Category II pilot in-the-loop oscillations analysis from robust stability methods

In this paper we deal with the analysis of pilot in-the-loop oscillations (PIO) of category II (with rate or position limiting, We propose an approach, based on robust stability analysis, which assumes that PIOs are characterized by a limit cycle behavior. In this way we obtain two different methods for the analysis of category LI PIOs; the first method replaces the nonlinear element (contained in the model of the rate or position 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 time-invariant gain may. be, however, optimistic in predicting PIOs for a given aircraft. Therefore a further method, based on stability analysis via Lur'e Lyapunov functions, is provided; such a method guarantees asymptotic stability of the nonlinear plant and can give conservative results. By the use of both methods, a complete analysis of the nonlinear system can be performed. The X-15 case study is considered to illustrate the effectiveness of the proposed methodology.