Observer-based motion control system for the approach ship with propeller and rudder in the process of underway replenishment

doi:10.1016/j.oceaneng.2021.108586

Ocean Engineering

Volume 222, 15 February 2021, 108586

https://doi.org/10.1016/j.oceaneng.2021.108586 Get rights and content

Highlights

•
An observer-based control strategy needs only position and heading of the ship.
•
A model considers wind, wave and currents, the hydrodynamic interaction and highline cable tension.
•
A novel ESO estimates the surge speed, sway speed, yaw rate and the total uncertainties.
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The propeller speed and rudder angle are considered as the control inputs for the approach ship.

Abstract

To avoid collisions between guide ship and approach ship during the underway replenishment process, it is important to maintain a certain distance between them. Based on trajectory tracking requirements, a control strategy suitable for engineering applications is proposed for an approach ship without velocity measurements. First, considering the effects of wind, waves, currents, hydrodynamic interactions and the highline cable system, models are established for the two ships. Second, a leader-follower approach is used to maintain the expected longitudinal and transverse distances between the two ships. Third, an extended state observer is designed according to the position, heading, propeller speed and rudder angle of the approach ship. Two time-varying parameters in the observer are estimated in the controller design process. Therefore, the linear speeds, yaw rate, and total system uncertainties can be observed. Fourth, the propeller speed and rudder angle, other than the surge force and steering moment, are considered as the control inputs, which are constructed by the command filter backstepping method. The stability of the proposed control system is verified. Finally, a simulation is performed to demonstrate the effectiveness of the proposed method.

Introduction

Underway replenishment (UNREP) has become a necessary process for global fleet operations. During replenishment, one of two ships will assume the role of guide ship and maintain a steady course and speed, while an approach ship will move alongside the guide ship to transfer cargoes such as food, fuel and fresh water. The motion control of the approach ship is typically achieved manually with the aid of GPS and radar and requires a helmsman with good steering skills (Kyrkjebø, 2007; Liu et al., 2007). However, external disturbances can hinder maintaining the expected longitudinal and transverse distances between the two ships by manual control (Skejic et al., 2009). Hence, it is necessary to develop a synchronization motion control system that can significantly improve maneuvering precision, increase supply efficiency and ensure the safety of both crews and cargoes.

In general, a leader-follower approach is used to realize the synchronized control of two ships engaged in underway replenishment (Liu et al., 2018; Gierusz et al., 2016). The basic concept involves the guide ship following a predefined straight path at a specified speed while the approach ship tracks a virtual trajectory that is constructed by the motion states of the guider and predefined replenishment distances (Wang, 1991).

In recent decades, numerous methods for the trajectory tracking control of underactuated ships have been studied. Considering the nonlinear characteristics of ship dynamics and the uncertainty of external disturbances, backstepping-based control strategies have been widely used in this field due to their excellent capability to control uncertain nonlinear systems (Zhao et al., 2019a, 2019b, 2020). Godhavn (1998) applied an adaptive backstepping technique to obtain a control law for trajectory tracking. Although the position tracking demand was satisfied, the heading of the ship was controlled indirectly, which caused a large heading error when it was required to turn. To overcome this problem, a high gain-based local exponential stabilization algorithm was developed to control the heading of the ship directly (Pettersen et al., 2001). Based on the assumption that the yaw rate was not zero, Jiang (2002) proposed a global asymptotic tracking control law in which the desired trajectory is generated by a virtual ship for curvilinear path-following tasks. Do et al. (2002) removed this assumption by constructing a new desired trajectory, and the desired surge speed and yaw rate were not required to be generated by the virtual ship. It should be noted that the above three approaches were all based on accurate mathematical models, which are usually unavailable in practice. By using adaptive laws with projection, a nonlinear adaptive control strategy was developed to control ships with unknown parameters (Do et al., 2004). In relevant studies, a neural network (NN) was combined with a backstepping method to address model uncertainties and time-varying disturbances (Zhang et al., 2014). However, all the abovementioned control methods did not fully consider external disturbances. During an UNREP, in addition to wind, waves and currents, hydrodynamic interactions and highline cable tension also exist. All these disturbances should be considered in the controller to improve the tracking accuracy.

