-learning function of the neural network so as to suppress buffeting, and therefore, the system performance is improved.

Description

A kind of unmanned airship Three-dimensional Track tracking

Technical field

The present invention relates to a kind of flight control method of field of aerospace, it provides a kind of neural networks sliding mode control method for unmanned airship Track In Track, belongs to automatic control technology field.

Background technology

Unmanned airship refers to that the gas (as helium, hydrogen etc.) that a kind of dependence is lighter than air produces the lift-off of quiet buoyancy, automatic flight control system is relied on to realize aircraft that is resident and low-speed maneuver of fixing a point, have that airborne period is long, load capacity is large, energy consumption is low, efficiency-cost ratio advantages of higher, be widely used in the fields such as reconnaissance and surveillance, earth observation, environmental monitoring, emergency disaster relief, scientific exploration, there is significant application value and wide application prospect, the current study hotspot having become aviation field.Track In Track refers to that unmanned airship is according to preset flight path (or way point) flight, to complete every aerial mission.The spatial movement of unmanned airship have non-linear, passage coupling, uncertain, be subject to the features such as external disturbance, therefore, flight tracking control becomes one of gordian technique that unmanned airship flight controls.Existing document mostly based on linearization kinetic model, does not consider non-linear factor and the coupling longitudinally and between horizontal sideway movement to the research of dirigible Track In Track method, only effective near equilibrium state.Sliding-mode control has strong robustness to model indeterminate and external interference, and the Track In Track for unmanned airship provides a kind of effective means.But the discontinuous switching characteristic that sliding formwork controls causes system to produce buffeting, becomes its significant shortcoming.

Summary of the invention

For solving the problem, the present invention proposes a kind of unmanned airship Three-dimensional Track tracking, and it is a kind of neural networks sliding mode control method.The present invention is directed to the Track In Track problem of unmanned airship, establish the mathematical model of its spatial movement; With this model for controll plant, sliding-mode control is adopted to devise flight tracking control rule; In order to suppress to buffet, with the input variable that sliding-mode surface and rate of change thereof are neural network, be that the output variable of neural network devises neural networks sliding mode control law with ride gain, utilize the self-learning function on-line tuning ride gain of neural network, to suppress to buffet thus to improve system performance.The closed-loop system controlled by the method can tenacious tracking instruction flight path, and has good robustness and dynamic property, for the Project Realization of unmanned airship flight tracking control provides effective scheme.

A kind of unmanned airship Three-dimensional Track of the present invention tracking, first by given instruction flight path and actual flight path error of calculation amount, then adopts sliding-mode control design flight tracking control rule, calculates flight tracking control amount; The buffeting caused is controlled for effectively suppressing sliding formwork, with the input variable that sliding-mode surface and rate of change thereof are neural network, be that the output variable of neural network devises neural networks sliding mode control law with ride gain, utilize the self-learning function on-line tuning ride gain of neural network.In practical application, dirigible flight path is obtained by integrated navigation system measurement, the controlled quentity controlled variable calculated is transferred to topworks can realize flight tracking control function by the method.

A kind of unmanned airship flight tracking control method, its concrete steps are as follows,

Step one: given instruction flight path (generalized coordinate): η _d=[x _d, y _d, z _d, θ _d, ψ _d, φ _d] ^t;

Step 2: the margin of error calculates: the margin of error e between computations flight path and actual flight path;

Step 3: sliding formwork design of control law: choose sliding-mode surface and Reaching Law, adopts sliding-mode control design flight tracking control rule, calculates flight tracking control amount u;

Step 4: Design of Neural Network Controller: the input variable being neural network with sliding-mode surface and rate of change thereof, be that the output variable of neural network devises neural networks sliding mode control law with ride gain, utilize the self-learning function on-line tuning ride gain of neural network, control the chattering phenomenon caused to suppress sliding formwork.

Wherein, the instruction flight path described in step one is generalized coordinate η _d=[x _d, y _d, z _d, θ _d, ψ _d, φ _d] ^t, x _d, y _d, z _d, θ _d, ψ _dand φ _dbe respectively instruction x coordinate, instruction y coordinate, instruction z coordinate, the instruction angle of pitch, instruction crab angle and instruction roll angle, subscript T represents vector or transpose of a matrix.

Wherein, the margin of error between the computations flight path described in step 2 and actual flight path, its computing method are:

e＝η _d-η＝[x _d-x,y _d-y,z _d-z,θ _d-θ,ψ _d-ψ,φ _d-φ] ^T (1)

η=[x, y, z, θ, ψ, φ] ^tfor actual flight path, x, y, z, θ, ψ, φ are respectively the x coordinate of actual flight path, y coordinate, z coordinate, the angle of pitch, crab angle and roll angle.

Wherein, the design sliding formwork control law described in step 3, calculate flight tracking control amount u, its method is: the mathematical model 1) setting up dirigible spatial movement

For ease of describing, coordinate system and the kinematic parameter of dirigible spatial movement are defined as follows.As shown in Figure 3, earth axes o is adopted _ex _ey _ez _ewith body coordinate system o _bx _by _bz _bbe described the spatial movement of dirigible, CV is centre of buoyancy, and CG is center of gravity, and centre of buoyancy is r to the vector of center of gravity _g=[x _g, y _g, z _g] ^t.Kinematic parameter defines: position P=[x, y, z] ^t, x, y, z is respectively the displacement of axis, side direction and vertical direction; Attitude angle Ω=[θ, ψ, φ] ^t, θ, ψ, φ are respectively the angle of pitch, crab angle and roll angle; Speed v=[u, v, w] ^t, u, v, w are respectively the speed of axis, side direction and vertical direction in body coordinate system; Angular velocity omega=[p, q, r] ^t, p, q, r are respectively rolling, pitching and yaw rate.Note generalized coordinate η=[x, y, z, θ, ψ, φ] ^t, generalized velocity is V=[u, v, w, p, q, r] ^t.

The mathematical model of dirigible spatial movement is described below:

$\stackrel{\·}{\mathrm{\η}}=J\left(\mathrm{\η}\right)=\left[\begin{array}{cc}{J}_1& 0_{3\×3}\\ 0_{3\×3}& J_2\end{array}\right]V---\left(2\right)$

$M\stackrel{\·}{V}=\stackrel{\‾}{N}+\stackrel{\‾}{G}+\stackrel{\‾}{\mathrm{\τ}}---\left(3\right)$

In formula

$J_1=\left[\begin{array}{ccc}\cos \mathrm{\ψ}\cos \mathrm{\θ}& \cos \mathrm{\ψ}\sin \mathrm{\θ}\sin \mathrm{\φ}-\sin \mathrm{\ψ}\cos \mathrm{\φ}& \cos \mathrm{\ψ}\sin \mathrm{\θ}\cos \mathrm{\φ}+\sin \mathrm{\ψ}\sin \mathrm{\φ}\\ \sin \mathrm{\ψ}\cos \mathrm{\θ}& \sin \mathrm{\ψ}\sin \mathrm{\θ}\sin \mathrm{\φ}+\cos \mathrm{\ψ}\cos \mathrm{\φ}& \sin \mathrm{\ψ}\sin \mathrm{\θ}\cos \mathrm{\φ}-\cos \mathrm{\ψ}\sin \mathrm{\φ}\\ -\sin \mathrm{\θ}& \cos \mathrm{\θ}\sin \mathrm{\φ}& \cos \mathrm{\θ}\cos \mathrm{\φ}\end{array}\right]---\left(4\right)$

$J_2=\left[\begin{array}{ccc}0& \cos \mathrm{\φ}& -\sin \mathrm{\φ}\\ 0& \sec \mathrm{\θ}\sin \mathrm{\φ}& \sec \mathrm{\θ}\cos \mathrm{\φ}\\ 1& \tan \mathrm{\θ}\sin \mathrm{\φ}& \tan \mathrm{\θ}\cos \mathrm{\φ}\end{array}\right]---\left(5\right)$

