The Web Winding System (WWS) knows several constraints such as the thermal effects caused by the frictions, and the mechanical effects provoked by metal elongation, that generates dysfunctions due to the influence of the process conditions. A major objective in the web winding system control design is: To obtain a precise thickness, with the best possible regularity when a sudden constraints occurs; To achieve stable rolling and ensure strip quality. This work presents the conception of a new law of nonlinear control of the WWS. This is the Backstepping method with introduction of integral actions. Furthermore, the simulation under the Matlab/Simulink software allows the highlighting performance of the control strategy adopted.

Robotic manipulators face significant control challenges in a wide range of industrial applications, where stability and reliability are essential for achieving operational objectives. This paper investigates nonlinear modeling and control strategies for a three Degree-of-Freedom (3-DOF) robot manipulator, focusing on dynamic complexities and employing advanced techniques like nonlinear backstepping design for trajectory tracking. The 3-DOF robot's nonlinear model is derived using Lagrange's equation. Subsequently, a backstepping control method is developed to manage the nonlinear behavior. Backstepping ensures precise trajectory tracking and global stability by systematically designing a Lyapunov function for each step, leading to a robust control law. The step-by-step nature of backstepping facilitates the design of controllers for 3-DOF robotic systems. Each joint can be controlled separately while ensuring the overall stability of the system, making the design process more manageable. Simulation results demonstrate the ability of the proposed control method to achieve fast and accurate tracking of reference setpoints, even under moderate control input variations. These results highlight the effectiveness of the approach in enhancing both accuracy and stability.