Nonlinear Control of a Helicopter Based Unmanned Aerial Vehicle Model

In this paper, output tracking control of a helicopter based unmanned aerial vehicle model is investigated. First, based on Newton-Euler equations, a dynamical model is derived by considering the helicopter as a rigid body upon which a set of forces and moments act. Second, we show that the model cannot be converted into a controllable linear system via exact state space linearization. In particular, for certain output functions, exact input-output linearization by state feedback results in unstable zero dynamics. Third, by neglecting weak couplings between forces and moments on the model, we apply input-output linearization to the approximate model for deriving an approximate control with positions and heading as the outputs . Given a bounded output trajectory, the tracking error of the original model by applying the approximate control is proved to be bounded. Finally, we prove by construction that the approximate model with the same outputs is differentially flat and hence the state and input can be expressed as functions of the outputs and their derivatives. This property is very useful for real-time trajectory generation. Based on natural time scale separation, we decompose the dynamics into two subsystems: inner and outer systems. A nonlinear controller, which is based on outer flatness property of the system, is proposed. Simulation results using output tracking controllers based on exact and approximate input-output linearization, and differentail flatness are presented. The controlled system with approximate control and outer flatness based control exhibits small control effort and stable behavior. The response of the controlled system using exact input-output linearization shows unstable pitch and roll dynamics which is shown as the non-minimum phase property of the system.