$M=\left[\begin{array}{cccccc}m+m_{11}& 0& 0& 0& {\mathrm{mz}}_G& -{\mathrm{my}}_G\\ 0& m+m_{22}& 0& -{\mathrm{mz}}_G& 0& {\mathrm{mx}}_G\\ 0& 0& m+m_{33}& {\mathrm{my}}_G& -{\mathrm{mx}}_G& 0\\ 0& {-\mathrm{mz}}_G& {\mathrm{my}}_G& I_x+I_{11}& 0& 0\\ {\mathrm{mz}}_G& 0& -{\mathrm{mx}}_G& 0& I_x+I_{22}& 0\\ 0& {\mathrm{mx}}_G& 0& -I_{\mathrm{xz}}& 0& I_x+I_{33}\end{array}\right]---\left(6\right)$

$\stackrel{\‾}{G}=\left[\begin{array}{c}(B-G)\sin \mathrm{\θ}\\ (G-B)\cos \mathrm{\θ}\sin \mathrm{\φ}\\ (G-B)\cos \mathrm{\θ}\cos \mathrm{\φ}\\ y_{G}G\cos \mathrm{\θ}\cos \mathrm{\φ}-z_{G}G\cos \mathrm{\θ}\sin \mathrm{\φ}\\ -x_{G}G\cos \mathrm{\θ}\cos \mathrm{\φ}-z_{G}G\sin \mathrm{\θ}\\ x_{G}G\cos \mathrm{\θ}\sin \mathrm{\φ}+y_{G}G\sin \mathrm{\θ}\end{array}\right]---\left(7\right)$

$\mathrm{\τ}=\left[\begin{array}{c}T\cos \mathrm{\μ}\cos \mathrm{\υ}\\ T\sin \mathrm{\μ}\\ T\cos \mathrm{\μ}\sin \mathrm{\υ}\\ T\sin \mathrm{\υ}{l}_y\\ T\cos \mathrm{\υ}{l}_z-T\sin \mathrm{\υ}{l}_x\\ T\cos \mathrm{\υ}{l}_z-T\sin \mathrm{\υ}{l}_x\end{array}\right]---\left(8\right)$

$\stackrel{\‾}{N}={[N_u,N_v,N_w,N_p,N_q,N_r]}^T---\left(9\right)$

Wherein

N _u＝(m+m ₂₂)vr-(m+m ₃₃)wq+m[x _G(p ²+r ²)-y _Gpq-z _Gpr]

(10)

+QV ^2/3(-C _Xcosαcosβ+C _Ycosαsinβ+C _Zsinα)

N _v＝(m+m ₃₃)wp-(m+m ₁₁)ur-m[x _Gpq-y _G(p ²+r ²)+z _Gqr]

(11)

+QV ^2/3(C _Xsinβ+C _Ycosβ)

N _w＝(m+m ₂₂)vp-(m+m ₁₁)uq-m[x _Gpr+y _Gqr-z _G(p ²+q ²)]

(12)

+QV ^2/3(-C _Xsinαsinβ+C _Ysinαcosβ-C _Zcosα)

N _p＝[(I _y+m ₅₅)-(I _z+I ₆₆)]qr+I _xzpq-I _xypr-I _yz(r ²-q ²)+

(13)

[mz _G(ur-wp)+y _G(uq-vp)]+QVC _l

N _q＝[(I _z+m ₆₆)-(I _x+I ₄₄)]pr+I _xyqr-I _yzpq-I _xz(p ²-r ²)

(14)

+m[x _G(vp-uq)-z _G(wp-vr)]+QVC _m

N _r＝[(I _y+m ₅₅)-(I _x+I ₄₄)]pq-I _xzqr-I _xy(q ²-p ²)+I _yzpr

(15)

+m[y _G(wq-vr)-x _G(ur-wp)]+QVC _n

In formula, m is dirigible quality, m ₁₁, m ₂₂, m ₃₃for additional mass, I ₁₁, I ₂₂, I ₃₃for additional inertial; Q is dynamic pressure, and α is the angle of attack, and β is yaw angle, C _x, C _y, C _z, C _l, C _m, C _nfor Aerodynamic Coefficient; I _x, I _y, I _zbe respectively around o _bx _b, o _by _b, o _bz _bprincipal moments; I _xy, I _xz, I _yzbe respectively about plane o _bx _by _b, o _bx _bz _b, o _by _bz _bproduct of inertia; T is thrust size, and μ is thrust vectoring and o _bx _bz _bangle between face, specifies that it is at o _bx _bz _bthe left side in face is just, υ is that thrust vectoring is at o _bx _bz _bthe projection in face and o _bx _bangle between axle, specifies that it is projected in o _bx _bjust be under axle; l _x, l _y, l _zrepresent that thrust point is apart from initial point o _bdistance.

Formula (3) is the expression formula about generalized velocity V, needs to be transformed to the expression formula about generalized coordinate η.

Can be obtained by formula (1):

$V=J^{-1}\left(\mathrm{\η}\right)\stackrel{\·}{\mathrm{\η}}=R\left(\mathrm{\η}\right)\stackrel{\·}{\mathrm{\η}}=\left[\begin{array}{cc}A& 0_{3\×3}\\ 0_{3\×3}& B\end{array}\right]\stackrel{\·}{\mathrm{\η}}---\left(16\right)$

In formula

J ^-1(η) be the inverse matrix of J (η).

$A=\left[\begin{array}{ccc}\cos \mathrm{\ψ}\cos \mathrm{\θ}& \sin \mathrm{\ψ}\cos \mathrm{\θ}& -\sin \mathrm{\θ}\\ \cos \mathrm{\ψ}\sin \mathrm{\θ}\sin \mathrm{\φ}-\sin \mathrm{\ψ}\cos \mathrm{\φ}& \sin \mathrm{\ψ}\sin \mathrm{\θ}\sin \mathrm{\φ}+\cos \mathrm{\ψ}\cos \mathrm{\φ}& \cos \mathrm{\θ}\sin \mathrm{\φ}\\ \cos \mathrm{\ψ}\sin \mathrm{\θ}\cos \mathrm{\φ}+\sin \mathrm{\ψ}\sin \mathrm{\φ}& \sin \mathrm{\ψ}\sin \mathrm{\θ}\cos \mathrm{\φ}-\cos \mathrm{\ψ}\sin \mathrm{\φ}& \cos \mathrm{\θ}\cos \mathrm{\φ}\end{array}\right]---\left(17\right)$

$B=\left[\begin{array}{ccc}0& -\sin \mathrm{\θ}& 1\\ \cos \mathrm{\φ}& \cos \mathrm{\θ}\sin \mathrm{\φ}& 0\\ -\sin \mathrm{\φ}& \cos \mathrm{\θ}\cos \mathrm{\φ}& 0\end{array}\right]---\left(18\right)$

To formula (16) differential, can obtain

$\stackrel{\·}{V}=\stackrel{\·}{R}\stackrel{\·}{\mathrm{\η}}+R\stackrel{\·\·}{\mathrm{\η}}---\left(19\right)$

In formula

$\stackrel{\·}{R}=\left[\begin{array}{cc}\stackrel{\·}{A}& 0_{3\×3}\\ 0_{3\×3}& \stackrel{\·}{B}\end{array}\right]---\left(20\right)$

Formula (19) premultiplication can obtain

$R^{T}M\stackrel{\·}{V}=R^{T}M\stackrel{\·}{R}\stackrel{\·}{\mathrm{\η}}+R^T\mathrm{MR}\stackrel{\·\·}{\mathrm{\η}}---\left(21\right)$

Composite type (3), formula (19) and formula (21) can obtain:

