Chaos control of third-order phase-locked loops using backstepping nonlinear controller

2004 ◽  
Vol 20 (4) ◽  
pp. 719-723 ◽  
Author(s):  
Ahmad M. Harb ◽  
Bassam A. Harb
Keyword(s):  
Chaos Control ◽  
Phase Locked Loops ◽  
Nonlinear Controller ◽  
Third Order

DYNAMICS AND CHAOS CONTROL OF NONLINEAR SYSTEMS WITH ATTRACTION/REPULSION FUNCTION

2008 ◽  
Vol 18 (08) ◽  
pp. 2345-2371 ◽  
Author(s):  
XIAN LIU ◽  
JINZHI WANG ◽  
ZHISHENG DUAN ◽  
LIN HUANG
Keyword(s):  
Absolute Stability ◽  
Chaos Control ◽  
Linear Matrix ◽  
Chaotic Attractors ◽  
Matrix Inequality ◽  
Third Order ◽  
Simple Method ◽  
Stabilizing Controller ◽  
The Given ◽  
Absolute Stability Theory

In this paper, a more general third-order chaotic system with attraction/repulsion function is introduced on the basis of [Duan et al., 2005]. A gallery of chaotic attractors, bifurcation diagrams and Lyapunov exponent spectra are presented to show the interesting phenomena of the given system. Based on the absolute stability theory and linear matrix inequality (LMI), a simple method of chaos control for the system is proposed and a stabilizing controller is derived such that chaos oscillations of the system disappear and all chaotic trajectories of it are led to certain equilibrium. Numerical simulations are provided to illustrate the efficiency of the proposed method.

Control Chaos of a Nonlinear Circuit System by Two Controllers

2012 ◽  
Vol 433-440 ◽  
pp. 2263-2269
Author(s):  
Bai Zhan Shi ◽  
Xiang Feng Gou ◽  
Quan Lei Chen
Keyword(s):  
Bifurcation Diagram ◽  
Phase Plane ◽  
Control Method ◽  
State Equation ◽  
Phase Portraits ◽  
Negative Capacitance ◽  
Nonlinear Controller ◽  
Third Order ◽  
Controlled System ◽  
Better Than

A third-order circuit system with nonlinear negative capacitance is studied. The dynamical equation and state equation of the system are established. By the phase portraits, the motions of the system are studied under the definite parameters. And by bifurcation diagram, the route from periodic motion to chaos is studied under the presented system parameters. Two controllers are constructed to control the chaos of a third-order circuit system with nonlinear negative capacitance. One controller is nonlinear and the other is linear. The phase plane portraits and bifurcation diagram of the controlled system are obtained. The effect of the nonlinear controller is better than the linear one. The threshold values of the control values of the two control method are obtained. The advantages of the two controlled methods are that the collect of the control signals are simple and can put on any time and the chaotic system can be asymptotically stabilized to equilibriums with small control. The orbits of the system can be controlled by these two methods according to our target.

Chaos control of 4D chaotic systems using recursive backstepping nonlinear controller

2009 ◽  
Vol 39 (1) ◽  
pp. 356-362 ◽  
Author(s):  
J.A. Laoye ◽  
U.E. Vincent ◽  
S.O. Kareem
Keyword(s):  
Chaos Control ◽  
Chaotic Systems ◽  
Nonlinear Controller
Sign in / Sign up

Export Citation Format

Share Document