5. Conclusions
In this work, a linear controllability approach is adopted to study airplane flight dynamics in different loss-of-control situations using different model sizes. For the conventional fourth-order longitudinal flight dynamics, we show that the system remains controllable if the elevator control input or the throttle regulation is lost. However, the elevator-only longitudinal controller relies on the available gravitational potential energy. To prevent such an exploitation, we added the altitude to the state variables and found that the resulting fifth-order longitudinal flight dynamics cannot be controlled using elevator only but is still controllable using thrust only. If all longitudinal kinematic variables are included (i.e., sixth-order flight dynamic model), linear controllability becomes deficient if either elevator or throttle is lost. In such a case, nonlinear controllability analysis is discussed and invoked because of its relaxed notions of controllability. On the other hand, the conventional fifth-order lateral flight dynamics is shown to be controllable using either aileron or rudder controls. Moreover, both aileron and rudder could be replaced with a differential thrust control input without diminishing linear controllability. We also stress the fact the system being controllable using only one controller does not guarantee equilibrium at the end state; i.e., the system may depart from such a state immediately after the excursion time. In this work, we also considered application of the linear controllability analysis to Thrust-only Flight Control Systems (TFCSs). We show that the desired flight path angle for landing-approach can be tracked using a TFCS without exceeding the thrust control input bounds even if the engine lag is considered. Then, we address some of the previously raised concerns about TFCSs. Firstly, we show that flight path angle regulation during the landingapproach is also achievable using TFCS even if Mδt = 0. Secondly, we confirm the previously raised issue that is both flight path angle and speed cannot be simultaneously regulated using TFCS during the landing-approach. Thirdly, we investigate the effect of slow engine dynamics on yaw damping in the case of rudder loss.