Delay and saturation in controlled aircraft dynamics (stability and oscillations)

One of the most active domains of Control saturated (bounded) control in time delay systems - meets on interesting field of applications in aircraft control and stabilisation. While control signals (both for thrust and attitude) are naturally bounded, time delay is used for modelling various uncertainties as the feedback control chain of the SAS (stability augmentation system) for the fast motion (short - period) subsystem or the pilot dynamics for the slow motion subsystem. The present paper deals Popov-type stability inequality deduced for bounded nonlinear functions. Since its was based on the integral form for state equations, it is valid for time delay systems also. While more difficult to apply this inequality seems less conservative than usual techniques. This analysis is performed on a linearized model of the fast motion subsystem. Nevertheless the model is in fact highly nonlinear because of various aerodynamic coefficient, which depend essentially on the attack angle - one the state variables. Among these nonlinearities the most influent on qualitative properties is the lift coefficient - a nonlinear function with an angular point corresponding to the so-called stall angle. If the linearisation is performed around this point, a piecewise linear system is obtained (with a discontinuous coefficient). In this system self-sustained oscillations may occur in a natural way. For the delayless case their study may be performed by usual state (phase) plane method. For time delay systems there is no reliable theory of Poincaré - Bendixon type but Yakubovich type self sustained oscillations may be considered.