---

Electromagnetic suspension technology has been developed in recent years due to advantages such as no contact and reduced friction. Of course, ensuring efficiency in these systems requires precise control of the position of the suspended object. Therefore, electromagnetic suspension is considered as a process by control engineers. The dynamics of electromagnetic suspension systems is nonlinear and also include model and parametric uncertainties such as the weight of the suspended object. In this paper, a finite time nonlinear hybrid method is used to stabilize the electromagnetic suspension system. Proof of finite time stability of the proposed method is performed using Lyapunov theory and a relation for calculating the convergence time depends on the controller gains is presented. To ensure the finite time convergence of the system state and output variables, the backstepping algorithm is used and in each step, the finite-time convergence theory is used. The controller designed in this paper is compared with the backsteping method and the superiority of the proposed method in various simulations is shown.

---

The control of unmanned aerial vehicles is a challenging problem due to their lightweight and intense coupling between longitudinal and lateral motion. Considering this issue, in this article, an automatic landing system for a fixed-wing unmanned aircraft exposed to wind disturbances and parametric uncertainties is designed using the backstepping algorithm and the disturbance observer-based sliding mode control. Two controllers are designed based on the backstepping algorithm and sliding mode control to stabilize the attitude angles. The longitudinal speed controller uses the sliding mode technique to maintain the total speed relative to the ground at a constant desired value in all landing phases. A nonlinear disturbance-observer is considered in the sliding mode controller structure to estimate wind disturbance and parametric uncertainty. The new robust automatic landing system is software implemented, and its performance is investigated by several numerical simulations; Lateral deviation relative to the runway is eliminated while the unmanned aerial vehicle maintains its desired trajectory slope angle in all phases of the landing at the desired value. Therefore, the results of numerical simulations prove that the new control structure is stable and robust against different initial conditions, different types of wind disturbances (wind shear and discrete gust), and parametric uncertainty.