Abstract

Various methods of stability analysis of an airplane with a MIMO control system are considered in the framework of frequency analysis. They assume that the control system is open for selected signal with other loops closed or that system is open for all signals of selected loops and allow solving the stability equation and calculating the eigenvalues of the matrix of transfer functions. It is shown that all methods deal with different forms of the same equation, and thus the equivalence of methods considered for calculating closed-loop stability domains is proved. The application of methods is demonstrated for calculation of stability domains for an airplane equipped with MIMO stability and control augmentation system in lateral motion that uses ailerons and rudder as control surfaces. It is shown that in the case of a MIMO system, an open-loop transfer function that defines closed-loop stability is a nonlinear function of control system gains; this introduces uncertainty to the concept of amplitude and phase margins.

中文翻译：

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基于频率法的多输入多输出控制系统飞机稳定性分析

摘要

在频率分析的框架内考虑了具有 MIMO 控制系统的飞机稳定性分析的各种方法。他们假设控制系统对选定的信号开放，而其他回路关闭，或者该系统对选定回路的所有信号开放，并允许求解稳定性方程并计算传递函数矩阵的特征值。结果表明，所有方法都处理同一方程的不同形式，从而证明了计算闭环稳定域所考虑方法的等效性。演示了方法的应用，用于计算配备 MIMO 稳定性和控制增强系统的飞机在横向运动中使用副翼和方向舵作为控制面的稳定性域。结果表明，在 MIMO 系统的情况下，定义闭环稳定性的开环传递函数是控制系统增益的非线性函数；这给幅度和相位裕度的概念带来了不确定性。