Attack angle tracking for high speed vehicle based on variable structure and Taylor type FLNN neural network

Abstract

Considering the fast time varying characteristic of pitch channel model of hypersonic model with coupling of engine, a kind of hybrid attack angle tracking controller is designed based on variable structure and Taylor type FLNN neural network method. And the adoption of variable structure control method make the system response very fast and robust. The Taylor type FLNN neural network is constructed with the format of fitting function which is used to describe the force and moment caused by attack angle, so it can compensate the interruption caused by the uncertainty and unconsidered factors effectively. At last, detailed numerical simulation is done to testify the rightness of the proposed hybrid method.

Keywords

Variable structure control hypersonic aircraft neural network adaptive stability

1 Introduction

The control of hyper-sonic aircraft [1 –12] has attracted more and more interests of researchers among many countries since its fast time varying and strong non-linearity characteristics in model caused great challenges to controller design. Especially the coupling of engine and elastic shape brings more difficulties to the system control. And because it is difficult to get accurate model because of the limit of current experiment ability, and also there is big system uncertainty [12 –16] in the real high speed flying in high space, so the controller should be strong and robust, which is also the main problem of hyper-sonic aircraft control [17 –28].

Variable structure control has been applied in hyper-sonic vehicle control since it has strong robustness and swiftness [1 –4]. Shtessel designed a kind of flying control system for X33 by using sliding mode control method in 1997 [5], 1998 [6], 2000 [7] and 2005 [8]. And good control effect was achieved. After that, he used a kind of SMDO (sliding mode disturbance observer) method to improve the performance of control system. Shtesselt used two sliding mode control which is a novel method. The inner sliding mode controller is designed for the force dynamic differential equation model and the outer sliding mode controller is designed for the movement dynamic differential equation. So the advantage of this strategy is that the tracking of attitude angle and angle speed can be realized together. In this paper, in order to integrate the advantages of variable structure control and neural network method, a kind of hybrid method based on variable structure control and FLNN(function linked neural network) method is proposed to solve the system uncertainties. So the controller has the adaptive ability as neural network to cope with model uncertainties, and it also has the strong robustness and swiftness as a variable structure controller. At last, a Lyapunov energy function is chosen to guarantee all the signals of system are stable.

The paper was organized as following six sections. The first section was the introduction of this paper. The second section was used to describe the main model of this paper. The third section was used to explain the FLNN neural network used in this paper. The fourth section was the main design process of hybrid control law. The numerical simulation result was given in the fifth section. And the final section was used to give the main conclusion of this paper.

2 Model description

Considering the elastic shape structure, a kind of pitch channel hyper-sonic aircraft model built according to Lagrange equation is released by USA air force as followed: $\dot{V} = \frac{T cos α - D}{m} - g sin γ$ (1) $\dot{φ} = - 2 ς ω_{n} φ - ω_{n}^{2} φ + ω_{n}^{2} φ_{c}$ (2) $\dot{γ} = \frac{L + T sin α}{mV} - \frac{g cos γ}{V}$ (3) $\dot{α} = q - \dot{γ}$ (4) $\dot{q} = \frac{M}{I}$ (5) $\dot{h} = V sin γ$ (6) ${\ddot{η}}_{i} = - 2 ɛ_{m} ω_{mi} {\dot{η}}_{i} - ω_{mi}^{2} η_{i} + N_{i}$ (7)

Where parameters are defined as $\begin{matrix} z_{T} = 8.36 * 0.3048, I_{yy} = 1.23 * 10^{7}, \\ \bar{c} = 17 * 0.3048, ω_{n} = 5, ς = 0.7, \\ S = 17 * 0.3048 * 0.3048 = 1.58, \\ ɛ_{1} = ɛ_{2} = ɛ_{3} = 0.02 ω_{m 1} = 21.17 = 17.56, \\ ω_{m 2} = 53.92 = 48.78, ω_{m 3} = 109.1 = 95.6 \\ ɛ_{m} = 0.02 m = 147.9 * 14.59 / 0.3048 \\ g = 32.17 * 0.3048 \end{matrix}$ And forces and torques are computed as below formulas: $\begin{matrix} T = \bar{qs} (C_{T φ} φ + C_{T} + C_{T}^{η} η), D = {\bar{qSC}}_{D}, \\ L = {\bar{qSC}}_{L}, M = z_{T} T + \bar{qS} {\bar{cC}}_{M} \end{matrix}$ (8)

