CN102707624B

CN102707624B - Design method of longitudinal controller region based on conventional aircraft model

Info

Publication number: CN102707624B
Application number: CN201210175030.7A
Authority: CN
Inventors: 史忠科
Original assignee: Northwestern Polytechnical University
Current assignee: Northwestern Polytechnical University
Priority date: 2012-05-31
Filing date: 2012-05-31
Publication date: 2014-08-06
Anticipated expiration: 2032-05-31
Also published as: CN102707624A

Abstract

The invention discloses a method for designing a longitudinal controller region based on a conventional model of an aircraft, which is used to solve the technical problem that the existing controller design method cannot directly determine the overall stability of a given flight region. This method obtains the equilibrium point when the control target altitude and Mach number are given through the aerodynamic force and moment equations, and uses the phase plane analysis model to determine the regional stability of the system. On this basis, the parameters of the feedback controller are determined, and the longitudinal motion of the aircraft Controlling avoids incorrect approximations such as ignoring aerodynamic effects and lateral heading effects in the moment equation, so that the controller can ensure the stability of the aircraft in the entire design area, reducing or even avoiding unstable and unsafe flight caused by the analysis model and so on.

Description

Design Method of Longitudinal Controller Area Based on Conventional Model of Aircraft

技术领域 technical field

本发明涉及一种飞行器纵向控制器设计方法，特别涉及一种基于飞行器常规模型的纵向控制器区域设计方法。The invention relates to a method for designing a longitudinal controller of an aircraft, in particular to a method for designing a region of a longitudinal controller based on a conventional model of an aircraft.