$M_{\mathrm{\η}}\left(\mathrm{\η}\right)\stackrel{\·\·}{\mathrm{\η}}+N_{\mathrm{\η}}(\mathrm{\η},\stackrel{\·}{\mathrm{\η}})\stackrel{\·}{\mathrm{\η}}+G_{\mathrm{\η}}\left(\mathrm{\η}\right)=\widehat{\mathrm{\τ}}---\left(22\right)$

In formula

M _η(η)＝R ^TMR (23)

$N_{\mathrm{\η}}(\mathrm{\η},\stackrel{\·}{\mathrm{\η}})=R^{T}M\stackrel{\·}{R}---\left(24\right)$

$G_{\mathrm{\η}}\left(\mathrm{\η}\right)=-R^T(\stackrel{\‾}{N}+\stackrel{\‾}{G})---\left(25\right)$

$\stackrel{\‾}{\mathrm{\τ}}=R^T\mathrm{\τ}---\left(26\right)$

With the mathematical model described by formula (22) for controlled device, adopt sliding-mode control design flight tracking control rule.Sliding formwork controls by designing suitable diverter surface and sliding formwork control law, make the Phase Pathway of system in finite time, arrive designed diverter surface and slide to equilibrium point so that suitable speed is asymptotic, thus the system that ensures has predetermined performance index.Its maximum advantage is uncertain to model and external interference has unchangeability.

2) sliding-mode surface design

Design sliding-mode surface is:

$s=\mathrm{ce}+\stackrel{\·}{e}---\left(27\right)$

Wherein, s=[s ₁, s ₂, s ₃, s ₄, s ₅, s ₆] ^t, c=diag (c ₁, c ₂, c ₃, c ₄, c ₅, c ₆), c _i> 0 (i=1,2,3,4,5,6).

Definition:

${\stackrel{\·}{\mathrm{\η}}}_r=\stackrel{\·}{\mathrm{\η}}-s={\stackrel{\·}{\mathrm{\η}}}_d-\mathrm{ce}---\left(28\right)$

Then sliding-mode surface can be expressed as:

$s=\stackrel{\·}{\mathrm{\η}}-{\stackrel{\·}{\mathrm{\η}}}_r---\left(29\right)$

3) choosing exponentially approaching rule is:

$\stackrel{\·}{s}=-\mathrm{\ρs}-\mathrm{ksign}\left(s\right)---\left(30\right)$

Wherein, ρ=diag (ρ ₁, ρ ₂, ρ ₃, ρ ₄, ρ ₅, ρ ₆), ρ i > 0, k=diag (k ₁, k ₂, k ₃, k ₄, k ₅, k ₆), k _i> 0 (i=1,2,3,4,5,6), sign () is sign function.

4) design sliding formwork control law, flight tracking control amount is:

$u=M_{\mathrm{\η}}{\stackrel{\·\·}{\mathrm{\η}}}_r+N_{\mathrm{\η}}{\stackrel{\·}{\mathrm{\η}}}_r+G_{\mathrm{\η}}-\mathrm{\ρs}-\mathrm{ksign}\left(s\right)---\left(31\right)$

In formula, k=[k ₁, k ₂, k ₃, k ₄, k ₅, k ₆] ^t.

Control law in formula (31) switches back and forth between different steering logics, causes sliding die to be buffeted near diverter surface, thus affects the dynamic property of control system, and buffeting problem becomes sliding formwork and controls significant shortcoming.Therefore, the present invention devises nerve network controller, effectively to suppress to buffet.

Wherein, the design nerve network controller described in step 4, its method for designing is:

1) input/output variable is selected

The input variable of nerve network controller is made to be i-th sliding-mode surface s _iand rate of change wherein s _i∈ s, i=1,2,3,4,5,6; Output variable is i-th ride gain k _i, wherein, k _i∈ k, i=1,2,3,4,5,6, thus can according to s _ichange on-line tuning k _ivalue.

2) neural network structure is designed

Neural network structure comprises input layer, hidden layer and output layer, as shown in Figure 4.

Input layer: the input variable choosing network is

Hidden layer: choose the basis function of Gaussian function as hidden node

$h_i=\exp \left(\frac{{\left|\right|x_N-{\mathrm{\μ}}_i\left|\right|}^2}{{\mathrm{\σ}}_i^2}\right)---\left(32\right)$

Wherein, μ _ibe the intermediate value of i-th Gaussian function, σ _ibe the standard deviation of i-th Gaussian function, || || represent euclideam norm.

Output layer: i-th output of network is

$k_i=\left|W^{T}H\right|=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{w}_i{h}_i---\left(33\right)$

Wherein, W=[w ₁, w ₂..., w _n] ^t, H=[h ₁, h ₂..., h _n] ^t, w _ibe i-th network weight, n is the nodes of network.

3) online design learning algorithm

The present invention adopts gradient descent method online design learning algorithm.Definition energy function

$E=\frac{1}{2}{e}^{T}e---\left(34\right)$

In formula, e is Track In Track error.

The on-line learning algorithm design of network gain w is as follows.

First Δ w is calculated:

$\mathrm{\Δw}=-{\mathrm{\λ}}_w\frac{\∂E}{\∂w}=-{\mathrm{\λ}}_{w}e\frac{\∂e}{\∂w}=-{\mathrm{\λ}}_{w}e\frac{\∂e}{\∂u}\frac{\∂u}{\∂k}\frac{\∂k}{\∂w}{\≈-\mathrm{\λ}}_w\mathrm{esign}\left(\frac{\∂e}{\∂u}\right)\frac{\∂u}{\∂k}\frac{\∂k}{\∂w}---\left(35\right)$

In formula, λ _wfor learning rate, and 0 < λ _w< 1.

Formula (31) asks local derviation to k, can obtain:

$\frac{\&PartialD;u}{\&PartialD;k}=-\mathrm{sign}\left(s\right)---\left(36\right)$

According to formula (33), k asks local derviation to w, can obtain:

$\frac{\&PartialD;k}{\&PartialD;w}=-H\left(x\right)\mathrm{sign}\left(w^{T}H\left(x\right)\right)---\left(37\right)$

Formula (36), formula (37) are substituted into formula (35), can obtain:

$\mathrm{\&Delta;w}\&ap;-{\mathrm{\&lambda;}}_w\mathrm{esign}\left(\frac{\&PartialD;e}{\&PartialD;u}\right)(-\mathrm{sign}\left(s\right)H\left(x\right))\mathrm{sign}\left(w^{T}H\left(x\right)\right)---\left(38\right)$

The learning algorithm of network weight is as follows:

w(t)＝w(t-1)+Δw(t)+γ _w(w(t)-w(t-1)) (39)

In formula, 0 < γ _w< 1.

Thus, on-line tuning ride gain k can be realized by above-mentioned nerve network controller.

Compared with prior art, the invention has the advantages that:

1) the method directly designs based on the non-linear dynamic model of dirigible spatial movement, consider every non-linear factor and the coupling longitudinally and between horizontal sideway movement, overcome the limitation that inearized model is only suitable for equilibrium state, widen the working point variation range of system.

2) the method can follow the tracks of arbitrary parameter instruction flight path, and can ensure the stability of system.

3) the method is by choosing suitable sliding-mode surface and Reaching Law design sliding formwork control law, and what make system uncertain and external disturbance to model has good robustness.

4) the method adopts neural network, is that the output variable of neural network devises neural networks sliding mode control law, utilizes the self-learning function on-line tuning ride gain of neural network with ride gain, effectively suppresses sliding formwork to control the chattering phenomenon caused.

Control engineering teacher can according to the given arbitrary instruction flight path of actual dirigible in application process, and the controlled quentity controlled variable obtained by the method is transferred to topworks realizes flight tracking control function.

