Nonlinear Control of Chaotic Circuits (original) (raw)
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Chaos control of the modified Chua’s circuit system
Physica D-nonlinear Phenomena, 2002
In this paper, a nonlinear controller called the backstepping controller is applied to suppress the chaotic motion of a modified Chua's circuit system. The new controller can drive the system to the exact reference state at any prescribed speed. Most importantly, the controller achieves global exponential stability in the sense that the attraction basin for the reference state is the entire state space. Previous controllers for the Chua's circuit can achieve only local stability in the sense that the attraction basin is a subset of the state space.
Nonlinear and Chaotic Circuits
We studied the behavior of nonlinear and chaotic circuits. The resonant frequency of an LRC circuit was experimentally determined, and the circuit was compared to a diodeinductor-resistor (DLR) circuit to explore the transition from nonlinearity to chaos. The internal resistance of the LRC inductor was found to be 123 ± 2 Ω, while the low amplitude diode capacitance of the DLR circuit was found to be 55.6 ± 0.7 pF. With the aid of a fast-Fourier-transform (FFT) oscilloscope function, four regimes of behavior in the DLR circuit were studied. Finally, an experiment on Chua's strange attractor circuit is proposed as a future project.
A Comprehensive Study and Analysis of the Chaotic Chua Circuit
Iraqi journal of science, 2022
was studied by taking several different values for the constant α and fixing the other three variables β, c and d with the values 25.58,-0.7142857, and-1.142, respectively. The purpose of this paper is to know the values by which the system transforms from a steady state to a chaotic state under the initial conditions x, y, and z that equal-1.6, 0 and 1.6 respectively. It was found that when the value of α is equal to 0, the Chua system is in a steady state, and when the value of α is equal to 9.5 and the wave is sinusoidal, the system is in oscillation, and when α is equal 13.4 the system is in a Quasi-chaotic state, and finally the system turns to the chaotic state when the value of α equals 15.05.
Chaotic dynamics with high complexity in a simplified new nonautonomous nonlinear electronic circuit
Chaos, Solitons & Fractals, 2009
A two dimensional nonautonomous dissipative forced series LCR circuit with a simple nonlinear element exhibiting an immense variety of dynamical features is proposed for the first time. Unlike the usual cases of nonlinear element, the nonlinear element used here possesses three segment piecewise linear character with one positive and one negative slope. This nonlinearity is verified to be sufficient to produce chaos with high complexity in many established nonautonomous nonlinear circuits, such as MLC, MLCV, driven Chua, etc., thus indicating an universal behavior similar to the familiar Chua's diode. The dynamics of the proposed circuit is studied experimentally, confirmed numerically, simulated through PSPICE and proved mathematically. An important feature of the circuit is its ability to show dual chaotic behavior.
Nonlinear electronic circuit, Part I: Multiple routes to chaos
Nonlinear Analysis: Theory, Methods & Applications, 2009
A nonlinear electronic oscillator, suitable for synchronized chaotic communication, is studied. This circuit is capable of transmitting discrete chaotic signals, although the chaotic modes of operation are controlled in an analog way. In Part I of this review paper the three routes to chaotic operation that appear, namely the period doubling, intermittency and crisis induced intermittency, are thoroughly studied and discussed. In all three routes to chaos the appropriate experimental distributions were calculated. Moreover, the chaotic nature of the circuit operation was evaluated by using the Grassberger-Procaccia method. Calculation of the corresponding minimum embedding dimension, the Kolmogorov-Sinai entropy as well as the maximal Lyapunov exponent give useful information in order to fully characterize the circuit operation.
Analysis, nonlinear control, and chaos generator circuit of another strange chaotic system
2012
In this paper, we introduce a new 3-dimensional quadratic continuous autonomous chaotic system. This system can generate strange and interesting attractors. Some basic dynamical properties, such as bifurcations, and chaotic behaviors of the new chaotic system are investigated analytically and numerically. We propose a nonlinear control scheme to discuss codimension 1 and 2 Hopf bifurcations. In addition, a new circuit implementation of the chaotic attractor is reported and examined in PSpice. The new system is suitable for purposefully generating chaos in chaos-based engineering applications.
IEEE Transactions on Circuits and Systems I-regular Papers, 2001
Two generic classes of chaotic oscillators comprising four different configurations are constructed. The proposed structures are based on the simplest possible abstract models of generic second-order RC sinusoidal oscillators that satisfy the basic condition for oscillation and the frequency of oscillation formulas. By linking these sinusoidal oscillator engines to simple passive first-order or second-order nonlinear composites, chaos is generated and the evolution of the two-dimensional sinusoidal oscillator dynamics into a higher dimensional state space is clearly recognized. We further discuss three architectures into which autonomous chaotic oscillators can be decomposed. Based on one of these architectures we classify a large number of the available chaotic oscillators and propose a novel reconstruction of the classical Chua's circuit. The well-known Lorenz system of equations is also studied and a simplified model with equivalent dynamics, but containing no multipliers, is introduced.
Dynamical Analysis, Electronic Circuit Design and Control Application of a Different Chaotic System
2020
In this study, the dynamic behavior of a chaotic system is explored and its dynamical analysis is performed by Lyapunov exponents, fractional dimension, dependence to initial conditions and bifurcation diagram. In addition, the bifurcation analysis of the system is studied with respect to a certain parameter. The electronic circuit implementation of a chaotic system is realized and compared with the phase portraits obtained from Matlab and circuit realization. Also, passive control technique is applied to stabilize and suppress the chaos in the chaotic system. Numerical simulations are presented to verify the theoretical analysis and the effectiveness of the proposed control method.
Chaotic Mathematical Circuitry
A Festschrift for Leon ChuaWith DVD-ROM, composed by Eleonora Bilotta, 2013
Following the worldwide tradition of use of Chuas circuits for various purposes, we introduce the paradigm of chaotic mathematical circuitry which shows some similarity to the paradigm of electronic circuitry-the design of electronic circuit-especially in the frame of chaotic attractors. An electronic circuit is composed of individual electronic components, such as capacitors, diodes, inductors, resistors, transistors and connected by conductive wires. Recently, in 2009, three more components discovered by L. O. Chua have been added to the set of devices, namely: memristors, memcapacitors and meminductors. In the same way a mathematical circuit is composed of individual components we design: generators, couplers, samplers, mixers, reducers and cascaders, connected by streams of data. The combination of such mathematical components allows many new applications in chaotic cryptography, genetic algorithms in optimization or in control.