背景技术 Background technique

飞行控制的基本目的是改善飞机的稳定性和操纵性，从而提高执行任务的能力；最近几十年来，随着飞机性能的不断提高，飞行控制技术发生了很大的变化，出现了主动控制技术、综合控制技术、自主飞行控制技术等先进的飞行控制技术，飞行控制系统与航电系统出现了高度综合化的趋势。现代高性能飞机对飞行控制系统提出了更高的要求，使用古典控制理论设计先进飞机的飞行控制系统已越来越困难；为了获得更好的飞行品质，许多现代控制方法被应用到飞机飞行控制系统的设计中，如线性二次型调节器／线性二次型高斯函数／回路传递恢复（LQR／LQG／LTR）方法、定量反馈方法、动态逆方法、反馈线性化方法、反步控制方法、滑模变结构控制方法等；这些方法都需要飞行器准确的数学模型，然而，飞行器模型是一个很复杂的非线性微分方程式，人们很难得到准确的数学模型；工程上，飞机模型都是在通过风洞实验和飞行试验得到的，实际飞行控制系统设计中还要考虑以下问题：(1)在已经建立起数学模型的飞机参数发生变化或存在结构不确定时，飞行控制系统应该具有小的灵敏度响应；(2)由于控制器频带比较宽，使得飞机性能受飞机结构和执行机构动态性能变化的影响比较有小的灵敏度响应比较大；(3)反馈控制器的设计虽然对飞行员指令会得到较理想的响应，但是对于外部干扰的响应可能会是破坏性的；(4)执行部件与控制元件存在制造容差，系统运行过程中也存在老化、磨损及环境和运行条件恶化等现象；(5)在实际工程问题中，通常对数学模型要人为地进行简化，去掉一些复杂的因素；为此，非线性H∞和μ综合鲁棒控制等非线性设计方法也在飞行控制器设计中得到广泛关注；上述方法，能够得到仅适于某个给定飞行状态的控制律结构及参数，在此基础上，需要逐次对整个飞行包线内不同飞行状态下的控制律设计，得到适于不同飞行状态的控制律结构和参数，并利用不同的方法进行控制律参数及结构的调整参数规律进行设计，最后得到一个适合于整个包线的完整的飞行控制律；依赖以上控制器设计方法，设计人员不能直接确定在给定飞行区域的稳定性；文献“Hsien-Keng Chenand Ching-I Lee，Anti-control of chaos in rigid body motion，Chaos，litons & Fractals，2004，Vol.21(4)：957-965”直接根据飞行器通用的气动力、力矩表达式进行了相平面分析，既不考虑飞行器机型、又不考虑气动导数；论文方法偏离实际太远，给出的结果不被人们认可。The basic purpose of flight control is to improve the stability and maneuverability of the aircraft, thereby improving the ability to perform tasks; in recent decades, with the continuous improvement of aircraft performance, great changes have taken place in flight control technology, and active control technology has emerged , integrated control technology, autonomous flight control technology and other advanced flight control technologies, the flight control system and avionics system have a highly integrated trend. Modern high-performance aircraft put forward higher requirements for the flight control system, and it is becoming more and more difficult to design the flight control system of advanced aircraft using classical control theory; in order to obtain better flight quality, many modern control methods are applied to aircraft flight control In system design, such as linear quadratic regulator/linear quadratic Gaussian function/loop transfer recovery (LQR/LQG/LTR) method, quantitative feedback method, dynamic inverse method, feedback linearization method, backstepping control method, Sliding mode variable structure control methods, etc.; these methods require accurate mathematical models of the aircraft, however, the aircraft model is a very complex nonlinear differential equation, it is difficult for people to obtain an accurate mathematical model; in engineering, aircraft models are all passed Based on wind tunnel experiments and flight tests, the following issues should also be considered in the design of the actual flight control system: (1) When the parameters of the aircraft that have established a mathematical model change or there is structural uncertainty, the flight control system should have a small sensitivity (2) Due to the relatively wide frequency band of the controller, the aircraft performance is relatively small due to the influence of the aircraft structure and the dynamic performance of the actuator, and the sensitivity response is relatively large; (3) Although the design of the feedback controller will have a greater effect on the pilot's instructions Ideal response, but the response to external disturbances may be destructive; (4) There are manufacturing tolerances in the actuator components and control components, and aging, wear and deterioration of the environment and operating conditions also exist during the operation of the system; (5) ) In practical engineering problems, the mathematical model is usually artificially simplified to remove some complicated factors; for this reason, nonlinear design methods such as nonlinear H∞ and μ-synthetic robust control are also widely used in the design of flight controllers Attention; the above method can obtain the control law structure and parameters only suitable for a given flight state. The control law structure and parameters of the state, and use different methods to design the control law parameters and the adjustment parameters of the structure, and finally get a complete flight control law suitable for the entire envelope; relying on the above controller design method, the designer The stability in a given flight area cannot be directly determined; the literature "Hsien-Keng Chenand Ching-I Lee, Anti-control of chaos in rigid body motion, Chaos, litons & Fractals, 2004, Vol.21(4): 957- 965” conducted phase plane analysis directly based on the common aerodynamic force and moment expressions of aircraft, without considering the aircraft type or aerodynamic derivative; the method deviated too far from reality, and the results given were not recognized by people.

发明内容 Contents of the invention

为了克服现有控制器设计方法不能直接确定给定飞行区域整体稳定性的不足，本发明提供一种基于飞行器常规模型的纵向控制器区域设计方法，该方法通过气动力、力矩方程得到给定控制目标高度、马赫数时的飞行器平稳平飞气流迎角和配平舵面，引入气流迎角等状态反馈控制器，采用相平面分析模型确定系统的区域稳定性，在此基础上确定反馈控制器的参数，直接对飞行器纵向运动进行控制，避免了力矩方程中忽略气动力作用和横航向影响等不正确近似，使得控制器在整个设计区域都能保证飞行器的稳定性，减少甚至避免了分析模型导致的不稳定、不安全飞行等问题发生。In order to overcome the deficiency that the existing controller design method cannot directly determine the overall stability of a given flight area, the present invention provides a method for designing a longitudinal controller area based on a conventional model of an aircraft. The airflow angle of attack and the trim rudder surface of the aircraft are stable at the target altitude and Mach number, the airflow angle of attack and other state feedback controllers are introduced, the regional stability of the system is determined by the phase plane analysis model, and the feedback controller is determined on this basis. Parameters, directly control the longitudinal motion of the aircraft, avoiding incorrect approximations such as ignoring the aerodynamic effects and lateral heading effects in the moment equation, so that the controller can ensure the stability of the aircraft in the entire design area, reducing or even avoiding the analysis model. Problems such as instability and unsafe flight occurred.