The aforementioned control methods suffer from three major problems. The first is the ‘explosion of terms’, which is caused by the redifferentiation of the virtual control inputs in the standard backstepping design process. The second is that the control inputs of these control systems are the surge force and yaw moment, which is puzzling for designers. Because for an underactuated ship, the actual control inputs are the propeller speed and rudder angle. The third problem is that all states of the ship are used as feedbacks for the controller, but the sway speed and yaw rate are usually unmeasurable. To address the second problem, Li et al. (2009a, 2009b) considered the rudder angle as a control input, but the propeller speed was not mentioned. Zhang et al. (2017) considered both actual control inputs, but it also need to measure the surge speed, sway speed and yaw rate. For the last problem, extended-state observers (ESOs) have been widely used to estimate unmeasured states and lumped uncertainties (Guo et al., 2012; Liu et al., 2019; Fu et al., 2015; Peng et al., 2018). Similar to the second drawback of the controllers introduced in the last section, in addition to the ship's position and heading, the abovementioned ESO also requires information on surge forces and yaw moments, which are difficult to obtain in practice. Inspired by this problem, a simplified dynamics model is proposed. The surge force is rewritten as a product of the propeller speed and an unknown time-varying parameter. The steering moment is constructed as the product of an unknown time-varying parameter and the rudder angle. A novel ESO is designed by replacing the force and moment with the propeller speed and rudder angle, respectively. Two direct adaptive laws are proposed in the controller design process to estimate these two parameters. In this way, we not only give full play to the advantages of the ESO-based backstepping design technique but also solve the problem where the control inputs cannot be used directly in engineering.

In this paper, all the aforementioned disturbances are considered. The command filtered backstepping approach (Wu et al., 2018) is combined with a novel ESO to design the motion controller of an approach ship by regarding the propeller speed and rudder angle as the control inputs. The main contributions of this paper are as follows: (a) The ‘explosion of terms’ problem is avoided by the command filter. (b) An ESO is designed based on the position, heading angle, propeller speed and rudder angle to observe the surge speed, sway speed, yaw rate and total uncertainties, which include the model uncertainties and external disturbances. Two time-varying parameters in the proposed ESO are estimated in the controller design process by two adaptive laws. (c) The actual propeller speed and rudder angle are considered the control inputs for the approach ship, which benefits implementation.

The rest of this paper is organized as follows. Mathematical models of the two ships and external disturbances are presented in the next section. In Section 3, the guidance law of the approach ship is derived. The ESO is designed in Section 4. Section 5 illustrates the controller design process, and simulation results are shown in Section 6. Section 7 concludes this paper.

Section snippets

Mathematical models of the two ships during replenishment

UNREP is a process that can be divided into three phases, as shown in Fig. 1: approaching, parallel motion and departure. The second phase is the key phase during which replenishment operations are conducted. Both ships must move with the same surge speed and heading angle.

Considering the motions in surge, sway and yaw, the 3-DOF kinematic model of ship can be expressed as: ${\dot{η}}_{i} = J (ψ_{i}) υ_{i} with J (ψ_{i}) = [\begin{array}{l} \cos ψ_{i} & - \sin ψ_{i} & 0 \\ \sin ψ_{i} & \cos ψ_{i} & 0 \\ 0 & 0 & 1 \end{array}], i = A, B$ where index $i$ represents guide ship A and approach ship B. $η_{i} = [x_{i}, y_{i},$

Guidance law design

The guidance law for approach ship B is derived in this section. It is assumed that guide ship A can precisely follow the predefined straight path at a constant surge speed. According to Fig. 5, to achieve the coordinated motion control of the guide ship and approach ship, a virtual trajectory with a relatively fixed distance from the trajectory of the guide one is obtained by the leader-follower approach. Based on this virtual trajectory, the desired heading angle for approach ship B can be

The ESO design

Based on the propeller speed $n_{P_{B}}$ , rudder angle $δ_{B}$ and measurable position vector $η_{B} = {[x_{B}, y_{B}, ψ_{B}]}^{T}$ of approach ship B, an ESO is proposed in this section to obtain the estimations of unmeasured speed vector $υ_{B} = {[u_{B}, v_{B}, r_{B}]}^{T}$ and total uncertainties $ζ = {[ζ_{u}, ζ_{v}, ζ_{r}]}^{T}$ .

Because the sideslip angle $β_{B}$ is very small, the effective attack angle $α_{R_{B}}$ shown in (3) can be approximately expressed as $α_{R_{B}} = δ_{B} + β_{B} \approx δ_{B}$ . Then, the steering moment can be rewritten as: $N_{R_{B}} = - (1 + α_{H}) x_{R_{B}} 0.5 ρ_{w} A_{R_{B}} V_{R_{B}}^{2} 6 λ_{R_{B}} / (λ_{R_{B}} + 2) \sin δ_{B} \cos δ_{B}$

We define $f ($

Controller design

In this section, the robust propeller speed and rudder angle control laws are designed for approach ship B. Fig. 6 illustrates the entire motion control strategy.

