CN108375907B - Adaptive compensation control method of hypersonic aircraft based on neural network - Google Patents

Adaptive compensation control method of hypersonic aircraft based on neural network Download PDF

Info

Publication number
CN108375907B
CN108375907B CN201810262739.8A CN201810262739A CN108375907B CN 108375907 B CN108375907 B CN 108375907B CN 201810262739 A CN201810262739 A CN 201810262739A CN 108375907 B CN108375907 B CN 108375907B
Authority
CN
China
Prior art keywords
function
elevator
hypersonic
radial basis
nonlinear
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201810262739.8A
Other languages
Chinese (zh)
Other versions
CN108375907A (en
Inventor
胡庆雷
李梓明
郭雷
王陈亮
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beihang University
Original Assignee
Beihang University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beihang University filed Critical Beihang University
Priority to CN201810262739.8A priority Critical patent/CN108375907B/en
Publication of CN108375907A publication Critical patent/CN108375907A/en
Application granted granted Critical
Publication of CN108375907B publication Critical patent/CN108375907B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Landscapes

  • Engineering & Computer Science (AREA)
  • Health & Medical Sciences (AREA)
  • Artificial Intelligence (AREA)
  • Computer Vision & Pattern Recognition (AREA)
  • Evolutionary Computation (AREA)
  • Medical Informatics (AREA)
  • Software Systems (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Feedback Control In General (AREA)
  • Control Of Position, Course, Altitude, Or Attitude Of Moving Bodies (AREA)

Abstract

本发明公开了一种基于神经网络的高超声速飞行器自适应补偿控制方法，包括以下步骤：建立高超声速飞行器的纵向动力学模型，并将其分解为姿态子系统和速度子系统；建立高超声速飞行器的升降舵故障模型；构建平滑函数来估计非线性输入饱和，并引入径向基函数神经网络来估计高超声速飞行器的纵向动力学模型中的非线性函数；通过反步法设计高超声速飞行器的自适应补偿控制器及相应的自适应参数更新律。本发明提供了一种考虑了升降舵故障以及输入饱和的径向基神经网络自适应补偿控制方法，解决了高超声速飞行器飞行过程中各类升降舵故障以及执行器饱和对飞行器的影响，保证了系统的容错能力和鲁棒性。

Figure 201810262739

The invention discloses a neural network-based adaptive compensation control method for a hypersonic aircraft, comprising the following steps: establishing a longitudinal dynamics model of the hypersonic aircraft, and decomposing it into an attitude subsystem and a velocity subsystem; establishing a hypersonic aircraft The elevator fault model of the hypersonic vehicle is constructed; a smooth function is constructed to estimate the nonlinear input saturation, and a radial basis function neural network is introduced to estimate the nonlinear function in the longitudinal dynamic model of the hypersonic vehicle; the adaptive design of the hypersonic vehicle is designed by the backstepping method Compensation controller and corresponding adaptive parameter update law. The present invention provides a radial basis neural network adaptive compensation control method that considers elevator faults and input saturation, solves the influence of various elevator faults and actuator saturation on the aircraft during the flight of a hypersonic aircraft, and ensures system reliability. Fault tolerance and robustness.

Figure 201810262739

Description

基于神经网络的高超声速飞行器自适应补偿控制方法Adaptive compensation control method for hypersonic vehicle based on neural network

技术领域technical field

本发明属于飞行器控制技术领域，具体来说，涉及一种基于神经网络的高超声速飞行器自适应补偿控制方法。The invention belongs to the technical field of aircraft control, and in particular relates to a neural network-based adaptive compensation control method for a hypersonic aircraft.

背景技术Background technique

近几年来，高超声速飞行器作为一种通往临近空间的可靠且经济的运输工具，吸引了极大的商业和军事关注。然而由于其特殊的构造，独特的飞行条件，导致高超声速飞行器对空气动力学参数极其敏感，以及其动力学特征的高度非线性，所有的这些因素使得高超声速飞行器的控制设计具有很大难度。In recent years, hypersonic vehicles have attracted significant commercial and military attention as a reliable and economical means of transportation to near space. However, due to its special structure and unique flight conditions, hypersonic vehicles are extremely sensitive to aerodynamic parameters, and their dynamic characteristics are highly nonlinear. All these factors make the control design of hypersonic vehicles very difficult.

运用径向基神经网络自适应补偿控制可以很好的解决系统中存在未知非线性环节这一问题，能保证系统在满足稳定性要求的同时达到相应的控制要求。目前为止，包括鲁棒控制，滑模控制以及线性二次控制等控制方法都已经被运用于高超声速飞行器纵向模型的控制设计，相比较于这些提到的控制方法，自适应反步控制提供了一种解决未知非线性模型的有效方法。一方面，在飞行器控制中，执行器饱和可能会导致控制效果恶化甚至完全失控，具有输入饱和特性系统的控制问题近些年来受到了极大的关注，通过构建辅助系统，系统输入饱和问题可以得到解决。但是当系统具有未知的时延环节时，辅助系统模型难以建立，并且给闭环系统稳定性分析造成很大难度，运用自适应补偿控制可以很好的解决系统中存在未知增益环节这一问题。另一方面，由于频繁的运作以及严酷的工作环境飞行器升降舵可能会受到故障的影响，这些故障对于飞行器而言时毁灭性的，而在现今的控制研究中故障模型的建立往往被假设为每一个升降舵只会发生一次故障，而且故障的模式(控制效果完全失效)以及参数不会发生改变。显然这是一种极端的情况，实际的飞行器升降舵故障所包含的类型是复杂的。本专利中所提出的升降舵故障模型可以很好的涵盖各种类型的故障，对故障的数目没有限制要求，更具实际性。Using radial basis neural network adaptive compensation control can well solve the problem of unknown nonlinear links in the system, and can ensure that the system can meet the corresponding control requirements while meeting the stability requirements. So far, control methods including robust control, sliding mode control, and linear quadratic control have been used in the control design of the longitudinal model of hypersonic vehicles. Compared with these mentioned control methods, adaptive backstepping control provides An efficient method for solving unknown nonlinear models. On the one hand, in aircraft control, actuator saturation may cause the control effect to deteriorate or even completely out of control. The control problem of systems with input saturation characteristics has received great attention in recent years. By building an auxiliary system, the system input saturation problem can be obtained. solve. However, when the system has an unknown time delay link, the auxiliary system model is difficult to establish, and it is very difficult to analyze the stability of the closed-loop system. The use of adaptive compensation control can solve the problem of unknown gain links in the system. On the other hand, due to the frequent operation and harsh working environment, the aircraft elevator may be affected by failures, which are destructive for the aircraft, and the establishment of failure models in current control research is often assumed for each The elevator will only fail once, and the mode of failure (complete failure of the control effect) and parameters will not change. Obviously this is an extreme case, and the types involved in actual aircraft elevator failures are complex. The elevator fault model proposed in this patent can well cover various types of faults, and there is no limit to the number of faults, which is more practical.

发明内容SUMMARY OF THE INVENTION

本发明解决的技术问题是：由于高超声速飞行器飞行过程中可能受到各方面扰动因素的影响，从而导致升降舵出现各类故障，以及高超声速飞行器在飞行过程中可能存在执行器输入饱和现象，本发明提供了一种考虑了升降舵故障以及输入饱和的径向基神经网络自适应补偿控制方法，解决了高超声速飞行器飞行过程中各类升降舵故障以及执行器饱和对飞行器的影响，保证了系统的容错能力和鲁棒性。The technical problems solved by the present invention are: due to the influence of various disturbance factors during the flight of the hypersonic aircraft, various types of elevator failures may occur, and the hypersonic aircraft may have actuator input saturation during the flight process. A radial basis neural network adaptive compensation control method considering elevator failure and input saturation is provided, which solves the influence of various elevator failures and actuator saturation on the aircraft during the flight of hypersonic aircraft, and ensures the fault tolerance of the system. and robustness.

为实现上述技术目的，本发明的技术方案如下：For realizing the above-mentioned technical purpose, the technical scheme of the present invention is as follows:

一种基于神经网络的高超声速飞行器自适应补偿控制方法，包括以下步骤：A neural network-based adaptive compensation control method for hypersonic aircraft, comprising the following steps:

S1：建立高超声速飞行器的纵向动力学模型，并将其分解为姿态子系统和速度子系统；S1: Establish the longitudinal dynamics model of hypersonic vehicle and decompose it into attitude subsystem and velocity subsystem;

S2：建立高超声速飞行器的升降舵故障模型；S2: Establish the elevator failure model of the hypersonic vehicle;

S3：构建平滑函数来估计非线性输入饱和，并引入径向基函数神经网络来估计高超声速飞行器的纵向动力学模型中非线性函数Fi(i＝1,2,3)；S3: Construct a smooth function to estimate the nonlinear input saturation, and introduce a radial basis function neural network to estimate the nonlinear function F i (i=1, 2, 3) in the longitudinal dynamics model of the hypersonic vehicle;

S4：通过反步法设计高超声速飞行器的自适应补偿控制器及相应的自适应参数更新律。S4: Design the adaptive compensation controller and the corresponding adaptive parameter update law of the hypersonic vehicle through the backstepping method.