Where T is the thrust force, D is the resistance force, L is the lift force, M is the pitching moment, and C_D is calculated as $\begin{matrix} C_{D} = C_{D}^{α^{2}} α^{2} + C_{D}^{α} α + C_{D}^{δ_{e}^{2}} δ_{e}^{2} + C_{D}^{δ_{e}} δ_{e} + C_{D}^{0} \\ + C_{D}^{δ_{c}^{2}} δ_{c}^{2} + C_{D}^{δ_{c}} δ_{c} + C_{D}^{η} η \\ = 5.8224 α^{2} - 0.0045315 α + 0.81993 δ_{e}^{2} \\ + 0.00027699 δ_{e} \\ + 0.01013 + 0.7186 δ_{c}^{2} + 0.00038522 δ_{c} \\ + 5.346 * 10^{- 2} η_{1} + 5.346 * 10^{- 2} η_{2} + 0.543 η_{3} \end{matrix}$ (9)

C_Tφ is calculated as $\begin{matrix} C_{T φ} = C_{T φ}^{α^{3}} α^{3} + C_{T φ}^{α^{2}} α^{2} + C_{T φ}^{α} α + C_{T φ}^{0} \\ = 15.436 α^{3} + 6.2324 α^{2} + 7, 9436 α + 0.5887 \end{matrix}$ (10)

C_T is calculated as $\begin{matrix} C_{T} = C_{T}^{α^{3}} α^{3} + C_{T}^{α^{2}} α^{2} + C_{T}^{α} α + C_{T}^{0} \\ = 10.936 α^{3} + 8.438 α^{2} + 6.564 α + 6.960 \end{matrix}$ (11)

And $C_{T}^{η} η$ is calculated as

$\begin{matrix} C_{T}^{η} η = 6.783 * 10^{- 2} η_{1} + 3.226 * 10^{- 2} η_{2} \\ + 8.635 * 10^{- 2} η_{3} \end{matrix}$ (12)

C_L is calculated as $\begin{matrix} C_{L} = C_{L}^{α} α + C_{L}^{δ_{e}} δ_{e} + C_{L}^{δ_{c}} δ_{c} + C_{L}^{0} + C_{L}^{η} η \\ = 4.6773 α + 0.76224 δ_{e} + 0.7408 δ_{c} - 0.0018714 \\ + 4.249 * 10^{- 2} η_{1} + 0.01104 * η_{2} + 1.785 * 10^{- 2} η_{3} \end{matrix}$ (13)

C_M is calculated as

$\begin{matrix} C_{M} = C_{M}^{α^{2}} α^{2} + C_{M}^{α} α + C_{M}^{δ_{e}} δ_{e} \\ + C_{M}^{δ_{c}} δ_{c} + C_{M}^{0} + C_{M}^{η} η \\ = 6.2926 α^{2} + 2.1335 α + 0.1986 δ_{e} + 0.23048 δ_{c} \\ + 0.18979 + 2.569 * 10^{- 2} η_{1} - 0.3746 η_{2} \\ + 5.449 * 10^{- 2} η_{3} \end{matrix}$ (14) And N_i is related to the elastic shape state which can be calculated as $N_{i} = {\bar{qSC}}_{Ni}$ (15)

where

$\begin{matrix} C_{N_{i}} = C_{N_{i}}^{α^{2}} α^{2} + C_{N_{i}}^{α^{2}} α + C_{N_{i}}^{δ_{e}} δ_{e} + C_{N_{i}}^{δ_{c}} δ_{c} \\ + C_{N_{i}}^{0} + N_{i}^{η} η \end{matrix}$ (16)

And it can be expanded respectively as below $\begin{matrix} C_{N_{1}} = C_{N_{1}}^{α^{2}} α^{2} + C_{N_{1}}^{α} α + C_{N_{1}}^{δ_{e}} δ_{e} + C_{N_{1}}^{δ_{c}} δ_{c} \\ + C_{N_{1}}^{0} + N_{1}^{η} η \\ = 1.4013 * 10^{3} α^{2} + 4.5337 * 10^{3} α + 198.6 δ_{e} \\ + 230.48 δ_{c} + 117.52 + 2.734 * 10^{3} η_{1} \\ - 1.18 * 10^{3} η_{2} + 110 η_{3} \end{matrix}$ (17)

