﻿ 改进神经网络动态逆着舰控制方法
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 哈尔滨工程大学学报  2018, Vol. 39 Issue (10): 1649-1654  DOI: 10.11990/jheu.201705004 0

### 引用本文

ZHOU Jun, JIANG Ju, YU Chaojun, et al. Carrier aircraft dynamic inversion landing control based on improved neural network[J]. Journal of Harbin Engineering University, 2018, 39(10), 1649-1654. DOI: 10.11990/jheu.201705004.

### 文章历史

Carrier aircraft dynamic inversion landing control based on improved neural network
ZHOU Jun, JIANG Ju, YU Chaojun, XIAO Dong
College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Abstract: Considering the modeling error and carrier airwake problems when landing carrier-based aircraft, a dynamic inverse control method based on an improved neural network is proposed to improve the accuracy and speed of the landing controller. The neural network is introduced into the dynamic inverse control to dynamically compensate the model error in order to meet the controller requirement. The convergence speed of the neural network is improved by introducing an adaptive learning rate. The simulation results show that the dynamic inversion controller based on the improved neural network has good inhibitory and compensatory effects on the system modeling error. The convergence rate is greatly improved and the steady-state error tends to zero. It also has a good inhibitory effect on the ship's airstream. It effectively maintains the attitude and speed of carrier-based aircraft and ensures safe landing.
Keywords: carrier-based aircraft    landing    modeling error    carrier airwake    neural network    adaption    dynamic inverse

1 舰载机着舰问题描述 1.1 舰载机着舰运动模型

 $\left\{ \begin{array}{l} \dot u = vr - wq - g\sin \theta + \frac{{{F_x}}}{m}\\ \dot v = - ur + wp + g\cos \theta \sin \phi + \frac{{{F_y}}}{m}\\ \dot w = uq - vp + g\cos \theta \cos \phi + \frac{{{F_z}}}{m} \end{array} \right.$ (1)

 $\left\{ \begin{array}{l} \dot p = \left( {{c_1}r + {c_2}p} \right)q + {c_3}\bar L + {c_4}N\\ \dot q = {c_5}pr - {c_6}\left( {{p^2} - {r^2}} \right) + {c_7}M\\ \dot r = \left( {{c_8}p - {c_2}r} \right)q + {c_4}L + {c_9}N \end{array} \right.$ (2)

 $\left\{ \begin{array}{l} \dot \phi = p + \left( {r\cos \phi + q\sin \phi } \right)\tan \theta \\ \dot \theta = q\cos \phi - r\sin \phi \\ \dot \psi = \frac{1}{{\cos \theta }}\left( {r\cos \phi + q\sin \phi } \right) \end{array} \right.$ (3)

1.2 舰艉气流模型

 Download: 图 1 三级海况下三个方向上舰艉气流 Fig. 1 Three directions carrier airwake under the third sea level
2 控制器设计 2.1 非线性动态逆舰载机着舰控制器设计

 $\mathit{\boldsymbol{x}} = {\left[ {\begin{array}{*{20}{c}} p&q&r&f&q&y&u&v&w \end{array}} \right]^{\rm{T}}}$

 Download: 图 2 动态逆控制简化模型 Fig. 2 Simplified model of dynamic inverse control

 ${{\mathit{\boldsymbol{\dot x}}}_{\rm{f}}} = {F_{\rm{f}}}\left( {{\mathit{\boldsymbol{x}}_{\rm{f}}}} \right) + {G_{\rm{f}}}\left( {{\mathit{\boldsymbol{x}}_{\rm{f}}}} \right)\mathit{\boldsymbol{u}}$ (4)
 ${{\mathit{\boldsymbol{\dot x}}}_{\rm{s}}} = {F_{\rm{s}}}\left( {{\mathit{\boldsymbol{x}}_{\rm{s}}}} \right) + {G_{\rm{s}}}\left( {{\mathit{\boldsymbol{x}}_{\rm{s}}}} \right){\mathit{\boldsymbol{x}}_{\rm{f}}}$ (5)

 ${{\mathit{\boldsymbol{\dot x}}}_{{\rm{sd}}}} = {\left[ {\begin{array}{*{20}{c}} {\dot \varphi }&{\dot \theta }&{\dot \psi } \end{array}} \right]^{\rm{T}}}$

 ${\mathit{\boldsymbol{x}}_{{\rm{fc}}}} = \mathit{\boldsymbol{G}}_{\rm{s}}^{ - 1}\left( {{\mathit{\boldsymbol{x}}_{\rm{s}}}} \right)\left[ {{{\mathit{\boldsymbol{\dot x}}}_{{\rm{sd}}}} - {F_{\rm{s}}}\left( {{\mathit{\boldsymbol{x}}_{\rm{s}}}} \right)} \right]$ (6)

 $u = \mathit{\boldsymbol{G}}_{\rm{f}}^{ - 1}\left( {{\mathit{\boldsymbol{x}}_{\rm{f}}}} \right)\left[ {{{\mathit{\boldsymbol{\dot x}}}_{{\rm{fd}}}} - {F_{\rm{f}}}\left( {{\mathit{\boldsymbol{x}}_{\rm{f}}}} \right)} \right]$ (7)

2.2 神经网络动态逆舰载机着舰控制器设计

 Download: 图 3 神经网络动态逆控制结构 Fig. 3 Structure of neural network dynamic inverse control

 $\mathit{\boldsymbol{\dot x}} = \mathit{\boldsymbol{f}} + g\mathit{\boldsymbol{u}} + \Delta$ (8)

 $\mathit{\boldsymbol{u}} = {\mathit{\boldsymbol{g}}^{ - 1}}\left( { - \mathit{\boldsymbol{f}} + \mathit{\boldsymbol{v}}} \right)$ (9)