进一步地，S1中，所述纵向动力学模型为：Further, in S1, the longitudinal dynamics model is:

Figure GDA0001674925600000021
Figure GDA0001674925600000021

Figure GDA0001674925600000022
Figure GDA0001674925600000022

Figure GDA0001674925600000023
Figure GDA0001674925600000023

Figure GDA0001674925600000024
Figure GDA0001674925600000024

Figure GDA0001674925600000025
Figure GDA0001674925600000025

其中，V，h，γ，α和q分别为速度，高度，航迹倾斜角，攻角和俯仰率；m,Re,μ和Iyy分别为飞行器质量，地球半径，万有引力常数和惯性力矩；T,D,L和Myy分别表示推力，阻力，升力和俯仰力矩。Among them, V, h, γ, α and q are the velocity, altitude, track inclination angle, angle of attack and pitch rate, respectively; m, R e , μ and I yy are the mass of the aircraft, the radius of the earth, the gravitational constant and the moment of inertia, respectively ; T, D, L and M yy represent thrust, drag, lift and pitching moment, respectively.

进一步地，S1中，所述姿态子系统的模型为：Further, in S1, the model of the attitude subsystem is:

Figure GDA0001674925600000026
Figure GDA0001674925600000026

Figure GDA0001674925600000027
Figure GDA0001674925600000027

Figure GDA0001674925600000031
Figure GDA0001674925600000031

y＝x1 y = x1

其中，状态变量x1＝γ，x2＝θp，x3＝q，θp为高超声速飞行器的俯仰角；f1(x1,V)，f3(x1,x2,x3,V)和g3(V)为通过径向基函数处理的非线性函数，f2和g2为已知常数；uj＝δej，j∈N表示第j个升降舵，N为非负整数集合，δej为第j个升降舵的偏转角；dj表示第j个偏转角的增益，sat(uj)为表示第j个升降舵的偏转角的饱和非线性函数。Among them, the state variables x 1 =γ, x 2 =θ p , x 3 =q, θ p is the pitch angle of the hypersonic vehicle; f 1 (x 1 ,V), f 3 (x 1 ,x 2 ,x 3 , V) and g 3 (V) are nonlinear functions processed by radial basis functions, f 2 and g 2 are known constants; u j =δ ej , j∈N represents the jth elevator, and N is non-negative Set of integers, δ ej is the deflection angle of the j-th elevator; d j represents the gain of the j-th deflection angle, and sat(u j ) is a saturated nonlinear function representing the deflection angle of the j-th elevator.

所述速度子系统的模型为：The model of the velocity subsystem is:

Figure GDA0001674925600000032
Figure GDA0001674925600000032

其中，fV(x1,x2,x3h,V)和gV(x1,x2,x3,h,V)是通过径向基函数处理的非线性函数；uV＝β，β为燃料当量比，sat(uV)为表示燃料当量比的饱和非线性函数。where f V (x 1 ,x 2 ,x 3 h,V) and g V (x 1 ,x 2 ,x 3 ,h,V) are nonlinear functions processed by radial basis functions; u V =β , β is the fuel equivalence ratio, and sat(u V ) is a saturated nonlinear function representing the fuel equivalence ratio.

进一步地，S2中，所述升降舵故障模型为：Further, in S2, the elevator failure model is:

Figure GDA0001674925600000033
Figure GDA0001674925600000033

其中，h∈N表示第h个故障，kj,h，

Figure GDA0001674925600000034
和
Figure GDA0001674925600000035
都是根据升降舵具体故障以及发生时间所确定的常数，其中0≤kj,h≤1，表示第j个升降舵发生第h个故障时第j个升降舵的健康指数，
Figure GDA0001674925600000036
和
Figure GDA0001674925600000037
分别表示第j个升降舵发生第h个故障的起始时间和结束时间，且
Figure GDA0001674925600000038
Figure GDA0001674925600000039
是分段连续的有界函数，用来表示第j个升降舵发生第h个故障时中的加性故障部分，vj(t)表示升降舵偏转角的控制信号。where h∈N denotes the hth fault, k j,h ,
Figure GDA0001674925600000034
and
Figure GDA0001674925600000035
are constants determined according to the specific failure of the elevator and the occurrence time, where 0≤k j,h ≤1, which means the health index of the j-th elevator when the j-th elevator has the h-th fault,
Figure GDA0001674925600000036
and
Figure GDA0001674925600000037
represent the start time and end time of the hth failure of the jth elevator, respectively, and
Figure GDA0001674925600000038
Figure GDA0001674925600000039
is a piecewise continuous bounded function, used to represent the additive fault part of the jth elevator when the hth fault occurs, v j (t) represents the control signal of the elevator deflection angle.

优选地，S3中，所述平滑函数是基于升降舵的偏转角输入饱和时构建的；Preferably, in S3, the smoothing function is constructed when the deflection angle input of the elevator is saturated;

所述平滑函数的形式如下：The smoothing function is of the form:

Figure GDA00016749256000000310
Figure GDA00016749256000000310

sat(uj)＝ψ(uj)+ψd(uj)sat(u j )=ψ(u j )+ψ d (u j )

其中，

Figure GDA00016749256000000311
ψd(uj)是一个有界函数；
Figure GDA00016749256000000312
和
Figure GDA00016749256000000313
分别代表uj的上界和下界；ψ(uj)＝ψauj，即sat(uj)＝ψauj+ψd(uj),ψa为连续有界的非线性函数。in,
Figure GDA00016749256000000311
ψ d (u j ) is a bounded function;
Figure GDA00016749256000000312
and
Figure GDA00016749256000000313
respectively represent the upper and lower bounds of u j ; ψ(u j )=ψ a u j , that is, sat(u j )=ψ a u j +ψ d (u j ), ψ a is a continuous and bounded nonlinear function .

优选地，S3中，所述平滑函数是基于燃料当量比输入饱和时构建的；Preferably, in S3, the smoothing function is constructed based on the input saturation of the fuel equivalence ratio;

所述平滑函数的形式如下：The smoothing function has the following form:

Figure GDA0001674925600000041
Figure GDA0001674925600000041

sat(uV)＝ψaVuV+ψdV(uV)sat(u V )=ψ aV u V +ψ dV (u V )

其中，

Figure GDA0001674925600000042
ψdV(uV)是一个有界函数；
Figure GDA0001674925600000043
和
Figure GDA0001674925600000044
分别代表uV的上界和下界；ψaV(uV)＝ψauV，即sat(uV)＝ψaVuV+ψdV(uV),ψaV为连续有界的非线性函数。in,
Figure GDA0001674925600000042
ψ dV (u V ) is a bounded function;
Figure GDA0001674925600000043
and
Figure GDA0001674925600000044
Represent the upper and lower bounds of u V ; _ function.

进一步地，S3中，所述引入径向基函数神经网络来估计系统中非线性函数Fi(i＝1,2,3)的具体形式如下：Further, in S3, the specific form of introducing the radial basis function neural network to estimate the nonlinear function F i (i=1, 2, 3) in the system is as follows:

Figure GDA0001674925600000045
Figure GDA0001674925600000045

其中，θi∈RN是径向基函数中的N个节点的最优权重向量，RN为N维实数空间，φi(ξi)＝[φi1(ξi),…,φiN(ξi)]T∈RN是径向基函数中的基函数向量；Δ(ξi)表示近似误差，δi为一常数，其中

Figure GDA0001674925600000046
οij和bi分别为径向基函数的中心和宽度；定义一个常数
Figure GDA0001674925600000047
Figure GDA0001674925600000048
是
Figure GDA0001674925600000049
的估计值，
Figure GDA00016749256000000410
为估计误差，gm是常数，且0＜gm≤min[inf{g1(V)},g2,inf{g3(V)},inf{gV(x1,x2,x3,h,V)}]。Among them, θ i ∈ R N is the optimal weight vector of N nodes in the radial basis function, R N is an N-dimensional real number space, φ i (ξ i )=[φ i1 (ξ i ),…,φ iN (ξ i )] T ∈R N is the basis function vector in the radial basis function; Δ(ξ i ) represents the approximation error, δ i is a constant, where
Figure GDA0001674925600000046
ο ij and b i are the center and width of the radial basis function, respectively; define a constant
Figure GDA0001674925600000047
Figure GDA0001674925600000048
Yes
Figure GDA0001674925600000049
the estimated value of ,
Figure GDA00016749256000000410
is the estimation error, g m is a constant, and 0<g m ≤min[inf{g 1 (V)},g 2 ,inf{g 3 (V)},inf{g V (x 1 ,x 2 ,x 3 ,h,V)}].