Accompanying drawing explanation

Fig. 1 is dirigible flight path control system structural drawing of the present invention

Fig. 2 is dirigible Three-dimensional Track control method flow chart of steps of the present invention

Fig. 3 is dirigible coordinate system of the present invention and kinematic parameter definition

Fig. 4 is neural network structure figure of the present invention

Fig. 5 is dirigible Three-dimensional Track tracking results of the present invention

Fig. 6 is dirigible Three-dimensional Track tracking error of the present invention

Fig. 7 is dirigible flight tracking control amount of the present invention

Fig. 8 is ride gain change curve of the present invention

In figure, symbol description is as follows:

η η=[x, y, z, θ, ψ, φ] ^tfor dirigible flight path, wherein x, y, z, θ, ψ, φ are respectively the x coordinate of actual flight path, y coordinate, z coordinate, the angle of pitch, crab angle and roll angle;

η _dη _d=[x _d, y _d, z _d, θ _d, ψ _d, φ _d] ^tfor instruction flight path, wherein x _d, y _d, z _d, θ _d, ψ _dand φ _dbe respectively instruction x coordinate, instruction y coordinate, instruction z coordinate, the instruction angle of pitch, instruction crab angle and instruction roll angle;

O _ex _ey _ez _eo _ex _ey _ez _erepresent earth axes;

O _bx _by _bz _bo _bx _by _bz _brepresent dirigible body coordinate system;

E e=[x _e, y _e, z _e, θ _e, ψ _e, φ _e] ^tfor flight tracking control error, be respectively the x error of coordinate of flight tracking control, y error of coordinate, z coordinate error;

U u=[τ _u, τ _v, τ _w, τ _l, τ _m, τ _n] ^tfor system control amount, τ _ufor axial control, τ _vfor side direction control, τ _wfor vertical direction control, τ _lfor roll unloads moment, τ _mpitch control subsystem moment, τ _nfor driftage control moment.

Below with reference to the drawings and specific embodiments, the present invention is described in further detail.

Embodiment

A kind of unmanned airship flight tracking control of the present invention method, its concrete steps are as follows:

Step one: given instruction flight path

Given instruction flight path is:

η _d=[x _d, y _d, z _d, θ _d, ψ _d, φ _d] ^t=[(3t) m, (0.93t) m, 10m, 0rad, 0.3rad, 0rad] ^t, x _d, y _d, z _d, θ _d, ψ _dand φ _dbe respectively instruction x coordinate, instruction y coordinate, instruction z coordinate, the instruction angle of pitch, instruction crab angle and instruction roll angle;

Step 2: the margin of error calculates

The margin of error between computations flight path and actual flight path:

e＝η _d-η＝[x _d-x,y _d-y,z _d-z,θ _d-θ,ψ _d-ψ,φ _d-φ] ^T，

Wherein, η=[x, y, z, θ, ψ, φ] ^tfor actual flight path, x, y, z, θ, ψ, φ are respectively the x coordinate of actual flight path, y coordinate, z coordinate, the angle of pitch, crab angle and roll angle, are consecutive variations value.

Initial flight path is:

η ₀＝[x ₀,y ₀,z ₀,θ ₀,ψ ₀,φ ₀] ^T＝[100m,-200m,5m,0.02rad,0.02rad,0.1rad] ^T。

Initial velocity:

V ₀＝[u ₀,v ₀,w ₀,p ₀,q ₀,r ₀] ^T＝[8m/s,0m/s,0m/s,0rad/s,0rad/s,0rad/s] ^T

Step 3: design sliding formwork control law:

1) mathematical model of dirigible spatial movement is set up

The mathematical model of dirigible spatial movement can be expressed as:

$\stackrel{\&CenterDot;}{\mathrm{\&eta;}}=J\left(\mathrm{\&eta;}\right)=\left[\begin{array}{cc}{J}_1& 0_{3\&times;3}\\ 0_{3\&times;3}& J_2\end{array}\right]V---\left(40\right)$

$M\stackrel{\&CenterDot;}{V}=\stackrel{\&OverBar;}{N}+\stackrel{\&OverBar;}{G}+\stackrel{\&OverBar;}{\mathrm{\&tau;}}---\left(41\right)$

In formula

$J_1=\left[\begin{array}{ccc}\cos \mathrm{\&psi;}\cos \mathrm{\&theta;}& \cos \mathrm{\&psi;}\sin \mathrm{\&theta;}\sin \mathrm{\&phi;}-\sin \mathrm{\&psi;}\cos \mathrm{\&phi;}& \cos \mathrm{\&psi;}\sin \mathrm{\&theta;}\cos \mathrm{\&phi;}+\sin \mathrm{\&psi;}\sin \mathrm{\&phi;}\\ \sin \mathrm{\&psi;}\cos \mathrm{\&theta;}& \sin \mathrm{\&psi;}\sin \mathrm{\&theta;}\sin \mathrm{\&phi;}+\cos \mathrm{\&psi;}\cos \mathrm{\&phi;}& \sin \mathrm{\&psi;}\sin \mathrm{\&theta;}\cos \mathrm{\&phi;}-\cos \mathrm{\&psi;}\sin \mathrm{\&phi;}\\ -\sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\sin \mathrm{\&phi;}& \cos \mathrm{\&theta;}\cos \mathrm{\&phi;}\end{array}\right]---\left(42\right)$

$J_2=\left[\begin{array}{ccc}0& \cos \mathrm{\&phi;}& -\sin \mathrm{\&phi;}\\ 0& \sec \mathrm{\&theta;}\sin \mathrm{\&phi;}& \sec \mathrm{\&theta;}\cos \mathrm{\&phi;}\\ 1& \tan \mathrm{\&theta;}\sin \mathrm{\&phi;}& \tan \mathrm{\&theta;}\cos \mathrm{\&phi;}\end{array}\right]---\left(43\right)$

$M=\left[\begin{array}{cccccc}m+m_{11}& 0& 0& 0& {\mathrm{mz}}_G& -{\mathrm{my}}_G\\ 0& m+m_{22}& 0& -{\mathrm{mz}}_G& 0& {\mathrm{mx}}_G\\ 0& 0& m+m_{33}& {\mathrm{my}}_G& -{\mathrm{mx}}_G& 0\\ 0& {-\mathrm{mz}}_G& {\mathrm{my}}_G& I_x+I_{11}& 0& 0\\ {\mathrm{mz}}_G& 0& -{\mathrm{mx}}_G& 0& I_x+I_{22}& 0\\ 0& {\mathrm{mx}}_G& 0& -I_{\mathrm{xz}}& 0& I_x+I_{33}\end{array}\right]---\left(44\right)$

$\stackrel{\&OverBar;}{G}=\left[\begin{array}{c}(B-G)\sin \mathrm{\&theta;}\\ (G-B)\cos \mathrm{\&theta;}\sin \mathrm{\&phi;}\\ (G-B)\cos \mathrm{\&theta;}\cos \mathrm{\&phi;}\\ y_{G}G\cos \mathrm{\&theta;}\cos \mathrm{\&phi;}-z_{G}G\cos \mathrm{\&theta;}\sin \mathrm{\&phi;}\\ -x_{G}G\cos \mathrm{\&theta;}\cos \mathrm{\&phi;}-z_{G}G\sin \mathrm{\&theta;}\\ x_{G}G\cos \mathrm{\&theta;}\sin \mathrm{\&phi;}+y_{G}G\sin \mathrm{\&theta;}\end{array}\right]---\left(45\right)$

$\mathrm{\&tau;}=\left[\begin{array}{c}T\cos \mathrm{\&mu;}\cos \mathrm{\&upsi;}\\ T\sin \mathrm{\&mu;}\\ T\cos \mathrm{\&mu;}\sin \mathrm{\&upsi;}\\ T\sin \mathrm{\&upsi;}{l}_y\\ T\cos \mathrm{\&upsi;}{l}_z-T\sin \mathrm{\&upsi;}{l}_x\\ T\cos \mathrm{\&upsi;}{l}_z-T\sin \mathrm{\&upsi;}{l}_x\end{array}\right]---\left(46\right)$

