Adaptive Synchronization of Chaotic Brushless DC Motors with Uncertain System Parameters Based on Lyapunov Stability theory

Author(s):  
Mu Feng Wang ◽  
Du Qu Wei
2008 ◽  
Vol 22 (15) ◽  
pp. 2453-2461 ◽  
Author(s):  
XINGYUAN WANG ◽  
YONG WANG

This paper analyzes the synchronization control of new chaotic systems called Lorenz-like systems. Based on the Lyapunov stability theory, an adaptive controller and a parameter update rule are designed. It is proved that the controller and update rule not only achieve self-synchronization of Lorenz-like systems but can also make the Lorenz-like system asymptotically synchronized with the Rössler system, and further identify the uncertain system parameters. Numerical simulations have shown the effectiveness of the adaptive controller.


2013 ◽  
Vol 401-403 ◽  
pp. 1657-1660
Author(s):  
Bin Zhou ◽  
Xiang Wang ◽  
Yu Gao ◽  
Shao Cheng Qu

An adaptive controller with adaptive rate is presented to synchronize two chaos systems and to apply to secure communication. Based on Lyapunov stability theory, a sufficient condition and adaptive control parameters are obtained. Finally, the simulation with synchronization and secure communication is given to show the effectiveness of the proposed method. Keywords: adaptive; synchronization; observer; controller.


2008 ◽  
Vol 22 (08) ◽  
pp. 1015-1023 ◽  
Author(s):  
XINGYUAN WANG ◽  
XIANGJUN WU

This paper studies the adaptive synchronization and parameter identification of an uncertain hyperchaotic Chen system. Based on the Lyapunov stability theory, an adaptive control law is derived to make the states of two identical hyperchaotic Chen systems asymptotically synchronized. With this approach, the synchronization and parameter identification of the hyperchaotic Chen system with five uncertain parameters can be achieved simultaneously. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.


2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Phuong Dam Thanh ◽  
Cat Pham Thuong

The problem of synchronization of chaotic State Controlled Cellular Neural Network (SC-CNN) with uncertain state template is investigated. In detail, the following three cases are solved: firstly, synchronization of two identical chaotic SC-CNNs with uncertain state template, secondly, synchronization of two nonidentical chaotic SC-CNNs with all uncertain state templates, and, thirdly, synchronization between chaotic SC-CNN with uncertain state template and different uncertain parameter chaotic systems. The controllers and update laws proposed in each case are proved closely based on Lyapunov stability theory. In addition, some illustrative corresponding examples are presented to demonstrate the effectiveness and usefulness of the proposed control laws.


2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Weiping Wang ◽  
Lixiang Li ◽  
Haipeng Peng ◽  
Jialiang Yuan ◽  
Jinghua Xiao ◽  
...  

This paper studies the synchronization of complex dynamical networks with multilinks and similar nodes. The dynamics of all the nodes in the networks are impossible to be completely identical due to the differences of parameters or the existence of perturbations. Networks with similar nodes are universal in the real world. In order to depict the similarity of the similar nodes, we give the definition of the minimal similarity of the nodes in the network for the first time. We find the threshold of the minimal similarity of the nodes in the network. If the minimal similarity of the nodes is bigger than the threshold, then the similar nodes can achieve synchronization without controllers. Otherwise, adaptive synchronization method is adopted to synchronize similar nodes in the network. Some new synchronization criteria are proposed based on the Lyapunov stability theory. Finally, numerical simulations are given to illustrate the feasibility and the effectiveness of the proposed theoretical results.


2014 ◽  
Vol 28 (05) ◽  
pp. 1450014
Author(s):  
PI LI ◽  
XING-YUAN WANG ◽  
PENG SUN ◽  
CHAO LUO ◽  
XIU-KUN WANG

In this paper, active control and adaptive control methods are applied, respectively. Adaptive control method is implemented when system parameters are unknown and active control method is applied when system parameters are known. Based on the Lyapunov stability theory, the controllers are designed to realize anti-synchronization, meanwhile, the update laws of parameters are proposed. The theoretical proof is given. And two groups of examples are shown to verify the effectiveness of the proposed schemes.


2018 ◽  
Vol 32 (31) ◽  
pp. 1850342 ◽  
Author(s):  
Shuang Liu ◽  
Qingyun Wang

In this paper, a separated sliding mode strategy is proposed for the synchronization of network systems. To break the predicament caused by the inhomogeneity of nodes coupling in complex network, a colored network with different node systems and edges is given. According to the nonlinear subsystem of the colored complex networks, a separated sliding mode controller is designed, while for the linear subsystem, some appropriate system parameters are established to implement synchronization. Then, based on the Lyapunov stability theory, the performance of the sliding mode controller is appraised through the synchronization for the colored networks consisting of different-dimensional systems and nonidentical interactions. In the end, two simulation illustrations are employed to demonstrate the presented control method.


2004 ◽  
Vol 14 (11) ◽  
pp. 3969-3979 ◽  
Author(s):  
E. M. ELABBASY ◽  
H. N. AGIZA ◽  
M. M. EL-DESSOKY

This paper addresses the synchronization problem of two modified Chen systems in the presence of unknown system parameters. One-way coupling and active control laws are applied to achieve the state synchronization of two identical modified Chen systems. Based on Lyapunov stability theory, active control laws are derived such that the two modified Chen systems are to be synchronized. Numerical simulations results are used to demonstrate the effectiveness of the proposed control methods.


2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Fan-di Zhang ◽  
Jin-ping Jia ◽  
Li-xin Yang

This paper investigates the adaptive cluster synchronization in the complex networks with different orders. By means of Lyapunov stability theory and the adaptive control technique, a novel adaptive synchronization controller is developed. To demonstrate the validity of the proposed method, the examples for the synchronization of systems with the chaotic and hyperchaotic node dynamics are presented.


Author(s):  
Umesh Kumar Soni ◽  
Ramesh Kumar Tripathi

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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