Exact Evaluation of Stability Margin of Multiloop Flight Control Systems

Abstract

ULTILOOP e ight control systems are widely used in the advanced aircraft in recent years. Such highly augmented aircraft have considerable potential in terms of e ying qualities. There are many design methods for the multiloop control system, but a method to exactly evaluate the stability margin for multiloop control systems has not been established yet.It is very important for the designers to exactly know the stability margin of the e ight control system because it directly comes to bear on e ight safety. MukhopadhyayandNewsom 1 studiedtheevaluationofmultiloop stability margin using singular values. In their study, square diagonalmatrix L = Diag[Kn exp( ju n)]wasintroduced atthe plant input to determine the range in which both Kn and u n can be changed simultaneously in allloops for which thesystemwouldremain stable. And, the relation between the singular value of the system return difference matrix r (I + FG) and the simultaneous gain and phase change [Kn, u n] was illustrated. But, predictions based on the singularvalue aregenerallyconservative.Toimprove theconservatism of these predictions, Ly 2 proposed a method using the eigenvalue norm j 1 + k [FG]j as a measure of robustness, and Yeh et al. 3 proposedamethodusing theeigenvaluemagnitude of thesystemreturn difference matrix j k [I + FG]j . But, these methods cannot be used to exactly evaluate the stability margin. In this Note, analysis methods for the exact evaluation of the stability margin of multiloop e ight control systems are presented. The minus inverse vector n and the open-loop transfer function for themultiloope ightcontrolsystem i 1/n vectorareintroduced.Both methods are the extension of that for single-loop control systems. Using these methods, the gain and phase margins of the system can be considered individually.