Abstract
This chapter describes a procedure to obtain an improved design model of ships subjected to the influence of currents and sea waves. The model structure is at the heart of the application of new techniques in control and estimation theory to the problem of Dynamic Positioning (DP) and wave filtering of marine vessels. The model proposed captures the physics of the problem at hand in an effective manner and includes the sea state as an uncertain parameter. This allows for the design of advanced control and estimation algorithms to solve the DP and wave filtering problems under different sea conditions. Numerical simulations, carried out using a high fidelity nonlinear DP system simulator, illustrate the performance improvement in wave filtering as a result of the use of the proposed model. Furthermore, using Monte-Carlo simulations the performance of three DP controllers, designed based on the plant model developed, is evaluated for different sea conditions. The first controller is a nonlinear multivariable PID controller with a passive observer. The second controller is of the Linear Quadratic Gaussian type and the third controller builds on \(\mathcal{H}_{\infty }\) control techniques using the mixed-μ synthesis methodology. The theoretical results are experimentally verified and the performance of wave filtering in DP systems operated with the controllers designed for different sea conditions are further examined by model testing a DP operated ship, the Cybership III, in a towing tank equipped with a hydraulic wavemaker.
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- 1.
In six degrees-of-freedom dynamics, (17.8) is written as \(M(w)\ddot{\eta }_{R\omega } + D_{p}(w)\dot{\eta }_{R\omega } + G\eta _{R\omega } =\tau _{\text{wave1}}\), where \(G \in \mathbb{R}^{6\times 6}\) is the linearized restoring coefficient matrix due to the gravity and buoyancy affecting heave, roll, and pitch only (see [26] for more details). Throughout this chapter a three degrees-of-freedom dynamics is used for the design purposes, while a six degrees-of-freedom dynamics is used in the simulation.
- 2.
- 3.
In long-crested irregular sea, the sea elevation can be assumed statistically stable. See [26] for details and differences between long- and short-crested seas.
- 4.
When designing observers for wave filtering in dynamic positioning, since the controller regulates the heading of the vessel, the designer can assign a new intensity to w b f; however, assigning the intensity of the noise in practice requires considerable expertise.
- 5.
- 6.
At this point, we should emphasize that the observers are designed according to the simple model of (17.10)–(17.15) [and (17.1)–(17.7)] while they are tested in the MCSim using a high fidelity model which captures hydrodynamic effects, generalized coriolis and centripetal accelerations, nonlinear damping and current forces, and generalized restoring forces. Moreover, in the MCSim the JONSWAP wave spectrum is used to simulate the waves while the observers are designed using a linear second order approximation of the spectrum.
- 7.
- 8.
All the results are presented in full scale. During the testing phase care was taken to ensure that all controllers were tuned to their best performance, so as to allow for a fair comparative study.
- 9.
For technical reasons in this experiment the tunnel thruster was deactivated.
- 10.
Before a DP system is functional, the state estimate of the filter in the DP system should converge to its steady state performance; this initialization may take tens of minutes.
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Acknowledgements
We thank our colleagues Asgeir J. Sørensen, A. Pedro Aguiar, N.T. Dong, and Thor I. Fossen for many discussions on wave filtering and adaptive estimation. We would also like to thank T. Wahl, M. Etemaddar, E. Peymani, M. Shapouri, and B. Ommani for their invaluable assistance during the model tests at MCLab. This work has been carried out at the Centre for Autonomous Marine Operations and Systems (AMOS) in collaboration with the Norwegian Marine Technology Research Institute (MARINTEK). The Norwegian Research Council is acknowledged as the main sponsor of AMOS. This work was supported by the Research Council of Norway through the Centres of Excellence funding scheme, Project number 223254—AMOS.
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Hassani, V., Pascoal, A.M. (2015). Wave Filtering and Dynamic Positioning of Marine Vessels Using a Linear Design Model: Theory and Experiments. In: Ocampo-Martinez, C., Negenborn, R. (eds) Transport of Water versus Transport over Water. Operations Research/Computer Science Interfaces Series, vol 58. Springer, Cham. https://doi.org/10.1007/978-3-319-16133-4_17
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