Numerical roll motion control by using fins based on the linear quadratic regulator and dynamic mode decomposition

Reducing the roll motion and acceleration of a ship is a critical concern for the safety and comfort requirement in a seaway. In this paper, the uncontrolled roll motion time series is obtained under the harsh beam sea simulation for a naval vessel using a single degree of freedom nonlinear equation of motion. Then the linear quadratic controller (LQR) controller is applied by utilizing one pair of fins (port and starboard) that were positioned amidship. The amplitude and rate saturations of the fins are taken into consideration in the simulations. The LQR controller is designed based on an analytical mathematical model, with the selection of appropriate controller parameters. Then, an estimation is made based on the dynamic mode decomposition method for the ship model by taking measurements from online states as if those are derived from the experimental measurements. Finally, the ‘estimated mathematical model’ is used for the LQR controller design. The results demonstrate the successfulness of the estimation process, with only minimal degradation in performance observed.