Three‐time scale singular perturbation control and stability analysis for an autonomous helicopter on a platform

SUMMARY 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.