Verification of equilibrium point stability for linearization of an aircraft model

Unmanned Air Vehicles (UAVs) are of vital importance in future aviation industry. A UAV is flown by an onboard controller which controls aircraft movements during flight. For convenient design of linear controllers, a stable operating point (equilibrium point) is required against which the aircraft model can be linearized. This paper aims at developing a technique for stability verification of such an operating point. For a nonlinear mathematical model of a UAV, its equilibrium point has been determined using an optimization scheme. The non-linear model is then linearized using Jacobian based numerical linearization technique. Due to insignificant values of coupling terms, the aircraft linear model is decoupled into longitudinal and lateral sub-models. The response of nonlinear model is compared to that of linearized sub-models by applying identical inputs to the both model types. Simulation results for both the cases are presented. It is concluded that this work presents a convenient technique to verify the stability of equilibrium point, leading to successful controller design.