# Concise Robust Control of the Nonlinear Ship in Course-Keeping Control
## 6 Conclusions  
In this paper, the 3 DOF ship course control method based on concise robust control was proposed, and the concise robust control algorithm was constructed on the grounds of the closed-loop gain-shaping algorithm, and the stability should be a guarantee thanks to the Lyapunov function. The ship course controller designed here has the ability to deal with the model perturbation, implying that this method could suppress disturbances including wind and wave under environmental uncertainty. The limitations of the study and additional studies required in the future are to carry out a ship trial test on a real ship, in order to verify the robustness further.  
(1) In this paper, the ability of concise robust control of model perturbation was verified. The control law designed according to the nominal model could effectively stabilize the perturbed model. The controller could not only realize the course keeping control but could also realize the tracking control of a continuously changing course periodically.  
(2) In this paper, the ability for concise robust control in suppressing environmental disturbance such as wind and wave was validated. The disturbance of wind and wave with scale 6 interference on the ship's course could be effectively suppressed by designing a door-closing slope for the closed-loop transfer function in the frequency domain. Compared  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Control Method** & **Max Rudder Angle (\(\lx@math@degree\))** & **Avg Rudder Angle (\(\lx@math@degree\))** & **Variance of** & **Time to 95\% Target Course** \\ \hline CROB \(-20\) dB & \(5.68\) & \(-2.94\) & \(5641.30\) & \(110.06\) \\ CROB \(-40\) dB & \(3.61\) & \(-2.95\) & \(90.45\) & \(209.09\) \\ CROB \(-60\) dB & \(3.20\) & \(-2.95\) & \(19.81\) & \(303.00\) \\ PID & \(4.56\) & \(-2.95\) & \(3189.80\) & \(154.90\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Concise robust control with wind–wave disturbance (\(500\) s–\(1000\) s).  
with the PID method based on backstepping, the rudder angle of steering gear could be significantly reduced and the wear of steering gear could be decreased significantly.  
(3) Keeping other conditions the same, the larger the closing slope of the closed-loop transfer function spectrum is, the stronger its resistance to external interference, but its sensitivity will also decrease accordingly. Therefore, it is necessary to select the proper door-closing slope of the closed-loop transfer function spectrum according to the actual situation.  
Conceptualization, C.Z. and J.Y.; Methodology, C.Z. and J.Y.; Validation, C.Z. and Y.G.; formal analysis, C.Z. and Y.G.; visualization, Y.G.; Software, C.Z. and Y.G.; Investigation, C.Z. and Y.G.; writing--review and editing, C.Z., J.Y., and Y.G. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (Nos. 61861017, 52062016, U2001213, 61971191, and 61661021), Key R & D Projects of Jiangxi Province (No. 20192 ACB50027), Jiangxi Science and Technology Transportation Department Project (No. HX2019-332), Key Projects of Jiangxi Provincial Department of Education(No. GJJ190296), Key R & D Projects of Jiujiang City (No. 20200069), Beijing Natural Science Foundation under Grant L182018 and L201011, National Key Research and Development Project (No. 2020 YFB1807204), open project of Shanghai Institute of Microsystem and Information Technology (No. 20190910), the Key project of Natural Science Foundation of Jiangxi Province (No. 20202 ACBL202006), Provincial Teaching Reform Research Key Project of Jiangxi Province (No. JXJG-20-5-3), Teaching Reform Project of Electronic Information Specialty Teaching Steering Committee (No. 2020-YB-55), Teaching Reform Research Project of Degree and Postgraduate Education in Jiangxi Province (No. JXYJG-2020-107).  
Not applicable.  
The data presented in this study are available on request from the corresponding authors.  
The authors declare no conflict of interest.