scholarly journals Hopf Bifurcation and Control of Magnetic Bearing System with Uncertain Parameter

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Jing Wang ◽  
Shaojuan Ma ◽  
Peng Hao ◽  
Hehui Yuan
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
Control Method ◽  
Magnetic Bearing ◽  
Uncertain Parameter ◽  
Equivalent Model ◽  
Linear Feedback ◽  
Feedback Control Method ◽  
And Control ◽  
Bearing System

In this paper, the Hopf bifurcation and control of the magnetic bearing system under an uncertain parameter are investigated. Firstly, the two-degree-of-freedom magnetic bearing system model with uncertain parameter is established. The method of orthogonal polynomial approximation is used to obtain the equivalent magnetic bearing model which is deterministic. Secondly, combining mathematical analysis tools and numerical simulations, the Hopf bifurcation of the equivalent model is analyzed. Finally, a hybrid feedback control method (linear feedback control method combined with nonlinear stochastic feedback control method) is introduced to control the Hopf bifurcation behavior of the magnetic bearing system.

LOCAL BIFURCATION CONTROL IN A ROTOR-MAGNETIC BEARING SYSTEM

2003 ◽  
Vol 13 (04) ◽  
pp. 951-956 ◽  
Author(s):  
J. C. JI ◽  
COLIN H. HANSEN
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
Normal Forms ◽  
Magnetic Bearing ◽  
Linear Feedback ◽  
Nonlinear Feedback Control ◽  
Nonlinear Feedback ◽  
Linear Feedback Control ◽  
Linearized System ◽  
Bearing System

Linear-plus-nonlinear feedback control is used to stabilize Hopf bifurcation in a rotor-magnetic bearing system, for which the linearized system possesses a double zero eigenvalues. The addition of nonlinear (quadratic) terms to the original linear feedback control formulation is used to modify the coefficients of the nonlinear terms in the reduced normal forms. It is found that feedback control incorporating certain quadratic terms renders the Hopf bifurcation supercritical. Finally, illustrative examples are given to verify the analytical results.

scholarly journals Adaptive Control of Chaos in Chua's Circuit

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Weiping Guo ◽  
Diantong Liu
Keyword(s):  
Feedback Control ◽  
Control Method ◽  
Equilibrium Points ◽  
Lyapunov Theory ◽  
Chua’S Circuit ◽  
Control Of Chaos ◽  
Chua's Circuit ◽  
Adaptive Technology ◽  
Feedback Control Method ◽  
And Control

A feedback control method and an adaptive feedback control method are proposed for Chua's circuit chaos system, which is a simple 3D autonomous system. The asymptotical stability is proven with Lyapunov theory for both of the proposed methods, and the system can be dragged to one of its three unstable equilibrium points respectively. Simulation results show that the proposed methods are valid, and control performance is improved through introducing adaptive technology.

scholarly journals Delay Feedback Control of the Lorenz-Like System

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Qin Chen ◽  
Jianguo Gao
Keyword(s):  
Hopf Bifurcation ◽  
Feedback Control ◽  
Control Method ◽  
Functional Differential Equations ◽  
Variable Parameter ◽  
Positive Equilibrium ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Feedback Control Method ◽  
Delay Feedback Control

We choose the delay as a variable parameter and investigate the Lorentz-like system with delayed feedback by using Hopf bifurcation theory and functional differential equations. The local stability of the positive equilibrium and the existence of Hopf bifurcations are obtained. After that the direction of Hopf bifurcation and stability of periodic solutions bifurcating from equilibrium is determined by using the normal form theory and center manifold theorem. In the end, some numerical simulations are employed to validate the theoretical analysis. The results show that the purpose of controlling chaos can be achieved by adjusting appropriate feedback effect strength and delay parameters. The applied delay feedback control method in this paper is general and can be applied to other nonlinear chaotic systems.

scholarly journals Linear Feedback Synchronization Used in the Three-Dimensional Duffing System

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Jian-qun Han ◽  
Xu-dong Shi ◽  
Hong Sun
Keyword(s):  
Feedback Control ◽  
Chaotic System ◽  
Control Method ◽  
Three Dimensional ◽  
Lyapunov Stability Theory ◽  
Linear Feedback ◽  
Nonlinear Feedback ◽  
Linear Feedback Control ◽  
Duffing System ◽  
Feedback Control Method

It has been realized that synchronization using linear feedback control method is efficient compared to nonlinear feedback control method due to the less computational complexity and the synchronization error. For the problem of feedback synchronization of Duffing chaotic system, in the paper, we firstly established three-dimensional Duffing system by method of variable decomposition and, then, studied the synchronization of Duffing chaotic system and designed the control law based on linear feedback control and Lyapunov stability theory. It is proved theoretically that the two identical integer order chaotic systems are synchronized analytically and numerically.

scholarly journals Stabilization of a Class of Complex Chaotic Systems by the Dynamic Feedback Control

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Zhi Liu ◽  
Rongwei Guo
Keyword(s):  
Feedback Control ◽  
Chaotic System ◽  
Control Method ◽  
Linear Feedback ◽  
Dynamic Feedback ◽  
Feedback Control Method ◽  
Dynamic Feedback Control ◽  
Complex Chaotic Systems ◽  
Complex Chaotic System ◽  
Theoretical Results

The stabilization problem of the complex chaotic system is investigated in this paper. First, a systematic method is proposed, by which a given complex chaotic system can be transformed into its equivalent real chaotic system. Then, both simple and physical controller is designed for the corresponding real chaotic system by the dynamic feedback control method, thereby the controller for the original complex chaotic system is obtained. Especially, for some complex system, the controller is obtained by the linear feedback control method. Finally, two illustrative examples with numerical simulations are used to verify the validity and effectiveness of the theoretical results.

EXPERIMENTAL EVIDENCE FOR SPATIOTEMPORAL STABILITY AND CONTROL OF A ONE-WAY OPEN CML

2002 ◽  
Vol 12 (12) ◽  
pp. 2937-2944 ◽  
Author(s):  
TAKUYA IMAI ◽  
KEIJI KONISHI ◽  
HIDEKI KOKAME ◽  
KENTARO HIRATA
Keyword(s):  
Feedback Control ◽  
Experimental Evidence ◽  
Control Method ◽  
Spatiotemporal Chaos ◽  
Coupled Map Lattice ◽  
Delayed Feedback Control ◽  
Electronic Circuits ◽  
Stability And Control ◽  
Feedback Control Method ◽  
And Control

We present an experimental evidence for spatiotemporal stability of a real one-way open coupled map lattice implemented by electronic circuits. Furthermore, it is shown that the decentralized delayed feedback control method can suppress the spatial instability and the spatiotemporal chaos in the coupled map lattice circuits.

Sign in / Sign up

Export Citation Format

Share Document