Robust adaptive first-second-order sliding mode control to stabilize the uncertain fin-roll dynamic

Controlling the roll motion involves several problems including incomplete measurements, external disturbances, and the model uncertainties. In this paper, the perturbed model for the roll-fin dynamics is extracted by considering the problems influencing the fin stabilizer system during ship sailing. The sliding mode control provides robust performance for the mentioned factors. Therefore, a sliding mode controller is designed based on the information about the upper bound of perturbations and wave excitation force. Inasmuch as the uncertainty bound is not usually known, a robust adaptive sliding mode controller is proposed. Although it has been proven that the proposed method is robust, the chattering phenomenon is accounted as a drawback of the sliding mode control. In order to overcome the chattering phenomenon, a second-order sliding mode is replaced by the first-order one to create an adaptive second-order sliding mode control. The simulation results show that the control strategy is effective to decrease the roll motion and robust to overcome the uncertainties and random waves.