Elsevier

Automatica

Volume 73, November 2016, Pages 207-214
Automatica

Brief paper
Robust dynamic positioning of ships with disturbances under input saturation

https://doi.org/10.1016/j.automatica.2016.06.020Get rights and content

Abstract

In the presence of unknown time-varying disturbances and input saturation, this paper develops a robust nonlinear control law for the dynamic positioning (DP) system of ships using a disturbance observer, an auxiliary dynamic system, and the dynamic surface control (DSC) technique. The disturbance observer is constructed to provide the estimates of unknown time-varying disturbances, the auxiliary dynamic system is employed to handle input saturation, and the DSC technique makes the designed DP control law be simple and easy to implement in practice. It is proved that the designed DP robust nonlinear control law can maintain ship’s position and heading at desired values, while guaranteeing the uniform ultimate boundedness of all signals in the DP closed-loop control system. Finally, simulations on a supply ship are carried out to demonstrate the effectiveness of the developed DP control law.

Introduction

A dynamic positioning (DP) system aims at regulating the horizontal position and heading of the vessel exclusively by means of its own propulsion system (Sørensen, 2011). Compared with the traditional anchor moored positioning, the DP mode has the advantages of working in the deep sea, high positioning accuracy, and avoiding damaging the seabed (Fossen, 2011). With the ocean exploration and exploitation moving into the deep and distant sea, the DP system has been increasingly used in offshore operations, such as offshore oil and gas drilling, underwater cable and pipe laying, and wreck investigation (Hassani, Sørensen, & Pascoal, 2013).

With the advances of the nonlinear control, the DP nonlinear control has gradually gained much attention. In 1990s, the DP nonlinear control laws were developed by using the backstepping method (Krstić, Kanellakopoulos, & Kokotović, 1995) in component form in Grøvlen and Fossen (1996) and in vector setting in Fossen and Grøvlen (1998), respectively, where disturbances due to waves, currents and wind were neglected. In Fossen and Strand (1999), Fossen and Strand proposed a passive observer with wave filtering for the DP system to estimate low-frequency positions and velocities of ships from noisy position measurements and bias states (environmental disturbances). Combining the passive observer and a proportional–derivative control law, Loria et al. presented a globally asymptotically stable controller for the DP system, the effectiveness of which was demonstrated by experimentation with a 1:70 scale model of a supply ship (Loria, Fossen, & Panteley, 2000). Benetazzo et al. presented a DP discrete variable-structure controller with Kalman filters estimating the disturbances, which exhibits better performance than the proportional–integral–derivative (PID) controller with the passive observer (Benetazzo, Ippoliti, Longhi, & Raspa, 2012). Considering the variations of sea states, Hassani et al. designed a bank of Kalman filters for the DP system to adapt to sea state variations using the multiple model adaptive estimate techniques (Hassani, Sørensen, Pascoal, & Aguiar, 2012). Nguyen et al. proposed a hybrid controller for the DP system using the supervisory switching control so that different controllers can be switched online according to sea state variations (Nguyen, Sørensen, & Quek, 2007). Considering unknown time-varying disturbances, Du et al. proposed a robust adaptive neural controller for the DP system, where ship unknown model dynamics and time-varying disturbances are compensated for by adaptive radial basis function (RBF) neural networks (Du, Yang, Wang, & Guo, 2013). In the presence of ship unknown dynamic parameters, unavailable velocities, and unknown time-varying disturbances, Du et al. developed an adaptive robust output feedback controller for the DP system by incorporating adaptive RBF neural networks and the high-gain observer into the vectorial backstepping method (Du, Hu, Liu, & Chen, 2015).

All aforementioned control design for the DP system did not take into account input saturation. Input saturation is a potential problem for the DP system since the commanded control inputs calculated by the DP controller are possibly constrained by the maximum forces and moment that the propulsion system can produce. This would give rise to degraded performance and even instability of the DP control system. Input saturation puts a challenge on the DP control design. In the presence of unknown constant disturbances and input saturation, Veksler et al. developed model predictive control (MPC) for the DP system combining DP control design with thrust allocation, where actuator saturation was handled in the optimization problem of MPC (Veksler, Johansen, Borrelli, & Realfsen, 2016); Perez and Donaire proposed DP proportional–integral control, where disturbances and input saturation were handled by the integral action with anti-windup scheme (Perez & Donaire, 2009); and Donaire and Perez proposed DP passivity-based control, where disturbances and input saturation were handled by using the integral action and anti-windup compensator in the port-Hamiltonian framework (Donaire & Perez, 2012).

In this paper, simultaneously considering unknown time-varying disturbances and input saturation, we develop a robust nonlinear control law for the DP system. To the best of the authors’ knowledge, it is the first time in the literature that unknown time-varying disturbances and input saturation are simultaneously dealt with in the DP control design. A disturbance observer is constructed to estimate unknown time-varying disturbances and an auxiliary dynamic system is employed to handle input saturation, on the basis of which the DP control law is designed by using the DSC technique.

