Longitudinal Absolute Stability of a BWB Aircraft-Pilot System with Saturated Actuator Model

This paper deals with the analysis of the P(ilot) I(n-the-Loop) O(scillations) of the second category (with rate and position liming in the closed loop pilot-vehicle system), caused by the dynamic coupling between the human pilot and the aircraft. The analysis is made in the context of the longitudinal motion and the theoretical model of the airplane presented in this article is a (B)lended(W)ing (B)ody tailless configuration. In what concerns the human operator, this is expressed by the Synchronous Pilot Model, which is represented by a simple gain, without a specific delay. The Routh-Hurwitz criterion is used in order to analyze the longitudinal stability of the low-order pilot-airplane system without the influence of actuator nonlinearity (this means that the unsaturated actuator model is employed for the mentioned algebraic criterion). Most emphasis is put on the frequency Popov criterion, which is used to investigate the absolute stability property of the short-period model in the presence of the actuator rate saturation, in the condition of the Lurie problem. The transfer function of the longitudinal BWB model, obtained from open-loop analysis, has a double pole at the origin and, for the absolute stability feedback structure that contains the nonlinearity of the saturation type, the Popov frequency-domain inequalities are applied to the PIO II problem in this critical case.