scholarly journals Synchronization of the Fractional-Order Brushless DC Motors Chaotic System

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Shiyun Shen ◽  
Ping Zhou
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Direct Method ◽  
Fractional Order Systems ◽  
Lyapunov Direct Method ◽  
Brushless Dc Motors ◽  
Brushless Dc ◽  
Dc Motors ◽  
Synchronization Scheme

Based on the extension of Lyapunov direct method for nonlinear fractional-order systems, chaos synchronization for the fractional-order Brushless DC motors (BLDCM) is discussed. A chaos synchronization scheme is suggested. By means of Lyapunov candidate function, the theoretical proof of chaos synchronization is addressed. The numerical results show that the chaos synchronization scheme is valid.

scholarly journals Stabilization of the FO-BLDCM Chaotic System in the Sense of Lyapunov

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Ping Zhou ◽  
Rongji Bai ◽  
Hao Cai
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Direct Method ◽  
Order System ◽  
Lyapunov Direct Method ◽  
Brushless Dc Motors ◽  
Brushless Dc ◽  
Dc Motors ◽  
System A ◽  
Control Scheme

Based on an integer-order Brushless DC motors (IO-BLDCM) system, we give a fractional-order Brushless DC motors (FO-BLDCM) system in this paper. There exists a chaotic attractor for fractional-order0.95<q≤1in the FO-BLDCM system. Furthermore, using the Lyapunov direct method for fractional-order system, a control scheme is proposed to stabilize the FO-BLDCM chaotic system in the sense of Lyapunov. Numerical simulation shows that the control scheme in this paper is valid for the FO-BLDCM chaotic system.

Chaos Synchronization of Fractional-Order Lur’e Systems

2020 ◽  
Vol 30 (14) ◽  
pp. 2050206
Author(s):  
Mohammed Salah Bouridah ◽  
Toufik Bouden ◽  
Müştak Erhan Yalçin
Keyword(s):  
Fractional Order ◽  
Chaos Synchronization ◽  
Direct Method ◽  
Linear Matrix ◽  
Lyapunov Direct Method ◽  
Lur’E Systems ◽  
Controller Gain ◽  
Error System ◽  
Synchronization Scheme ◽  
Order Four

Based on some essential concepts of fractional calculus and the theorem related to the fractional extension of Lyapunov direct method, we present in this paper a synchronization scheme of fractional-order Lur’e systems. A quadratic Lyapunov function is chosen to derive the synchronization criterion. The derived criterion is a suffcient condition for the asymptotic stability of the error system, formulated in the form of linear matrix inequality (LMI). The controller gain can be achieved by solving the LMI. The proposed scheme is illustrated for fractional-order Chua’s circuits and fractional-order four-cell CNN. Numerical results, which agree well with the proposed theorem, are given to show the effectiveness of this scheme.

scholarly journals Control and Synchronization of the Fractional-Order Lorenz Chaotic System via Fractional-Order Derivative

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Ping Zhou ◽  
Rui Ding
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Stability Theory ◽  
Chaos Synchronization ◽  
Equilibrium Points ◽  
Order Derivative ◽  
Fractional Order Systems ◽  
Fractional Order Derivative ◽  
Lorenz Chaotic System ◽  
Control And Synchronization

The unstable equilibrium points of the fractional-order Lorenz chaotic system can be controlled via fractional-order derivative, and chaos synchronization for the fractional-order Lorenz chaotic system can be achieved via fractional-order derivative. The control and synchronization technique, based on stability theory of fractional-order systems, is simple and theoretically rigorous. The numerical simulations demonstrate the validity and feasibility of the proposed method.

scholarly journals Circuit Implementation Synchronization between Two Modified Fractional-Order Lorenz Chaotic Systems via a Linear Resistor and Fractional-Order Capacitor in Parallel Coupling

