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 II PIOs; the e rst method replaces the nonlinear element (contained in the model of the rate or position limited actuator ) by a linear time-invariantgainand isshownto beequivalenttotheclassicaldescribingfunction analysis,withtheadvantageof preventing thecomputational dife culties of the describing function approach. Theanalysis via time-invariant gain may be, however, optimistic in predicting PIOs for a given aircraft. Therefore a further method, based on stability analysisvia Lur’ eLyapunov functions, isprovided;such a method guaranteesasymptoticstability ofthenonlinear 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.