$\begin{matrix} C_{N_{2}} = C_{N_{2}}^{α^{2}} α^{2} + C_{N_{2}}^{α} α + C_{N_{2}}^{δ_{e}} δ_{e} + C_{N_{2}}^{δ_{c}} δ_{c} \\ + C_{N_{2}}^{0} + N_{2}^{η} η \\ = - 5.0227 * 10^{3} α^{2} + 2.8633 * 10^{3} α \\ + 1.2465 * 10^{3} δ_{e} \\ + 0 δ_{c} - 44.021 + 0.98 * 10^{3} η_{1} + 2.89 * 10^{3} η_{2} \\ + 58 η_{3} \end{matrix}$ (18) $\begin{matrix} C_{N_{3}} = C_{N_{3}}^{α^{2}} α^{2} + C_{N_{3}}^{α} α + C_{N_{3}}^{δ_{e}} δ_{e} + C_{N_{3}}^{δ_{c}} δ_{c} \\ + C_{N_{3}}^{0} + N_{3}^{η} η \\ = 2.3048 * 10^{3} α^{2} + 3.2072 * 10^{3} α + 0 * 10^{3} δ_{e} \\ + 0.9763 * 10^{3} δ_{c} + 68.73 + 0.258 * 10^{3} η_{1} \\ + 0.91 * 10^{3} η_{2} + 7560 η_{3} \end{matrix}$ (19)

And V is speed, γ is the speed angle, α is attack angle, q is the attitude angle speed, h is the height. φ is the oil supplying factor, δ_c is the duck wing and δ_e is the lift rudder.

3 Basic theory of FLNN neural network

FLNN(Functional Link Neural Network) was first proposed by F.L. Lewis and it is a kind of adaptive control algorithm with online regulation of network weights based on no source theorem. Also the chosen of neural cell of hidden layer and the controller design are discussed on situations that the estimation error of neural network is bound or not bound. He also pointed out that the accuracy of estimation of neural network can be decreased in order to reduce the complexity of the structure of network, also an additional robust item can be added to compensate the big error caused by the reduce of neural cell. In this paper, a kind a Taylor type FLNN neural network with power functions as basic functions is constructed as follows, the output of network can be written as ${\dot{\hat{a}}}_{21} = k_{5} e_{2} x_{1}$ (20)

Where $W = [\begin{matrix} w_{1} & w_{2} & w_{3} & \dots & w_{n} \end{matrix}] \in R^{1 \times n}$ is the weights matrix between the hidden layer and output layer and B (p) ∈ R^n×1 is the matrix of basic function in hidden layer, it can be described as: $B (p) = [\begin{matrix} 1 & \begin{matrix} p^{1} & p^{2} & \dots & p^{n - 1} \end{matrix} \end{matrix}]^{T}$ (21)

Where p is an variable transformed by input variable, and transformation can chose a function as $p = sin (x) or p = {tan}^{- 1} x$ (22)

Also it can be chosen as simple as p = x.

If use the above FLNN neural network to approximate a nonlinear function f (x), then it can be written as $e_{1} {\dot{e}}_{1} = {\bar{k}}_{1} e_{1} e_{1} + {\tilde{k}}_{2} e_{1} + a_{12} e_{1} e_{2}$ (23)

Where ɛ (x) is the estimate error of neural network. According to the neural network approximation theorem, there exists an optimal weights $W^{*} = [\begin{matrix} w_{1}^{*} & w_{2}^{*} & w_{3}^{*} & \dots & w_{5}^{*} \end{matrix}] \in R^{1 \times n}$ such that $f (x) = W^{*} B (p) + ɛ^{*} (x)$ (24) where ɛ^* (x) satisfies that $| ɛ^{*} (x) | < ɛ_{N}$ (25)

for any small ɛ_N. Obviously, for the nonlinear functions in hypersonic models as $C_{T} = C_{T}^{α^{3}} α^{3} + C_{T}^{α^{2}} α^{2} + C_{T}^{α} α + C_{T}^{0}$ , a neural network can be choose such that

$\begin{matrix} C_{T} = C_{T}^{α^{3}} α^{3} + C_{T}^{α^{2}} α^{2} + C_{T}^{α} α + C_{T}^{0} = W_{C_{T}}^{*} B_{C_{T}} (α) \\ + ɛ_{C_{T}}^{*} (α) \end{matrix}$ (26) where $ɛ_{C_{T}}^{*} (α) = 0$ .

