# Concise Robust Control of the Nonlinear Ship in Course-Keeping Control
## 2 Basic Structure of Ship Course Control System  
The basic structure of the ship course control system is shown in Figure 1. The structure of ship course control mainly includes a controller, steering gear model, ship motion mathematical model, wind wave, and other external interferences.  
In Figure 1, \(\psi_{d}\) is the setting target course; \(\psi\) is the current course; \(\Delta\psi\) is the course deviation between the target course and current course; \(\delta_{r}\) is the control rudder angle output from the controller; \(\delta\) is the rudder angle after considering the characteristic limitation of the steering gear; \(\delta_{w}\) is the equivalent rudder angle of external interference such as wind and waves.  
The basic process of ship course control mainly involves the following four steps:  
(1) The rudder angle is applied to adjust the ship's course when the ship is sailing. The ship course control input is obtained by comparing the target course with the current course, and the controller output is calculated according to the control law design.  
(2) Because the actual rudder angle output is limited by the characteristics of the steering gear, the limitation contains the maximum rudder angle limit and the rudder angular velocity limit. After the correction, the rudder angle output satisfying the characteristics of the steering gear is obtained, and the rectified rudder angle output is closer to reality after considering the characteristic limitation of the steering gear.  
(3) The mathematical model of ship motion produces the corresponding yawing under the action of the input rudder angle, and the corresponding equivalent rudder angle output is obtained under the effect of external wind and wave interference; hence, the actual heading output is obtained after the superposition of the two. At this time, the output heading includes wind-wave interference. In this way, we can handle both the wind and wave via the equivalent input rudder angle, instead of dealing with the wind and wave themselves. This makes the control system more concise. For Beaufort scale 6, the wave disturbance model driven by Gaussian white noise is as below:  
\[\psi_{H}=\frac{0.4198s}{s^{2}+0.3638s+0.3675}w_{H} \tag{1}\]  
where \(\psi_{H},s,w_{H}\) are the Gaussian white noise, Laplace operator, and high-frequency wave disturbance, respectively. For more detailed information, please refer to reference [24; 25].  
(4) The actual course is fed back to the controller through the compass and other sensors. The variance is obtained by comparing with the target course; thus, the controller completes the closed-loop cycle.  
From the basic structure of the ship course controller, it can be seen that the mathematical model and controller of ship motion are the core of the whole system. The mathematical model of ship motion is the mathematical abstraction of the actual ship, which reflects the dynamic and kinematic characteristics of the actual ship to a certain extent; hence, it can be regarded as an approximation of the actual ship. The controller is a device to calculate the control rudder angle according to the course deviation and control law designed. The performance of the controller directly affects the energy consumption of the ship and the wear and tear of the steering gear.  
Figure 1: The basic structure for ship course control in simulation.