飞机偏航角控制系统的稳定性仿真与分析

摘要

用李雅普诺夫直接法分析了具有非线性部分的飞机偏航角控制系统的绝对稳定性问题。根据系统构成与动态方程，以递增叠加法求得李雅普诺夫函数及其导数，由此得出系统绝对稳定的条件。采用波波夫谐波线性化方法，确定非线性部分的取值范围。然后在仿真计算中采用波波夫稳定判据，证明在改变系统参数的情况下，系统稳定性将随之改变，表明李雅普诺夫直接法所得的系统绝对稳定性条件能够对系统稳定判断起到较好的指导效果。%The absolute stability of an aircraft’s yaw-angle control system was studied based on the Lyapunov direct method. The configuration and dynamic equations of the control system were given. The Lyapunov function and its derivatives were derived by superposition method. The absolute stability condition was also obtained. Using Popov harmonic linearization, the maximum value of nonlinear part was determined. Then Popov stability criterion was introduced to simulate the absolute stability with various parameter settings of the system. Simulation results indicate that the absolute stability condition can be applied to judge the stability of the system effectively.