• helicopter control;
  • nonlinear systems;
  • singular perturbation;
  • asymptotic stability;
  • mathematical upper bounds


A three-time scale singular perturbation control law is designed for a nonlinear helicopter model in vertical flight. The proposed control law is based on time scale decomposition and is able to achieve the desired altitude by selecting a desired angular velocity and the associated collective pitch angle of the blades. The stability of the system is performed by presenting a stability analysis for generic three-time scale singularly perturbed systems, which allows to construct a composite Lyapunov function for the resultant closed-loop system by using time scale separation and also providing mathematical expressions for the upper bounds of the singularly perturbed parameters that define the three-time scale. Numerical results on both, the singular perturbation control strategy and the stability analysis, are also presented for the studied nonlinear highly coupled helicopter model. Copyright © 2012 John Wiley & Sons, Ltd.