Rudder angle

A control system may have several feedback control loops. For example, with a ship autopilot, the rudder-angle control loop is termed the minor loop, whereas the heading control loop is referred to as the major loop. When analysing multiple loop systems, the minor loops are considered first, until the system is reduced to a single overall closed-loop transfer function. 

The training file eonsisted of input data of the form Time elapsed t kT), Rudder angle 6(kT), Engine speed n(kT) with eorresponding output data Forward veloeity u kT), Lateral veloeity v(kT), Yaw-rate r kT). 

So, for example, with the ship model shown in Figure 10.26, the inverse model eould be trained with time, forward veloeity, lateral veloeity and yaw-rate as input data and rudder angle and engine speed as output data. 

Further, taking into account constraints for turning angle we assume staring rudder angle... 

Similar to the Real Time Simulation (RTS) technique the manoeuvring indices rudder angle, engine revolutions, drift indices, proximity to fixed points and towing force can be analysed in dependence on environmental conditions. 

The effect of water depth to draft ratio and influence of rudder angle examined on big physical model with geometrical scale 1 16 was presented in (Abramowicz-Gerigk, 2010 Abramowicz-Gerigk, 2011). The mean axial velocities v of propeller jet behind the rudder in deep water (water depth to ship draft ratio h/T = 3) and shallow water (h/T = 1.2) conditions related to —jet velocity in deep water with rudder angle 0 are presented in Table 1. 

In 2011 Ryan and Hamill (Ryan Hamill, 2011) presented the findings from the experiment of a ship berthing alongside a quay wall and the effect of rudder angle on the magnitude of the scouring. 

ABSTRACT In this paper the Internal Model Control (IMC) approach for marine autopilot system is presented. The inversion by feedback techniques are employed for reahzation of inversion such nonlinear characteristics as saturation of rudder angle and rudder rate. The extension of the model and inverse model to a nonlinear form enabled to achieve a significant improvement in the control performance. 

To prevent this, in the proposed control structure such a model was introduced which parameters depending on shaft velocity n and the rudder angle 5. This will ensure better quality of the model in a wider range of changes of the state variables of a system. 

Figure 3. Steering gear scheme. 5 - rudder angle... 

The differential equation (12) could not been employed to create a model of the ship because the step response of the considered container ship for larger rudder angle is oscillatory. Therefore, the transfer function (21) has been selected, which step response better reflects the behavior of the ship in the responding set point. 

The parameters k, Ti, T2, Ts, as known, depend on ship velocity and it is necessary to calculate or to identify them. For this study, the parameters are identified to expend this model to a wider range of rudder angles. In Figures 5,6 are presented simulation results for Si =1 and =10 , by =100... 

The relations between particular parameters and rudder angle are presented in graphical form in Figures 7-10. 

The concept of extension the linear Intemal Model Control to a nonlinear form allowed to obtain a more accuracy model what also improved the control performance, which is expressed by reducing the overshoot and settling time for a wide range of work points. In this study the parametric model of the process was created by means of identification based of an open-loop step response by different rudder angle thereby the different ship velocity components. The proposed controller can be successfully used to reach a new set-point of course and also after the necessary modifications also in vessel maneuvering along a desired path. 

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