$\stackrel{\&OverBar;}{N}={[N_u,N_v,N_w,N_p,N_q,N_r]}^T---\left(47\right)$

Wherein

N _u＝(m+m ₂₂)vr-(m+m ₃₃)wq+m[xG(p ²+r ²)-y _Gpq-z _Gpr]

(48)

+QV ^2/3(-C _Xcosαcosβ+C _Ycosαsinβ+C _Zsinα)

N _v＝(m+m ₃₃)wp-(m+m ₁₁)ur-m[x _Gpq-y _G(p ²+r ²)+z _Gqr]

(49)

+QV ^2/3(C _Xsinβ+C _Ycosβ)

N _w＝(m+m ₂₂)vp-(m+m ₁₁)uq-m[x _Gpr+y _Gqr-z _G(p ²+q ²)]

(50)

+QV ^2/3(-C _Xsinαsinβ+C _Ysinαcosβ-C _Zcosα)

N _p＝[(I _y+m ₅₅)-(I _z+I ₆₆)]qr+I _xzpq-I _xypr-I _yz(r ²-q ²)+

(51)

[mz _G(ur-wp)+y _G(uq-vp)]+QVC _l

N _q＝[(I _z+m ₆₆)-(I _x+I ₄₄)]pr+I _xyqr-I _yzpq-I _xz(p ²-r ²)

(52)

+m[x _G(vp-uq)-z _G(wp-vr)]+QVC _m

N _r＝[(I _y+m ₅₅)-(I _x+I ₄₄)]pq-I _xzqr-I _xy(q ²-p ²)+I _yzpr

(53)

+m[y _G(wq-vr)-x _G(ur-wp)]+QVC _n

In formula, m is dirigible quality, m ₁₁, m ₂₂, m ₃₃for additional mass, I ₁₁, I ₂₂, I ₃₃for additional inertial; Q is dynamic pressure, and α is the angle of attack, and β is yaw angle, C _x, C _y, C _z, C _l, C _m, C _nfor Aerodynamic Coefficient; I _x, I _y, I _zbe respectively around o _bx _b, o _by _b, o _bz _bprincipal moments; I _xy, I _xz, I _yzbe respectively about plane o _bx _by _b, o _bx _bz _b, o _by _bz _bproduct of inertia; T is thrust size, and μ is thrust vectoring and o _bx _bz _bangle between face, specifies that it is at o _bx _bz _bthe left side in face is just, υ is that thrust vectoring is at o _bx _bz _bthe projection in face and o _bx _bangle between axle, specifies that it is projected in o _bx _bjust be under axle; l _x, l _y, l _zrepresent that thrust point is apart from initial point o _bdistance.

Formula (41) is the expression formula about generalized velocity V, needs to be transformed to the expression formula about generalized coordinate η.

Can be obtained by formula (40):

$V=J^{-1}\left(\mathrm{\&eta;}\right)\stackrel{\&CenterDot;}{\mathrm{\&eta;}}=R\left(\mathrm{\&eta;}\right)\stackrel{\&CenterDot;}{\mathrm{\&eta;}}=\left[\begin{array}{cc}A& 0_{3\&times;3}\\ 0_{3\&times;3}& B\end{array}\right]\stackrel{\&CenterDot;}{\mathrm{\&eta;}}---\left(54\right)$

In formula, J ^-1(η) be the inverse matrix of J (η),

$A=\left[\begin{array}{ccc}\cos \mathrm{\&psi;}\cos \mathrm{\&theta;}& \sin \mathrm{\&psi;}\cos \mathrm{\&theta;}& -\sin \mathrm{\&theta;}\\ \cos \mathrm{\&psi;}\sin \mathrm{\&theta;}\sin \mathrm{\&phi;}-\sin \mathrm{\&psi;}\cos \mathrm{\&phi;}& \sin \mathrm{\&psi;}\sin \mathrm{\&theta;}\sin \mathrm{\&phi;}+\cos \mathrm{\&psi;}\cos \mathrm{\&phi;}& \cos \mathrm{\&theta;}\sin \mathrm{\&phi;}\\ \cos \mathrm{\&psi;}\sin \mathrm{\&theta;}\cos \mathrm{\&phi;}+\sin \mathrm{\&psi;}\sin \mathrm{\&phi;}& \sin \mathrm{\&psi;}\sin \mathrm{\&theta;}\cos \mathrm{\&phi;}-\cos \mathrm{\&psi;}\sin \mathrm{\&phi;}& \cos \mathrm{\&theta;}\cos \mathrm{\&phi;}\end{array}\right]---\left(55\right)$

$B=\left[\begin{array}{ccc}0& -\sin \mathrm{\&theta;}& 1\\ \cos \mathrm{\&phi;}& \cos \mathrm{\&theta;}\sin \mathrm{\&phi;}& 0\\ -\sin \mathrm{\&phi;}& \cos \mathrm{\&theta;}\cos \mathrm{\&phi;}& 0\end{array}\right]---\left(56\right)$

To formula (54) differential, can obtain

$\stackrel{\&CenterDot;}{V}=\stackrel{\&CenterDot;}{R}\stackrel{\&CenterDot;}{\mathrm{\&eta;}}+R\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&eta;}}---\left(57\right)$

In formula

$\stackrel{\&CenterDot;}{R}=\left[\begin{array}{cc}\stackrel{\&CenterDot;}{A}& 0_{3\&times;3}\\ 0_{3\&times;3}& \stackrel{\&CenterDot;}{B}\end{array}\right]---\left(58\right)$

Formula (57) premultiplication can obtain

$R^{T}M\stackrel{\&CenterDot;}{V}=R^{T}M\stackrel{\&CenterDot;}{R}\stackrel{\&CenterDot;}{\mathrm{\&eta;}}+R^T\mathrm{MR}\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&eta;}}---\left(59\right)$

Composite type (41), formula (57) and formula (59) can obtain:

$M_{\mathrm{\&eta;}}\left(\mathrm{\&eta;}\right)\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&eta;}}+N_{\mathrm{\&eta;}}(\mathrm{\&eta;},\stackrel{\&CenterDot;}{\mathrm{\&eta;}})\stackrel{\&CenterDot;}{\mathrm{\&eta;}}+G_{\mathrm{\&eta;}}\left(\mathrm{\&eta;}\right)=\widehat{\mathrm{\&tau;}}---\left(60\right)$

In formula

M _η(η)＝R ^TMR (61)

$N_{\mathrm{\&eta;}}(\mathrm{\&eta;},\stackrel{\&CenterDot;}{\mathrm{\&eta;}})=R^{T}M\stackrel{\&CenterDot;}{R}---\left(62\right)$

$G_{\mathrm{\&eta;}}\left(\mathrm{\&eta;}\right)=-R^T(\stackrel{\&OverBar;}{N}+\stackrel{\&OverBar;}{G})---\left(63\right)$

$\stackrel{\&OverBar;}{\mathrm{\&tau;}}=R^T\mathrm{\&tau;}---\left(64\right)$

Dirigible parameter in the present embodiment sees the following form.

Dirigible parameter list

2) sliding-mode surface is chosen

Choosing sliding-mode surface is:

$s=\mathrm{ce}+\stackrel{\&CenterDot;}{e}$

Wherein, c=diag (c ₁, c ₂, c ₃, c ₄, c ₅, c ₆)=diag (2,2,2,2,2,2).

3) choosing exponentially approaching rule is:

$\stackrel{\&CenterDot;}{s}=-\mathrm{\&rho;s}-\mathrm{ksign}\left(s\right)---\left(65\right)$

4) design sliding formwork control law, calculating flight tracking control amount is:

$u=M_{\mathrm{\&eta;}}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&eta;}}}_r+N_{\mathrm{\&eta;}}{\stackrel{\&CenterDot;}{\mathrm{\&eta;}}}_r+G_{\mathrm{\&eta;}}-\mathrm{\&rho;s}-\mathrm{ksign}\left(s\right)---\left(65\right)$

Wherein, control law gain is chosen for

ρ＝diag(ρ ₁,ρ ₂,ρ ₃,ρ ₄,ρ ₅,ρ ₆)＝diag(80,80,80,20,20,20),

k＝diag(k ₁,k ₂,k ₃,k ₄,k ₅,k ₆)＝diag(20,20,20,5,25,25).