本发明解决其技术问题所采用的技术方案：一种基于飞行器常规模型的纵向控制器区域设计方法，其特点是包括以下步骤：The technical scheme that the present invention solves its technical problem adopts: a kind of longitudinal controller region design method based on conventional model of aircraft, it is characterized in that comprising the following steps:

1、根据气动力、力矩方程：1. According to the aerodynamic force and torque equation:

在q=0，确定给定控制目标高度和马赫数时的平衡点δ_s，α_s；at q=0, Determine the equilibrium point δ _s , α _s for a given control target altitude and Mach number;

式中：q为俯仰角速度，α为气流迎角，β为侧滑角，υ为俯仰角，为滚转角，p为滚转角速度，r为偏航角速度，δ为包含升降舵、油门开度、鸭翼等在内的输入向量，g为重力加速度，I_x为绕轴x的转动惯量，I_y为绕轴y的转动惯量，I_xz为乘积转动惯量，V₀为空速，M_q、Z_q、f_q、f_α为有关函数表达式，δ_s，α_s分别为对应控制目标高度、马赫数时的平飞配平舵面和平飞气流迎角；In the formula: q is the pitch angular velocity, α is the airflow angle of attack, β is the sideslip angle, υ is the pitch angle, is the roll angle, p is the roll angular velocity, r is the yaw angular velocity, δ is the input vector including elevator, throttle opening, canard, etc., g is the acceleration of gravity, I _x is the moment of inertia around the axis x, I _y is the moment of inertia around the axis y, I _xz is the product moment of inertia, V ₀ is the airspeed, M _q , Z _q , f _q , f _α are related function expressions, δ _s , α _s are the heights of the corresponding control targets , level flight trim rudder surface and level flight airflow angle of attack at Mach number;

2、选取反馈控制器表达式为：2. Select the feedback controller expression as:

δ=δ₀+k(α，q，υ)δ=δ ₀ +k(α,q,υ)

满足条件：α=α_s q=0时，δ=δ_s；Satisfied conditions: α=α _s q=0, δ=δ _s ;

其中：δ₀为舵面输入的常数值，k(α，q，υ)为待确定的反馈控制函数；Wherein: _δ0 is a constant value input by the rudder surface, and k(α, q, υ) is the feedback control function to be determined;

3、在给定飞行区域内，采用以下相平面分析模型3. In a given flight area, the following phase plane analysis model is used

分析系统收敛性，根据收敛性指标和平衡点条件：α=α_s q=0及δ=δ_s时，δ=δ_s共同确定反馈控制器的参数；To analyze the convergence of the system, according to the convergence index and the equilibrium point condition: when α=α _s q=0 and δ=δ _s , δ=δ _s jointly determine the parameters of the feedback controller;

其中：in:

本发明的有益效果是：通过气动力、力矩方程得到给定控制目标高度和马赫数时的平衡点，采用相平面分析模型确定系统的区域稳定性，在此基础上确定反馈控制器的参数，直接对飞行器纵向运动进行控制，避免了力矩方程中忽略气动力作用和横航向影响等不正确近似，使得控制器在整个设计区域都能保证飞行器的稳定性，减少甚至避免了分析模型导致的不稳定、不安全飞行等问题发生。The beneficial effect of the present invention is: obtain the equilibrium point when given control target height and Mach number through aerodynamic force, torque equation, adopt phase plane analysis model to determine the regional stability of the system, determine the parameter of feedback controller on this basis, Directly control the longitudinal motion of the aircraft, avoiding incorrect approximations such as ignoring the aerodynamic effect and lateral direction influence in the moment equation, so that the controller can ensure the stability of the aircraft in the entire design area, reducing or even avoiding the error caused by the analysis model. Problems such as stability and unsafe flight occurred.

下面结合实施例对本发明作详细说明。The present invention is described in detail below in conjunction with embodiment.

