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 character ized 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 nonlin ear element (contained in the model of the rate or position limited actuato r) by a linear time-invariant gain and is shown to be equivalent to the cla ssical describing function analysis, with the advantage of preventing the c omputational difficulties of the describing function approach. The analysis via time-invariant gain may. be, however, optimistic in predicting PIOs fo r a given aircraft. Therefore a further method, based on stability analysis via Lur'e Lyapunov functions, is provided; such a method guarantees asympt otic stability of the nonlinear plant and can give conservative results. By the use of both methods, a complete analysis of the nonlinear system can b e performed. The X-15 case study is considered to illustrate the effectiven ess of the proposed methodology.