Step 4: design nerve network controller:

1) input/output variable is selected

The input variable of nerve network controller is made to be i-th sliding-mode surface s _iand rate of change wherein s _i∈ s, i=1,2,3,4,5,6; Output variable is i-th ride gain k _i, wherein, k _i∈ k, i=1,2,3,4,5,6, thus can according to s _ichange on-line tuning k _ivalue.

2) neural network structure is designed

Neural network structure comprises input layer, hidden layer and output layer.

Input layer: the input variable choosing network is

Hidden layer: choose the basis function of Gaussian function as hidden node

$h_i=\exp \left(\frac{{\left|\right|x_N-{\mathrm{\&mu;}}_i\left|\right|}^2}{{\mathrm{\&sigma;}}_i^2}\right)---\left(66\right)$

Wherein, μ _ibe the intermediate value of i-th Gaussian function, σ _ibe the standard deviation of i-th Gaussian function, get μ _i=30, σ _i=5.

Output layer: i-th output of network is

$k_i=\left|W^{T}H\right|=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i{h}_i---\left(67\right)$

Wherein, H=[h ₁, h ₂..., h _n] ^t, W=[w ₁, w ₂..., w _n] ^t, w _ibe i-th network weight, n is the nodes of network, gets W=[30,30,30] ^t.

3) online design learning algorithm

The on-line learning algorithm design of network gain W is as follows.

First Δ w is calculated:

$\mathrm{\&Delta;w}\&ap;-{\mathrm{\&lambda;}}_w\mathrm{esign}\left(\frac{\&PartialD;e}{\&PartialD;u}\right)(-\mathrm{sign}\left(s\right)H\left(x\right))\mathrm{sign}\left(w^{T}H\left(x\right)\right)---\left(68\right)$

Wherein, λ is got _w=0.8.

The learning algorithm of network weight is as follows:

w(t)＝w(t-1)+Δw(t)+γ _w(w(t)-w(t-1)) (69)

Wherein, γ is got _w=0.05.

Thus, on-line tuning ride gain can be realized by above-mentioned nerve network controller.

Dirigible Three-dimensional Track tracking results in embodiment as shown in Figure 5-Figure 8.Fig. 5 gives dirigible Three-dimensional Track tracking results, can be obtained by Fig. 5: dirigible, can trace command flight path exactly by initial position, demonstrates the validity of Track In Track method proposed by the invention; Fig. 6 gives Track In Track error, can be obtained by Fig. 6: the Track In Track method in the present invention has higher control accuracy.Fig. 7 gives flight tracking control amount curve over time, can be obtained by Fig. 7, and controlled quentity controlled variable can meet the demand of Track In Track, and without chattering phenomenon.Fig. 8 gives ride gain curve over time, can be obtained by Fig. 8, and ride gain can according to sliding-mode surface and rate of change on-line tuning adaptively thereof.

The above is only the preferred embodiment of the present invention, protection scope of the present invention be not only confined to above-described embodiment, and all technical schemes belonged under thinking of the present invention all belong to protection scope of the present invention.Should propose, for those skilled in the art, improvements and modifications without departing from the principles of the present invention, these improvements and modifications also should be considered as protection scope of the present invention.

Claims (2)

1. a unmanned airship Three-dimensional Track tracking, is characterized in that: first by given instruction flight path and actual flight path error of calculation amount, then adopts sliding-mode control design flight tracking control rule, calculates flight tracking control amount; Again with the input variable that sliding-mode surface and rate of change thereof are neural network, be that the output variable of neural network devises neural networks sliding mode control law with ride gain, utilize the self-learning function on-line tuning ride gain of neural network.

2. unmanned airship Three-dimensional Track tracking according to claim 1, is characterized in that:

Step one: given instruction flight path: η _d=[x _d, y _d, z _d, θ _d, ψ _d, φ _d] ^t; Wherein: x _d, y _d, z _d, θ _d, ψ _dand φ _dbe respectively instruction x coordinate, instruction y coordinate, instruction z coordinate, the instruction angle of pitch, instruction crab angle and instruction roll angle, subscript T represents vector or transpose of a matrix

Step 2: the margin of error calculates: the margin of error e between computations flight path and actual flight path, and its computing method are:

e＝η _d-η＝[x _d-x,y _d-y,z _d-z,θ _d-θ,ψ _d-ψ,φ _d-φ] ^T (1)

Wherein: η=[x, y, z, θ, ψ, φ] ^tfor actual flight path, x, y, z, θ, ψ, φ are respectively the x coordinate of actual flight path, y coordinate, z coordinate, the angle of pitch, crab angle and roll angle;

Step 3: sliding formwork design of control law: choose sliding-mode surface and Reaching Law, adopt sliding-mode control design flight tracking control rule, calculate flight tracking control amount u, concrete grammar is as follows:

1) mathematical model of dirigible spatial movement is set up

Coordinate system and the kinematic parameter of dirigible spatial movement are defined as follows: adopt earth axes o _ex _ey _ez _ewith body coordinate system o _bx _by _bz _bbe described the spatial movement of dirigible, CV is centre of buoyancy, and CG is center of gravity, and centre of buoyancy is r to the vector of center of gravity _g=[x _g, y _g, z _g] ^t; Kinematic parameter defines: position P=[x, y, z] ^t, x, y _{, z}be respectively the displacement of axis, side direction and vertical direction; Attitude angle Ω=[θ, ψ, φ] ^t, θ, ψ, φ are respectively the angle of pitch, crab angle and roll angle; Speed v=[u, v, w] ^t, u, v, w are respectively the speed of axis, side direction and vertical direction in body coordinate system; Angular velocity omega=[p, q, r] ^t, p, q, r are respectively rolling, pitching and yaw rate; Note generalized coordinate η=[x, y, z, θ, ψ, φ] ^t, generalized velocity is V=[u, v, w, p, q, r] ^t;

The mathematical model of dirigible spatial movement is described below:

$\stackrel{\&CenterDot;}{\mathrm{\&eta;}}=J\left(\mathrm{\&eta;}\right)\left[\begin{array}{cc}{J}_1& 0_{3\&times;3}\\ 0_{3\&times;3}& J_2\end{array}\right]V---\left(2\right)$

$M\stackrel{\&CenterDot;}{V}=\stackrel{\&OverBar;}{N}+\stackrel{\&OverBar;}{G}+\stackrel{\&OverBar;}{\mathrm{\&tau;}}---\left(3\right)$

In formula

$J_1=\left[\begin{array}{ccc}\cos \mathrm{\&psi;}\cos \mathrm{\&theta;}& \cos \mathrm{\&psi;}\sin \mathrm{\&theta;}\sin \mathrm{\&phi;}-\sin \mathrm{\&psi;}\cos \mathrm{\&phi;}& \cos \mathrm{\&psi;}\sin \mathrm{\&theta;}\cos \mathrm{\&phi;}+\sin \mathrm{\&psi;}\sin \mathrm{\&phi;}\\ \sin \mathrm{\&psi;}\cos \mathrm{\&theta;}& \sin \mathrm{\&psi;}\sin \mathrm{\&theta;}\sin \mathrm{\&phi;}+\cos \mathrm{\&psi;}\cos \mathrm{\&phi;}& \sin \mathrm{\&psi;}\sin \mathrm{\&theta;}\cos \mathrm{\&phi;}-\cos \mathrm{\&psi;}\sin \mathrm{\&phi;}\\ -\sin \mathrm{\&theta;}& \cos \mathrm{\&theta;}\sin \mathrm{\&phi;}& \cos \mathrm{\&theta;}\cos \mathrm{\&phi;}\end{array}\right]---\left(4\right)$

