New criteria for the analysis of PIO based on robust stability methods

Abstract

In this paper we deal with the analysis of Pilot in the Loop Oscillations (PIO) of Category II (with rate and position limiting). We propose an approach, based on robust stability analysis, which assumes that PI0 are characterized by a lit cycle behaviour. In this way we obtain two different criteria for the analysis of Category II PIO; the first criterion replaces the nonlinear element (contained in the model of the rate limited actuator) by a linear time-invariant gain and is shown to be equivalent to the classical Describing Function analysis, with the advantage of preventing the computational difficulties of the Describing Function approach. The analysis via timeinvariant gain may be, however, optimistic in assessing PI0 proneness of a given aircraft. Therefore a further criterion (based on stability analysis via Lur’e Lyapunov functions) is provided; such criterion guarantees asymptotic stability of the nonlinear plant and may give conservative results. By the use of both methods a complete analysis of the nonlinear system can be performed. Several case studies are provided to illustrate the effectiveness of the proposed methodologies.