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Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems
Karthikeyan Rajagopal, Anitha Karthikeyan* and Prakash Duraisamy**
Abstract In this paper we investigate the control of three-dimensional non-autonomous fractionalorder uncertain model of a permanent magnet synchronous generator (PMSG) via a adaptive control technique. We derive a dimensionless fractional order model of the PMSM from the integer order presented in the literatures. Various dynamic properties of the fractional order model like Eigen values, Lyapunov exponents, bifurcation and bicoherence are investigated. The system chaotic behavior for various orders of fractional calculus are presented. Nonlinear adaptive controllers and adaptive sliding mode controllers are derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the robust controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results derived through which we show that for the derived adaptive controller and the parameter update law, the origin of the system for any bounded initial conditions is asymptotically stable.
Keyword Chaos suppression, Fractional order systems, Permanent magnet synchronous generator, Bifurcation, Lyapunov stability, LabVIEW, FPGA
Status Before proofreading
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