进一步地，S4中，所述通过反步法设计高超声速飞行器的自适应补偿控制器及相应的自适应参数更新律的具体形式如下：Further, in S4, the specific form of the adaptive compensation controller and the corresponding adaptive parameter update law designed by the backstepping method for the hypersonic aircraft is as follows:

定义误差变量s1、s2、s3：Define error variables s 1 , s 2 , s 3 :

s1＝x1-γr s 1 =x 1 -γ r

s2＝x2-x2d s 2 =x 2 -x 2d

s3＝x3-x3d s 3 =x 3 -x 3d

其中，γr为航迹倾斜角γ的控制信号，定义hr为高度h的参考信号，选取

Figure GDA00016749256000000411
以保证当γ追踪其控制信号γr时，h追踪其参考信号hr；x2d为姿态子系统第一状态方程
Figure GDA00016749256000000412
的虚拟控制信号，x3d为姿态子系统第二状态方程
Figure GDA00016749256000000413
的虚拟控制信号；Among them, γ r is the control signal of the track inclination angle γ , and hr is defined as the reference signal of the height h.
Figure GDA00016749256000000411
To ensure that when γ tracks its control signal γ r , h tracks its reference signal hr ; x 2d is the first state equation of the attitude subsystem
Figure GDA00016749256000000412
The virtual control signal of x 3d is the second state equation of the attitude subsystem
Figure GDA00016749256000000413
the virtual control signal;

所述姿态子系统的虚拟控制器设计如下：The virtual controller of the attitude subsystem is designed as follows:

Figure GDA0001674925600000051
Figure GDA0001674925600000051

Figure GDA0001674925600000052
Figure GDA0001674925600000052

x2d对应的自适应参数更新律为：The adaptive parameter update law corresponding to x 2d is:

Figure GDA0001674925600000053
Figure GDA0001674925600000053

x3d对应的自适应参数更新律为：The adaptive parameter update law corresponding to x 3d is:

Figure GDA0001674925600000054
Figure GDA0001674925600000054

所述姿态子系统的实际控制器设计如下：The actual controller design of the attitude subsystem is as follows:

Figure GDA0001674925600000055
Figure GDA0001674925600000055

vj对应的自适应参数更新律为：The adaptive parameter update law corresponding to v j is:

Figure GDA0001674925600000056
Figure GDA0001674925600000056

Figure GDA0001674925600000057
Figure GDA0001674925600000057

Figure GDA0001674925600000058
Figure GDA0001674925600000058

定义Vr为速度V的参考信号，

Figure GDA0001674925600000059
为V的追踪误差，所述速度子系统的控制器为：Define V r as the reference signal of speed V,
Figure GDA0001674925600000059
is the tracking error of V, the controller of the velocity subsystem is:

Figure GDA00016749256000000510
Figure GDA00016749256000000510

uV对应的自适应参数更新律为：The adaptive parameter update law corresponding to u V is:

Figure GDA00016749256000000511
Figure GDA00016749256000000511

Figure GDA00016749256000000512
Figure GDA00016749256000000512

Figure GDA00016749256000000513
Figure GDA00016749256000000513

其中，

Figure GDA00016749256000000514
ε(t)＝[d1(ψa1u1+ψd1),d2(ψa2u2+ψd2),…,dn(ψanun+ψdn)]T，
Figure GDA00016749256000000515
Figure GDA00016749256000000516
Figure GDA00016749256000000517
和
Figure GDA00016749256000000518
分别为ζ和p的估计值，
Figure GDA00016749256000000519
和
Figure GDA00016749256000000520
分别为ζV和pV的估计值，ξ1＝(x1,γr,h,V)T，
Figure GDA0001674925600000061
ξV＝(x1,x2,x3,h,V)T，∈，ci，λi和μi均为正常数。in,
Figure GDA00016749256000000514
ε(t)=[d 1 (ψ a1 u 1 +ψ d1 ),d2(ψ a2 u 2 +ψ d2 ),…,d n (ψ an u n +ψ dn )] T ,
Figure GDA00016749256000000515
Figure GDA00016749256000000516
Figure GDA00016749256000000517
and
Figure GDA00016749256000000518
are the estimated values of ζ and p, respectively,
Figure GDA00016749256000000519
and
Figure GDA00016749256000000520
are the estimated values of ζ V and p V , respectively, ξ 1 =(x 1 ,γ r ,h,V) T ,
Figure GDA0001674925600000061
ξ V =(x 1 ,x 2 ,x 3 ,h,V) T , ∈, c i , λ i and μ i are all positive numbers.

本发明的有益效果：Beneficial effects of the present invention:

(1)与现有的飞行器设计过程中建立的故障模型相比，本发明中所建立的故障模型更适用于高超声速飞行器升降舵故障的一般情况，可以很好的涵盖各种类型的故障，更加符合实际。(1) Compared with the fault model established in the existing aircraft design process, the fault model established in the present invention is more suitable for the general situation of hypersonic aircraft elevator failure, and can well cover various types of faults, more Realistic.

(2)与传统的高超声速飞行器的自适应控制方法相比，本发明通过建立平滑函数，解决了执行器的输入饱和问题，有利于反步法在自适应设计过程中得以直接使用。(2) Compared with the traditional adaptive control method of hypersonic aircraft, the present invention solves the problem of input saturation of the actuator by establishing a smooth function, which is beneficial to the direct use of the backstepping method in the adaptive design process.

(3)本发明通过引入径向基函数神经网络，解决了自适应补偿控制系统设计中的未知的非线性函数所带来的不便，并且通过定义关于神经网络最优权重向量的函数，使得无论神经网络最优权重向量维数多大，自适应参数更新律中每一步内只需更新一个参数，大大减小了计算量。(3) The present invention solves the inconvenience caused by the unknown nonlinear function in the design of the adaptive compensation control system by introducing the radial basis function neural network, and by defining the function of the optimal weight vector of the neural network, no matter How large is the optimal weight vector dimension of the neural network, only one parameter needs to be updated in each step in the adaptive parameter update law, which greatly reduces the amount of calculation.

附图说明Description of drawings

为了更清楚地说明本发明实施例或现有技术中的技术方案，下面将对实施例中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本发明的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings required in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some of the present invention. In the embodiments, for those of ordinary skill in the art, other drawings can also be obtained according to these drawings without any creative effort.

图1为本方法的流程图；Fig. 1 is the flow chart of this method;

图2为本方法的系统框图；Fig. 2 is the system block diagram of this method;

图3为本方法中高度h跟踪高度参考信号hr的Matlab仿真结果图，其中横坐标表示时间(单位为s)，纵坐标表示高度(单位为ft)；Fig. 3 is the Matlab simulation result diagram of height h tracking height reference signal h r in this method, wherein the abscissa represents time (unit is s), and the ordinate represents height (unit is ft);

图4为本方法中速度V跟踪速度参考信号Vr的Matlab仿真结果图，其中横坐标表示时间(单位为s)，纵坐标表示速度(单位为ft/s)。Figure 4 is a graph of the Matlab simulation result of the speed V tracking the speed reference signal V r in this method, wherein the abscissa represents time (unit is s), and the ordinate represents speed (unit is ft/s).

具体实施方式Detailed ways

下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员所获得的所有其他实施例，都属于本发明保护的范围。The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art fall within the protection scope of the present invention.

如图1所示，基于神经网络的高超声速飞行器自适应补偿控制方法，包括以下步骤：As shown in Figure 1, the neural network-based adaptive compensation control method for hypersonic aircraft includes the following steps:

S1：建立一种标准的高超声速飞行器纵向动力学模型，并将其分解为姿态子系统和速度子系统；S1: Establish a standard hypersonic vehicle longitudinal dynamics model and decompose it into attitude subsystem and velocity subsystem;

建立一种标准的高超声速飞行器的纵向动力学模型如下：The longitudinal dynamics model of a standard hypersonic vehicle is established as follows:

Figure GDA0001674925600000071
Figure GDA0001674925600000071

Figure GDA0001674925600000072
Figure GDA0001674925600000072

Figure GDA0001674925600000073
Figure GDA0001674925600000073

Figure GDA0001674925600000074
Figure GDA0001674925600000074

Figure GDA0001674925600000075
Figure GDA0001674925600000075

其中，V，h，γ，α和q分别为速度，高度，航迹倾斜角，攻角和俯仰率；m,Re,μ和Iyy分别为飞行器质量，地球半径，万有引力常数和惯性力矩，取m＝9375kg,Re＝20903500ft和Iyy＝7×106bf·ft；T,D,L和Myy分别表示推力，阻力，升力和俯仰力矩。Among them, V, h, γ, α and q are the velocity, altitude, track inclination angle, angle of attack and pitch rate, respectively; m, R e , μ and I yy are the mass of the aircraft, the radius of the earth, the gravitational constant and the moment of inertia, respectively , take m=9375kg, Re =20903500ft and I yy =7×10 6 bf·ft; T, D, L and My yy represent thrust, drag, lift and pitch moment respectively.

