Fractional order adaptive sliding mode control for nonlinear anti-roll of ship

  Objectives  In order to solve the problem of ship nonlinear rolling control, a fractional order adaptive sliding mode control (FOASMC) algorithm is proposed.

  Methods  First, the spectral density of random waves, spectral density of wave inclination and spectrum of waves acting on ships are calculated using a random wave model with long peak waves. The rolling angle tracking error of the system is then verified on the basis of Lyapunov stability theory. Moreover, the switching function is designed to make the system robust to uncertainties and external disturbances. Finally, the effects of fractional order, control law gain and sliding surface mode gain are analyzed.

  Results  The results show that the mean rolling angle and standard deviation of FOASMC are smaller than those of basic sliding mode control (SMC) for various speeds and wave directions. For example, when the ship's speed is 10 m/s and the encountering wave direction is five degrees, the average rolling angle is 25.89% of the basic SMC, and the mean square deviation is 14.32% of the basic SMC.

  Conclusions  It is proven that the proposed control algorithm has good stabilization effectiveness at various navigation speeds and encountering wave directions, as well as such advantages as strong robustness, continuous control input and no high gain.