Time delay Duffing’s systems: chaos and chatter control

Rusinek, Rafał; Mitura, Andrzej; Warmiński, Jerzy

doi:10.1007/s11012-014-9874-4

Cited by 15 publications

(5 citation statements)

References 27 publications

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“…As the control uses the current state and one delay period, when the perturbation is small it presents low-quality stabilization, for example during high periodic orbits [27].…”

Section: Tdasmentioning

confidence: 99%

Analysis and Control of Chaos in the Boost Converter with ZAD, FPIC, and TDAS

2022

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This paper presents an analysis and control of chaos in the boost converter controlled with zero average dynamics, fixed-point induced control, and time-delayed autosynchronization techniques. First, the existence of chaos is demonstrated numerically when positive Lyapunov exponents are found in the controlled system, for a range from k1=−0.26 to k1=0.4387, when k2=0.5. Additionally, chaos is also found for a range from k1=−0.435 to k1=0.26, when k2=−0.5. Subsequently, fixed-point-induced control and time-delayed autosynchronization techniques are used to control the chaos. The results show that both techniques are useful to control the chaos in the boost converter. Furthermore, the fixed-point-induced control technique allows better regulation than the time-delayed autosynchronization technique. Moreover, when only the fixed-point induced control technique is used on the boost converter with a time delay, the results were not good enough to stabilize orbits. The stability is validated by calculating the Lyapunov exponents.

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“…As the control uses the current state and one delay period, when the perturbation is small it presents low-quality stabilization, for example during high periodic orbits [27].…”

Section: Tdasmentioning

confidence: 99%

Analysis and Control of Chaos in the Boost Converter with ZAD, FPIC, and TDAS

2022

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“…In order to demonstrate the proposed method for solving the fractional order derivatives and/or delayed systems, three numerical examples which have been taken from recent publications (Leung, Guo, and Myers 2012;Leung, Yang, and Zhu 2014;Rusinek, Mitura, and Warminski 2014) are considered. The equations of motion are given by:…”

Section: System Equations Of Motionmentioning

confidence: 99%

“…The structural parameters is taken from an example in Eq. (7) of Rusinek, Mitura, and Warminski (2014). The first ten integer harmonic numbers are kept in the multiharmonic expansion, otherwise metioned.…”

Section: Optimization Problem Formulationmentioning

confidence: 99%

Stability analysis of duffing oscillator with time delayed and/or fractional derivatives

Liao

2015

Mechanics Based Design of Structures and Machines

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The periodic motions of the fractional order and/or delayed nonlinear systems are investigated in the frequency domain using a harmonic balance method with the analytical gradients of the nonlinear quality constraints and the sensitivity information of the Fourier coefficients can also obtained. The properties of fractional order derivatives and trigonometric functions are utilized to construct the fractional order derivatives, delayed and product operational matrices. The operational matrices are used to derive the analytical formulas of nonlinear systems of algebraic equations. The stability of periodic solutions for the delayed nonlinear systems is identified by an eigenvalue analysis of quasi polynomials characteristic equations. Sensitivity analysis is performed to study the influence of the structural parameters on the system responses. Finally, Downloaded by [New York University] at 04:02 25 July 2015 2three numerical examples are presented to illustrate the validity and feasibility of the developed method. It is concluded that the proposed methodology has the potential to facilitate highly efficient optimization, as well as sensitivity and uncertainty analysis of nonlinear systems with fractional derivatives and/or time delayed.

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“…From the current theoretical researches and experimental verifications, we found that chattering impact leads to energy transfer and dissipation, causes the system vibration and noise, and reduces mechanical efficiency. Accordingly, many scholars have devoted to the study of chattering prediction and suppression, reducing or eliminating the harm of chattering-impact vibration to the system [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Effects of Differently Located Clearance on the Dynamic Responses of a Two‐Degree‐of‐Freedom Vibration System

Yang

Luo

2021

Shock and Vibration

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The mechanical model of a two-degree-of-freedom forced harmonic vibration system with multiclearance rigid constraints is established, considering the location schemes of symmetrical both-sided clearance and asymmetrical multiple clearance. Existence domains, correlative distributions, and bifurcation scenarios of periodic vibrations are analyzed using multiparameter and multiperformance cosimulation. Pattern diversity, distribution, and occurrence mechanism of the subharmonic impact motion sequences in the tongue-shaped transition regions among the neighboring fundamental periodic motions of the vibration systems are investigated. The emergent behavior of sticking process of fundamental periodic vibration, the occurrence law of chattering-impact motion, and the interaction of different modes of sticking are discussed. According to the sampling ranges of parameters, three multiple heterogeneous constraint conditions are explored; the effects of differently clearance location and values on the dynamic responses and the transition region of fundamental periodic vibrations and subharmonic motions are particularly analyzed. Hence, the reasonable clearance arrangement scheme and numerical optimization combination are determined and the ideal parameter domain of the vibration system is obtained.

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Time delay Duffing’s systems: chaos and chatter control

Cited by 15 publications

References 27 publications

Analysis and Control of Chaos in the Boost Converter with ZAD, FPIC, and TDAS

Analysis and Control of Chaos in the Boost Converter with ZAD, FPIC, and TDAS

Stability analysis of duffing oscillator with time delayed and/or fractional derivatives

Effects of Differently Located Clearance on the Dynamic Responses of a Two‐Degree‐of‐Freedom Vibration System

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