建立高超声速飞行器的姿态子系统的模型如下：The model for establishing the attitude subsystem of the hypersonic vehicle is as follows:

Figure GDA0001674925600000076
Figure GDA0001674925600000076

Figure GDA0001674925600000077
Figure GDA0001674925600000077

Figure GDA0001674925600000078
Figure GDA0001674925600000078

y＝x1 y = x1

其中，状态变量x1＝γ，x2＝θp，x3＝q，θp为高超声速飞行器的俯仰角；f1(x1,V)，f3(x1,x2,x3,V)和g3(V)为通过径向基函数处理的非线性函数，f2和g2为已知常数；uj＝δej，j∈N表示第j个升降舵，N为非负整数集合，δej为第j个升降舵的偏转角；dj表示第j个偏转角的增益，sat(uj)为表示第j个升降舵的偏转角的饱和非线性函数。Among them, the state variables x 1 =γ, x 2 =θ p , x 3 =q, θ p is the pitch angle of the hypersonic vehicle; f 1 (x 1 ,V), f 3 (x 1 ,x 2 ,x 3 , V) and g 3 (V) are nonlinear functions processed by radial basis functions, f 2 and g 2 are known constants; u j =δ ej , j∈N represents the jth elevator, and N is non-negative Set of integers, δ ej is the deflection angle of the j-th elevator; d j represents the gain of the j-th deflection angle, and sat(u j ) is a saturated nonlinear function representing the deflection angle of the j-th elevator.

建立高超声速飞行器的速度子系统的模型如下：The model of the velocity subsystem of the hypersonic vehicle is established as follows:

Figure GDA0001674925600000081
Figure GDA0001674925600000081

其中，fV(x1,x2,x3h,V)和gV(x1,x2,x3,h,V)是通过径向基函数处理的非线性函数；uV＝β，β为燃料当量比，高超声速飞行器的飞行速率主要由燃料当量比β决定，故选取其为输入；sat(uV)为表示燃料当量比的饱和非线性函数。where f V (x 1 ,x 2 ,x 3 h,V) and g V (x 1 ,x 2 ,x 3 ,h,V) are nonlinear functions processed by radial basis functions; u V =β , β is the fuel equivalence ratio, the flight speed of the hypersonic vehicle is mainly determined by the fuel equivalence ratio β, so it is selected as the input; sat(u V ) is a saturated nonlinear function representing the fuel equivalence ratio.

S2：建立高超声速飞行器的升降舵故障模型；S2: Establish the elevator failure model of the hypersonic vehicle;

建立一种具有一般性的升降舵故障模型如下：A general elevator fault model is established as follows:

Figure GDA0001674925600000082
Figure GDA0001674925600000082

其中，h∈N表示第h个故障，kj,h，

Figure GDA0001674925600000083
和
Figure GDA0001674925600000084
都是根据升降舵具体故障以及发生时间所确定的常数，其中0≤kj,h≤1，表示第j个升降舵发生第h个故障时第j个升降舵的健康指数，
Figure GDA0001674925600000085
和
Figure GDA0001674925600000086
分别表示第j个升降舵发生第h个故障的起始时间和结束时间，且
Figure GDA0001674925600000087
Figure GDA0001674925600000088
是分段连续的有界函数，用来表示第j个升降舵发生第h个故障时中的加性故障部分，vj(t)表示升降舵偏转角的控制信号。本发明建立的故障模型相比于普通的故障模型更具有普遍性，可以表示两种不同的故障：where h∈N denotes the hth fault, k j,h ,
Figure GDA0001674925600000083
and
Figure GDA0001674925600000084
are constants determined according to the specific failure of the elevator and the occurrence time, where 0≤k j,h ≤1, which means the health index of the jth elevator when the hth failure of the jth elevator occurs,
Figure GDA0001674925600000085
and
Figure GDA0001674925600000086
represent the start time and end time of the hth failure of the jth elevator, respectively, and
Figure GDA0001674925600000087
Figure GDA0001674925600000088
is a piecewise continuous bounded function, used to represent the additive fault part of the jth elevator when the hth fault occurs, v j (t) represents the control signal of the elevator deflection angle. Compared with ordinary fault models, the fault model established by the present invention is more general and can represent two different faults:

第一种故障：当0≤kj,h≤1时，第j个升降舵失去了其部分有效性并且受到额外的故障

Figure GDA0001674925600000089
的影响，
Figure GDA00016749256000000810
First fault: when 0≤k j,h ≤1, the jth elevator loses some of its validity and suffers from additional faults
Figure GDA0001674925600000089
Impact,
Figure GDA00016749256000000810

第二种故障：当kj,h＝0时，升降舵完全失控，不再受控制信号控制，

Figure GDA00016749256000000811
The second fault: when k j,h = 0, the elevator is completely out of control and is no longer controlled by the control signal,
Figure GDA00016749256000000811

S3：构建平滑函数来估计非线性输入饱和，并引入径向基函数神经网络来估计高超声速飞行器的纵向动力学模型中的非线性函数Fi(i＝1,2,3)；S3: Build a smooth function to estimate nonlinear input saturation, and introduce a radial basis function neural network to estimate the nonlinear function F i (i=1, 2, 3) in the longitudinal dynamics model of the hypersonic vehicle;

对于升降舵的偏转角输入饱和的情况，构建平滑函数的形式如下：For the case where the deflection angle input of the elevator is saturated, the smooth function is constructed in the following form:

Figure GDA00016749256000000812
Figure GDA00016749256000000812

sat(uj)＝ψ(uj)+ψd(uj)sat(u j )=ψ(u j )+ψ d (u j )

其中，

Figure GDA00016749256000000813
ψd(uj)是一个有界函数；
Figure GDA00016749256000000814
和
Figure GDA00016749256000000815
分别代表uj的上界和下界；ψ(uj)＝ψauj，即sat(uj)＝ψauj+ψd(uj),ψa为连续有界的非线性函数。in,
Figure GDA00016749256000000813
ψ d (u j ) is a bounded function;
Figure GDA00016749256000000814
and
Figure GDA00016749256000000815
respectively represent the upper and lower bounds of u j ; ψ(u j )=ψ a u j , that is, sat(u j )=ψ a u j +ψ d (u j ), ψ a is a continuous and bounded nonlinear function .

对于燃料当量比输入饱和的情况，构建平滑函数的形式如下：For the case where the fuel equivalence ratio input is saturated, the smoothing function is constructed as follows:

Figure GDA00016749256000000816
Figure GDA00016749256000000816

sat(uV)＝ψaVuV+ψdV(uV)sat(u V )=ψ aV u V +ψ dV (u V )

其中，

Figure GDA0001674925600000091
ψdV(uV)是一个有界函数；
Figure GDA0001674925600000092
和
Figure GDA0001674925600000093
分别代表uV的上界和下界；ψaV(uV)＝ψauV，即sat(uV)＝ψaVuV+ψdV(uV),ψaV为连续有界的非线性函数。in,
Figure GDA0001674925600000091
ψ dV (u V ) is a bounded function;
Figure GDA0001674925600000092
and
Figure GDA0001674925600000093
Represent the upper and lower bounds of u V ; _ function.

