Bifurcation Analysis and Chaos Control of a Fractional Order Portal Frame with Nonideal Loading Using Adaptive Sliding Mode Control

Rajagopal, Karthikeyan; Karthikeyan, Anitha; Duraisamy, Prakash

doi:10.1155/2017/2321060

Cited by 6 publications

(4 citation statements)

References 41 publications

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“…The sliding mode control is free from chattering effects, so it is more suitable for control of complex nonlinear systems like the fractional-order Willamowski-Rössler chemical system [5]. For systems suffering from external disturbances and/or parameter uncertainties, the sliding mode controller adapts to the sliding condition first so the adaptive sliding mode control algorithm is introduced [7]. Nonlinear phenomena in complex systems such as voltage collapse and oscillatory phenomenon in power systems can be studied using the chaos theory.…”

Section: Chaos Suppression In the Phase Converter Circuitmentioning

confidence: 99%

“…Nonlinear behaviors, especially chaotic phenomena of the three-phase voltage source inverter (VSI) with hysteresis current comparator, are studied [3]. Chaotic behavior of various types of switching converters is discussed in [2,[4][5][6][7]; the analytical model of switching converters with piecewise switched circuits is developed during the 1970s. The changes in the switching state in power converters results in nonsmooth system trajectories, and hence, it demands nonlinear methods for analysis.…”

Section: Introductionmentioning

confidence: 99%

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No Chattering and Adaptive Sliding Mode Control of a Fractional‐Order Phase Converter with Disturbances and Parameter Uncertainties

et al. 2018

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Discussing the dynamical properties of various power system models is of significant importance in order to understand its complete behavior. Even though there are many literatures discussing about the chaotic behavior shown by phase converter circuits, none of them have reported the hazardous phenomenon of multistability. In this paper, we derive the fractional-order model of a phase converter circuit and investigate its dynamics. Bifurcation of the system with the parameters and fractional order are investigated. A forward and backward continuation scheme is adopted to display various coexisting attractors; the property of multistability is also discussed. Using forward and backward continuation, various coexisting attractors and the property of multistability are discussed. Two different sliding mode controllers for controlling chaotic oscillations with model disturbances and parameter uncertainties are derived, and the effectiveness of the controllers is discussed with numerical simulations.

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Section: Chaos Suppression In the Phase Converter Circuitmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

No Chattering and Adaptive Sliding Mode Control of a Fractional‐Order Phase Converter with Disturbances and Parameter Uncertainties

et al. 2018

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“…Observing how many coexisting attractors are present in the system and investigating the parameter range and corresponding initial conditions are very important. Many literatures showed the coexistence of attractors in mechanical systems and studied their behaviors [24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Route to Chaos and Bistability Analysis of Quasi-Periodically Excited Three-Leg Supporter with Shape Memory Alloy

2020

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In this paper, the effect of quasi-periodic excitation on a three-leg supporter configured with shape memory alloy is investigated. We derived the equation of motion for the system using the supporter configuration and polynomial constitutive model of the shape memory alloys (SMAs) based on Falk model. Two sets of parameters and symmetric initial conditions are used to analyze the system. The system responded with a chaotic attractor and a strange nonchaotic attractor. Coexistence of these attractors is studied and discussed with corresponding phase portrait, bifurcation plot, and cross section of basin of attraction. We confirm the quasi-periodic excitation results with generation of strange nonchaotic attractors as discussed in the literature. The special properties like symmetricity and bistability are revealed and the parameter ranges of existence of such behaviors are discussed. The system is analyzed for different phases and the existence of bistability in martensite phase and transition phase is explained. While the system enters into austenite phase, the bistability behavior vanishes. The results provide insight knowledge into dynamical response of a quasi-periodically excited SMA leg support system and will be useful for design improvements and controller design.

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“…Some of the common applications of chaotic systems in science and engineering are chemical reactors, Brusselators, dynamos, tokamak systems, biology models, neurology, ecology models, and memristive devices. Chaotic phenomenon was observed in several mechanical systems [2]. Chaos may be described as bounded random like motion exhibited by deterministic nonlinear systems characterized by their sensitivity to initial conditions.…”

Section: Introductionmentioning

confidence: 99%

Multistability in Horizontal Platform System with and without Time Delays

Rajagopal

Duraisamy

Weldegiorgis

2018

Shock and Vibration

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Chaotic behavior and bifurcation analysis of horizontal platform systems (HPS) have been investigated widely by many researchers. However, the multistable features of such systems have not been investigated, and hence we identified the multistable parameter and investigated the coexisting attractors of the HPS. To understand the effects of time delays on the nonautonomous and autonomous HPS, we introduced a constant time delay in the state feedback variable. Investigation of the bifurcation of the time delayed HPS with time delay and parameters reveals that the system behavior differs between the autonomous and nonautonomous HPS. To investigate the multistability existence in time delayed HPS, we plot the bifurcation of the autonomous HPS and show the multistability and coexisting attractors.

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Bifurcation Analysis and Chaos Control of a Fractional Order Portal Frame with Nonideal Loading Using Adaptive Sliding Mode Control

Cited by 6 publications

References 41 publications

No Chattering and Adaptive Sliding Mode Control of a Fractional‐Order Phase Converter with Disturbances and Parameter Uncertainties

No Chattering and Adaptive Sliding Mode Control of a Fractional‐Order Phase Converter with Disturbances and Parameter Uncertainties

Route to Chaos and Bistability Analysis of Quasi-Periodically Excited Three-Leg Supporter with Shape Memory Alloy

Multistability in Horizontal Platform System with and without Time Delays

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