Decoupling of a Class of Nonlinear Systems and Its Application to an Aircraft Control Problem

The necessary and sufficient condition for decoupling a nonlinear system with state feedback is obtained. It is shown that when this condition is satisfied there exists a control law which makes each output variable of the dynamical system independently controllable with a separate input. The theory is then applied to an aircraft control problem where the implication of the theoretical results is discussed. The objective of the aircraft control problem is to decouple the vertical and the horizontal path angles of the flight trajectory relative to earth-fixed axes. The aircraft equations are simplified by postulating a rudder control law which maintains zero sideslip velocity in flight. The control laws for the elevator and aileron which decouple the simplified aircraft model are obtained. The control system is then evaluated in a simulation study to show that it indeed decouples the flight path angles.