# Particle Swarm Optimization of a Passivity-Based Controller for Dynamic Positioning of Ships

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. The Port-Hamiltonian Modeling of the Surface Ship

#### 2.1. The DP System Overview

- Power System. It compromises all components and units responsible to supply the DP system with its power requirements including: Prime movers, Generators, Switchboards, Electrical distribution system (cabling and piping), transformers. It may also include more advanced subsystems for energy storage and power management purposes.
- Thruster system. The vessel’s horizontal motion is influenced and controlled by means of thrusters and propellers which are also the sole source of position/heading keeping. They supply the DP system with thrust force and direction and it includes thrusters with electronic drive units, propellers and rudders, cabling and piping and other associated auxiliary subsystems.
- Control System. it compromises all hardware and software components including processors and computers, joystick control unit, Sensors and instrumentation and signal processing units, Position and heading reference systems (navigation, acoustic, microwaves and laser systems), operator and display panels.

#### 2.2. The Mathematical Model

**O**and (X,Y,Z) coordinates, and the body coordinate frame, which is fixed to the ship and moves along with it, with

**b**origin and $(x,y,z)$ coordinates.

## 3. The IDA-PBC Controller Design

**Proposition**

**1.**

**Remark**

**1.**

**Proof**

**of**

**Proposition**

**1.**

**Condition**

**1.**

**Remark**

**2.**

## 4. The PSO Method for DP of Ship

#### 4.1. An Overview of PSO Method

#### 4.2. Application of PSO Algorithm for DP of Ship

#### 4.3. Convergence to the Optimal Solution Using PSO Method

## 5. Numerical Simulations

#### 5.1. A Comparison between the Modified and the Original Controllers

#### 5.2. The PSO Tuning of the Proposed Controller

#### 5.3. The Robustness of the Proposed Controller

## 6. Conclusions and Future Work

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Ship motion in 6-DOF [24].

Time Characteristics | Modified Controller | Original Controller |
---|---|---|

${\mathit{q}}_{\mathbf{1}}$ Rise time(s) | 40.7935 | 59.0104 |

${\mathit{q}}_{\mathbf{1}}$ Settling time(s) | 457.7632 | 1062.9 |

${\mathit{q}}_{\mathbf{1}}$ Overshoot percentage | 41.0047 | 49.7733 |

${\mathit{q}}_{\mathbf{2}}$ Rise time(s) | 47.6423 | 46.8955 |

${\mathit{q}}_{\mathbf{2}}$ Settling time(s) | 480.8057 | 765.8472 |

${\mathit{q}}_{\mathbf{2}}$ Overshoot percentage | 44.4818 | 59.0281 |

${\mathit{q}}_{\mathbf{3}}$ Rise time(s) | 5.4699 | 5.3337 |

${\mathit{q}}_{\mathbf{3}}$ Settling time(s) | 9.1445 | 41.6431 |

${\mathit{q}}_{\mathbf{3}}$ Overshoot percentage | 1.3724 (under) | 11.4531 (under) |

Parameter Name | Value |
---|---|

Maximum iteration | 500 |

Swarm Size | 30 |

Self-Weight acceleration coefficient (${c}_{1}$) | 1.494 |

Social-Weight acceleration coefficient (${c}_{2}$) | 1.494 |

Inertia weight (w) | 0.729 |

kq1 range | 0.001–10 |

kq2 range | 0.001–10 |

kq3 range | 0.001–10 |

Time Characteristics | Without PSO | with PSO |
---|---|---|

${\mathit{q}}_{\mathbf{1}}$ Rise time(s) | 40.7935 | 17.0299 |

${\mathit{q}}_{\mathbf{1}}$ Settling time(s) | 457.7632 | 277.9465 |

${\mathit{q}}_{\mathbf{1}}$ Overshoot percentage | 41.0047 | 5.6116 |

${\mathit{q}}_{\mathbf{2}}$ Rise time(s) | 47.6423 | 15.9123 |

${\mathit{q}}_{\mathbf{2}}$ Settling time(s) | 480.8057 | 398.5471 |

${\mathit{q}}_{\mathbf{2}}$ Overshoot percentage | 44.4818 | 7.9774 |

${\mathit{q}}_{\mathbf{3}}$ Rise time(s) | 5.4699 | 3.4137 |

${\mathit{q}}_{\mathbf{3}}$ Settling time(s) | 9.1445 | 6.2746 |

${\mathit{q}}_{\mathbf{3}}$ Overshoot percentage | 1.3724 (under) | 0.6043 (under) |

**Table 4.**Codes of sea state [39].

Sea State Code | Description of Sea | Wave Height Observed (m) | World Wide Probability (%) |
---|---|---|---|

0 | Calm (glassy) | 0 | - |

1 | Calm (ripples) | 0–0.1 | 11.2486 |

2 | Smooth | 0.1–0.5 | - |

3 | Slight | 0.5–1.25 | 31.6851 |

4 | Moderate | 1.25–2.5 | 40.1944 |

5 | Rough | 2.5–4.0 | 12.8005 |

6 | Very rough | 4.0–6.0 | 3.0253 |

7 | High | 6.0–9.0 | 0.9263 |

8 | Very high | 9.0–14.0 | 0.1190 |

9 | Extreme | Over 14.0 | 0.0009 |

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**MDPI and ACS Style**

Ryalat, M.; Salim Damiri, H.; ElMoaqet, H.
Particle Swarm Optimization of a Passivity-Based Controller for Dynamic Positioning of Ships. *Appl. Sci.* **2020**, *10*, 7314.
https://doi.org/10.3390/app10207314

**AMA Style**

Ryalat M, Salim Damiri H, ElMoaqet H.
Particle Swarm Optimization of a Passivity-Based Controller for Dynamic Positioning of Ships. *Applied Sciences*. 2020; 10(20):7314.
https://doi.org/10.3390/app10207314

**Chicago/Turabian Style**

Ryalat, Mutaz, Hazem Salim Damiri, and Hisham ElMoaqet.
2020. "Particle Swarm Optimization of a Passivity-Based Controller for Dynamic Positioning of Ships" *Applied Sciences* 10, no. 20: 7314.
https://doi.org/10.3390/app10207314