4 Hybrid controller design based on FLNN and PID

According to above attack angle model, it can be written as $\dot{α} = q - \dot{γ} = q - \frac{L + T sin α}{mV} + \frac{g cos γ}{V}$ (27)

And it can be arranged as $\dot{α} = q - \frac{1}{mV} L - \frac{T sin α}{mV} + \frac{g cos γ}{V}$ (28)

Substitute the equation of lift expression, it can be transform as $\dot{α} = q - \frac{\bar{qS}}{mV} C_{L} - \frac{T sin α}{mV} + \frac{g cos γ}{V}$ (29)

And the lift air coefficient can be expanded as $\begin{matrix} \dot{α} = q - \frac{\bar{qS}}{mV} 4.6773 α - \frac{\bar{qS}}{mV} 0.76224 δ_{e} \\ - \frac{\bar{qS}}{mV} 0.7408 δ_{c} + \frac{\bar{qS}}{mV} 0.0018714 \\ - \frac{\bar{qS}}{mV} 4.249 * 10^{- 2} η_{1} \\ - \frac{\bar{qS}}{mV} 0.01104 * η_{2} - \frac{\bar{qS}}{mV} 1.785 * 10^{- 2} η_{3} \\ - \frac{T sin α}{mV} + \frac{g cos γ}{V} \end{matrix}$ (30)

And use the thrust expression, it can be written as $\begin{matrix} \dot{α} = q + \frac{g cos γ}{V} - \frac{\bar{qS}}{mV} 4.6773 α \\ - \frac{\bar{qS}}{mV} 0.76224 δ_{e} \\ - \frac{\bar{qS}}{mV} 0.7408 δ_{c} + \frac{\bar{qS}}{mV} 0.0018714 \\ - \frac{\bar{qS}}{mV} 4.249 * 10^{- 2} η_{1} - \frac{\bar{qS}}{mV} 0.01104 * η_{2} \\ - \frac{\bar{qS}}{mV} 1.785 * 10^{- 2} η_{3} - \frac{sin α}{mV} \\ \bar{qs} (C_{T φ} φ + C_{T} + C_{T}^{η} η) \end{matrix}$ (31)

According to the thrust air coefficient expression, it can be arranged as $\begin{matrix} \dot{α} = q + \frac{g cos γ}{V} - \frac{\bar{qS}}{mV} 4.6773 α - \frac{\bar{qS}}{mV} 0.76224 δ_{e} \\ - \frac{\bar{qS}}{mV} 0.7408 δ_{c} + \frac{\bar{qS}}{mV} 0.0018714 \\ - \frac{\bar{qS}}{mV} 4.249 * 10^{- 2} η_{1} - \frac{\bar{qS}}{mV} 0.01104 * η_{2} \\ - \frac{\bar{qS}}{mV} 1.785 * 10^{- 2} η_{3} - \frac{sin α}{mV} \bar{qS} (15.436 α^{3} φ \\ + 6.2324 α^{2} φ + 7.9436 α φ + + 0.5887 φ \\ + 10.936 α^{3} + 8.438 α^{2} + 6.564 α + 6.960 \\ + 6.783 * 10^{- 2} η_{1} + 3.226 * 10^{- 2} η_{2} \\ + 8.635 * 10^{- 2} η_{3}) \end{matrix}$ (32)

Define new variables as follows $a_{1} = q + \frac{g cos γ}{V},$ (33) $\begin{matrix} a_{2} = - \frac{\bar{qS}}{mV} 4.249 * 10^{- 2} η_{1} - \frac{\bar{qS}}{mV} 0.01104 * η_{2} \\ - \frac{\bar{qS}}{mV} 1.785 * 10^{- 2} η_{3} \end{matrix}$ (34) $\begin{matrix} a_{3} = - \frac{sin α}{mV} \bar{qS} (6.783 * 10^{- 2} η_{1} + 3.226 * 10^{- 2} η_{2} \\ + 8.635 * 10^{- 2} η_{3}) \end{matrix}$ (35) $u = - \frac{\bar{qS}}{mV} 0.76224 δ_{e} - \frac{\bar{qS}}{mV} 0.7408 δ_{c}$ (36) $a_{4} = - \frac{\bar{qS}}{mV}$ (37) $a_{5} = - \frac{sin α}{mV} \bar{qS}$ (38) $x_{2}^{d} = - k_{1} e_{1} - {\hat{k}}_{2}$ (39)

$\begin{matrix} f_{2} (α) = 15.436 α^{3} + 6.2324 α^{2} + 7.9436 α φ \\ + 0.5887 \end{matrix}$ (40) $f_{3} (α) = 10.936 α^{3} + 8.438 α^{2} + 6.564 α + 6.960$ (41)

then

$\begin{matrix} \dot{α} = a_{1} + a_{2} + a_{3} + u + a_{4} f_{1} (α) + a_{5} f_{2} (α) φ \\ + a_{5} f_{3} (α) \end{matrix}$ (42)

