Journal
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
Volume 23, Issue 7-8, Pages 1231-1238Publisher
WALTER DE GRUYTER GMBH
DOI: 10.1515/ijnsns-2020-0127
Keywords
Caputo fractional approach; controller; fractional-order system; ship power system
Funding
- Center for Nonlinear Systems, Chennai Institute of Technology, India [CIT/CNS/2020/RD/063]
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The ship power system is studied using a fractional-order approach, with observation of a chaotic attractor and calculation of the fractional-order form using the Adam-Bashforth-Moulton method. Lyapunov exponents and bifurcation diagrams are analyzed, and a fractional-order controller is designed to remove chaotic dynamics, demonstrating its effectiveness through time plots simulation.
In this research, the ship power system is studied with a fractional-order approach. A 2-D model of a two-generator parallel-connected is considered. A chaotic attractor is observed for particular parameter values. The fractional-order form is calculated with the Adam-Bashforth-Moulton method. The chaotic response is identified even for the order 0.99. Phase portrait is generated using the Caputo derivative approach. Wolf's algorithm is used to calculate Lyapunov exponents. For the considered values of parameters, one positive Lyapunov exponent confirms the existence of chaos. Bifurcation diagrams are presented to analyze the various dynamical behaviors and bifurcation points. Interestingly, the considered system is multistable. Also, antimonotonicity, period-doubling, and period halving are observed in the bifurcation diagram. As the last step, a fractional-order controller is designed to remove chaotic dynamics. Time plots are simulated to show the effectiveness of the controller.
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