Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems

2017 ◽  
Vol 6 (2) ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Anitha Karthikeyan ◽  
Prakash Duraisamy
Keyword(s):  
Permanent Magnet ◽  
Fractional Order ◽  
Dynamic Properties ◽  
Synchronous Generator ◽  
Adaptive Controller ◽  
Control Technique ◽  
Order Model ◽  
Permanent Magnet Synchronous Generator ◽  
Chaos Suppression ◽  
Fractional Order Model

AbstractIn this paper we investigate the control of three-dimensional non-autonomous fractional-order 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. An adaptive controller is 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.

Chaos Suppression in Fractional Order Permanent Magnet Synchronous Motor and PI controlled Induction motor by Extended Back stepping Control

2016 ◽  
Vol 5 (4) ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Anitha Karthikeyan ◽  
Prakash Duraisamy
Keyword(s):  
Permanent Magnet ◽  
Induction Motor ◽  
Fractional Order ◽  
Permanent Magnet Synchronous Motor ◽  
Synchronous Motor ◽  
Control Technique ◽  
Order Model ◽  
Chaos Suppression ◽  
Fractional Order Model ◽  
Back Stepping Control

AbstractIn this paper we investigate the control of three-dimensional non-autonomous fractional-order model of a permanent magnet synchronous motor (PMSM) and PI controlled fractional order Induction motor via recursive extended back stepping control technique. A robust generalized weighted controllers are derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the 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.

Switched Fractional Order Model Reference Adaptive Control for an Automatic Voltage Regulator

2021 ◽  
Author(s):  
Norelys Aguila-Camacho ◽  
Jorge E. García-Bustos ◽  
Eduardo I. Castillo-López
Keyword(s):  
Fractional Order ◽  
Adaptive Controller ◽  
System Response ◽  
Voltage Regulator ◽  
Order Model ◽  
Model Reference ◽  
Fractional Order Model ◽  
Automatic Voltage Regulator ◽  
Adaptive Laws ◽  
Model Reference Adaptive

Abstract This paper presents the design and implementation of a Switched Fractional Order Model Reference Adaptive Controller (SFOMRAC) for an Automatic Voltage Regulator (AVR). The fractional orders, adaptive gains and switching times of the controller adaptive laws are tuned offline, using Particle Swarm Optimization (PSO). The functional to be optimized contains not only parameters of the AVR response but also the control energy. The obtained controllers are compared to non switched Integer Order Model Reference Adaptive Controller (IOMRAC) and non switched Fractional Order Model Reference Adaptive Controller (FOMRAC) proposed previously for this process, showing that the SFOMRAC can improve both, the system response and the control energy used.

scholarly journals Dynamic Analysis of the Viscoelastic Pipeline Conveying Fluid with an Improved Variable Fractional Order Model Based on Shifted Legendre Polynomials

2019 ◽  
Vol 3 (4) ◽  
pp. 52
Author(s):  
Yuanhui Wang ◽  
Yiming Chen
Keyword(s):  
Numerical Method ◽  
Fractional Order ◽  
Legendre Polynomials ◽  
Dynamic Properties ◽  
Fluid Velocity ◽  
Nonlinear Function ◽  
Order Model ◽  
Shifted Legendre Polynomials ◽  
Fractional Order Model ◽  
Conveying Fluid

Viscoelastic pipeline conveying fluid is analyzed with an improved variable fractional order model for researching its dynamic properties accurately in this study. After introducing the improved model, an involuted variable fractional order, which is an unknown piecewise nonlinear function for analytical solution, an equation is established as the governing equation for the dynamic displacement of the viscoelastic pipeline. In order to solve this class of equations, a numerical method based on shifted Legendre polynomials is presented for the first time. The method is effective and accurate after the numerical example verifying. Numerical results show that how dynamic properties are influenced by internal fluid velocity, force excitation, and variable fractional order through the proposed method. More importantly, the numerical method has shown great potentials for dynamic problems with the high precision model.

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