$J_2=\left[\begin{array}{ccc}0& \cos \mathrm{\&phi;}& -\sin \mathrm{\&phi;}\\ 0& \sec \mathrm{\&theta;}\sin \mathrm{\&phi;}& \sec \mathrm{\&theta;}\cos \mathrm{\&phi;}\\ 1& \tan \mathrm{\&theta;}\sin \mathrm{\&phi;}& \tan \mathrm{\&theta;}\cos \mathrm{\&phi;}\end{array}\right]---\left(5\right)$

$M=\left[\begin{array}{cccccc}m+m_{11}& 0& 0& 0& {\mathrm{mz}}_G& -{\mathrm{my}}_G\\ 0& m+m_{22}& 0& -{\mathrm{mz}}_G& 0& {\mathrm{mx}}_G\\ 0& 0& m+m_{33}& {\mathrm{my}}_G& -{\mathrm{mx}}_G& 0\\ 0& -{\mathrm{mz}}_G& {\mathrm{my}}_G& I_x+I_{11}& 0& 0\\ {\mathrm{mz}}_G& 0& -{\mathrm{mx}}_G& 0& I_x+I_{22}& 0\\ 0& {\mathrm{mx}}_G& 0& -I_{\mathrm{xz}}& 0& I_x+I_{33}\end{array}\right]---\left(6\right)$

$\stackrel{\&OverBar;}{G}\left[\begin{array}{c}(B-G)\sin \mathrm{\&theta;}\\ (G-B)\cos \mathrm{\&theta;}\sin \mathrm{\&phi;}\\ (G-B)\cos \mathrm{\&theta;}\cos \mathrm{\&phi;}\\ y_{G}G\cos \mathrm{\&theta;}\cos \mathrm{\&phi;}-z_{G}G\cos \mathrm{\&theta;}\sin \mathrm{\&phi;}\\ -x_{G}G\cos \mathrm{\&theta;}\cos \mathrm{\&phi;}-z_{G}G\sin \mathrm{\&theta;}\\ x_{G}G\cos \mathrm{\&theta;}\sin \mathrm{\&phi;}+y_{G}G\sin \mathrm{\&theta;}\end{array}\right]---\left(7\right)$

$\mathrm{\&tau;}=\left[\begin{array}{c}T\cos \mathrm{\&mu;}\cos \mathrm{\&upsi;}\\ T\sin \mathrm{\&mu;}\\ T\cos \mathrm{\&mu;}\sin \mathrm{\&upsi;}\\ T\sin \mathrm{\&upsi;}{l}_y\\ T\cos {\mathrm{\&upsi;l}}_z-T\sin {\mathrm{\&upsi;l}}_x\\ T\cos {\mathrm{\&upsi;l}}_z-T\sin {\mathrm{\&upsi;l}}_x\end{array}\right]---\left(8\right)$

$\stackrel{\&OverBar;}{N}=[N_u,N_v,N_w,N_p,N_q,N_r{]}^T---\left(9\right)$

Wherein

N _u＝(m+m ₂₂)vr-(m+m ₃₃)wq+m[x _G(p ²+r ²)-y _Gpq-z _Gpr]

(10)

+QV ^2/3(-C _X cosαcosβ+C _Y cosαsinβ+C _Z sinα)

N _v＝(m+m ₃₃)wp-(m+m ₁₁)ur-m[x _Gpq-y _G(p ²+r ²)+z _Gqr]

(11)

+QV ^2/3(C _X sinβ+C _Y cosβ)

N _w＝(m+m ₂₂)vp-(m+m ₁₁)uq-m[x _Gpr+y _Gqr-z _G(p ²+q ²)]

(12)

+QV ^2/3(-C _X sinαsinβ+C _Y sinαcosβ-C _Z cosα)

N _p＝[(I _y+m ₅₅)-(I _z+I ₆₆)]qr+I _xzpq-I _xypr-I _yz(r ²-q ²)+

(13)

[mz _G(ur-wp)+y _G(uq-vp)]+QVC _l

N _q＝[(I _z+m ₆₆)-(I _x+I ₄₄)]pr+I _xyqr-I _yzpq-I _xz(p ²-r ²)

(14)

+m[x _G(vp-uq)-z _G(wp-vr)]+QVC _m

N _r＝[(I _y+m ₅₅)-(I _x+I ₄₄)]pq-I _xzqr-I _xy(q ²-p ²)+I _yzpr

(15)

+m[y _G(wq-vr)-x _G(ur-wp)]+QVC _n

In formula, m is dirigible quality, m ₁₁, m ₂₂, m ₃₃for additional mass, I ₁₁, I ₂₂, I ₃₃for additional inertial; Q is dynamic pressure, and α is the angle of attack, and β is yaw angle, C _x, C _y, C _z, C _l, C _m, C _nfor Aerodynamic Coefficient; Ix, Iy, Iz are respectively around o _bx _b, o _by _b, o _bz _bprincipal moments; Ixy, Ixz, Iyz are respectively about plane o _bx _by _b, o _bx _bz _b, o _by _bz _bproduct of inertia; T is thrust size, and μ is thrust vectoring and o _bx _bz _bangle between face, specifies that it is at o _bx _bz _bthe left side in face is just, υ is that thrust vectoring is at o _bx _bz _bthe projection in face and o _bx _bangle between axle, specifies that it is projected in o _bx _bjust be under axle; l _x, l _y, l _zrepresent that thrust point is apart from initial point o _bdistance;

Formula (3) is the expression formula about generalized velocity V, needs to be transformed to the expression formula about generalized coordinate η;

Can be obtained by formula (1):

$V=J^{-1}\left(\mathrm{\&eta;}\right)\stackrel{\&CenterDot;}{\mathrm{\&eta;}}=R\left(\mathrm{\&eta;}\right)\stackrel{\&CenterDot;}{\mathrm{\&eta;}}=\left[\begin{array}{cc}{J}_1& 0_{3\&times;3}\\ 0_{3\&times;3}& J_2\end{array}\right]\stackrel{\&CenterDot;}{\mathrm{\&eta;}}---\left(16\right)$

In formula

J ^-1(η) be the inverse matrix of J (η);

$A=\left[\begin{array}{ccc}\cos \mathrm{\&psi;}\cos \mathrm{\&theta;}& \sin \mathrm{\&psi;}\cos \mathrm{\&theta;}& -\sin \\ \cos \mathrm{\&psi;}\sin \mathrm{\&theta;}\sin \mathrm{\&phi;}-\sin \mathrm{\&psi;}\cos \mathrm{\&phi;}& \sin \mathrm{\&psi;}\sin \mathrm{\&theta;}\sin \mathrm{\&phi;}+\cos \mathrm{\&psi;}\cos \mathrm{\&theta;}& \cos \mathrm{\&theta;}\sin \mathrm{\&phi;}\\ \cos \mathrm{\&psi;}\sin \mathrm{\&theta;}\cos \mathrm{\&phi;}+\sin \mathrm{\&psi;}\sin \mathrm{\&phi;}& \sin \mathrm{\&psi;}\sin \mathrm{\&theta;}\cos \mathrm{\&phi;}-\cos \mathrm{\&psi;}\sin \mathrm{\&phi;}& \cos \mathrm{\&theta;}\cos \mathrm{\&phi;}\end{array}\right]---\left(17\right)$

$B=\left[\begin{array}{ccc}0& -\sin \mathrm{\&theta;}& 1\\ \cos \mathrm{\&phi;}& \cos \mathrm{\&theta;}\sin \mathrm{\&phi;}& 0\\ -\sin \mathrm{\&phi;}& \cos \mathrm{\&theta;}\cos \mathrm{\&phi;}& 0\end{array}\right]---\left(18\right)$

