Dynamics Analysis and Synchronization in Relay Coupled Fractional Order Colpitts Oscillators

2018 ◽  
pp. 317-356
Author(s):  
Kammogne Soup Tewa Alain ◽  
Kengne Romanic ◽  
Ahmad Taher Azar ◽  
Sundarapandian Vaidyanathan ◽  
Fotsin Hilaire Bertrand ◽  
...  
Keyword(s):  
Fractional Order ◽  
Phase Synchronization ◽  
Lyapunov Stability Theory ◽  
Order System ◽  
Colpitts Oscillator ◽  
Multiple Attractors ◽  
Chua’S Oscillator ◽  
Colpitts Circuit ◽  
Innovative Work ◽  
Novel Method

In this chapter, the dynamics of a particular topology of Colpitts oscillator with fractional order dynamics is presented. The first part is devoted to the dynamics of the model using standard nonlinear analysis techniques including time series, bifurcation diagrams, phase space trajectories plots, and Lyapunov exponents. One of the major results of this innovative work is the numerical finding of a parameter region in which the fractional order Colpitts oscillator's circuit experiences multiple attractors' behavior. This phenomenon was not reported previously in the Colpitts circuit (despite the huge amount of related research works) and thus represents an enriching contribution to the understanding of the dynamics of Chua's oscillator. The second part of this chapter deals with the synchronization of fractional order system. Based on fractional-order Lyapunov stability theory, this chapter provides a novel method to achieve generalized and phase synchronization of two and network fractional-order chaotic Colpitts oscillators, respectively.

Nonlinear dynamic system identification using neuro-fractional-order Hammerstein model

2017 ◽  
Vol 40 (13) ◽  
pp. 3872-3883 ◽  
Author(s):  
Mohammad-Reza Rahmani ◽  
Mohammad Farrokhi
Keyword(s):  
Fractional Order ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic System ◽  
Lyapunov Stability Theory ◽  
The State ◽  
Order System ◽  
Hammerstein Model ◽  
Identification Algorithm ◽  
State Variables ◽  
State Matrix

This paper presents a neuro-fractional-order Hammerstein model with a systematic identification algorithm for identifying unknown nonlinear dynamic systems. The proposed model consists of a Radial Basis Function Neural Network (RBF NN) followed by a Fractional-Order System (FOS). The proposed identification scheme is performed in two stages. First, the fractional-order and the number of state variables (or degree) of the state-space realization of the FOS are estimated in the frequency domain. Then, the parameters of the RBF NN (the weights, centers and widths of the Gaussian functions) and the state matrix of the FOS are determined using the time domain data via the Lyapunov stability theory. Simulating as well as experimental examples are provided to verify the effectiveness of the proposed method. The identification results show that the proposed neuro-fractional-order Hammerstein modeling is superior as compared with the existing Hammerstein modeling in literature.

scholarly journals Optimal tuning PID controller of unstable fractional order system by desired transient characteristics using RIM

2019 ◽  
Vol 14 (3) ◽  
pp. 1177
Author(s):  
Phu Tran Tin ◽  
Le Anh Vu ◽  
Minh Tran ◽  
Nguyen Quang Dung ◽  
Tran Thanh Trang
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Interpolation Method ◽  
Optimal Solution ◽  
Practical Method ◽  
Fractional Order System ◽  
Order System ◽  
The Novel ◽  
Transient Characteristics ◽  
Novel Method

<p>In this paper, we propose the method of tuning a conventional PID controller for unstable transient characteristics. The results show that: 1) This is the novel practical method based on the desired settling time and overshoot percentage; 2) The results are close to the desired parameters; 3) The novel method can tune an unstable fractional order system by real interpolation method (RIM); 4) The novel method is simplicity and computer efficiency; 5) The novel method can find an optimal solution for tuning task in both academic and industrial purposes.</p>

Adaptive Synchronization of a Stochastic Fractional-Order System

2015 ◽  
Vol 733 ◽  
pp. 939-942
Author(s):  
Xiao Jun Liu
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Stochastic System ◽  
Fractional Order System ◽  
Adaptive Synchronization ◽  
Order System ◽  
Unknown Parameters ◽  
Adaptive Laws

In this paper, adaptive synchronization of a stochastic fractional-order system with unknown parameters is studied. Firstly, the stochastic system is reduced into the equivalent deterministic one with Laguerre approximation. Then, the synchronization for the system is realized by designing appropriate controllers and adaptive laws of the unknown parameters. Numerical simulations are carried out to demonstrate the effectiveness of the controllers and laws.

A UNIFIED FRAMEWORK FOR SYNCHRONIZATION AND CONTROL OF DYNAMICAL SYSTEMS

1994 ◽  
Vol 04 (04) ◽  
pp. 979-998 ◽  
Author(s):  
CHAI WAH WU ◽  
LEON O. CHUA
Keyword(s):  
Dynamical Systems ◽  
Chaotic Systems ◽  
Main Tool ◽  
Lyapunov Stability Theory ◽  
Asymptotical Stability ◽  
Unified Framework ◽  
Partial Synchronization ◽  
Chua’S Oscillator ◽  
And Control

In this paper, we give a framework for synchronization of dynamical systems which unifies many results in synchronization and control of dynamical systems, in particular chaotic systems. We define concepts such as asymptotical synchronization, partial synchronization and synchronization error bounds. We show how asymptotical synchronization is related to asymptotical stability. The main tool we use to prove asymptotical stability and synchronization is Lyapunov stability theory. We illustrate how many previous results on synchronization and control of chaotic systems can be derived from this framework. We will also give a characterization of robustness of synchronization and show that master-slave asymptotical synchronization in Chua’s oscillator is robust.

scholarly journals Sliding Mode Control and Modified Generalized Projective Synchronization of a New Fractional-Order Chaotic System

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Junbiao Guan ◽  
Kaihua Wang
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Secure Communication ◽  
Sliding Mode ◽  
Projective Synchronization ◽  
Control Technique ◽  
Order System ◽  
Mode Control ◽  
The Stability

A new fractional-order chaotic system is addressed in this paper. By applying the continuous frequency distribution theory, the indirect Lyapunov stability of this system is investigated based on sliding mode control technique. The adaptive laws are designed to guarantee the stability of the system with the uncertainty and external disturbance. Moreover, the modified generalized projection synchronization (MGPS) of the fractional-order chaotic systems is discussed based on the stability theory of fractional-order system, which may provide potential applications in secure communication. Finally, some numerical simulations are presented to show the effectiveness of the theoretical results.

FINDING PARAMETERS FOR CHUA’S OSCILLATOR WHICH IS TOPOLOGICALLY CONJUGATE TO SYSTEMS WITH A SCALAR NONLINEARITY

1995 ◽  
Vol 05 (03) ◽  
pp. 895-899 ◽  
Author(s):  
CHAI WAH WU ◽  
LEON O. CHUA
Keyword(s):  
Vector Field ◽  
Large Class ◽  
Vector Fields ◽  
Colpitts Oscillator ◽  
Chua’S Oscillator ◽  
Scalar Nonlinearity

Chua’s oscillator is topologically conjugate to a large class of vector fields with a scalar non-linearity. In this letter, we give an algorithm which, given a vector field in this class, finds the parameters for Chua’s oscillator for which Chua’s oscillator is topologically conjugate to it. We illustrate this by transforming Sparrow’s system and the chaotic Colpitts oscillator into equivalent Chua’s oscillators.

Sign in / Sign up

Export Citation Format

Share Document