Oscillation Susceptibility Analysis along the Path of the Longitudinal Flight Equilibriums in ADMIRE Model

Our goal is the oscillation susceptibility analysis in the framework of a nonlinear mathematical model in the so-called ADMIRE or Aero Data Model in a Research Environment. First, we analyze the oscillation susceptibility along the path of the longitudinal flight equilibriums when the flight control system (FCS) is decoupled. After that, a similar analysis is undertaken in the case when the FCS is coupled. For decoupled FCS, it is shown that on the path of the longitudinal flight equilibriums there exists a saddle-node where stability is lost and fold bifurcation occurs. Maneuvers are simulated showing the effect of an instantaneous change of the elevator angle, and the evolution of the unstable equilibriums (due to the maneuvers) to the corresponding exponentially stable equilibriums. It is shown numerically that at the saddle-node oscillations occur when the elevator angle is less than the critical value and the start is from the saddle-node. More precisely, it is shown that if the plane state parameters coincide with the saddle-node coordinates and the elevator angle is changed instantaneously from the critical value to a value which is less than this value, then two of the state parameters $\left(\alpha ,q\right)$ begin to oscillate with the same period and the third parameter $\left(\theta \right)$ increases, tending to infinity. Thus, the orbit of the system evolves spiraling. It is shown also, that if the elevator angle is reset, the plane returns to a stable equilibrium. Therefore, a soft or no catastrophic stability loss takes place. When the FCS is coupled, the plane for every value of the amplification factor has a unique equilibrium which is exponentially stable and attracts all the equilibriums which exist in decoupled case. In this case, there are no bifurcation points on the equilibrium path. The dependence of the equilibrium and of the relaxation period on the amplification factor value is found numerically. Finally, it is concluded that when the FCS is decoupled, then along the path of the longitudinal equilibriums oscillations can occur, but when the FCS is coupled and the pilot can modify (instantaneously) only the amplifier factor value, then the vehicle, defined by the considered numerical data, is not anymore susceptible to oscillation.