Section snippets

Problem formulation

Two right-hand coordinate frames are defined as indicated in Fig. 1. The earth-fixed frame OX0Y0Z0 is an inertial coordinate frame. The origin O of the earth-fixed frame can be chosen as any point on the earth’s surface. The axis OX0 is directed to the north, OY0 is directed to the east, and OZ0 points towards the center of the earth. The body-fixed frame AXYZ is a moving coordinate frame which is fixed to the ship. The origin A of the body-fixed frame is located at the gravity center of the

Disturbance observer design

In this subsection, we construct the disturbance observer (6)–(7) for the unknown time-varying disturbances d(t) as follows (Do, 2010): dˆ(t)=q(t)+K0Mνq̇(t)=K0q(t)K0(Dν+τ+K0Mν) where dˆ(t)R3 is the estimate of d(t), q(t)R3 is the auxiliary state vector of the disturbance observer, and K0=K0TR3×3 is a positive definite design matrix.

Define the disturbance estimation error vector d̃(t)R3 of the observer as d̃=dˆd. From (6), (7), (2), we have dˆ̇=K0qK0(Dν+τ+K0Mν)+K0(Dν+τ+d)=K0(q+K0Mνd

Simulations

In this section, the simulations on Northern Clipper are carried out to evaluate the performance of the proposed DP control law. Further, we compare our proposed DP control law with the PID control law. The dynamic parameters in the motion model (1)–(2) of Northern Clipper are detailed in Alme (2008). The saturation limits of Northern Clipper are given in Table 1 (Alme, 2008).

Conclusion

In this paper, a control scheme combining a disturbance observer and an auxiliary dynamic system with DSC has been proposed for the DP system of ships with unknown time-varying disturbances and input saturation. Input saturation is dealt with in the DP control design by introducing the auxiliary dynamic system. Any priori knowledge of time-varying disturbances is not required through constructing the disturbance observer. The proposed DP control law is simple and easy to implement in practice

Acknowledgments

This work was supported partly by the National Natural Science Foundation of China (51579026, 51079013), partly by the Program for Liaoning Excellent Talents in University (LR2015007), partly by the Technology Foundation for Selected Overseas Chinese Scholar, the Ministry of Human Resources and Social Security of the People’s Republic of China, and partly by the Fundamental Research Funds for the Central Universities (3132016020).

Jialu Du received the B.E. degree in automatic control, the M.Sc. degree in power drive and automation, and the Ph.D. degree in marine engineering from Dalian Maritime University, Dalian, China, in 1988, 1991, and 2005, respectively. She was a Visiting Scholar with the Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway, and with the Cymer Center for Control Systems and Dynamics, University of California at San Diego, La Jolla, CA, USA. She

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  • Cited by (346)

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    Jialu Du received the B.E. degree in automatic control, the M.Sc. degree in power drive and automation, and the Ph.D. degree in marine engineering from Dalian Maritime University, Dalian, China, in 1988, 1991, and 2005, respectively. She was a Visiting Scholar with the Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway, and with the Cymer Center for Control Systems and Dynamics, University of California at San Diego, La Jolla, CA, USA. She is currently a Professor with the School of Information Science and Technology, Dalian Maritime University. Her current research interests include nonlinear control theory, intelligent control, and ship motion control.

    Xin Hu received the B.E. degree in information and computing science from Ludong University, Yantai, China, in 2012. He is currently pursuing the Ph.D. degree with the School of Information Science and Technology, Dalian Maritime University, Dalian, China. His current research interests include nonlinear control theory, intelligent control, and ship motion control.

    Miroslav Krstić holds the Alspach endowed chair and is the founding director of the Cymer Center for Control Systems and Dynamics at UC San Diego. He also serves as Associate Vice Chancellor for Research at UCSD. Krstic is Fellow of IEEE, IFAC, ASME, SIAM, and IET (UK), Associate Fellow of AIAA, and foreign member of the Academy of Engineering of Serbia. He has received the PECASE, NSF Career, and ONR Young Investigator awards, the Axelby and Schuck paper prizes, the Chestnut textbook prize, the ASME Nyquist Lecture Prize, and the first UCSD Research Award given to an engineer. Krstic has coauthored eleven books on adaptive, nonlinear, and stochastic control, extremum seeking, control of PDE systems including turbulent flows, and control of delay systems.

    Yuqing Sun received the M.Sc. degree and the Ph.D. degree in marine engineering from Dalian Maritime University, Dalian, China, in 1989 and 1996, respectively. He is currently a Professor with the School of Marine Engineering, Dalian Maritime University. His current research interests include mechatronics, ship’s auxiliary machinery, hydraulic drive and control, refrigeration technique.

    The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Abdelhamid Tayebi under the direction of Editor Toshiharu Sugie.

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