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Journal of Applied Nonlinear Dynamics 6(4) (2017) 521--530 | DOI:10.5890/JAND.2017.12.007

Jimmie C. Oxley$^{1}$; James L. Smith$^{1}$; Sayavur I. Bakhtiyarov$^{2}$; Philipp M. Baldovi$^{2}$

$^{1}$ Department of Chemistry, DHS Center of Excellence in Explosives, University of Rhode Island, Kingston, 51 Lower College Rd, RI 02881, USA

$^{2}$ Mechanical Engineering Department, New Mexico Institute of Mining and Technology, 801 Leroy Place, Socorro, NM 87801, USA

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Abstract

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.

Acknowledgments

This study was performed under an appointment to the U.S. Department of Homeland Security (DHS) Science & Technology (S&T) Directorate Office of University Programs Summer Research Team Program for Minority Serving Institutions, administered by the Oak Ridge Institute for Science and Education (ORISE) through an interagency agreement between the U.S. Department of Energy (DOE) and DHS. ORISE is managed by ORAU under DOE contract number DE-SC0014664. All opinions expressed in this paper are the author’s and do not necessarily reflect the policies and views of DHS, DOE, or ORAU/ORISE.

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