PIO II — a unifying point of view

In the context of the P(ilot) I(n-the-Loop) O(scillations), the second category PIO II is triggered by the position and rate limiters that account for saturation. Since saturation is a sector restricted nonlinear function, the PIO II problem may be tackled within the theory of the absolute stability. Consequently some three basic PIO II approaches (robust control, Popov approach and the IQC approach) turn out to be of the same methodological family. This philosophy is illustrated on the short period dynamics of the aircraft; the Popov frequency domain inequality approach is used but the sector condition is fulfilled only on a finite state space domain; the estimate of this domain is obtained using a Liapunov function that is associated to the Popov frequency domain inequality that is fulfilled.