通过引入径向基函数神经网络来估计高超声速飞行器的纵向动力学模型中非线性函数Fi(i＝1,2,3)，将其表示如下：The nonlinear function F i (i=1, 2, 3) in the longitudinal dynamics model of the hypersonic vehicle is estimated by introducing the radial basis function neural network, which is expressed as follows:

Fi(ξi)＝θi Tφi(ξi)+Δ(ξi),|Δ(ξi)|≤δi F i (ξ i )=θ i T φ i (ξ i )+Δ(ξ i ),|Δ(ξ i )|≤δ i

其中，θi∈RN是径向基函数中的N个节点的最优权重向量，RN为N维实数空间，φi(ξi)＝[φi1(ξi),…,φiN(ξi)]T∈RN是径向基函数中的基函数向量；Δ(ξi)表示近似误差，δi为一常数，其中

Figure GDA0001674925600000094
οij和bi分别为径向基函数的中心和宽度；定义一个常数
Figure GDA0001674925600000095
Figure GDA0001674925600000096
是
Figure GDA0001674925600000097
的估计值，
Figure GDA0001674925600000098
为估计误差，gm是常数，且0＜gm≤min[inf{g1(V)},g2,inf{g3(V)},inf{gV(x1,x2,x3,h,V)}]。本发明中用到径向基函数神经网络进行近似的几处非线性环节如下所示：
Figure GDA0001674925600000099
Figure GDA00016749256000000910
其中ξ1＝(x1,γr,h,V)T，
Figure GDA00016749256000000911
ξV＝(x1,x2,x3,h,V)T。Among them, θ i ∈ R N is the optimal weight vector of N nodes in the radial basis function, R N is an N-dimensional real number space, φ i (ξ i )=[φ i1 (ξ i ),…,φ iN (ξ i )] T ∈R N is the basis function vector in the radial basis function; Δ(ξ i ) represents the approximation error, δ i is a constant, where
Figure GDA0001674925600000094
ο ij and b i are the center and width of the radial basis function, respectively; define a constant
Figure GDA0001674925600000095
Figure GDA0001674925600000096
Yes
Figure GDA0001674925600000097
the estimated value of ,
Figure GDA0001674925600000098
is the estimation error, gm is a constant, and 0<g m ≤min[inf{g 1 (V)},g 2 ,inf{g 3 (V)},inf{g V (x 1 ,x 2 ,x 3 ,h,V)}]. In the present invention, several nonlinear links used for approximation by radial basis function neural network are as follows:
Figure GDA0001674925600000099
Figure GDA00016749256000000910
where ξ 1 =(x 1 ,γ r ,h,V) T ,
Figure GDA00016749256000000911
ξ V =(x 1 ,x 2 ,x 3 ,h,V) T .

S4：通过反步法设计高超声速飞行器的自适应补偿控制器及相应的自适应参数更新律；S4: Design the adaptive compensation controller and the corresponding adaptive parameter update law of the hypersonic vehicle through the backstepping method;

定义误差变量s1、s2、s3：Define error variables s 1 , s 2 , s 3 :

s1＝x1-γr s 1 =x 1 -γ r

s2＝x2-x2d s 2 =x 2 -x 2d

s3＝x3-x3d s 3 =x 3 -x 3d

其中，γr为航迹倾斜角γ的控制信号，定义hr为高度h的控制信号，选取

Figure GDA00016749256000000912
以保证当γ追踪其控制信号γr时，h追踪其控制信号hr；x2d为姿态子系统第一状态方程
Figure GDA00016749256000000913
的虚拟控制信号，x3d为姿态子系统第二状态方程
Figure GDA00016749256000000914
的虚拟控制信号；Among them, γ r is the control signal of the track inclination angle γ , and hr is defined as the control signal of the height h.
Figure GDA00016749256000000912
To ensure that when γ tracks its control signal γ r , h tracks its control signal hr ; x 2d is the first state equation of the attitude subsystem
Figure GDA00016749256000000913
The virtual control signal of x 3d is the second state equation of the attitude subsystem
Figure GDA00016749256000000914
the virtual control signal;

所述姿态子系统的虚拟控制器设计如下：The virtual controller of the attitude subsystem is designed as follows:

Figure GDA0001674925600000101
Figure GDA0001674925600000101

Figure GDA0001674925600000102
Figure GDA0001674925600000102

x2d对应的自适应参数更新律为：The adaptive parameter update law corresponding to x 2d is:

Figure GDA0001674925600000103
Figure GDA0001674925600000103

x3d对应的自适应参数更新律为：The adaptive parameter update law corresponding to x 3d is:

Figure GDA0001674925600000104
Figure GDA0001674925600000104

所述姿态子系统的实际控制器设计如下：The actual controller design of the attitude subsystem is as follows:

Figure GDA0001674925600000105
Figure GDA0001674925600000105

vj对应的自适应参数更新律为：The adaptive parameter update law corresponding to v j is:

Figure GDA0001674925600000106
Figure GDA0001674925600000106

Figure GDA0001674925600000107
Figure GDA0001674925600000107

Figure GDA0001674925600000108
Figure GDA0001674925600000108

定义Vr为速度V的参考信号，

Figure GDA0001674925600000109
为V的追踪误差，所述速度子系统的控制器为：Define V r as the reference signal of speed V,
Figure GDA0001674925600000109
is the tracking error of V, the controller of the velocity subsystem is:

Figure GDA00016749256000001010
Figure GDA00016749256000001010

uV对应的自适应参数更新律为：The adaptive parameter update law corresponding to u V is:

Figure GDA00016749256000001011
Figure GDA00016749256000001011

Figure GDA00016749256000001012
Figure GDA00016749256000001012

Figure GDA00016749256000001013
Figure GDA00016749256000001013

其中，

Figure GDA00016749256000001014
ε(t)＝[d1(ψa1u1+ψd1),d2(ψa2u2+ψd2),…,dn(ψanun+ψdn)]T，
Figure GDA00016749256000001015
Figure GDA00016749256000001016
Figure GDA00016749256000001017
和
Figure GDA00016749256000001018
分别为ζ和p的估计值，
Figure GDA00016749256000001019
和
Figure GDA00016749256000001020
分别为ζV和pV的估计值，ξ1＝(x1,γr,h,V)T，
Figure GDA00016749256000001021
ξV＝(x1,x2,x3,h,V)T，∈，ci，λi和μi均为正常数。in,
Figure GDA00016749256000001014
ε(t)=[d 1 (ψ a1 u 1 +ψ d1 ),d2(ψ a2 u 2 +ψ d2 ),…,d n (ψ an u n +ψ dn )] T ,
Figure GDA00016749256000001015
Figure GDA00016749256000001016
Figure GDA00016749256000001017
and
Figure GDA00016749256000001018
are the estimated values of ζ and p, respectively,
Figure GDA00016749256000001019
and
Figure GDA00016749256000001020
are the estimated values of ζ V and p V , respectively, ξ 1 =(x 1 ,γ r ,h,V) T ,
Figure GDA00016749256000001021
ξ V =(x 1 ,x 2 ,x 3 ,h,V) T , ∈, c i , λ i and μ i are all positive numbers.

基于以上步骤的控制方法的系统框图如图2所示，自适应控制器通过对给定的信号(高度参考信号hr和速度参考信号Vr)以及系统的状态信息进行综合计算，从而得到升降舵和燃料节流阀的控制信号，进而对系统进行控制，图中箭头方向表示信号传递方向。The system block diagram of the control method based on the above steps is shown in Figure 2. The adaptive controller obtains the elevator by comprehensively calculating the given signals (altitude reference signal hr and speed reference signal V r ) and the state information of the system. And the control signal of the fuel throttle valve, and then control the system, the direction of the arrow in the figure indicates the direction of signal transmission.

本实施例中选取以下参数对本方法进行matlab仿真实现：∈＝0.1，c1＝40，c2＝7，c3＝5，cV＝5，λ1＝0.1，λ2＝0.1，λ3＝0.1，λ4＝0.15，λ5＝0.25，μ1＝0.3，μ2＝0.3，μ3＝0.3，μ4＝0.2，μ5＝0.2，μV1＝μV2＝μV3＝0.1，λV1＝λV2＝λV3＝0.1。对于径向基函数神经网络的宽度以及中心点的选取如下：b1＝b2＝b3＝10，bV＝15。对于ο1＝(ο11,ο12,ο13,ο14)，ο1j分别选自矩阵

