Nonsmooth control based on finite-time disturbance estimator for the translational oscillator with a rotational actuator system with nonvanishing disturbances

In this article, the stabilization and disturbance estimation of the translational oscillator with a rotational actuator with nonvanishing disturbances are considered. Different from existing methods, a disturbance estimator is designed to eliminate the effects of unexpected external disturbances. As far as we know, this article presents the first finite-time disturbance-estimator-based nonsmooth control scheme for the translational oscillator with a rotational actuator system. Specifically, first, a series of changes of coordinates is made for the model of the translational oscillator with a rotational actuator system. Then, a disturbance estimator is presented to estimate uncertain disturbances and a nonsmooth control scheme is designed to ensure the convergence of all the states. Furthermore, rigorous theoretical analysis is given. Finally, simulation tests are carried out and the obtained results demonstrate that the designed approach exhibits better control performance and stronger robustness than the existing methods.