To formula (16) differential, can obtain

$\stackrel{\&CenterDot;}{V}=\stackrel{\&CenterDot;}{R}\stackrel{\&CenterDot;}{\mathrm{\&eta;}}+R\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&eta;}}---\left(19\right)$

In formula

$\stackrel{\&CenterDot;}{R}=\left[\begin{array}{cc}\stackrel{\&CenterDot;}{A}& 0_{3\&times;3}\\ 0_{3\&times;3}& \stackrel{\&CenterDot;}{B}\end{array}\right]---\left(20\right)$

Formula (19) premultiplication can obtain

$R^{T}M\stackrel{\&CenterDot;}{V}=R^{T}M\stackrel{\&CenterDot;}{R}\stackrel{\&CenterDot;}{\mathrm{\&eta;}}+R^T\mathrm{MR}\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&eta;}}---\left(21\right)$

Composite type (3), formula (19) and formula (21) can obtain:

$M_{\mathrm{\&eta;}}\left(\mathrm{\&eta;}\right)\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&eta;}}+N_{\mathrm{\&eta;}}(\mathrm{\&eta;},\stackrel{\&CenterDot;}{\mathrm{\&eta;}})\stackrel{\&CenterDot;}{\mathrm{\&eta;}}+G_n\left(\mathrm{\&eta;}\right)=\widehat{\mathrm{\&tau;}}---\left(22\right)$

In formula

M _η(η)＝R ^TMR (23)

$N_{\mathrm{\&eta;}}(\mathrm{\&eta;},\stackrel{\&CenterDot;}{\mathrm{\&eta;}})=R^{T}M\stackrel{\&CenterDot;}{R}---\left(24\right)$

$G_{\mathrm{\&eta;}}\left(\mathrm{\&eta;}\right)=-R^T(\stackrel{\&OverBar;}{N}+\stackrel{\&OverBar;}{G})---\left(25\right)$

$\stackrel{\&OverBar;}{\mathrm{\&tau;}}=R^T\mathrm{\&tau;}---\left(26\right)$

With the mathematical model described by formula (22) for controlled device, adopt sliding-mode control design flight tracking control rule;

2) sliding-mode surface design

Design sliding-mode surface is:

$s=\mathrm{ce}+\stackrel{\&CenterDot;}{e}---\left(27\right)$

Wherein, s=[s ₁, s ₂, s ₃, s ₄, s ₅, s ₆] ^t, c=diag (c ₁, c ₂, c ₃, c ₄, c ₅, c ₆), c _i> 0 (i=1,2,3,4,5,6);

Definition:

${\stackrel{\&CenterDot;}{\mathrm{\&eta;}}}_r=\stackrel{\&CenterDot;}{\mathrm{\&eta;}}-s={\stackrel{\&CenterDot;}{\mathrm{\&eta;}}}_d-\mathrm{ce}---\left(28\right)$

Then sliding-mode surface can be expressed as:

$s=\stackrel{\&CenterDot;}{\mathrm{\&eta;}}-{\stackrel{\&CenterDot;}{\mathrm{\&eta;}}}_r---\left(29\right)$

3) choosing exponentially approaching rule is:

$\stackrel{\&CenterDot;}{s}=\mathrm{\&rho;s}-\mathrm{k\; sign}\left(s\right)---\left(30\right)$

Wherein, ρ=diag (ρ ₁, ρ ₂, ρ ₃, ρ ₄, ρ ₅, ρ ₆), ρ _i> 0, k=diag (k ₁, k ₂, k ₃, k ₄, k ₅, k ₆), k _i> 0 (i=1,2,3,4,5,6), sign () is sign function;

4) design sliding formwork control law, flight tracking control amount is:

$u=M_{\mathrm{\&eta;}}{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&eta;}}}_r+N_{\mathrm{\&eta;}}{\stackrel{\&CenterDot;}{\mathrm{\&eta;}}}_r+G_{\mathrm{\&eta;}}-\mathrm{\&rho;s}-\mathrm{k\; sign}\left(s\right)---\left(31\right)$

In formula, k=[k ₁, k ₂, k ₃, k ₄, k ₅, k ₆] ^t;

Step 4: Design of Neural Network Controller: the input variable being neural network with sliding-mode surface and rate of change thereof, be that the output variable of neural network devises neural networks sliding mode control law with ride gain, utilize the self-learning function on-line tuning ride gain of neural network, control the chattering phenomenon caused to suppress sliding formwork;

1) input/output variable is selected

The input variable of nerve network controller is made to be i-th sliding-mode surface s _iand rate of change wherein s _i∈ s, i=1,2,3,4,5,6; Output variable is i-th ride gain k _i, wherein, k _i∈ k, i=1,2,3,4,5,6, thus can according to s _ichange on-line tuning k _ivalue;

2) neural network structure is designed

Neural network structure comprises input layer, hidden layer and output layer;

Input layer: the input variable choosing network is

Hidden layer: choose the basis function of Gaussian function as hidden node

$h_i=\exp \left(\frac{{\left|\right|x_N-{\mathrm{\&mu;}}_i\left|\right|}^2}{{\mathrm{\&sigma;}}_i^2}\right)---\left(32\right)$

Wherein, μ _ibe the intermediate value of i-th Gaussian function, σ _ibe the standard deviation of i-th Gaussian function, || || represent euclideam norm;

Output layer: i-th output of network is

$k_i=\left|W^{T}H\right|=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{w}_i{h}_i---\left(33\right)$

Wherein, W=[w ₁, w ₂..., w _n] ^t, H=[h ₁, h ₂..., h _n] ^t, w _ibe i-th network weight, n is the nodes of network;

3) online design learning algorithm

Adopt gradient descent method online design learning algorithm; Definition energy function

$E=\frac{1}{2}{e}^{T}e---\left(34\right)$

In formula, e is Track In Track error;

The on-line learning algorithm design of network gain w is as follows:

First Δ w is calculated:

$\mathrm{\&Delta;s}=-{\mathrm{\&lambda;}}_w\frac{\&PartialD;E}{\&PartialD;w}=-{\mathrm{\&lambda;}}_{w}e\frac{\&PartialD;e}{\&PartialD;w}=-{\mathrm{\&lambda;}}_{w}e\frac{\&PartialD;e}{\&PartialD;u}\frac{\&PartialD;u}{\&PartialD;k}\frac{\&PartialD;k}{\&PartialD;w}\&ap;-{\mathrm{\&lambda;}}_w\mathrm{esign}\left(\frac{\&PartialD;e}{\&PartialD;u}\right)\frac{\&PartialD;u}{\&PartialD;k}\frac{\&PartialD;k}{\&PartialD;w}---\left(35\right)$

In formula, λ _wfor learning rate, and 0 < λ _w< 1;

Formula (31) asks local derviation to k, can obtain:

$\frac{\&PartialD;u}{\&PartialD;k}=-\mathrm{sign}\left(s\right)---\left(36\right)$

According to formula (33), k asks local derviation to w, can obtain:

$\frac{\&PartialD;k}{\&PartialD;w}=-H\left(x\right)\mathrm{sign}\left(w^{T}H\left(x\right)\right)---\left(37\right)$

Formula (36), formula (37) are substituted into formula (35), can obtain:

$\mathrm{\&Delta;w}\&ap;-{\mathrm{\&lambda;}}_w\mathrm{esign}\left(\frac{\&PartialD;e}{\&PartialD;u}\right)(-\mathrm{sign}\left(s\right)H\left(x\right))\mathrm{sign}\left(w^{T}H\left(x\right)\right)---\left(38\right)$

The learning algorithm of network weight is as follows:

w(t)＝w(t-1)+Δw(t)+γ _w(w(t)-w(t-1)) (39)

In formula, 0 < γ _w< 1;

Thus, on-line tuning ride gain k can be realized by above-mentioned nerve network controller.