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Course-keeping with roll damping control for ships using rudder and fin

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Abstract

To resolve the severe wear problems of steering engine and fin stabilizer, the nonlinear response characteristics of steering engine and fin stabilizer are studied by analyzing sea trial data of ship Yukun. The nonlinear response characteristics are summarized and applied to a rudder and fin hybrid control system. Decoupling, \(\hbox {H}_\infty\) and \({\rm H}_2\) controllers are designed to achieve low control frequency for it. Simulations show that all the three controllers can achieve excellent course-keeping and roll damping performances, and their control frequencies and amplitudes are consistent with those of nautical practice. It can be found that \(\hbox {H}_2\) controller achieves the best response performance of course-keeping and energy saving performance for rudder engine; \(\hbox {H}_\infty\) controller achieves the best response performance for roll damping; Decoupling controller has the best energy saving performance for fin stabilizer. When the Beaufort wind force scale is increased from 6 to 8 and model perturbation is involved, \(\hbox {H}_2\) controller shows the best robustness of control performance and control input. In addition, the designed low-order controllers can reduce hardware cost for autopilot realization in nautical field.

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Abbreviations

\(N_\delta\) :

Total number of steering

\(M_\delta\) :

Averaged steering amplitude

\(\psi\) :

Heading angle

\(\psi _\varDelta\) :

Changed heading angle

\(n_\delta\) :

The number of steering

\(m_\delta\) :

The amplitude of steering

\(T_\mathrm {c}\) :

Time of sea trial

\(m_\delta\) :

The amplitude of steering

\(\phi\) :

Roll angle

\(\delta\) :

Rudder angle

\(\sigma\) :

Fin angle

u :

Surge speed

v :

Sway speed

\(\tau\) :

Steering period

r(t):

Input signal

e(t):

Error signal

\(J_E\) :

Objective function

\(V_\mathrm s\) :

Ship speed

\(V_\mathrm R\) :

Relative wind speed

\(\psi _\mathrm R\) :

Relative wind direction

\(V_\mathrm {w}\) :

Absolute wind speed

\(\psi _\mathrm {w}\) :

Absolute wind direction

\(V_\mathrm {c}\) :

Absolute current speed

\(\psi _\mathrm {c}\) :

Absolute current direction

\(\delta _\mathrm {wind}\) :

Rudder angle induced by average wind

\(W_\mathrm {c}\) :

Second-order oscillation system

G :

Controlled plant

D :

Decoupling controller

K :

\(\hbox {H}_\infty\) controller

Q :

\(\hbox {H}_2\) controller

A :

System matrix

B :

Control matrix

C :

Measurement matrix

U :

Input matrix

s :

Laplacian operator

\(S_{\psi }\) :

Desired heading

\(S_{\phi }\) :

Desired roll angle

\(T_{\psi }\) :

Actual heading

\(T_{\phi }\) :

Actual roll angle

\(U_{\delta }\) :

Input rudder angle

\(U_{\sigma }\) :

Input fin angle

\(A_{\psi }\) :

Mean absolute error of heading

\(A_{\phi }\) :

Mean absolute error of roll damping

\(I_{\delta }\) :

Mean absolute input of rudder angle

\(I_{\sigma }\) :

Mean absolute input of fin angle

O-\(X_0Y_0Z_0\) :

Space fixed coordinate system

\(x_0\),\(y_0\) :

Ship position

o-xyz :

Body fixed coordinate system

CFD:

Computational fluid dynamics

MIMO:

Multi-input multi-output

SISO:

Single input single output

RGA:

Relative gain array

RHP:

Right half plane

MPC:

Model predictive control

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Authors and Affiliations

  1. State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai, 200240, China

    Zhiheng Zhang & Xinshu Zhang

  2. Collaborative Innovation Center for Advanced Ship and Deep Sea Exploration (CISSE), Shanghai, 200240, China

    Zhiheng Zhang & Xinshu Zhang

Authors
  1. Zhiheng Zhang
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  2. Xinshu Zhang
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Correspondence to Xinshu Zhang.

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Zhang, Z., Zhang, X. Course-keeping with roll damping control for ships using rudder and fin. J Mar Sci Technol 26, 872–882 (2021). https://doi.org/10.1007/s00773-020-00779-6

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  • DOI: https://doi.org/10.1007/s00773-020-00779-6

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