Landing trajectories improvement of a vertical takeoff and landing aircraft systems considering linear quadratic regulator strategy

Abstract

Controlling the landing path trajectories of a vertical takeoff and landing aircraft is a challenge that requires an accurate design algorithm. This study introduces an innovative approach to investigate the dynamic of such vehicles and implement an automatic controller such that the aircraft follows a desired landing path trajectory. By linearizing the governing equations of the aircraft around a specific reference path, the linear model of the aircraft system is established. The bank angle is used as the primary control input to adjust landing profile and ballistic paths, while landing speed is treated as an independent state variable. This design algorithm involves creating a linear quadratic regulator controller gain that minimizes the cost function of the aircraft system, establishing dynamic state equations. The Hamiltonian function is employed to generate and solve both state and co-state equations under specific boundary conditions, culminating in the solution of the Riccati matrix. Finally, the controller's performance is tested with different initial state values. Results reveal significant improvements in stability and performance considering the landing path. However, challenges such as conflicts between system states, control gain saturation, and abrupt state changes remain key design hinders. This study offers a sufficient method for controlling such an aircraft using linear control algorithms, which can be more efficient and cost-effective than complex nonlinear algorithms. By simplifying control systems, this approach ensures stable and effective flight operations, making it a valuable advancement in the field of vertical takeoff and landing aircraft technology.