Figure GDA0001674925600000111
的第j行，并进行排列组合，进而总共得到34＝81个不同的ο1值，即对于φ1(ξ1)＝[φ11(ξ1),…,φ1N(ξ1)]T∈RN总共使用了81个径向基函数，N＝81。对于ο2＝(ο21,ο22,ο23,ο24,ο25)，ο2j分别选自矩阵
Figure GDA0001674925600000112
的第j行，并进行排列组合，进而总共得到35＝243个不同的ο2值，即对于φ2(ξ2)＝[φ21(ξ2),…,φ2N(ξ2)]T∈RN总共使用了243个径向基函数，N＝243。对于ο3＝(ο31,ο32,ο33,ο34,ο35,ο36,ο37)，ο3j分别选自矩阵
Figure GDA0001674925600000113
的第j行，并进行排列组合，进而总共得到37＝2187个不同的ο3值，即对于φ3(ξ3)＝[φ31(ξ3),…,φ3N(ξ3)]T∈RN总共使用了2187个径向基函数，N＝2187。对于οV＝(οV1,οV2,οV3,οV4,οV5)，οVj分别选自矩阵
Figure GDA0001674925600000121
的第j行，并进行排列组合，进而总共得到35＝243个不同的οV值，即对于φV(ξV)＝[φV1(ξV),…,φVN(ξV)]T∈RN总共使用了243个径向基函数，N＝243。In this embodiment, the following parameters are selected to carry out matlab simulation implementation of this method: ∈=0.1, c 1 =40, c 2 =7, c 3 =5, c V =5,λ 1 =0.1,λ 2 =0.1,λ 3 =0.1, λ 4 =0.15, λ 5 =0.25, μ 1 =0.3, μ 2 =0.3, μ 3 =0.3, μ 4 =0.2, μ 5 =0.2, μ V1 =μ V2 =μ V3 =0.1,λ V1 =λ V2 =λ V3 =0.1. The selection of the width and center point of the radial basis function neural network is as follows: b 1 =b 2 =b 3 =10, b V =15. For ο 1 =(ο 11 ,ο 12 ,ο 13 ,ο 14 ), ο 1j are respectively selected from the matrix
Figure GDA0001674925600000111
The jth row of , and permutation and combination, and then get a total of 3 4 =81 different ο 1 values, that is, for φ 1 (ξ 1 )=[φ 11 (ξ 1 ),...,φ 1N (ξ 1 )] T ∈ R N uses a total of 81 radial basis functions, N=81. For ο 2 =(ο 21 ,ο 22 ,ο 23 ,ο 24 ,ο 25 ), ο 2j are respectively selected from the matrix
Figure GDA0001674925600000112
The jth row of , and permutation and combination, and then get a total of 3 5 =243 different ο 2 values, that is, for φ 2 (ξ 2 )=[φ 21 (ξ 2 ),...,φ 2N (ξ 2 )] T ∈ R N uses a total of 243 radial basis functions, N=243. For ο 3 = (ο 31 ,ο 32 ,ο 33 ,ο 34 ,ο 35 ,ο 36 ,ο 37 ), ο 3j are respectively selected from the matrix
Figure GDA0001674925600000113
The jth row of , and permutation and combination, and then get a total of 3 7 =2187 different ο 3 values, that is, for φ 3 (ξ 3 )=[φ 31 (ξ 3 ),...,φ 3N (ξ 3 )] T ∈ R N uses a total of 2187 radial basis functions, N=2187. For ο V = (ο V1 ,ο V2 ,ο V3 ,ο V4 ,ο V5 ), ο Vj are selected from the matrix
Figure GDA0001674925600000121
The jth row of , and permutation and combination, and then get a total of 3 5 =243 different ο V values, that is, for φ V (ξ V )=[φ V1 (ξ V ),...,φ VN (ξ V )] T ∈ R N uses a total of 243 radial basis functions, N=243.

如图3和图4所示，通过Matlab仿真，可以得到基于径向基神经网络的自适应补偿控制方法，可以实现在高超声速飞行器存在升降舵故障以及执行器饱和情况下，高度和速度分别跟踪其控制信号，且能够满足跟踪误差足够小的性能要求，本方法具有较强容错能力和鲁棒性。As shown in Figure 3 and Figure 4, through Matlab simulation, an adaptive compensation control method based on radial basis neural network can be obtained, which can realize that in the case of elevator failure and actuator saturation of hypersonic aircraft, the altitude and speed can track its speed respectively. control signal, and can meet the performance requirements of sufficiently small tracking error, the method has strong fault tolerance and robustness.

以上所述仅为本发明的较佳实施例而已，并不用以限制本发明，凡在本发明的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本发明的保护范围之内。The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the scope of the present invention. within the scope of protection.

Claims (9)

