In this paper, the problems of stabilization and disturbance rejection in the control of class I of underactuated mechanical systems (UMS) are addressed. Based on a global change of coordinates, the original dynamic model is transformed into a strict-feedback form and a Super-Twisting (STW) controller is designed to resolve the stabilization problem. To deal with the problem of uncertainties and external disturbances in UMS, a disturbance observer (DO) is proposed for the estimation of the input disturbances in the aim of compensating them in the controller and improving the performance and robustness of the resulting closed-loop system. Indeed, the proposed observer-based scheme is compared with the standard STW controller. Both controllers have been implemented and validated through real-time experiments on the inertia wheel inverted pendulum. The obtained results show clearly the superiority of the proposed observer-based STW control scheme and its effectiveness in terms of external disturbance rejection.

In this paper, the control problem of a class I of underactuated mechanical systems (UMSs) is addressed. The considered class includes nonlinear UMSs with two degrees of freedom and one control input. Firstly, we propose the design of a robust integral of the sign of the error (RISE) control law, adequate for this special class. Based on a change of coordinates, the dynamics is transformed into a strict-feedback (SF) form. A Lyapunov-based technique is then employed to prove the asymptotic stability of the resulting closed-loop system. Numerical simulation results show the robustness and performance of the original RISE toward parametric uncertainties and disturbance rejection. A comparative study with a conventional sliding mode control reveals a significant robustness improvement with the proposed original RISE controller. However, in real-time experiments, the amplification of the measurement noise is a major problem. It has an impact on the behaviour of the motor and reduces the performance of the system. To deal with this issue, we propose to estimate the velocity using the robust Levant differentiator instead of the numerical derivative. Real-time experiments were performed on the testbed of the inertia wheel inverted pendulum to demonstrate the relevance of the proposed observer-based RISE control scheme. The obtained real-time experimental results and the obtained evaluation indices show clearly a better performance of the proposed observer-based RISE approach compared to the sliding mode and the original RISE controllers.

No abstract

No abstract

No abstract