# An Offshore Self-Stabilized System Based on Motion Prediction and Compensation Control

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## Abstract

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## 1. Introduction

## 2. Ship Motion Prediction

#### 2.1. Ship Motion Modelling

#### 2.2. Autoregression Model and Parameter Initialization

#### 2.3. Parameter Update and Motion Prediction

## 3. Self-Stabilized System Design

#### 3.1. Inverse Kinematics Modeling

#### 3.2. Motion Compensation Control

## 4. Experiments and Analysis

#### 4.1. Motion Prediction

#### 4.2. Compensation Control

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Parameter identification and multistep prediction based on the autoregression model of ship motion.

**Figure 4.**Motion prediction of a ship in class 3–5 sea conditions. (

**a**) Class 3 rolling; (

**b**) Class 3 pitching; (

**c**) Class 4 rolling; (

**d**) Class 4 pitching; (

**e**) Class 5 rolling; (

**f**) Class 5 pitching.

**Figure 5.**Self−stabilization in 1DOF sin motion condition. (

**a**) Roll angle $\approx $ 5 deg; (

**b**) Pitch angle $\approx $ 5 deg; (

**c**) Roll angle $\approx $ 10 deg; (

**d**) Pitch angle $\approx $ 10 deg.

**Figure 6.**Self-Stabilized control in 3–5 level sea conditions. (

**a**) Class 3 rolling; (

**b**) Class 3 pitching; (

**c**) Class 4 rolling; (

**d**) Class 4 pitching; (

**e**) Class 5 rolling; (

**f**) Class 5 pitching.

Class 3 | Class 4 | Class 5 | |
---|---|---|---|

Roll | 0.581 | 0.658 | 0.733 |

Pitch | 0.543 | 0.577 | 0.922 |

1-DOF Motion | Maximum Error (deg) | Mean Error (deg) |
---|---|---|

roll angle $\approx $ 5 deg | 0.50 | 0.19 |

roll angle $\approx $ 10 deg | 0.82 | 0.40 |

pitch angle $\approx $ 5 deg | 0.55 | 0.20 |

pitch angle $\approx $ 10 deg | 0.88 | 0.42 |

Sea Condition | Maximum Error (deg) | Mean Error (deg) |
---|---|---|

class 3 rolling | 0.61 | 0.25 |

class 3 pitching | 0.50 | 0.19 |

class 4 rolling | 0.85 | 0.40 |

class 4 pitching | 0.68 | 0.29 |

class 5 rolling | 1.60 | 0.66 |

class 5 pitching | 0.96 | 0.39 |

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## Share and Cite

**MDPI and ACS Style**

Liu, Y.; Yuan, H.; Xiao, Z.; Xiao, C.
An Offshore Self-Stabilized System Based on Motion Prediction and Compensation Control. *J. Mar. Sci. Eng.* **2023**, *11*, 745.
https://doi.org/10.3390/jmse11040745

**AMA Style**

Liu Y, Yuan H, Xiao Z, Xiao C.
An Offshore Self-Stabilized System Based on Motion Prediction and Compensation Control. *Journal of Marine Science and Engineering*. 2023; 11(4):745.
https://doi.org/10.3390/jmse11040745

**Chicago/Turabian Style**

Liu, Yanhua, Haiwen Yuan, Zeyu Xiao, and Changshi Xiao.
2023. "An Offshore Self-Stabilized System Based on Motion Prediction and Compensation Control" *Journal of Marine Science and Engineering* 11, no. 4: 745.
https://doi.org/10.3390/jmse11040745