附图说明 Description of drawings

图1是本发明方法的相平面图实例，图1中，横坐标为α，单位为弧度，纵坐标为单位为弧度/秒。Fig. 1 is the phase plane example of the inventive method, and among Fig. 1, abscissa is α, and unit is radian, and ordinate is Units are radians/second.

具体实施方式 Detailed ways

以F-8飞机为例对具体实施方式进行说明。The specific implementation will be described by taking the F-8 aircraft as an example.

$\overset{\cdot &Center Dot;}{α α} = = ((11 - - 0.088 0.088 α α - - {α α}^{22})) q q - - 0.877 0.877 α α + + 0.47 0.47 {α α}^{22} + + 3.846 3.846 {α α}^{33} - - 0.215 0.215 {δ δ}_{e e} + + 0.28 0.28 {α α}^{22} {δ δ}_{e e} + + 0.47 0.47 {δ δ}_{e e}^{22} α α + + 0.63 0.63 {δ δ}_{e e}^{33}$

$\overset{\cdot \cdot}{q q} = = - - 0.396 0.396 q q - - 4.208 4.208 α α - - 0.47 0.47 {α α}^{22} - - 3.564 3.564 {α α}^{33} - - 20.967 20.967 {δ δ}_{e e} + + 6.265 6.265 {α α}^{22} {δ δ}_{e e} + + 4646 {δ δ}_{e e}^{22} + + 61.4 61.4 {δ δ}_{e e}^{33}$

取q=0，时，可得非线性代数方程组：Take q=0, , the system of nonlinear algebraic equations can be obtained:

$00 = = - - 0.877 0.877 α α + + 0.47 0.47 {α α}^{22} + + 3.846 3.846 {α α}^{33} - - 0.215 0.215 {δ δ}_{e e} + + 0.28 0.28 {α α}^{22} {δ δ}_{e e} + + 0.47 0.47 {δ δ}_{e e}^{22} α α + + 0.63 0.63 {δ δ}_{e e}^{33}$

$00 = = - - 4.208 4.208 α α - - 0.47 0.47 {α α}^{22} - - 3.564 3.564 {α α}^{33} - - 20.967 20.967 {δ δ}_{e e} + + 6.265 6.265 {α α}^{22} {δ δ}_{e e} + + 4646 {δ δ}_{e e}^{22} + + 61.4 61.4 {δ δ}_{e e}^{33}$

由该方程可以确定出在控制目标为当前高度和马赫数时的平衡点δ_es=0，α_s=0；From this equation, the balance point δ _es =0, α _s =0 can be determined when the control target is the current height and Mach number;

其中：δ_es，α_s分别为对应控制目标高度、马赫数时的平飞配平升降舵偏角和平飞气流迎角；Among them: δ _es , α _s are respectively the level flight trim elevator deflection angle and the level flight airflow angle of attack corresponding to the control target altitude and Mach number;

δ_e=k₀+k₁αδ _e =k ₀ +k ₁ α

满足条件：α=α_s q=0时，δ_e=δ_es；Satisfy the condition: when α=α _s q=0, δ _e =δ _es ;

3、在给定气流迎角和迎角导数的初值-0.5≤α₀≤0.5弧度、弧度/秒对应的飞行区域内，采用以下相平面分析模型3. The initial value of the given airflow angle of attack and angle of attack derivative -0.5≤α ₀ ≤0.5 radians, In the flight area corresponding to rad/s, the following phase plane analysis model is used

$\frac{{d d}^{22} α α}{{dt dt}^{22}} = = {d d}_{00} ((- - 4.208 4.208 α α - - 0.47 0.47 {α α}^{22} - - 3.564 3.564 {α α}^{33} - - 20.967 20.967 {δ δ}_{e e} + + 6.265 6.265 {α α}^{22} {δ δ}_{e e} + + 4646 {δ δ}_{e e}^{22} + + 61.4 61.4 {δ δ}_{e e}^{33}))$

$- d_{1} (\overset{\cdot}{α} + 0.877 α - 0.47 α^{2} - 3.846 α^{3} + 0.215 δ_{e} - 0.28 α^{2} δ_{e} - 0.47 δ_{e}^{2} α - 0.63 δ_{e}^{3}) - 0.877 \overset{\cdot}{α}$ 分析系 $- d_{1} (\overset{\cdot}{α} + 0.877 α - 0.47 α^{2} - 3.846 α^{3} + 0.215 δ_{e} - 0.28 α^{2} δ_{e} - 0.47 δ_{e}^{2} α - 0.63 δ_{e}^{3}) - 0.877 \overset{&Center Dot;}{α}$ Department of Analysis

$+ + 0.94 0.94 α α \overset{\cdot \cdot}{α α} + + 11.538 11.538 {α α}^{22} \overset{. .}{α α} - - 0.215 0.215 {\overset{\cdot &Center Dot;}{δ δ}}_{e e} + + 0.28 0.28 {α α}^{22} {\overset{\cdot &Center Dot;}{δ δ}}_{e e} + + 0.56 0.56 α α \overset{\cdot \cdot}{α α} {δ δ}_{e e} + + 0.47 0.47 {δ δ}_{e e}^{22} \overset{\cdot \cdot}{α α} + + 0.94 0.94 {δ δ}_{e e} {\overset{\cdot \cdot}{δ δ}}_{e e} α α + + 1.89 1.89 {δ δ}_{e e}^{22} {\overset{\cdot \cdot}{δ δ}}_{e e}$

统收敛性，根据收敛性指标和平衡点条件：α=α_s q=0及δ_e=δ_es时，确定反馈控制器的参数为k₀=0，k₁=1/4.9826521，对应相平面图如图1所示；其中d₀=1-0.088α-α²， $d_{1} = 0.396 + [(0.088 + 2 α) \overset{\cdot}{α}] / (1 - 0.088 α - α^{2}) .$ System convergence, according to the convergence index and equilibrium point conditions: when α=α _s q=0 and δ _e =δ _es , the parameters of the feedback controller are determined as k ₀ =0, k ₁ =1/4.9826521, corresponding to the phase plane diagram As shown in Figure 1; where d ₀ =1-0.088α-α ² , $d_{1} = 0.396 + [(0.088 + 2 α) \overset{&Center Dot;}{α}] / (1 - 0.088 α - α^{2}) .$

由图1的相平面图可知，在初值-0.5≤α₀≤0.5弧度、弧度/秒的全部飞行区域内，所设计的控制器使得系统是渐近稳定的，达到了全飞行区域的稳定控制效果。It can be seen from the phase plane diagram in Figure 1 that at the initial value -0.5≤α ₀ ≤0.5 radians, In the entire flight area of rad/s, the designed controller makes the system asymptotically stable, achieving the stable control effect of the entire flight area.

Claims

1. a kind of longitudinal control region design method based on aircraft conventional model, it is characterized in that comprising the following steps:

(a) According to the aerodynamic force and moment equation:

exist Determine the equilibrium point δ _s , α _s for a given control target height and Mach number;

In the formula: q is the pitch angular velocity, α is the airflow angle of attack, β is the sideslip angle, is the pitch angle, is the roll angle, p is the roll angular velocity, r is the yaw angular velocity, δ is the input vector including elevator, throttle opening and canard, g is the acceleration of gravity, I _x is the moment of inertia around the axis x, I _y is the moment of inertia around the axis y, I _xz is the product moment of inertia, V ₀ is the airspeed, M _q , Z _q , f _q , f _α are related function expressions, δ _s , α _s are the corresponding control target altitude, Level flight trim rudder surface and level flight airflow angle of attack at Mach number;

(b) Select the feedback controller expression as:

Satisfy the condition: when α=α _s q=0, δ=δ _s ;

Where: δ ₀ is the constant value input by the rudder surface, is the feedback control function to be determined;

(c) In a given flight area, use the following phase plane analysis model

To analyze the convergence of the system, according to the convergence index and the equilibrium point condition: when α=α _s q=0 and δ=δ _s , δ=δ _s jointly determine the parameters of the feedback controller;

in: