应用H_∞-范数进行多通道气动伺服弹性系统的频域稳定性分析

Exploring Differently Frequency Domain Analysis of MIMO AeroServo Elasticity(ASE) System Stability Using H-Infinity-Norm

气动伺服弹性稳定性分析是现代飞机设计中必须考虑的课题。给出了多输入/多输出气动伺服弹性系统的频域运动方程,并由系统稳定性理论得出,在气动伺服弹性稳定临界点附近,系统的H∞-范数趋于无穷大。据此,发展了一种应用H∞-范数进行频域气动伺服弹性稳定性分析的方法。针对某型飞机及其偏航/滚转增稳回路构成的多输入/多输出气动伺服弹性系统,采用该方法求得其闭环稳定临界点,与p-k法计算结果符合较好。分析结果还表明:考虑增稳系统的影响后,飞机气动伺服弹性稳定边界,相对于无控飞机的颤振速度有所降低;对临界稳定模态进行限幅滤波后,减小了不利耦合,使气动伺服弹性稳定性得到提高。

Sections 1 through 3 of the full paper explain our different exploration mentioned in the title,whose core consists of：（1） we derive the equations of motion in frequency domain for a multiple-input and multiple-output（MIMO） ASE system;（2） using the system stability theory,we prove that the H-infinity-norm of the frequency response function matrix of the ASE system is close to the infinity near the critical point of aeroservoelastic stability;（3） based on this unique property,we use the H-infinity-norm to develop a method for frequency domain analysis of ASE system stability so as to determine the instability boundary of the ASE system.Section 4 simulates a certain aircraft that is equipped with MIMO flight control system for yaw loop and roll loop to analyze the stability of the ASE system;the numerical results,given in Tables 1 and 2,and their analysis show preliminarily that：（1） the ASE system stability obtained with our frequency domain analysis method agrees well with that obtained with the p-k method,which is closely related to Ref.7 by Rodden and Johnson;（2） the stability boundary of the ASE system of the aircraft is smaller than that of the aircraft which is not equipped with the MIMO flight control system;（3） with the notch filter added to the control system for suppressing the critical mode,our frequency domain analysis method shows that the critical stability boundary increases prominently.