Coefficients Extraction of Model and Constrained Controller Design for Fin-Roll Stabilizer System in a Fishing Boat
Authors: Malekizade Hamid , Moaveni Bijan , Jahed-Motlagh Mohammad Reza , Esmailian Ehsan , Avili Mohammad Ghomi 
Published: October 2017

This study aimed at stabilizing and decreasing the fishing boat's nonlinear roll motion using a fin-roll stabilizer. To do so, numerical and analytical modeling have been introduced. In addition, a numerical method and empirical formulas for calculating the coefficients of the model are used. A Computational fluid dynamics (CFD) method is employed to analyze both the fluid flow and its effect on the fin performance. Constrained linear quadratic regulator (LQR) controller is designed and used to control the roll motion in the presence of operational constraints of the fin's actuator. To boost the validity of results, the performance of this controller is compared with a conventional proportional-integral-derivative (PID) controller. Simulation results demonstrate the significant amount of reduction in roll amplitude.

1. Introduction
Roll motion is one of the most important motions of a ship at sea. The accelerations due to wave-induced roll motions negatively influence a fishing boat's performance by limiting the comfort, workability, and safety (Perez & Blanke 2012).
The roll stabilization systems have widely been studied for more than three decades (Perez & Blanke 2012), and various types of antirolling devices have been introduced to reduce the undesirable roll motion (Lloyd 1989). The use of an active fin stabilizer has been considered as the most effective antirolling technique for ships normally operating at some forward speeds (Sellars & Martin 1992). This reduces the roll motion by controlling the mechanical angle of the fin according to the ship roll angle and roll rate (Stallard 1961).
There are two main constraints of fin stabilizers including saturation of the mechanical fin angle and dynamic stall (Ghaemi et al. 2009). These two constraints cause a performance degradation in the fishing boats. Dynamic stall is a nonlinear phenomenon caused by unsteady hydrodynamic effects leading to roll moment loss when the angle of attack exceeds a certain threshold (Perez & Goodwin 2008). Also, it depends on the lift coefficient which can be changed in line with the effective angle of attack between the flow and the fin. Therefore, to analyze the behavior of fin and calculate the lift coefficient, the experimental results (Lee et al. 2000), the computational fluid dynamics (CFD) method, (Surendran et al. 2007) and the empirical formulas are used (Whicker & Fehlner 1958). Taylan (1996, 1999, 2000) studied the nonlinear roll motion model. In those studies, the nonlinear restoring terms were considered as a third order polynomial. Likewise, the nonlinear damping term was regarded as a second order polynomial. In the study by Surendran and Venkata Ramana Reddy (2002), a comprehensive research was conducted regarding the roll dynamics of a Ro-Ro ship, taking into account the many types of combinations of loads in linear and nonlinear forms. In the study by Alarçin (2014), the nonlinear mathematical model of roll was introduced for a fishing boat in the presence of wave disturbance.