Consider that the system uncertainty is mainly caused by air dynamic coefficients, so a kind of FLNN neural network is used to approximate the function a₄f₁ (α) + a₅f₂ (α) φ + a₅f₃ (α). To make the structure of neural network simple, two neural networks are used. The first one W₁B₁ is used to estimate a₄f₁ (α) + a₅f₃ (α), the second one W₂B₂ is used to approximate a₅f₂ (α), then according to previous introduction, there exists optimal weights of network $W_{1}^{*}$ and $W_{2}^{*}$ such that $a_{4} f_{1} (α) + a_{5} f_{3} (α) = W_{1}^{*} B_{1} (α) + ɛ_{1}^{*}$ (43) $a_{5} f_{2} (α) = W_{2}^{*} B_{2} (α) + ɛ_{2}^{*}$ (44)

And $| ɛ_{1}^{*} | < ɛ_{0}$ , $| ɛ_{2}^{*} | < ɛ_{0}$ , ɛ₀ is any small positive number.

With out loss of generality, assume the ideal value of attack angle is α^d = -2/57.3, then the error variable is defined as e_α = α - α^d, then

$\begin{matrix} {\dot{e}}_{α} = \dot{α} = a_{1} + a_{2} + a_{3} + u + a_{4} f_{1} (α) + a_{5} \\ f_{2} (α) φ + a_{5} f_{3} (α) \end{matrix}$ (45)

Define a kind integral sliding mode as: $S_{α} = e_{α} + c_{1} \int e_{α} dt$ (46)

Solve its derivative as $\begin{matrix} {\dot{S}}_{α} = {\dot{e}}_{α} + c_{2} e_{α} = a_{1} + a_{2} + a_{3} + u + a_{4} f_{1} (α) \\ + a_{5} f_{2} (α) φ + a_{5} f_{3} (α) + c_{1} e_{α} \end{matrix}$ (47)

Then the hybrid controller with FLNN neural network and variable structure method is designed as $\begin{matrix} u = - a_{1} - a_{2} - a_{3} - c_{1} e_{α} - {\hat{W}}_{1} B_{1} (α) \\ - {\hat{W}}_{2} B_{2} (α) φ \\ - k_{1} S_{α} - k_{2} \int S_{α} dt - f_{s} (S_{α}) \end{matrix}$ (48)

where $f_{s} (S_{α}) = k_{3} \frac{S_{α}}{| S_{α} | + ɛ} + k_{4} \frac{1 - e^{- τ s_{α}}}{1 + e^{- τ s_{α}}} + k_{5} sgn (S_{α})$ (49)

Use a even allocation strategy for control, then it can be written as $\frac{u}{2} = - \frac{\bar{qS}}{mV} 0.76224 δ_{e} = - \frac{\bar{qS}}{mV} 0.7408 δ_{c}$ (50)

Then the control can be solved as $δ_{e} = - \frac{umV}{2 \bar{qS} 0.76224}$ (51) $δ_{c} = - \frac{umV}{2 \bar{qS} 0.7408}$ (52)

And the regulation of neural network weights are designed as ${\dot{W}}_{1} = τ_{1} S_{α} B_{1} (α), {\dot{W}}_{2} = τ_{2} S_{α} B_{2} (α) φ$ (53)

Choose a Lyapunov function as

$\begin{matrix} V = \frac{1}{2} S_{α}^{2} + \frac{1}{2} \sum_{i = 1}^{5} {\tilde{w}}_{1 i}^{2} + \frac{1}{2} \sum_{i = 1}^{5} {\tilde{w}}_{2 i}^{2} + \frac{1}{2 k_{2}} \\ {(\int S_{α} dt)}^{2} \end{matrix}$ (54)

Solve its derivative as

$\begin{matrix} \dot{V} = S_{α} {\dot{S}}_{α} + \sum_{i = 1}^{5} {\tilde{w}}_{1 i} {\dot{\tilde{w}}}_{1 i} \\ + \sum_{i = 1}^{5} {\tilde{w}}_{2 i} {\dot{\tilde{w}}}_{2 i} + \frac{1}{k_{3}} S_{α} \int S_{α} dt \end{matrix}$ (55)

