PIO I-II tendencies case study. Part 1. Mathematical modeling Adrian TOADER, Ioan URSU atoader@incas.ro iursu@incas.ro “Elie Carafoli” National Institute for Aerospace Research Abstract In the paper, a study is performed from the perspective of giving a method to reduce the conservatism of the well known PIO (Pilot-Induced Oscillation) criteria in predicting the susceptibility of an aircraft to this very harmful phenomenon. There are three interacting components of a PIO – the pilot, the vehicle, and the trigger (in fact, the hazard). The study, conceived in two parts, aims to underline the importance of human pilot model involved in analysis. In this first part, it is shown, following classical sources, how the LQG theory of control and estimation is used to obtain a complex model of human pilot. The approach is based on the argument, experimentally proved, that the human behaves “optimally” in some sense, subject to his inherent psychophysical limitations. The validation of such model is accomplished based on the experimental model of a VTOL-type aircraft. Then, the procedure of inserting typical saturation nonlinearities in the open loop transfer function is presented. A second part of the paper will illustrate PIO tendencies evaluation by means of a grapho-analytic method. 1. Introduction From the Wright Flyer to fly-by-wire, the phenomenon of pilot-induced oscillation (PIO) has been observed on almost every aircraft, either prototype, experimental or operational, military or commercial. Thus, PIO remains a permanent challenge for the aircrafts designers. PIO is a phenomenon usually due to adverse aircraft-pilot coupling 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” [1]. “Tight closed loop control” concerns as a rule takeoff, landing, aerial refueling, and formation flying. PIO supposes to have the pilot in the closed loop, but it should be emphasized that there is no blame placed on the pilot for the resulting oscillation (therefore other designations, such as: pilot-in-the loop oscillation or aircraft-pilot coupling have been suggested instead of PIO). Indeed, PIO is homologated as factual if there is at least one measurable aircraft state that is 180 degrees out of phase with at least one measurable pilot control input [2]. In other words, PIO is triggered as an aircraft motion totally adverse to pilot intentions and efforts (the third interacting component of the PIO is “a trigger” [2], i.e., in fact, the hazard). PIOs have caused numerous accidents with results ranging from minor damage to total loss of the aircraft and pilot. Predicting PIO is difficult and becomes even more difficult with the advent of new technologies such as active control and fly-by-wire flight control systems. This has been demonstrated by recent events involving Boeing 767 & 777, YF- 22A, YF-16, JAS-39, X-5, X-15, Shuttle, Falcon 900 and the list can continue [2]. Theoretical studies and flight test methods lead, however, to recommended practices exposing PIO tendencies, if they exist, so that the catastrophic events can be minimized or eliminated. According to common references (see, for example, [3]), PIOs are categorized depending essentially on the degree of nonlinearity in the event: INCAS BULLETIN, Volume 2, Number 1/ 2010 91