A fractional-order ship power system: chaos and its dynamical properties

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Prakash Duraisamy ◽  
Goitom Tadesse ◽  
Christos Volos ◽  
Fahimeh Nazarimehr ◽  
...  
Keyword(s):  
Power System ◽  
Fractional Order ◽  
Chaotic Dynamics ◽  
Period Doubling ◽  
Order Form ◽  
Dynamical Behaviors ◽  
Fractional Order Controller ◽  
Parameter Values ◽  
Ship Power System ◽  
D Model

Abstract 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.

A fractional-order ship power system with extreme multistability

2021 ◽  
Vol 106 (1) ◽  
pp. 1027-1040
Author(s):  
Haoyu Zhang ◽  
Kehui Sun ◽  
Shaobo He
Keyword(s):  
Power System ◽  
Fractional Order ◽  
Extreme Multistability ◽  
Ship Power System

CHAOTIC DYNAMICS OF A SIMPLE PARAMETRICALLY DRIVEN DISSIPATIVE CIRCUIT

2011 ◽  
Vol 21 (07) ◽  
pp. 1927-1933 ◽  
Author(s):  
P. PHILOMINATHAN ◽  
M. SANTHIAH ◽  
I. RAJA MOHAMED ◽  
K. MURALI ◽  
S. RAJASEKAR
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Exponents ◽  
Chaotic Dynamics ◽  
Period Doubling ◽  
Classic Period ◽  
Control Signal ◽  
Period Doubling Bifurcation ◽  
Chaotic Circuit ◽  
Route To Chaos ◽  
Parameter Values

We introduce a simple parametrically driven dissipative second-order chaotic circuit. In this circuit, one of the circuit parameters is varied by an external periodic control signal. Thus by tuning the parameter values of this circuit, classic period-doubling bifurcation route to chaos is found to occur. The experimentally observed phenomena is further validated through corresponding numerical simulation of the circuit equations. The periodic and chaotic dynamics of this model is further characterized by computing Lyapunov exponents.

Periodic-Doubling Bifurcation of a Circuit With a Fractional-Order Memristor

2019 ◽  
Author(s):  
Yajuan Yu ◽  
Yangquan Chen
Keyword(s):  
Fractional Order ◽  
Memory Loss ◽  
Period Doubling ◽  
Hysteresis Loops ◽  
State Variables ◽  
Discontinuous Change ◽  
Dynamical Behaviors ◽  
Sinusoidal Current ◽  
Memristive Circuit ◽  
Theoretical Analyses

Abstract A new fractional-order current-controlled memristor is proposed by the fact of the memory loss. Excited by sinusoidal current, the generalized hysteresis loops of the new fractional-order memristor are no longer symmetrical to the origin and the time to reach the steady state is longer than the integer-order memristor’s. The dynamical behaviors of a new fractional-order memristive circuit system whose state variables have different derivation orders are investigated by theoretical analyses and simulated numerically. It is shown that the new fractional-order memristive circuit system goes into chaos by period-doubling bifurcation; the periodic windows are induced by the discontinuous change of derivative order between variables.

Frequency regulation of a RES integrated power system with AC/DC parallel link employing a fuzzy tuned fractional order controller

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Anurekha Nayak ◽  
Manoj Kumar Maharana ◽  
Gayadhar Panda
Keyword(s):  
Power System ◽  
Fractional Order ◽  
Power Plants ◽  
Fuzzy Logic Controller ◽  
Thermal Power ◽  
Frequency Deviation ◽  
Frequency Regulation ◽  
High Voltage Direct Current ◽  
Fractional Order Controller ◽  
Operational Efficacy

Abstract This paper demonstrates the operational efficacy of a newly proposed fuzzy tuned fractional order controller to offer an improved frequency regulation of a multi area renewable energy source (RES) integrated nonlinear power system. The effect of governor dead band nonlinearity and generation rate constraint of hydro and thermal power plants are considered in the system. Moreover, a proposed appropriate High voltage direct current (HVDC) tie line model is incorporated in this work, to verify the frequency deviation. Different test cases are applied to verify the robustness of the controllers on frequency response. The superiority of the proposed controller upon Proportional integral and derivative (PID), fuzzy logic controller and fuzzy PID controller in minimizing frequency deviation has been verified through MATLAB SIMULINK environment.

CHAOTIC DYNAMICS OF A FIVE-DIMENSIONAL NONLINEAR NETWORK

2007 ◽  
Vol 18 (03) ◽  
pp. 335-342
Author(s):  
XUEWEI JIANG ◽  
DI YUAN ◽  
YI XIAO
Keyword(s):  
Lyapunov Exponent ◽  
Power Spectrum ◽  
Chaotic Dynamics ◽  
Period Doubling ◽  
Chinese Traditional Medicine ◽  
Bifurcation Diagrams ◽  
Nonlinear Network ◽  
Dynamical Behaviors ◽  
Lyapunov Exponent Spectrum ◽  
Period Doubling Bifurcations

The dynamics of a five-dimensional nonlinear network based on the theory of Chinese traditional medicine is studied by the Lyapunov exponent spectrum, Poincaré, power spectrum and bifurcation diagrams. The result shows that this system has complex dynamical behaviors, such as chaotic ones. It also shows that the system evolves into chaos through a series of period-doubling bifurcations.

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