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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

Nonlinear analysis of the yaw motion of a mariner vehicle under PDμ control

Journal of Applied Nonlinear Dynamics 6(4) (2017) 531--545 | DOI:10.5890/JAND.2017.12.008

C. A. Kitio kwuimy; C. Nataraj

Villanova Center for Analytics of Dynamic Systems (, Villanova University, Villanova, PA 19085

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This paper considers a mariner under PDμ controller and analyses the effects of controller parameters on the yaw rate by using the Nomoto model. The Nomoto model describing the time evolution of the yaw rate of the steering dynamics of a mariner is reduced to an asymmetric Duffing oscillator with fractional order derivative. Under the approximation of calm water, the steady behavior of the mariner shows an “imperfect” supercritical pitchfork bifurcation. Region of safe behavior is identified and strategy to reduce the yaw rate by an appropriated selection of controller parameters are discussed. The frequency analysis of the mariner shows the prominence of hysteresis is reduced for small order of the fractional derivative as well as the amplitude of the yaw rate. Evidence of chaotic response is illustrated using robust chaotic indicators such as the Lyapunov exponent and the fast Fourier transform.


Dr. Kwuimy was supported by the US Office of Naval Research under the grant ONR N00014-08-1-0435. We deeply appreciate this support. Our gratitude to the program managers, Mr Anthony Seman III and Capt. Lynn Petersen for their support and guidance.


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