1.一种基于神经网络的高超声速飞行器自适应补偿控制方法，其特征在于，包括以下步骤：1. a hypersonic aircraft adaptive compensation control method based on neural network, is characterized in that, comprises the following steps: S1：建立高超声速飞行器的纵向动力学模型，并将其分解为姿态子系统和速度子系统；S1: Establish the longitudinal dynamics model of hypersonic vehicle and decompose it into attitude subsystem and velocity subsystem; S2：建立高超声速飞行器的升降舵故障模型；S2: Establish the elevator failure model of the hypersonic vehicle; S3：构建平滑函数来估计非线性输入饱和，并引入径向基函数神经网络来估计高超声速飞行器的纵向动力学模型中的非线性函数Fi，i＝1,2,3；S3: Build a smooth function to estimate nonlinear input saturation, and introduce a radial basis function neural network to estimate the nonlinear function F i in the longitudinal dynamics model of the hypersonic vehicle, i=1, 2, 3; S4：通过反步法设计高超声速飞行器的自适应补偿控制器及相应的自适应参数更新；S4: Design the adaptive compensation controller of the hypersonic vehicle and update the corresponding adaptive parameters through the backstepping method; S4中，所述通过反步法设计高超声速飞行器的自适应补偿控制器及相应的自适应参数更新律的具体形式如下：In S4, the specific form of designing the adaptive compensation controller and the corresponding adaptive parameter update law of the hypersonic aircraft through the backstepping method is as follows: 定义误差变量s1、s2、s3：Define error variables s 1 , s 2 , s 3 : s1＝x1-γr s 1 =x 1 -γ r s2＝x2-x2d s 2 =x 2 -x 2d s3＝x3-x3d s 3 =x 3 -x 3d 其中，状态变量x1＝γ，x2＝θp，x3＝q，θp为高超声速飞行器的俯仰角，q为俯仰率，γr为航迹倾斜角γ的控制信号，定义hr为高度h的参考信号，选取
Figure FDA0002630910150000011
以保证当γ追踪其控制信号γr时，h追踪其参考信号hr；x2d为姿态子系统第一状态方程
Figure FDA0002630910150000012
的虚拟控制信号，x3d为姿态子系统第二状态方程
Figure FDA0002630910150000013
的虚拟控制信号；Among them, the state variables x 1 =γ, x 2 =θ p , x 3 =q, θ p is the pitch angle of the hypersonic vehicle, q is the pitch rate, γ r is the control signal of the track inclination angle γ , and the definition hr is the reference signal of height h, choose
Figure FDA0002630910150000011
To ensure that when γ tracks its control signal γ r , h tracks its reference signal hr ; x 2d is the first state equation of the attitude subsystem
Figure FDA0002630910150000012
The virtual control signal of x 3d is the second state equation of the attitude subsystem
Figure FDA0002630910150000013
the virtual control signal; 所述姿态子系统的虚拟控制器设计如下：The virtual controller of the attitude subsystem is designed as follows:
Figure FDA0002630910150000014
Figure FDA0002630910150000014
Figure FDA0002630910150000015
Figure FDA0002630910150000015
 x2d对应的自适应参数更新律为：The adaptive parameter update law corresponding to x 2d is:
Figure FDA0002630910150000016
Figure FDA0002630910150000016
 x3d对应的自适应参数更新律为：The adaptive parameter update law corresponding to x 3d is:
Figure FDA0002630910150000017
Figure FDA0002630910150000017
 所述姿态子系统的实际控制器设计如下：The actual controller design of the attitude subsystem is as follows:
Figure FDA0002630910150000021
Figure FDA0002630910150000021
 vj对应的自适应参数更新律为：The adaptive parameter update law corresponding to v j is:
Figure FDA0002630910150000022
Figure FDA0002630910150000022
Figure FDA0002630910150000023
Figure FDA0002630910150000023
Figure FDA0002630910150000024
Figure FDA0002630910150000024
 定义一个常数
Figure FDA0002630910150000025
Figure FDA0002630910150000026
是
Figure FDA0002630910150000027
的估计值，
Figure FDA0002630910150000028
为估计误差，gm是常数，且0＜gm≤min[inf{g1(V)},g2,inf{g3(V)},inf{gV(x1,x2,x3,h,V)}]；define a constant
Figure FDA0002630910150000025
Figure FDA0002630910150000026
Yes
Figure FDA0002630910150000027
the estimated value of ,
Figure FDA0002630910150000028
is the estimation error, g m is a constant, and 0<g m ≤min[inf{g 1 (V)},g 2 ,inf{g 3 (V)},inf{g V (x 1 ,x 2 ,x 3 ,h,V)}]; 定义Vr为速度V的参考信号，
Figure FDA0002630910150000029
为V的追踪误差，所述速度子系统的控制器为：Define V r as the reference signal of speed V,
Figure FDA0002630910150000029
is the tracking error of V, the controller of the velocity subsystem is:
Figure FDA00026309101500000210
Figure FDA00026309101500000210
 uV对应的自适应参数更新律为：The adaptive parameter update law corresponding to u V is:
Figure FDA00026309101500000211
Figure FDA00026309101500000211
Figure FDA00026309101500000212
Figure FDA00026309101500000212
Figure FDA00026309101500000213
Figure FDA00026309101500000213
 其中，
Figure FDA00026309101500000214
ε(t)＝[d1(ψa1u1+ψd1),d2(ψa2u2+ψd2),…,dn(ψanun+ψdn)]T，
Figure FDA00026309101500000215
Figure FDA00026309101500000216
和
Figure FDA00026309101500000217
分别为ζ和p的估计值，
Figure FDA00026309101500000218
和
Figure FDA00026309101500000219
分别为ζV和pV的估计值，ξ1＝(x1,γr,h,V)T，
Figure FDA00026309101500000220
ξV＝(x1,x2,x3,h,V)T，∈1，∈2，ci，λi和μi均为正常数。in,
Figure FDA00026309101500000214
ε(t)=[d 1 (ψ a1 u 1 +ψ d1 ),d 2 (ψ a2 u 2 +ψ d2 ),…,d n (ψ an u n +ψ dn )] T ,
Figure FDA00026309101500000215
Figure FDA00026309101500000216
and
Figure FDA00026309101500000217
are the estimated values of ζ and p, respectively,
Figure FDA00026309101500000218
and
Figure FDA00026309101500000219
are the estimated values of ζ V and p V , respectively, ξ 1 =(x 1 ,γ r ,h,V) T ,
Figure FDA00026309101500000220
ξ V =(x 1 ,x 2 ,x 3 ,h,V) T , ∈ 1 , ∈ 2 , c i , λ i and μ i are all positive numbers. 2.如权利要求1所述的方法，其特征在于，S1中，所述纵向动力学模型为：2. The method of claim 1, wherein in S1, the longitudinal dynamics model is:
Figure FDA00026309101500000221
Figure FDA00026309101500000221
Figure FDA0002630910150000031
Figure FDA0002630910150000031
Figure FDA0002630910150000032
Figure FDA0002630910150000032
Figure FDA0002630910150000033
Figure FDA0002630910150000033
Figure FDA0002630910150000034
Figure FDA0002630910150000034
 其中，V，h，γ和α分别为速度，高度，航迹倾斜角和攻角；m，Re，μ和Iyy分别为飞行器质量，地球半径，万有引力常数和惯性力矩；T，D，L和Myy分别表示推力，阻力，升力和俯仰力矩。Among them, V, h, γ and α are the speed, altitude, track inclination angle and angle of attack, respectively; m, Re, μ and I yy are the mass of the aircraft, the radius of the earth, the gravitational constant and the moment of inertia, respectively; T, D, L and M yy represent thrust, drag, lift and pitch moment, respectively. 3.如权利要求2所述的方法，其特征在于，S1中，所述姿态子系统的模型为：3. The method of claim 2, wherein in S1, the model of the attitude subsystem is:
Figure FDA0002630910150000035
Figure FDA0002630910150000035
Figure FDA0002630910150000036
Figure FDA0002630910150000036
Figure FDA0002630910150000037
Figure FDA0002630910150000037
 y＝x1 y = x1 其中，f1(x1,V)，f3(x1,x2,x3,V)和g3(V)为通过径向基函数处理的非线性函数，f2和g2为已知常数；uj＝δej，j∈N表示第j个升降舵，N为非负整数集合，δej为第j个升降舵的偏转角；dj表示第j个偏转角的增益，sat(uj)为表示第j个升降舵的偏转角的饱和非线性函数；where f 1 (x 1 ,V), f 3 (x 1 ,x 2 ,x 3 ,V) and g 3 (V) are nonlinear functions processed by radial basis functions, and f 2 and g 2 are u j =δ ej , j∈N represents the j-th elevator, N is the set of non-negative integers, δ ej is the deflection angle of the j-th elevator; d j represents the gain of the j-th deflection angle, sat(u j ) is a saturated nonlinear function representing the deflection angle of the jth elevator; 所述速度子系统的模型为：The model of the velocity subsystem is:
Figure FDA0002630910150000038
Figure FDA0002630910150000038
 其中，fV(x1,x2,x3h,V)和gV(x1,x2,x3,h,V)是通过径向基函数处理的非线性函数；uV＝β，β为燃料当量比，sat(uV)为表示燃料当量比的饱和非线性函数。where f V (x 1 ,x 2 ,x 3 h,V) and g V (x 1 ,x 2 ,x 3 ,h,V) are nonlinear functions processed by radial basis functions; u V =β , β is the fuel equivalence ratio, and sat(u V ) is a saturated nonlinear function representing the fuel equivalence ratio. 4.如权利要求3所述的方法，其特征在于，S2中，所述升降舵故障模型为：4. The method of claim 3, wherein in S2, the elevator failure model is:
Figure FDA0002630910150000039
Figure FDA0002630910150000039
 其中，h∈N表示第h个故障，kj,h，
Figure FDA00026309101500000310
和
Figure FDA00026309101500000311
都是根据升降舵具体故障以及发生时间所确定的常数，其中0≤kj,h≤1，表示第j个升降舵发生第h个故障时第j个升降舵的健康指数，
Figure FDA00026309101500000312
和
Figure FDA00026309101500000313
分别表示第j个升降舵发生第h个故障的起始时间和结束时间，where h∈N denotes the hth fault, k j,h ,
Figure FDA00026309101500000310
and
Figure FDA00026309101500000311
are constants determined according to the specific failure of the elevator and the occurrence time, where 0≤k j,h ≤1, which means the health index of the jth elevator when the hth failure of the jth elevator occurs,
Figure FDA00026309101500000312
and
Figure FDA00026309101500000313
represent the start time and end time of the hth failure of the jth elevator, respectively, 且
Figure FDA00026309101500000314
是分段连续的有界函数，用来表示第j个升降舵发生第h个故障时中的加性故障部分，vj(t)表示升降舵偏转角的控制信号。and
Figure FDA00026309101500000314
is a piecewise continuous bounded function, used to represent the additive fault part of the jth elevator when the hth fault occurs, v j (t) represents the control signal of the elevator deflection angle. 5.如权利要求4所述的方法，其特征在于，S3中，所述平滑函数是基于升降舵的偏转角输入饱和时构建的。5. The method of claim 4, wherein, in S3, the smoothing function is constructed based on when the deflection angle input of the elevator is saturated. 6.如权利要求4所述的方法，其特征在于，S3中，所述平滑函数是基于燃料当量比输入饱和时构建的。6. The method of claim 4, wherein, in S3, the smoothing function is constructed based on the saturation of the fuel equivalence ratio input. 7.如权利要求5所述的方法，其特征在于，所述平滑函数的形式如下：7. The method of claim 5, wherein the smoothing function has the following form:
Figure FDA0002630910150000041
Figure FDA0002630910150000041
 sat(uj)＝ψ(uj)+ψd(uj)sat(u j )=ψ(u j )+ψ d (u j ) 其中，
Figure FDA0002630910150000042
ψd(uj)是一个有界函数；
Figure FDA0002630910150000043
和
Figure FDA0002630910150000044
分别代表uj的上界和下界；ψ(uj)＝ψauj，即sat(uj)＝ψauj+ψd(uj),ψa为连续有界的非线性函数。in,
Figure FDA0002630910150000042
ψ d (u j ) is a bounded function;
Figure FDA0002630910150000043
and
Figure FDA0002630910150000044
respectively represent the upper and lower bounds of u j ; ψ(u j )=ψ a u j , that is, sat(u j )=ψ a u j +ψ d (u j ), ψ a is a continuous and bounded nonlinear function . 8.如权利要求6所述的方法，其特征在于，所述平滑函数的形式如下：8. The method of claim 6, wherein the smoothing function has the following form:
Figure FDA0002630910150000045
Figure FDA0002630910150000045
 sat(uV)＝ψaVuV+ψdV(uV)sat(u V )=ψ aV u V +ψ dV (u V ) 其中，
Figure FDA0002630910150000046
ψdV(uV)是一个有界函数；
Figure FDA0002630910150000047
和
Figure FDA0002630910150000048
分别代表uV的上界和下界；ψaV(uV)＝ψauV，即sat(uV)＝ψaVuV+ψdV(uV)，ψaV为连续有界的非线性函数。in,
Figure FDA0002630910150000046
ψ dV (u V ) is a bounded function;
Figure FDA0002630910150000047
and
Figure FDA0002630910150000048
Represent the upper and lower bounds of u V ; _ function. 9.如权利要求7或8所述的方法，其特征在于，S3中，所述引入径向基函数神经网络来估计高超声速飞行器的纵向动力学模型中非线性函数Fi，i＝1,2,3的具体形式如下：9. The method according to claim 7 or 8, wherein in S3, the radial basis function neural network is introduced to estimate the nonlinear function F i in the longitudinal dynamics model of the hypersonic aircraft, i=1, The specific forms of 2 and 3 are as follows: Fi(ξi)＝θi Tφi(ξi)+Δ(ξi)，|Δ(ξi)|≤δi F i (ξ i )=θ i T φ i (ξ i )+Δ(ξ i ), |Δ(ξ i )|≤δ i 其中，θi∈RN是径向基函数中的N个节点的最优权重向量，RN为N维实数空间，φi(ξi)＝[φi1(ξi),…,φiN(ξi)]T∈RN是径向基函数中的基函数向量；Δ(ξi)表示近似误差，δi为一常数，其中
Figure FDA0002630910150000049
οij和bi分别为径向基函数的中心和宽度；定义一个常数
Figure FDA00026309101500000410
Figure FDA00026309101500000411
是
Figure FDA00026309101500000412
的估计值，
Figure FDA00026309101500000413
为估计误差，gm是常数，且0＜gm≤min[inf{g1(V)},g2,inf{g3(V)},inf{gV(x1,x2,x3,h,V)}]。Among them, θ i ∈ R N is the optimal weight vector of N nodes in the radial basis function, R N is an N-dimensional real number space, φ i (ξ i )=[φ i1 (ξ i ),…,φ iN (ξ i )] T ∈R N is the basis function vector in the radial basis function; Δ(ξ i ) represents the approximation error, δ i is a constant, where
Figure FDA0002630910150000049
ο ij and b i are the center and width of the radial basis function, respectively; define a constant
Figure FDA00026309101500000410
Figure FDA00026309101500000411
Yes
Figure FDA00026309101500000412
the estimated value of ,
Figure FDA00026309101500000413
is the estimation error, g m is a constant, and 0<g m ≤min[inf{g 1 (V)},g 2 ,inf{g 3 (V)},inf{g V (x 1 ,x 2 ,x 3 ,h,V)}].
CN201810262739.8A 2018-03-28 2018-03-28 Adaptive compensation control method of hypersonic aircraft based on neural network Active CN108375907B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201810262739.8A CN108375907B (en) 2018-03-28 2018-03-28 Adaptive compensation control method of hypersonic aircraft based on neural network

