Gain-Phase Margin Analysis of Pilot-Induced Oscillations for Limit-Cycle Prediction

Abstract

This investigation attempts to forecast the limit cycles of pilot-induced oscillations (PIOs) by combining the gain-phase margin tester, the M-locus, and the parameter plane methods. First, one position- or rate-limited nonlinear element is linearized by the conventional means of describing functions. The stability of an equivalent linearized system with adjustable parameters is then analyzed using stability equations and the parameter plane method. Additionally, the minimum gain-phase margin of the PIO system at which a limit cycle can occur is determined by inserting the gain-phase margin tester into the forward open-loop system. Moreover, a simple method is developed to identify the intersections of the M locus and the constant gain and phase boundaries in the parameter plane. In so doing the exact relationship between the gain-phase margin and the characteristics of the limit cycle can be clearly determined. The results of this study demonstrate that these procedures can enhance the analysis of PIO over analysis by other methods in the literature. This approach is extended to PIO analysis with multiple nonlinearities.