Résumé
In this paper, RISE Controller (Robust Integral of the Sign of the Error) is proposed for class I of Underactuated mechanical systems. This class is characterized by two degrees of freedom and one control input. This approach is based on a global change of coordinates where the system is transformed into cascade strict feedback form. Through this transformation, two novel desired trajectories are proposed for the design of the controller. Experimentally, implementation of this approach has some drawbacks. Most of real systems are only equipped with position sensors (i.e. encoders). Velocities and accelerations are usually non-measurable. Indeed, the RISE controller is depending on the first derivative of the position measurement of the system. Furthermore, experimental quantities contain a noisy measurement and the latter is amplified in the computation of the velocity in real time. This may decrease the performance of the closed loop system. To overcome, these drawbacks, a HOSM differentiator is used to estimate, the velocity measurement of the system. To validate the effectiveness of this approach, extensive real-time experiments are conducted for the stabilization of the Inertia Wheel Inverted Pendulum (IWIP), where the system is under unmatched disturbances.