2021 ◽  
Vol 2021 ◽  
pp. 1-8 ◽  
Author(s):  
Juan Liu ◽  
Xuefeng Cheng ◽  
Ping Zhou
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
Lorenz Chaotic System ◽  
Simulation Results ◽  
Synchronization Scheme

In this study, a modified fractional-order Lorenz chaotic system is proposed, and the chaotic attractors are obtained. Meanwhile, we construct one electronic circuit to realize the modified fractional-order Lorenz chaotic system. Most importantly, using a linear resistor and a fractional-order capacitor in parallel coupling, we suggested one chaos synchronization scheme for this modified fractional-order Lorenz chaotic system. The electronic circuit of chaos synchronization for modified fractional-order Lorenz chaotic has been given. The simulation results verify that synchronization scheme is viable.

scholarly journals Stability Analysis of Fractional-Order Nonlinear Systems with Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Yu Wang ◽  
Tianzeng Li
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Fractional Order ◽  
Direct Method ◽  
Sufficient Conditions ◽  
Delay System ◽  
Fractional Order Systems ◽  
Lyapunov Direct Method ◽  
Definition Of ◽  
Fractional Order Nonlinear System

Stability analysis of fractional-order nonlinear systems with delay is studied. We propose the definition of Mittag-Leffler stability of time-delay system and introduce the fractional Lyapunov direct method by using properties of Mittag-Leffler function and Laplace transform. Then some new sufficient conditions ensuring asymptotical stability of fractional-order nonlinear system with delay are proposed firstly. And the application of Riemann-Liouville fractional-order systems is extended by the fractional comparison principle and the Caputo fractional-order systems. Numerical simulations of an example demonstrate the universality and the effectiveness of the proposed method.

Recent Challenges and Advances in the Sensorless Commutation of Brushless DC Motors

2020 ◽  
Vol 13 ◽  
Author(s):  
Umesh Kumar Soni ◽  
Ramesh Kumar Tripathi
Keyword(s):  
Initial Position ◽  
Position Estimation ◽  
Current Response ◽  
Flux Linkage ◽  
Brushless Dc Motors ◽  
Position Sensing ◽  
Brushless Dc ◽  
Dc Motors ◽  
Reverse Torque ◽  
Position Detection

Background: Brushless DC motors are highly efficient motors due to its high torque to weight ratio, compact design, high speed operating capability and higher power density. Conventional Hall sensor based rotor position sensing is affected by the heating, vibration, interference and noise. Objective: The innovative, cost effective and easily implementable sensorless techniques are essential in order to achieve high efficiency, reduced current and reduced torque pulsations. Further, a delay free, high load fast startup is also important issue. Methods: In this paper an extensive review of various techniques based on the detection of freewheeling diode current, phase back EMF zero crossoing point detection, back EMF integration method and third harmonic back EMF was done. The study and effect of various PWM strategies on back EMF detection was studied. Later on the sensorless schemes based on flux linkage estimation and flux linkage increment were introduced. The load torque observers, unknown input observers, sliding mode observers, L∞-induced observers, H ∞ - deconvolution filter for back EMF estimation were also reviewed. As the brushless DC motors have no back EMF at starting and for back EMF based commutation a minimum speed is required for sufficient back EMF. Therefore various strategies of open and close-loop reduced current startup have been studied to achieve effective commutation without reverse torque. Initial position detection (IPD) schemes, which are mostly based on saliency and current response to inductance variation, is effective where reverse torque is strictly prohibited. A detailed review of these initial position detection techniques (IPD) has also been presented. Results: The detailed mathematical and graphical analysis has been presented here in order to understand the working of the state-of-art sensorless techniques. Conclusion: The back EMF detection using direct and indirect methods of terminal voltage filtering have the problem of delay and attenuation, PWM noise, freewheeling diode spikes and disturbance in detected back EMFs is a drawback. The parameter detuning, underestimation and overestimation, offset problem, system noise and observer gain variation etc. limit the applicability of observer based technique. Therefore, a more robust and precise position estimation scheme is essential.

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