The study of nonlinear systems and chaos is of great importance to science and engineering mainly because real systems are inherently nonlinear and linearization is only valid near the operating point. The interest in chaos was increased when Lorenz accidentally discovered the sensitivity to initial condition during his simulation work on weather prediction. When a nonlinear system is exhibiting deterministic chaos, it is very difficult to predict its response under external disturbances. This behavior is a double-edged weapon. From a control and synchronization point of view, this proposes a challenge. On the other hand, from a communications and encryption perspective, this provides a higher level of security. This chapter is a survey of the recent contributions in engineering applications of fractional order chaotic continuous-time systems. The applications include but not limited to: communication and encryption, FPGA implementations, synchronization and control, modeling of electric motors, and biomedical applications. © 2018 Elsevier Inc. All rights reserved.
FPGA implementation of integer/fractional chaotic systems
Chaotic systems have remarkable importance in capturing some complex features of the physical process. Recently, fractional calculus becomes a vigorous tool in characterizing the dynamics of complex systems. The fractional-order chaotic systems increase the chaotic behavior in new dimensions and add extra degrees of freedom, which increase system controllability. In this chapter, FPGA implementation of different integer and fractional-order chaotic systems is presented. The investigated integer-order systems include Chua double scroll chaotic system and the modified Chua N-scroll chaotic system. The investigated fractional-order systems include Chua, Yalcin et al., Ozuogos et al., and Tang et al., chaotic systems. These systems are implemented and simulated based on the Grunwald–Letnikov (GL) definition with different window sizes. The parameters effect, along with different GL window sizes is investigated where some interesting chaotic behaviors are obtained. The proposed FPGA implementation utilizes fewer resources and has high throughput. Experimental results are provided on a digital oscilloscope. © Springer Nature Switzerland AG 2020.
Experimental investigation of methyl-orange removal using eco-friendly cost-effective materials raw fava bean peels and their formulated physical, and chemically activated carbon
The discharge of effluents from dye industries into water streams poses a significant environmental and public health risk. In response, eco-friendly adsorbents derived from agricultural waste, such as Fava Bean Peels (R–FBP), have been investigated as potential materials for the removal of such pollutants. In this study, R–FBP and their corresponding physical and chemically activated carbon (P-RFB-AC and C-FBP-AC) were synthesized using H3PO4 acid and characterized using FT-IR, and SEM analyses. An optimization process was conducted to determine the optimum conditions for achieving high Methyl Orange (M. Orange) removal efficiencies using the prepared materials, namely R–FBP, P-RFB-AC, and C-FBP-AC. The adsorption mechanism was examined by analyzing the isotherm and kinetics. The results revealed that the physical raw-activated carbon exhibited the highest removal efficiency of 96.8% compared to other materials. This outcome was achieved through the use of ANN combined with Moth Search Algorithm (MSA), which was found to be the most effective model for achieving the highest M. Orange removal efficiency from Physical raw fava bean activated carbon. Under parameters of 1000 mg/l M. Orange concentration, 2 g/l dose, 15 min contact time, and 120 rpm shaking, the best experimental and predicted removal efficiencies for physical-activated carbon fava bean rind were 96.8 RE%, 96.01 indicated RSM RE%, and 95.75 predicted ANN RE%. The highest experimental and predicted removal efficiencies for the H3PO4 chemical activated carbon fava bean peel were 94%RE. This study aimed to develop an economical solution for treating industrial wastewater contaminated with anionic M. Orange dye using raw fava bean peel and their generated activated carbon, in both physical and chemical forms. The Temkin and Langmuir isotherm models were found to best fit the data for raw fava bean peel, while Temkin agreed well with the data from physical-activated carbon. Temkin and Freundlich’s models were fitted with the H3PO4 chemical activated carbon. Pseudo-second-order kinetics was identified as the most suitable model for both physically and chemically activated carbons. Future research may explore the capacity of the produced activated carbon-based algae to extract a wider range of contaminants from contaminated wastewater. In summary, this work contributes to the development of eco-friendly and cost-effective methods for removing dyes, specifically M. Orange, from industrial effluents. By synthesizing and characterizing R–FBP and their relative activated carbon, the adsorption mechanism was studied, and the optimum conditions for achieving high M. Orange removal efficiencies were determined. The results showed that physical raw-activated carbon exhibited the highest removal efficiency, and pseudo-second-order kinetics was the most suitable model for both physically and chemically activated carbon. © 2023 The Authors