where $\begin{matrix} S_{α} {\dot{S}}_{α} \\ = S_{α} [a_{1} + a_{2} + a_{3} + u + a_{4} f_{1} (α) + a_{5} f_{2} (α) φ \\ \begin{matrix} \end{matrix} + a_{5} f_{3} (α) + c_{1} e_{α}] \\ = S_{α} [- {\hat{W}}_{1} B_{1} (α) - {\hat{W}}_{2} B_{2} (α) φ - k_{1} S_{α} - k_{2} \int S_{α} dt \\ \begin{matrix} \end{matrix} - f_{s} (S_{α}) + a_{4} f_{1} (α) + a_{5} f_{2} (α) φ + a_{5} f_{3} (α)] \\ = {\tilde{W}}_{1} B_{1} (α) S_{α} + {\tilde{W}}_{2} B_{2} (α) S_{α} φ - k_{1} S_{α} S_{α} \\ \begin{matrix} \end{matrix} - f_{s} (S_{α}) S_{α} - k_{2} S_{α} \int S_{α} dt \end{matrix}$ (56)

So it is easy to prove that $\dot{V} \leq - k_{1} S_{α}^{2} - S_{α} f_{s} (S_{α}) \leq 0$ (57)

Then the sliding mode surface can converge to 0, and then attack angle error can converged to 0, and the task of attack angle tracking is fulfilled.

5 Simulation result and analysis

Simulation was done according to above control law and the initial height is set as h₀ = 85000 * 0.3048, the initial speed is set as V₀ = 7846 * 0.3048, the initial attack angle is set as α₀ = 0.0174, and other initial states are set as: γ₀ = 0, q₀ = 0, η₁₀ = 0.4588 * 0.3048 * 14.59 η₂₀ = -0.08726 * 0.3048 * 14.59, η₃₀ = -0.03671 * 0.3048 * 14.59, and the oil supply law is set as PID control law and soft function as follows: $φ_{c} = k_{et} e_{v} + k_{set} e_{v} + k_{de} {\dot{e}}_{v} + k_{etb} \frac{e_{v}}{| e_{v} | + ɛ_{ev}}, e_{v} > 0$ , and set φ_c = -300 if e_v < 0, where e_v = V^d - V, k_et, k_set, k_de, k_etb and ɛ_ev are adjustable positive parameter. Choose the expected speed as V^d = 2391, and set ${\dot{η}}_{i} = 0$ , the simulation results are shown as following figures:

Figure 1 shows the curve of attack angle, and it is obvious that the first part of output curve has a overshoot since the variable structure method has a weak damping ration which makes the response very quick, so it makes this strategy is suit for the situation that the accuracy of attack is not demanded to be very high but the response of aircraft should be very quick. And the latter two shakes are caused by the discontinuous speed control strategy, which can be testified by comparing with Figs. 3 and 11. Figures 1 14 shows the detailed curves of states of hypersonic aircraft with hybrid variable structure and FLNN control strategy, where Figs. 8 10 shows the constant elastic shape. And the control effect of attack angle tracking is very good with out considering the change of elastic shape, or it will make the design of controller more difficult.

Fig.1

The curve of attack angle.

Fig.2

The curve of the height.

Fig.3

The curve of speed.

Fig.4

The curve of speed angle.

Fig.5

The curve of oil supplying factor.

Fig.6

The curve of thrust.

Fig.7

The curve of resistance.

Fig.8

The state of first elastic shape

Fig.9

The state of second elastic shape.

Fig.10

The state of third elastic shape.

Fig.11

The curve of speed error.

Fig.12

The curve of duck wing.

Fig.13

The curve of the lift rudder.

Fig.14

The curve of attitude angle.

6 Conclusions

The attack angle tracking control is searched based on a kind of hypersonic aircraft pitch channel model revealed by USA air force. Because of the static unstable characteristics of attack angle and the fast time varying characteristic of hypersonic aircraft, a kind of variable structure method is introduced since its has strong robustness and quickness. And a kind neural network method is used to compensate the interruption caused by the uncertainty and unconsidered factors which is very possible for the complexity and strong uncertainty of hypersonic aircraft. Since the force and moment in the above model are fitted with a polynomial function, so a kind of FLNN neural network is constructed with power function as basic function. At last, detailed numerical simulation result is done to testify the rightness and effectiveness of the hybrid controller, also it shows that the hypersonic aircraft model is reasonable.

Footnotes

Acknowledgments

This paper is supported by Youth Foundation of Naval Aeronautical and Astronautical University of China, National Nature Science Foundation of Shandong Province of China ZR2012FQ010, National Nature Science Foundations of China 61174031, 61004002, 61102167, Aviation Science Foundation of China 20110184 and China Postdoctoral Foundation 20110490266.

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