Because approach ship B is required to perform a trajectory tracking task, the two controllers need to force approach ship B to track the specified virtual trajectory. The tracking errors presented below are arranged for the controller design (Zhang et al., 2017): $[\begin{array}{l} x_{e_{B}} \\ y_{e_{B}} \\ ψ_{e_{B}} \end{array}] = J^{T} (ψ_{B}) [\begin{array}{l} x_{d_{B}} - x_{B} \\ y_{d_{B}} - y_{B} \\ ψ_{d_{B}} - ψ_{B} \end{array}]$ where $η_{d_{B}} = {[\begin{array}{l} x_{d_{B}} & y_{d_{B}} & ψ_{d_{B}} \end{array}]}^{T}$ shown in

Simulation studies

Scale models of ‘MARINER’ and ‘ESSO OSAKA’ are applied in a simulation to verify the feasibility and effect of the control strategy. The ‘ESSO OSAKA’ acts as guide ship A, and ‘MARINER’ acts as approach ship B, which is equipped with a single propeller and only one rudder. Their dimensions are displayed in Table 1. It should be noted that further information on the propulsion and rudder parameters for the scale models of ‘MARINER’ and ‘ESSO OSAKA’ are listed in Chislett et al. (1965) and Dand

Conclusions

A leader-follower motion control strategy based on a newly designed ESO and command filtered adaptive backstepping technique is presented for an approach ship engaged in an underway replenishment operation when only the position and heading of the approach ship are available. The propeller speed and rudder angle are regarded as the control inputs for the studied ship. Based on the proposed ESO, the unmeasured states as well as the total uncertainties can be accurately estimated simultaneously.

CRediT authorship contribution statement

Yuxian Huang: Conceptualization, Methodology, Software, Writing - original draft. Yifei Hu: Software, Writing - original draft. Jinbo Wu: Conceptualization, Methodology, Writing - review & editing. Chenghao Zeng: Investigation, Visualization, Writing - review & editing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grant 51979117.

References (35)

K. Do et al.
Robust adaptive path following of underactuated ships
Automatica
(2004)
Z. Jiang
Global tracking control of underactuated ships by Lyapunov's direct method
Automatica
(2002)
Z. Li et al.
Design, analysis and experimental validation of a robust nonlinear path following controller for marine surface vessels
Automatica
(2009)
L. Liu et al.
State recovery and disturbance estimation of unmanned surface vehicles based on nonlinear extended state observers
Ocean Eng.
(2019)
R. Skejic et al.
Modeling and control of underway replenishment operations in calm water
G. Zhang et al.
ESO-based path following control for underactuated vehicles with the safety prediction obstacle avoidance mechanism
Ocean. Eng.
(2019)
K. Zhao et al.
Tracking control of MIMO nonlinear systems under full state constraints: a single-parameter adaptation approach free from feasibility conditions
Automatica
(2019)
S. Boyd et al.
Linear matrix inequality in system and control theory
Studies in Applied Mathematics
(1994)
M.S. Chislett et al.
Planar motion mechanism tests and full-scale steering and manoeuvring predictions for a mariner class vessel. Hydro- and Aerodynamisk Lab., Lyngby, Denmark
Tech. Rep. H
(1965)
I.W. Dand et al.
Maneuvering Experiments Using Two Geosims of the Esso Osaka
(1983)

K. Do et al.

Underactuated ship global tracking under relaxed conditions

IEEE Trans. Automat. Contr.

(2002)

W. Dong et al.

Command filtered adaptive backstepping

IEEE Trans. Contr. Syst. Technol.

(2012)

T.I. Fossen

Guidance and Control of Ocean Vehicles

(1994)

M. Fu et al.

Nonlinear extended state observer for path following control of underactuated marine surface vessel

M. Fu et al.

Alongside replenishment tracking control of the supply ship under the influence of the highline cable tension

J.M. Godhavn et al.

Nonlinear and adaptive backstepping designs for tracking control of ships

Int. J. Adapt. Contr. Signal Process.

(1998)

B. Guo et al.

On convergence of non-linear extended state observer for multi-input multi-output systems with uncertainty

IET Control Theory & Appl.

(2012)

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View full text

Observer-based motion control system for the approach ship with propeller and rudder in the process of underway replenishment

Highlights

Abstract

Introduction

Section snippets

Mathematical models of the two ships during replenishment

Guidance law design

The ESO design

Controller design

Simulation studies

Conclusions

CRediT authorship contribution statement

Declaration of competing interest

Acknowledgments

Automatica

Automatica

Automatica

Ocean Eng.

Ocean. Eng.

Automatica

Linear matrix inequality in system and control theory

Studies in Applied Mathematics

Planar motion mechanism tests and full-scale steering and manoeuvring predictions for a mariner class vessel. Hydro- and Aerodynamisk Lab., Lyngby, Denmark

Tech. Rep. H

Maneuvering Experiments Using Two Geosims of the Esso Osaka

Underactuated ship global tracking under relaxed conditions

IEEE Trans. Automat. Contr.

Command filtered adaptive backstepping

IEEE Trans. Contr. Syst. Technol.

Guidance and Control of Ocean Vehicles

Nonlinear extended state observer for path following control of underactuated marine surface vessel

Alongside replenishment tracking control of the supply ship under the influence of the highline cable tension

Nonlinear and adaptive backstepping designs for tracking control of ships

Int. J. Adapt. Contr. Signal Process.

On convergence of non-linear extended state observer for multi-input multi-output systems with uncertainty

IET Control Theory & Appl.