Control of Chua's Circuit

Baker, D.C.; Burden, John

doi:10.1142/9789812798855_0027

Cited by 7 publications

(9 citation statements)

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“…Figure 5(d) shows the sliding surface without large changing in this case. These results show that the proposed control scheme results in fast setting time and smaller maximum control input by comparing against those obtained by state space techniques [Hartly & Mossayebi, 1993] and [Hwang et al, 1996]. The comparison is shown in Table 1.…”

Section: Regulation Of the Desired States Without Disturbancementioning

confidence: 78%

“…Considering a cubic Chua's circuit with disturbances, a control signal u is applied to the third state which would represent the addition of a voltage source in series with the inductor [Hartly & Mossayebi, 1993]. The dynamics of the controlled system can be described aṡ…”

Section: The Cubic Chua's Circuit Systemmentioning

confidence: 99%

“…From the typical root locus analysis of a linearized cubic Chua's circuit system [Hartly & Mossayebi, 1993], the result indicated that the control of state x 1 is the most difficult. In this study, the control objective is to regulate state x 1 (t) to the desired state…”

Section: Control Of the Cubic Chua's Circuit Systemmentioning

confidence: 99%

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Sliding Mode Control of Chaos in the Cubic Chua's Circuit System

Jang

Chen

2002

Int. J. Bifurcation Chaos

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In this paper, a sliding mode controller is applied to control the cubic Chua's circuit system. The sliding surface of this paper used is one dimension higher than the traditional surface and guarantees its passage through the initial states of the controlled system. Therefore, using the characteristic of this sliding mode we aim to design a controller that can meet the desired specification and use less control energy by comparing with the result in the current existing literature. The results show that the proposed controller can steer Chua's circuit system to the desired state without the chattering phenomenon and abrupt state change.

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Section: Regulation Of the Desired States Without Disturbancementioning

confidence: 78%

Section: The Cubic Chua's Circuit Systemmentioning

confidence: 99%

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Sliding Mode Control of Chaos in the Cubic Chua's Circuit System

Jang

Chen

2002

Int. J. Bifurcation Chaos

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“…One of the smooth functions similar to the original three-segment piecewise-linear nonlinearity is a cubic polynomial. Several papers chose Chua's circuit with a cubic nonlinearity [Altman, 1993a[Altman, , 1993bHuang et al, 1996;Hartley, 1993;Khibnik et al, 1993;Zhong, 1994;Pivka et al, 1996;Bykov, 1998;Tang & Man, 1998;Liao & Chen, 1998;Yang et al, 1998;Algaba et al, 1999Algaba et al, , 2000Algaba et al, , 2001Eltawil & Elwakil, 1999;Collantes & Suarez, 2000;Ge & Wang, 2000;Yang & Chua, 2001;Jang et al, 2002;O'Donoghue et al, 2005]. A cubic nonlinearity can also be realized by simple practical circuits [O'Donoghue et al, 2005].…”

Section: Piecewise-linear and Cubic Nonlinearitymentioning

confidence: 99%

A Gallery of Attractors From Smooth Chua's Equation

Tsuneda

2005

Int. J. Bifurcation Chaos

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In this tutorial paper, we present some interesting phenomena from Chua's equation with a cubic nonlinearity as well as that with a piecewise-linear characteristic, where a cubic polynomial approximates the original three-segment piecewise-linear function. A gallery of attractors and bifurcation diagrams obtained by numerical simulations are presented. We hope this will motivate researchers to study the smooth version of this extremely simple yet versatile equation with more than 20 attractors.

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“…The original Chua's circuit system contains a piecewise linear resistor. Hartley [10] suggested that the piecewise linear function can be replaced by a cubic polynomial with no major change in the system's dynamical characteristics. For chaos control of modified Chua's circuit system, there is an ocean of excellent works, see the monographs [1,3,6,[17][18][19][20][21] and references therein.…”

Section: Introductionmentioning

confidence: 99%