题 目 基于气动力控制的导弹姿态
控制律设计
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摘 要
对于大气层内飞行的导弹，为了使其准确的完成飞行，首要任务是使其姿态
保持稳定。导弹的姿态控制系统是导弹飞行成败的关键系统之一，姿态控制过程
和方法一直备受关注，它在导弹设计、使用、储存的整个生命周期中都意义重大。
在此背景下，本文针对大气层内导弹的姿态控制方法进行研究。
首先建立了一系列坐标系来描述大气层内导弹的飞行特性，包括弹体坐标系、
地面惯性坐标系、速度坐标系和弹道坐标系，之后对这些坐标系之间的变转换关
系进行了推导。然后，推导计算大气层内导弹的动力学方程组、运动学方程组、
攻角和侧滑角计算模型、弹道倾角和弹道偏角计算模型、气动力模型、气动力矩
模型以及重力模型，由上述模型得出导弹的姿态控制系统数学模型。由于大气层
内导弹的姿态控制数学模型具有强耦合、非线性的特点，因此先对其进行解耦和
线性化处理，而后进行控制器设计。本文应用小扰动假设下的线性化方法，分别
建立了各通道的传递函数。之后，运用 PD 控制方法对三个通道的控制律分别进
行设计，使导弹能在要求时间内达到目标姿态。最后，设计 MATLAB 仿真程序，
对控制律进行仿真验证，并对仿真结果进行分析。
仿真结果表明，对大气层内导弹姿态控制模型进行线性化及各通道解耦处理
后，应用 PD 控制方法设计控制律，能够使系统实现快速、稳定的达到目标姿态
的目的。
关键词 大气层内导弹；气动力控制；模型线性化；PD 控制；仿真
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Abstract
Missile flying within the atmosphere in order to make the accurate completion of
the flight, the first task is to make its attitude stability. The attitude of the missile
control system is a key system of missile flight success, attitude control process and
method has attracted much attention. It is significant in the entire life cycle of missile
design, use, and storage.
In this paper, a series of coordinate systems are established to describe the flight
of missile in atmosphere , including missile body coordinate system, ground inertial
coordinate system, velocity coordinate system and ballistic coordinate system, then
the transformation relation between these coordinate systems is deduced. Then,
according to the missile kinetic equations,missile kinematics equations, angle of
attack and side slip angle calculation model, trajectory angle and trajectory angle
calculation model, aerodynamic model, aerodynamic moment model and gravity
model, the attitude of the aircraft is obtained mathematical model of control system.
Because the mathematical model of attitude control of atmospheric missile has strong
coupling and nonlinear characteristics, it is decoupled and linearized first, and then
the controller is designed. In this paper, the transfer function of each channel is
established by using the linearization method under the assumption of small
disturbance. At the same time, the coupling of pitch, yaw and roll of the three
channels is also relieved. Then, the PD control method is used to design the control
law of the three channels, so that the missile can reach the target attitude accurately in
the required time. Finally, the MATLAB simulation program is designed to verify the
control law, and the simulation results are analyzed.
According to the design of controller and mathematical simulation and result
analysis show that after the linearization of the atmospheric missile attitude control
model and the decoupling of each channel, the PD control method is used to design
the control law, and the system can achieve the target position quickly and stably.
Keywords:A missile that flies in the atmosphere; aerodynamic force control; model
linearization; PD control; simulation
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