 $\mathit{\boldsymbol{\dot x}} = \mathit{\boldsymbol{v}} + \Delta$ (10)

 $\mathit{\boldsymbol{v}} = {\mathit{\boldsymbol{v}}_{\rm{p}}} + {{\mathit{\boldsymbol{\dot x}}}_{\rm{c}}} - {\mathit{\boldsymbol{v}}_{{\rm{ad}}}}$ (11)

 $\left\{ \begin{array}{l} \mathit{\boldsymbol{e}} = {\mathit{\boldsymbol{x}}_{\rm{c}}} - \mathit{\boldsymbol{x}}\\ \mathit{\boldsymbol{\dot e}} = {{\mathit{\boldsymbol{\dot x}}}_{\rm{c}}} - \mathit{\boldsymbol{\dot x}} \end{array} \right.$ (12)

 $\mathit{\boldsymbol{\dot e}} = - {k_{\rm{p}}}\mathit{\boldsymbol{e}} + \left( {{\mathit{\boldsymbol{v}}_{{\rm{ad}}}} - \Delta } \right)$ (13)

2.3 神经网络的构造

 ${y_i} = \sum\limits_{j = 1}^{{N_2}} {\left[ {{\mathit{\boldsymbol{w}}_{ij}}\sigma \left( {\sum\limits_{k = 1}^{{N_1}} {{v_{j{\rm{k}}}}{{\bar x}_{\rm{k}}}} + {\theta _{{\rm{v}}j}}} \right) + {\theta _{{\rm{w}}i}}} \right]}$ (14)

 $\sigma \left( z \right) = \frac{1}{{1 + {\mathit{\boldsymbol{e}}^{ - az}}}}$

 $\mathit{\boldsymbol{x}} = {\left[ {1,{x_1},{x_2}, \cdots ,{x_{{N_1}}}} \right]^{\rm{T}}}$ (15)
 $\mathit{\boldsymbol{y}} = {\left[ {1,{y_1},{y_2}, \cdots ,{y_{{N_3}}}} \right]^{\rm{T}}}$ (16)
 $\mathit{\boldsymbol{\sigma }}\left( z \right) = {\left[ {1,\sigma \left( {{z_1}} \right),\sigma \left( {{z_2}} \right), \cdots ,\sigma \left( {{z_{{N_2}}}} \right)} \right]^{\rm{T}}}$ (17)

 ${\mathit{\boldsymbol{W}}^{\rm{T}}} = \left[ {{\theta _{{\rm{w}}i}}\left| {{\mathit{\boldsymbol{w}}_{ij}}} \right.} \right],{\mathit{\boldsymbol{V}}^{\rm{T}}} = \left[ {{\theta _{{\rm{v}}i}}\left| {{\mathit{\boldsymbol{v}}_{ij}}} \right.} \right]$ (18)

 $\mathit{\boldsymbol{y}} = {\mathit{\boldsymbol{W}}^{\rm{T}}}\mathit{\boldsymbol{\sigma }}\left( {{\mathit{\boldsymbol{V}}^{\rm{T}}}\mathit{\boldsymbol{x}}} \right)$ (19)

 $\mathit{\boldsymbol{\dot W}} = - \left\{ {\left( {\mathit{\boldsymbol{\sigma }} - {{\sigma '}_z}{\mathit{\boldsymbol{V}}^{\rm{T}}}\mathit{\boldsymbol{x}}} \right)\mathit{\boldsymbol{e}} + \lambda \left\| \mathit{\boldsymbol{e}} \right\|\mathit{\boldsymbol{W}}} \right\}{\mathit{\Gamma }_W}$ (20)
 $\mathit{\boldsymbol{\dot V}} = - \left\{ {\mathit{\boldsymbol{xeW}}{{\sigma '}_z} + \lambda \left\| \mathit{\boldsymbol{e}} \right\|\mathit{\boldsymbol{V}}} \right\}{\mathit{\Gamma }_V}$ (21)

 $\mathit{\boldsymbol{ \boldsymbol{\varGamma} }}\left( k \right) = \left\{ {\begin{array}{*{20}{c}} \begin{array}{l} {k_1}\mathit{\boldsymbol{ \boldsymbol{\varGamma} }}\left( {k - 1} \right),\\ \mathit{\boldsymbol{ \boldsymbol{\varGamma} }}\left( {k - 1} \right),\\ {k_2}\mathit{\boldsymbol{ \boldsymbol{\varGamma} }}\left( {k - 1} \right), \end{array}&\begin{array}{l} E\left( {k - 1} \right) > E\left( k \right)\\ E\left( {k - 1} \right) = E\left( k \right)\\ E\left( {k - 1} \right) < E\left( k \right) \end{array} \end{array}} \right.$ (22)

3 着舰仿真

 Download: 图 4 各方法控制效果对比 Fig. 4 Comparison of control effects of various methods

 Download: 图 5 一般动态逆控制效果曲线 Fig. 5 Response curves of control using general dynamic inverse
 Download: 图 6 改进神经网络动态控制效果曲线 Fig. 6 Response curves of control using dynamic inverse based on improved neural network
4 结论

1) 动态逆控制方法能有效解决舰载机着舰非线性控制问题，同时采用快慢子系统分别求逆方法很好地解决了输入输出变量不相等不能求全逆问题。

2) 神经网络动态逆控制方法对建模误差以及舰艉气流干扰具有很好的抑制作用，能有效控制舰载机着舰轨迹，保证安全着舰。

3) 通过引入自适应学习率，使学习率随误差的改变而改变，从而有效提高神经网络的收敛速度，满足舰载机着舰对速度和精度的要求。

4) 对于恶劣海况，神经网络动态逆控制方法比一般控制方法能更加有效保证舰载机着舰安全。

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