Crystal violet removal using bimetallic Fe0–Cu and its composites with fava bean activated carbon
Nano zero-valent iron (nZVI), bimetallic nano zero-valent iron-copper (Fe0– Cu), and fava bean activated carbon-supported bimetallic nano zero-valent iron-copper (AC-Fe0-Cu) are synthesized and characterized using DLS, zeta potential, FT-IR, XRD, and SEM. The maximum removal capacity is demonstrated by bimetallic Fe0–Cu, which is estimated at 413.98 mg/g capacity at pH 7, 180 min of contact duration, 120 rpm shaking speed, ambient temperature, 100 ppm of C.V. dye solution, and 1 g/l dosage. The elimination capability of the H2SO4 chemical AC-Fe0-Cu adsorbent is 415.32 mg/g under the same conditions but with a 150 ppm C.V. dye solution. The H3PO4 chemical AC-Fe0-Cu adsorbent achieves a removal capacity of 413.98 mg/g under the same conditions with a 350 ppm C.V. dye solution and a 1.5 g/l dosage. Optimal conditions for maximum removal efficiency are determined by varying pH (3–9), time intervals (15–180 min), and initial dye concentrations (25–1000 ppm). Kinetic and isothermal models are used to fit the results of time and concentration experiments. The intra-particle model yields the best fit for bimetallic Fe0–Cu, H2SO4 chemical AC- Fe0–Cu, and H3PO4 chemical AC-Fe0-Cu, with corrected R-Squared values of 0.9656, 0.9926, and 0.964, respectively. The isothermal results emphasize the significance of physisorption and chemisorption in concentration outcomes. Response surface methodology (RSM) and artificial neural networks (ANN) are employed to optimize the removal efficiency. RSM models the efficiency and facilitates numerical optimization, while the ANN model is optimized using the moth search algorithm (MSA) for optimal results. © 2023
Preparation and Characterization of nZVI, Bimetallic Fe 0-Cu, and Fava Bean Activated Carbon-Supported Bimetallic AC-F e 0-Cu for Anionic Methyl Orange Dye Removal
Nano zero-valent iron (nZVI), bimetallic Nano zero-valent iron-copper (Fe 0- Cu), and fava bean activated carbon-supported with bimetallic Nano zero-valent iron-copper (AC-F e 0-Cu) were prepared and characterized by DLS, FT-IR, XRD, and SEM. The influence of the synthesized adsorbents on the adsorption and removal of soluble anionic methyl orange (M.O) dye was investigated using UV-V spectroscopy. The influence of numerous operational parameters was studied at varied pH (3–9), time intervals (15–180 min), and dye concentrations (25–1000 ppm) to establish the best removal conditions. The maximum removal efficiency of M.O. using the prepared adsorbent materials reached about 99%. The removal efficiency is modeled using response surface methodology (RSM). The Bimetallic Fe -Cu, the best experimental and predicted removal efficiency is 96.8% RE. For the H2SO4 chemical AC- Fe -Cu, the best experimental and removal efficiency is 96.25% RE. The commercial AC-Fe0–Cu, the best experimental and predicted removal efficiency is 94.93%RE. This study aims to produce low-cost adsorbents such as Bimetallic Fe0-Cu, and Fava Bean Activated Carbon-Supported Bimetallic AC-Fe0-Cu to treat the industrial wastewater from the anionic methyl orange (M.O) dye and illustrate its ability to compete H2SO4 chemical AC-Fe0-Cu, and commercial AC-Fe0-Cu. © 2023, The Author(s).
High-performance fractional anisotropic diffusion filter for portable applications
Anisotropic diffusion is one of the most effective methods used in image processing. It can be used to eliminate the small textures of an image while preserving its significant edges. In this paper, a new anisotropic diffusion filter is proposed based on a fractional calculus kernel rather than integer kernel to improve the overall performance of the filter. Integer and fractional anisotropic filters are implemented using the Genesys-2 FPGA kit to utilize the efficiency of parallelism in FPGAs. Integer and fractional anisotropic filters are tested against the achievable PSNR value vs the number of iterations. The proposed fractional anisotropic filter has a better PSNR value using a smaller number of iterations, reducing the power and area compared to integer anisotropic filter. The proposed filter can be used in image smoothing, edge detection, image segmentation, image denoising, and cartooning. In addition, the proposed filter reduces the power consumption by 58.2% compared to integer-order filters, which makes the proposed filter suitable for battery-based applications. © 2023, The Author(s).
