# Cascade Control of Active Heave Compensation Nonlinear System for Marine Crane

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Dynamic Model of AHC System

#### 2.1. AHC System Description

#### 2.2. Mathematical Model of AHC System

- 1.
- The hydraulic pipeline is short, and the friction loss and dynamic of the pipeline are neglected;
- 2.
- The pressure of each working chamber of the hydraulic cylinder is equal;
- 3.
- The temperature and bulk modulus of elasticity of hydraulic oil are constants;
- 4.
- The hydraulic cylinder ignores the external leakage, and the internal leakage is laminar flow [18].

- 1.
- The slide valve is an ideal four-side slide valve with zero opening, four throttle ports matching and symmetry;
- 2.
- The flow at the throttling window is turbulent;
- 3.
- Flow variation in response to valve spool displacement and valve pressure drop can occur instantaneously.

**Assumption**

**1.**

**Assumption**

**2.**

## 3. DOB-ANCC Controller Design

#### 3.1. Adaptive Law Design for Uncertain Parameters

#### 3.2. Disturbance Force Observer Design

#### 3.3. DOB-ANCC Nonlinear Cascade Control Based on Backstepping Method

#### 3.3.1. Step 1

#### 3.3.2. Step 2

#### 3.3.3. Step 3

## 4. Simulations

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Chen, H.; Wang, X.; Benbouzid, M.; Charpentier, J.F.; Aϊt-Ahmed, N.; Han, J. Improved Fractional-Order PID Controller of a PMSM-Based Wave Compensation System for Offshore Vessel Cranes. J. Mar. Sci. Eng.
**2022**, 10, 1238. [Google Scholar] [CrossRef] - Calnan, C.; Bauer, R.J.; Irani, R.A. Reference-point algorithms for active motion compensation of towed bodies. IEEE J. Ocean. Eng.
**2018**, 44, 1024–1040. [Google Scholar] [CrossRef] - Southerland, A. Mechanical systems for ocean engineering. Nav. Eng. J.
**1970**, 82, 63–74. [Google Scholar] [CrossRef] - Woodacre, J.; Bauer, R.; Irani, R. Hydraulic valve-based active-heave compensation using a model-predictive controller with non-linear valve compensations. Ocean Eng.
**2018**, 152, 47–56. [Google Scholar] [CrossRef] - Do, K.D. Boundary control design for extensible marine risers in three-dimensional space. J. Sound Vib.
**2017**, 388, 1–19. [Google Scholar] [CrossRef] - Richter, M.; Schaut, S.; Walser, D.; Schneider, K.; Sawodny, O. Experimental validation of an active heave compensation system: Estimation, prediction and control. Control Eng. Pract.
**2017**, 66, 1–12. [Google Scholar] [CrossRef] - Ren, H.P.; Jiao, S.S.; Wang, X.; Kaynak, O. Fractional order integral sliding mode controller based on neural network: Theory and electro-hydraulic benchmark test. IEEE/Asme Trans. Mechatron.
**2021**, 27, 1457–1466. [Google Scholar] [CrossRef] - Bozkurt, B.; Ertogan, M. Heave and horizontal displacement and anti-sway control of payload during ship-to-ship load transfer with an offshore crane on very rough sea conditions. Ocean Eng.
**2023**, 267, 113309. [Google Scholar] [CrossRef] - Ngo, Q.H.; Nguyen, N.P.; Nguyen, C.N.; Tran, T.H.; Ha, Q.P. Fuzzy sliding mode control of an offshore container crane. Ocean Eng.
**2017**, 140, 125–134. [Google Scholar] [CrossRef] - Yang, T.; Sun, N.; Chen, H.; Fang, Y. Neural network-based adaptive antiswing control of an underactuated ship-mounted crane with roll motions and input dead zones. IEEE Trans. Neural Netw. Learn. Syst.
**2019**, 31, 901–914. [Google Scholar] [CrossRef] [PubMed] - Guo, K.; Li, M.; Shi, W.; Pan, Y. Adaptive tracking control of hydraulic systems with improved parameter convergence. IEEE Trans. Ind. Electron.
**2021**, 69, 7140–7150. [Google Scholar] [CrossRef] - Puller, T.; Lecchini-Visintini, A. A simplified model of a fueldraulic actuation system with application to load estimation. Proc. Inst. Mech. Eng. Part I J. Syst. Control Eng.
**2019**, 233, 570–581. [Google Scholar] [CrossRef] - Yang, G.; Yao, J. Output feedback control of electro-hydraulic servo actuators with matched and mismatched disturbances rejection. J. Frankl. Inst.
**2019**, 356, 9152–9179. [Google Scholar] [CrossRef] - Han, J. From PID to active disturbance rejection control. IEEE Trans. Ind. Electron.
**2009**, 56, 900–906. [Google Scholar] [CrossRef] - Jia, W.; Luo, M.; Ni, F. Stochastic Dynamics of Suspension System in Maglev Train: Governing Equations for Response Statistics and Reliability. Int. J. Struct. Stab. Dyn.
**2023**, 1, 2350192. [Google Scholar] [CrossRef] - Yang, Y.; Hua, C.; Guan, X. Adaptive fuzzy finite-time coordination control for networked nonlinear bilateral teleoperation system. IEEE Trans. Fuzzy Syst.
**2013**, 22, 631–641. [Google Scholar] [CrossRef] - Guo, K.; Wei, J.H.; Tian, Q.Y. Disturbance observer based position tracking of electro-hydraulic actuator. J. Cent. South Univ.
**2015**, 22, 2158–2165. [Google Scholar] [CrossRef] - Yan, Y.; Fan, Y.; Qiu, H.; Yang, Z. Research on double cylinder synchronous linear loading system based on sliding mode control with exponentially converging disturbance observer. J. Phys. Conf. Ser.
**2022**, 2383, 012065. [Google Scholar] [CrossRef]

Parameter | Value | Unit | Parameter | Value | Unit |
---|---|---|---|---|---|

A_{1} | 1.113 × 10^{−2} | m^{2} | V_{01} | 1.15 × 10^{−2} | m^{3} |

A_{2} | 5.6 × 10^{−3} | m^{2} | V_{02} | 0.57 × 10^{−3} | m^{3} |

C_{ip} | 1.4 × 10^{9} | m^{3}/(s·Pa) | k_{d} | 1.25 × 10^{−3} | m/v |

β_{e} | 1.4 × 10^{9} | Pa | β | 4.956 × 10^{−1} |

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

k_{11} | 2 |

k_{12} | 15 |

k_{13} | 4 |

K_{21} | 8 |

η_{1} | 4 × 10^{9} |

η_{2} | 5 × 10^{9} |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Xu, J.; Wang, Y.; Ma, J.; Zhan, Y.
Cascade Control of Active Heave Compensation Nonlinear System for Marine Crane. *J. Mar. Sci. Eng.* **2023**, *11*, 1092.
https://doi.org/10.3390/jmse11051092

**AMA Style**

Xu J, Wang Y, Ma J, Zhan Y.
Cascade Control of Active Heave Compensation Nonlinear System for Marine Crane. *Journal of Marine Science and Engineering*. 2023; 11(5):1092.
https://doi.org/10.3390/jmse11051092

**Chicago/Turabian Style**

Xu, Jianan, Yiming Wang, Junling Ma, and Yong Zhan.
2023. "Cascade Control of Active Heave Compensation Nonlinear System for Marine Crane" *Journal of Marine Science and Engineering* 11, no. 5: 1092.
https://doi.org/10.3390/jmse11051092