Robust Control of a 3-DOF Helicopter with Input Dead-Zone

This chapter deals with the tracking control problem of a three-degree-of-freedom (3-DOF) helicopter. The system dynamics are given by a mathematical model that considers the existence of a dead-zone phenomenon in the actuators, as well as a first-order dynamic that adds a lag in the system input. This leads to obtain an eighth-order model where the positions are the only available measurements of the system. The control problem is solved using nonlinear \( {\mathcal{H}}_{\infty } \) synthesis of time-varying systems, the dead-zone is compensated using its inverse model, and a reference model is used to deal with the first-order dynamic in the actuators. Numerical results show the effectiveness of the proposed method, which also considers external perturbations and parametric variations.