LONGITUDINAL STABILITY ANALYSIS OF A UAV UNDER THE UNCERTAINTY OF TWO STABILITY DERIVATIVES

Abstract

The longitudinal stability of an aircraft is analyzed using root locations of the transfer function’s denominator (the characteristic equation). This transfer function is obtained by linearizing aircraft dynamic model at a certain operation point (altitude and speed). However, aircraft have varying stability derivatives, therefore dynamic behavior, for different flight phases such as takeoff, cruise, and landing. Thus the stability analysis of the characteristic equation can be said to be valid only for a single flight condition. In fact, stability derivatives vary with flight conditions, so an analysis that includes all possible stability derivatives in the flight envelope is required to guarantee stability. In this study, the two most variable stability derivatives in the transfer function were taken as uncertain parameters. Gridding these two parameters to check the stability of the unmanned aerial vehicle for all possible flight conditions is a possible method, but it is very time-consuming, and it cannot assure the stability theoretically. A new simple approach is developed by using the Edge and Bialas theorems, which guarantees stability despite the uncertainty of two stability derivatives. The problem is reduced to the analysis of four polynomials. With the eigenvalues of just four polynomials, the stability characteristics of an airplane for a given flight envelope can be easily determined.