Control of roll motion via optimal control methods based on linear matrix inequalities

The roll motion in ship motions is critically important. It is known that particularly high-amplitude roll motions cause the capsize of ships that remove from safe zones. For this reason, the roll motion of the ships must be kept at stable points in different sea states. In order to evaluate the roll motion, it is accurately necessary to analyze the parameters of the motion. Especially, the damping and restoring coefficients directly effect on the dynamic of ships. These coefficients can be found empirically or experimentally. After these parameters have been defined, the characteristic values of the ship are also assessed, with this way the necessary conditions for interaction with the motion are prepared. In recent years, roll stabilizer systems have been applied to many ships in order to reduce the amplitude of the roll motion and improve the maneuverability of the ships. The use of different control methods is rapidly increasing with the applications. In this study, the dynamics of roll motion for two different types of ship, fishing ship and planning hull were investigated. The damping values of the roll motion are found empirically and by means of the method proposed by Ikeda based on experimental results. These parameters are combined with the characteristic values of the ships, then it is ensured that the requirements for controller design. The fin roll stabilizing system is used to keep the roll motion in stable regions and lifting coefficients of fin roll stabilizing system were found in the results of CFD analyzes. LMI based state feedback H2 and H∞ controller designs and Backstepping controller design are applied for different ship types. As a result of the simulations, it is stated that the H∞ controller gives successful results compared to other controllers. Robust and saturated H∞ controller especially designed for high speed ship, Although the values in the saturation matrix vary by %57, It has been shown that it can reduce the roll amplitudes at different speeds. Considering the changing parameters during the operation with the controller structures, It presented a dynamic and realistic results were obtained. This study takes into account the ship dynamics that change momentarily, It is provided to ease future studies.