Chaos analysis of Buck converter with non-singular fractional derivative

Liao, Xiaozhong; Ran, Manjie; Yu, Donghui; Lin, Da; Yang, Ruocen

doi:10.1016/j.chaos.2022.111794

Cited by 11 publications

(5 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In further works we will extend the applicability of the combined method of the Modified Atangana-Baleanu fractional derivative and the MHPM to solve other complex phenomena like those described by the fractional Fisher equation, the fractional diffusion equation, the fractional Klein-Gordon equation and other important fractional equations relevant in physics, engineering, and other areas like those discussed previously in the [28][29][30][31][32][33][34][35][36][37][38][39]. In all these research that involves fractional derivatives with non singular fractional to fulfill the Figure 3.…”

Section: Discussionmentioning

confidence: 88%

“…Important real data studies that consider the Atangana-Baleanu fractional derivatives for the diarrhea transmission dynamics, epidemiological model related with the chickenpox disease and for the blood ethanol concentration, have shown that this type of fractional derivative provides better statistical results if they are compared with the same classical models or with Caputo and Caputo-Fabrizio fractional derivatives [28][29][30] . Other recent applications of the non singular kernel fractional derivatives have been considered in real data studies showing that actual capacitors and inductors possess inherently fractional order properties like the dissipative effects into the electrical circuits [31]. Additionally modeling the behavior of cells and tissues and the understanding of the overall biological function and behavior of living systems can be improved using fractional [32]; for example current results have shown that the fractional memory influences induce stabilization of immune systems in such a way that the equilibrium states have been reached with greater efficiency that in classical integer order model [33].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New modied Atangana-Baleanu fractional derivative applied to solve nonlinear fractional dierential equations

Yépez-Martínez¹,

Gómez‐Aguilar²,

İnç³

2023

Phys. Scr.

View full text Add to dashboard Cite

The main goal of this work is to present a new modified version of the Atangana-Baleanu fractional derivative with Mittag-Leffler non-singular kernel and strong memory. This proposal presents important advantages when specific initial conditions are impossed. The new modified version of the Atangana-Baleanu fractional derivative with Mittag-Leffler non-singular kernel has been constructed considering the fulfillment of the initial conditions with special interest because they are decisive in the obtaintion of analytical and numerical solutions of the fractional differential equations. The advantage of this new fractional derivative in the fulfilling of initial conditions plays a central role for the implementation of different perturbative analytical methods, such as the homotopy perturbation method and the modified homotopy perturbation method. These methods will be applied to solve nonlinear fractional differential equations. This novel modified derivative can be applied in the future in different mathematical modeling areas where satisfy the initial conditions is of great relevance to get more accurate description of real-world problems.

show abstract

Section: Discussionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

New modied Atangana-Baleanu fractional derivative applied to solve nonlinear fractional dierential equations

Yépez-Martínez¹,

Gómez‐Aguilar²,

İnç³

2023

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…The C-F definition-based system modeling method can characterize the properties that Caputo definition-based fractional-order models cannot accurately represent [42][43][44][45]. The results indicate that the C-F definition can accurately characterize the nonlinear characteristics of capacitor voltage and inductor current in DC-DC converters, simplify the circuit topology, and make the electrical characteristics of the models closer to the actual circuits [46][47][48]. However, these studies only consider the operating conditions of resistive loads.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Analysis of Caputo–Fabrizio Definition-Based Fractional-Order Boost Converter with Inductive Loads

Yu,

Liao,

Wang

2024

Fractal Fract

Self Cite

View full text Add to dashboard Cite

This paper proposes a modeling and analysis method for a Caputo–Fabrizio (C-F) definition-based fractional-order Boost converter with fractional-order inductive loads. The proposed method analyzes the system characteristics of a fractional-order circuit with three state variables. Firstly, this paper constructs a large signal model of a fractional-order Boost converter by taking advantage of the state space averaging method, providing accurate analytical solutions for the quiescent operating point and the ripple parameters of the circuit with three state variables. Secondly, this paper constructs a small signal model of the C-F definition-based fractional-order Boost converter by small signal linearization, providing the transfer function of the fractional-order system with three state variables. Finally, this paper conducts circuit-oriented simulation experiments where the steady-state parameters and the transfer function of the circuit are obtained, and then the effect of the order of capacitor, induced inductor, and load inductor on the quiescent operating point and ripple parameters is analyzed. The experimental results show that the simulation results are consistent with those obtained by the proposed mathematical model and that the three fractional orders in the fractional model with three state variables have a significant impact on the DC component and steady-state characteristics of the fractional-order Boost converter. In conclusion, the proposed mathematical model can more comprehensively analyze the system characteristics of the C-F definition-based fractional-order Boost converter with fractional-order inductive loads, benefiting the circuit design of Boost converters.

show abstract

“…Another application for which a high-frequency, tunable FOE is required in the literature is, for example, the fractional-order DC-DC buck converter [8,16], which offers additional degrees of freedom and increases the flexibility of the design. If the conventional integer-order buck converter cannot be reduced to the required voltage gain by adjusting the duty cycle, the fractional-order buck converter can further reduce the voltage gain by adjusting the fractional order to meet the system requirements.…”

Section: Introductionmentioning

confidence: 99%

Digitally Controlled Fractional-Order Elements Using OTA-C Structures

Emanovic,

Vonic,

Jurisic

et al. 2024

Electronics

View full text Add to dashboard Cite

This article presents an active realisation of an electronically controlled FO capacitor or a constant phase element (CPE) and an FO inductor (FOI) in the form of an integrated circuit. The realisation is demonstrated using an OTA-C structure in AMS 0.35 μm C35B4C3 technology. The same core is used for both realisations of CPE and FOI, and the angles can be realised in all four quadrants. The realisation of active constant-phase elements using OTAs with MOS transistors in the saturation region is proposed. The operating frequency is in the high range of 7–350 kHz, with a centre frequency of 50 kHz. A tuning method is proposed using different bias currents of the OTAs, which in turn are digitally controlled to obtain the desired parameters such as impedance and angle of an element. The linearisation of the individual OTAs is achieved by source degeneration. The newly introduced minimax approximation is used to design three non-integer orders of 1/3, 1/2, and 2/3. The integrated circuit was designed with a total area of 710 × 1127 µm2. The power consumption of the entire system is 12.37 mW.

show abstract

Chaos analysis of Buck converter with non-singular fractional derivative

Cited by 11 publications

References 32 publications

New modied Atangana-Baleanu fractional derivative applied to solve nonlinear fractional dierential equations

New modied Atangana-Baleanu fractional derivative applied to solve nonlinear fractional dierential equations

Modeling and Analysis of Caputo–Fabrizio Definition-Based Fractional-Order Boost Converter with Inductive Loads

Digitally Controlled Fractional-Order Elements Using OTA-C Structures

Contact Info

Product

Resources

About