A robust stability analysis approach for prediction of pilot in the loop oscillations

In this paper we deal with the analysis of Category II (nonlinear) Pilot in the Loop Oscillations (PIO). They are originated by a misadaptation between the pilot and the aircraft during some tasks in which tight closed loop control of the aircraft is required from the pilot, with the aircraft not responding to pilot commands as expected by the pilot himself. We propose a novel approach, based on robust stability analysis, which assumes that PIO are characterized by a limit cycle behaviour. In this approach the nonlinear elements are substituted by fictitious linear parameters, which can be considered time-invariant or time-varying. In the first case, by using ROBAN, a software tools based on polynomials methods developed by the authors, our approach is shown to recover the results of the Describing Function approach in the search for limit cycles. When the parameter is assumed to be time-varying, another method, based on the Quadratic Stability approach, gives a result which guarantees asymptotic stability (a stronger condition than the simple non existence of limit cycles) of the original nonlinear system. By the use of both methods a complete analysis of the nonlinear system can be performed. Finally, to demonstrate the use of the new proposed method in the prediction of Category II PIO, we apply our technique to a case study, namely the X-15 Landing Flare PIO [10].