Nonlinear disturbance observer based sliding mode control for a benchmark system with uncertain disturbances

Taking uncertain disturbances into account, the control problem of the translational oscillator with a rotational actuator (TORA) is considered in this paper. Motivated by the desire to attenuate influences from unknown disturbances/uncertainties, the disturbance-observer-based methodology is utilized. Specifically, a system model with a cascade structure for the TORA system is obtained after a series of coordinate transformations. Then, inspired by the backstepping control technique, for the first subsystem, a virtual control variable is introduced and an error-signal-based system is designed. Next, an estimator is presented and used to estimate unknown disturbances, based upon which a sliding mode control approach is devised to ensure the underactuated TORA system is asymptotically stable at the origin. Finally, the applicability and robustness of the designed control method are examined via three group numerical simulation tests.