A Unified FPGA Realization for Fractional-Order Integrator and Differentiator
This paper proposes a generic FPGA realization of an IP core for fractional-order integration and differentiation based on the Grünwald–Letnikov approximation. All fractional-order dependent terms are approximated to simpler relations using curve fitting to enable an efficient hardware realization. Compared to previous works, the proposed design introduces enhancements in the fractional-order range covering both integration and differentiation. An error analysis between software and hardware results is presented for sine, triangle and sawtooth signals. The proposed generic design is realized on XC7A100T FPGA achieving frequency of 9.328 MHz and validated experimentally for a sine input signal on the oscilloscope. The proposed unified generic design is suitable for biomedical signal processing applications. In addition, it can be employed as a laboratory tool for fractional calculus education. © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
CORDIC-Based FPGA Realization of a Spatially Rotating Translational Fractional-Order Multi-Scroll Grid Chaotic System
This paper proposes an algorithm and hardware realization of generalized chaotic systems using fractional calculus and rotation algorithms. Enhanced chaotic properties, flexibility, and controllability are achieved using fractional orders, a multi-scroll grid, a dynamic rotation angle(s) in two- and three-dimensional space, and translational parameters. The rotated system is successfully utilized as a Pseudo-Random Number Generator (PRNG) in an image encryption scheme. It preserves the chaotic dynamics and exhibits continuous chaotic behavior for all values of the rotation angle. The Coordinate Rotation Digital Computer (CORDIC) algorithm is used to implement rotation and the Grünwald–Letnikov (GL) technique is used for solving the fractional-order system. CORDIC enables complete control and dynamic spatial rotation by providing real-time computation of the sine and cosine functions. The proposed hardware architectures are realized on a Field-Programmable Gate Array (FPGA) using the Xilinx ISE 14.7 on Artix 7 XC7A100T kit. The Intellectual-Property (IP)-core-based implementation generates sine and cosine functions with a one-clock-cycle latency and provides a generic framework for rotating any chaotic system given its system of differential equations. The achieved throughputs are (Formula presented.) Mbits/s and (Formula presented.) Mbits/s for two- and three-dimensional rotating chaotic systems, respectively. Because it is amenable to digital realization, the proposed spatially rotating translational fractional-order multi-scroll grid chaotic system can fit various secure communication and motion control applications. © 2022 by the authors.
An Encryption Application and FPGA Realization of a Fractional Memristive Chaotic System
The work in this paper extends a memristive chaotic system with transcendental nonlinearities to the fractional-order domain. The extended system’s chaotic properties were validated through bifurcation analysis and spectral entropy. The presented system was employed in the substitution stage of an image encryption algorithm, including a generalized Arnold map for the permutation. The encryption scheme demonstrated its efficiency through statistical tests, key sensitivity analysis and resistance to brute force and differential attacks. The fractional-order memristive system includes a reconfigurable coordinate rotation digital computer (CORDIC) and Grünwald–Letnikov (GL) architectures, which are essential for trigonometric and hyperbolic functions and fractional-order operator implementations, respectively. The proposed system was implemented on the Artix-7 FPGA board, achieving a throughput of 0.396 Gbit/s. © 2023 by the authors.
Arithmetic optimization approach for parameters identification of different PV diode models with FOPI-MPPT
The Maximum Power Point Tracker (MPPT) provides the most efficient use of a Photo-voltaic system independent of irradiance or temperature fluctuations. This paper introduces the modeling and control of a photo-voltaic system operating at MPPT using the arithmetic optimization algorithm (AOA). The single and double Photo-voltaic models are investigated. Their optimal unknown parameters are extracted using AOA based on commercial Photo-voltaic datasheets. A comparison is performed between these optimal parameters extracted by AOA and other optimization techniques presented in the literature. These parameters generate the P – V and I – V curves for the studied models considering the temperature factor. A good match is achieved relative to the manufacturer data. A DC-DC boost converter is used as a link between the PV modules and the load. The converter duty cycle is adjusted, varying the climatic conditions using three cases: without a controller, using PI controller, and using the fractional-order PI controller (FOPI). The AOA is employed to set the optimum controllers parameters to maintain the impedance matching between the PV modules and the load. The FOPI shows a significant improvement in controlling the system performance. © 2021 THE AUTHORS