For transportation aircraft, the primary control objective for an autopilot system engaged during approach and landing is relative to the flight path tracking on the basis of highly simplified linear models of flight dynamics. The dynamics governing the flight path of an aircraft are in general highly nonlinear and involve complex physics for which no accurate models are available. In this paper a nonlinear model describing the longitudinal equations of motion in strick feedback form is derived. Backstepping is utilized for the construction of a globally stabilizing controller with a number of free parameters. It is implemented a controller with an internal loop controls involving the pitch rate of the aircraft and an external loop which includes angle of attack, path angle and pitch angle. Finally, nonlinear simulation results for a longitudinal model of a transportation aircraft are displayed and discussed.

Nowadays, the development of electric vehicles has become a general trend. Electrical vehicles have improved their performance, and have been made suitable for commercial and domestic use during the last decades. The proportional–integral–differential (PID) controller has been widely used in the industrial field. It has a simple structure, and can be easily realized. The recursive backstepping design methodology is originally introduced inadaptive control theory to systematically construct the feedback control law, the parameter adaptation law and the associated Lyapunov function for a class of nonlinear systems satisfying certain structured properties. the backstepping control (BKC)  is used to improve the robustness and real-time performance of the electrical vehicle system. Numerical simulation results show the effectiveness of this approach.