State space modelling approach for rudder roll stabilization
The control objective of the Rudder Roll Stabilization (RRS) system is to deploy the rudder, which is primarily a path controlling device, to reduce the roll motion without interference in heading of ship. To achieve the control of both roll and yaw motions, the only control input is the rudder angle and hence the RRS system is referred as a Single Input, Two Output (SITO) system. Rudder roll stabilization is insignificant at low forward speed of the ship, but can give significant control at higher speed when fast rudder movement is applied. This paper presents a closed loop state space model for accurate simulations on rudder roll stabilization in irregular seas considering the 3-degree of freedom motions, i.e., sway, roll and yaw. The computational model is developed to analyze the effect of the rudder movement on sway, roll and yaw in forward speed conditions in irregular sea conditions. The Sea State conditions are modelled as wave perturbation models using the method of shaping filter established by filtered white noise. The control system has been designed using optimal linear quadratic regulator (LQR) method. The control loop contains both the signal for the autopilot action to trigger the heading angle correction as well as the signal for rudder based roll motion control. The simulations are carried out with rudder roll control system ON and OFF mode to analyze the effect of the rudder on steering and motion stabilization. In both cases the autopilot is in active mode to correct deviations in the course heading. The simulations are analyzed for three different ship speeds in two different Seas State conditions with a low and fast rudder movement to show the efficacy of the model. The performance is evaluated and presented based on the RMS value. Since the rudder based roll motion stabilization may also result in unnecessary motions of sway and yaw, besides the desirable roll reduction, the result presents the sway-roll-yaw responses as applicable under the particular speed and Sea State conditions.