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201810262739.8A CN108375907B (en) 2018-03-28 2018-03-28 Adaptive compensation control method of hypersonic aircraft based on neural network

Publications (2)

Publication Number Publication Date
CN108375907A CN108375907A (en) 2018-08-07
CN108375907B true CN108375907B (en) 2020-11-10

Family

ID=63031779

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201810262739.8A Active CN108375907B (en) 2018-03-28 2018-03-28 Adaptive compensation control method of hypersonic aircraft based on neural network

Country Status (1)

Country Link
CN (1) CN108375907B (en)

Families Citing this family (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN109062055A (en) * 2018-09-10 2018-12-21 南京航空航天大学 A kind of Near Space Flying Vehicles control system based on Back-stepping robust adaptive dynamic surface
CN108919651B (en) * 2018-09-26 2020-09-01 北京航空航天大学 An adaptive fault-tolerant control method for hypersonic aircraft considering actuator input constraints
CN109508035B (en) * 2018-12-24 2021-11-26 南京邮电大学 Multi-region hierarchical unmanned aerial vehicle formation path planning method based on distributed control
CN110231774A (en) * 2019-04-08 2019-09-13 天津大学 Disturbance-observer becomes air intake duct hypersonic aircraft fuzzy coordinated control method
CN110187713A (en) * 2019-04-12 2019-08-30 浙江大学 A Longitudinal Control Method of Hypersonic Vehicle Based on Online Identification of Aerodynamic Parameters
CN110340898B (en) * 2019-08-22 2020-12-01 北京航空航天大学 An adaptive fault-tolerant control method for a free-floating space manipulator
CN110488852B (en) * 2019-08-28 2020-12-01 北京航空航天大学 A full-profile adaptive control method for hypersonic aircraft
CN110673472B (en) * 2019-09-09 2022-06-28 南京理工大学 Adaptive Robust Control Method Based on Neural Network Compensation for Dead Zone Inversion Error
CN111007724A (en) * 2019-12-19 2020-04-14 哈尔滨工业大学 A Quantitative Tracking Control Method for Specified Performance of Hypersonic Aircraft Based on Interval Type II Fuzzy Neural Network
CN111158398A (en) * 2020-01-15 2020-05-15 哈尔滨工业大学 Adaptive control method for hypersonic vehicle considering angle of attack constraints
CN112558484A (en) * 2020-12-29 2021-03-26 彩虹无人机科技有限公司 Design method of controller for displaying and considering dynamic characteristics of aircraft actuating mechanism
CN113961010B (en) * 2021-08-26 2023-07-18 中国科学院合肥物质科学研究院 Tracking control method for quadrotor plant protection UAV

Family Cites Families (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5102072A (en) * 1990-11-19 1992-04-07 General Dynamics Corporation, Convair Division Adaptive gain and phase controller for autopilot for a hypersonic vehicle
US6882992B1 (en) * 1999-09-02 2005-04-19 Paul J. Werbos Neural networks for intelligent control
CN102880052B (en) * 2012-09-29 2014-12-31 西北工业大学 Time scale function decomposition based hypersonic aircraft actuator saturation control method
CN104898682B (en) * 2015-05-05 2017-10-31 南京航空航天大学 A kind of hypersonic aircraft reenters posture fault tolerant control method
CN105843077B (en) * 2016-04-07 2019-03-29 杭州电子科技大学 A kind of gain switching method of Spacecraft Rendezvous system and maximum domain of attraction estimation
CN106842912B (en) * 2016-11-30 2020-08-14 南京航空航天大学 Hypersonic speed maneuvering flight control surface saturation robust control method
CN106934120B (en) * 2017-02-23 2020-02-11 哈尔滨工业大学 Three-dimensional guidance law design method for intercepting hypersonic aircraft based on forward guidance
CN107479384B (en) * 2017-09-05 2019-10-22 西北工业大学 Neural network compound learning non-backstepping control method for hypersonic vehicle

Also Published As

Publication number Publication date
CN108375907A (en) 2018-08-07

Similar Documents

Publication Publication Date Title
CN108375907B (en) Adaptive compensation control method of hypersonic aircraft based on neural network
CN108919651B (en) An adaptive fault-tolerant control method for hypersonic aircraft considering actuator input constraints
CN107450324B (en) Adaptive fault-tolerant control method for hypersonic vehicle considering angle of attack constraint
CN107390531B (en) Control method of hypersonic vehicle with finite time convergence of parameter learning
CN103616816B (en) A kind of hypersonic aircraft elevator fault control method
CN102749851B (en) Fine anti-interference tracking controller of flexible hypersonic vehicle
Jiang et al. Adaptive neural observer‐based backstepping fault tolerant control for near space vehicle under control effector damage
CN102880052B (en) Time scale function decomposition based hypersonic aircraft actuator saturation control method
CN110109361B (en) Rapid smooth self-adaptive sliding mode control method for hypersonic aircraft
CN109358634B (en) A robust adaptive control method for hypersonic aircraft
CN107479383B (en) Neural network compound learning control method for hypersonic vehicle based on robust design
CN113485304B (en) Aircraft hierarchical fault-tolerant control method based on deep learning fault diagnosis
CN108663940B (en) Aircraft neural network lea rning control method based on the compound estimation of lump
CN113268084B (en) Intelligent fault-tolerant control method for unmanned aerial vehicle formation
CN104199286A (en) Hierarchical dynamic inverse control method for flight vehicle based on sliding mode interference observer
CN108776434B (en) Rapid self-adaptive sliding mode fault-tolerant control method for hypersonic aircraft
CN105676852B (en) Small-sized depopulated helicopter is unpowered to learn model structure Adaptive Attitude control method
CN105182742A (en) Elastic body aircraft adaptive constrained tracking control indirect method
CN109062055A (en) A kind of Near Space Flying Vehicles control system based on Back-stepping robust adaptive dynamic surface
CN110879535B (en) Sliding mode fault-tolerant control method of T-S fuzzy UMV
CN105137999A (en) Aircraft tracking control direct method with input saturation
CN115079574B (en) Distributed fault compensation method for flexible hypersonic aircraft
CN112379595B (en) A Learning Control Method for Compound Disturbances for Nonlinear Strict Feedback Switching Systems
CN107908114A (en) Aircraft robust nonlinear control method and robust controller system
CN110362110B (en) Fixed self-adaptive neural network unmanned aerial vehicle track angle control method

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant