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摘要四旋翼飞行器是近年来自动控制领域的一个研究热点，关于四旋翼飞行器也有了很多成熟并付诸实用的控制理论。四旋翼飞行器作为一个结构复杂的系统，从控制结构角度可以分为姿态控制和位置控制。其中姿态控制对于微小变化要比位置控制敏感的多，也即姿态状态量变化速度比位置状态量的快很多。传统控制器的设计很难在兼顾两个量级上的时间常数的同时，保证控制精度。本文基于奇异摄动的思想，建立四旋翼飞行器的奇异摄动模型，并分别设计LQR与控制控制器，提高控制器的控制精度。
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主要工作如下：
(1) 建立并分析四旋翼飞行器的动力学模型，给出4种分运动，包括升降运动、航向运动、俯仰运动以及横滚运动。在此基础上，使用小扰动法进一步得出各个分运动的线性化模型。再根据奇异摄动理论，我们利用从线性化模型中分解出快慢子系统。
(2) 根据LQR控制理论分别设计四旋翼飞行器的线性化模型控制器与奇异摄动模型控制器，将控制器应用于原非线性系统，并对比其控制效果。仿真结果表明奇异摄动模型下的控制器在欧拉角状态的快速性上占优。
(3) 根据H∞控制理论分别设计四旋翼飞行器的线性化模型控制器与奇异摄动模型控制器，将控制器应用于原非线性系统，并对比其控制效果。仿真结果表明奇异摄动模型下的控制器在欧拉角抗扰性上占优。19183
(4) 对比H∞控制控制器与LQR控制器的抗扰性能。理论上，H∞算法在抗扰性上有较好的表现，仿真结果也验证了这一点。
关键字：四旋翼飞行器 奇异摄动 LQR控制 H∞控制 抗扰性
Title High-frequency Dynamic of Unmanned Quatodrotor Simulation and Analysis
Abstract
Quadrotor is a research hotspot in the automatic control field in recent years, and it also has a lot of mature and practical control theories. As a system of complex structure, it can be pided into attitude control and position control from the perspective of control structure. Attitude control is more sensitive to small changes than position control, in other words the changing speed of state variable of attitude control is much faster than that of position control. So it is difficult to design a traditional controller to meet control accuracy at the same time of considering time constant of different orders of magnitude.
In this paper, a model of singular perturbation is established based on the theory of singular perturbation, with LQR and H∞ controllers being given, to improve control accuracy.
The main work in this paper is as follows:
(1) Established and analyzed the dynamic model of quadrotor, gave four
kinds of independent moments which includes lifting movement, heading the movement, pitch and roll motion movement. Then deduced the linear model of each moment with the small perturbation method and got fast subsystem and slow subsystem from the linear model based on singular perturbation theory.
(2) Designed controllers of linear model and singular perturbation model respectively based on LQR control theory, and applied them to the original nonlinear system to compare the control performances. The simulation results show that the controller based on singular perturbation model is advance in rapidity of Euler angles.
(3) Designed controllers of linear model and singular perturbation model respectively based on H∞ control theory, and applied them to the original nonlinear system to compare the control performances. The simulation results show that the controller based on singular perturbation model is advance in disturbance rejection of Euler angles.
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