This chapter introduces two FPGA implementations of the fractional-order operators: the Caputo and the Grünwald-Letnikov (GL) derivatives. First, the Caputo derivative is realized using nonuniform segmentation to reduce the size of the Look-Up Table. The Caputo implementation introduced can generate derivatives of previously defined functions only. Generic and complete hardware architecture of the GL operator is realized with different memory window sizes. The generic architecture is used as a block to implement several fractional-order chaotic systems. The investigated systems include Borah, Chen, Liu, Li, and Arneodo fractional-order chaotic systems. Different interesting attractors are realized under various parametric changes with distinct step sizes for different fractional orders. To verify the chaotic behavior of the generated attractors, the Maximum Lyapunov Exponent is calculated for each system at different parameter values. © 2018 Elsevier Inc. All rights reserved.
Fractional-Order Filter Design
One of the advantages of fractional order is the extra degree of freedom added by the fractional-order parameters, which enrich the analysis with more details in new dimensions. This chapter introduces factional-order conventional filters of orders ?, 2?, and 3?. The general transfer functions of continuous-time filters (low-pass, high-pass, and band-pass filters) to the noninteger-order (fractional-order) domain are investigated. Also, mathematical expressions for the maximum and minimum frequencies, the half power frequencies, and the right-phase frequencies are derived. In addition, the effect of the transfer function parameters on the filter poles and hence the stability is introduced. Numerical spice results are introduced to validate the theoretical findings. Several passive and active filters are studied to validate the concept. This chapter also investigates the effect of an inserted delay parameter on the filter main frequencies. Different filter responses are obtained from the general delayed transfer function. Two delay examples are investigated. © 2018 Elsevier Inc. All rights reserved.
A survey on memristor active emulation circuits in the fractional-order domain
Chua postulated a new element called a memristor, contributing flux and charge link. The main characteristic of the memristor is a pinched hysteresis double loop with one pinched point. The memristor’s realization in the fractional-order domain increases the hysteresis loop area’s controllability and frequency range. Besides, the fractional-higher-order memristor is realized, achieving more than a pinched point with changes of the pinched point’s location at different values of a. The commercial memristor device is absent until now. For this purpose, scientists concentrated on modeling the memristor achieving its characteristics, and applied it with other circuit elements. This chapter is intended to study the previously proposed memristor emulator in a fractional-order domain dependent on commercial active building blocks. The memristance emulation circuits are classified into four categories: circuits based on operational amplifiers, second-generation current conveyor family circuits, current-feedback operational amplifiers, and complementary metal-oxide semiconductors. The introduced circuits are compared, also the PSPICE, and experimental results confirm the selected circuits. © 2022 Elsevier Inc. All rights reserved.
Observability of speed DC motor with self-tuning fuzzy-fractional-order controller
The DC motor is one of the simplest electrical machines used in industry since it is controlled by direct voltages and currents. These configurations have various advantages, allowing the machine to be adapted to the constraints of its specific application. The present chapter analyzes the DC motor with separate excitation without the use of a speed sensor to approximate the rotor speed. An analysis of the stability of the rotor speed estimation is performed. Enhanced control of the direct action is integrated into the adaptive observer to decrease the roundness capability of the model and simplify implementation. Design guidelines for the feedback gain and speed fractional controller whose parameters are automatically adjusted using intelligent fuzzy logic techniques are also provided to ensure system stability throughout the operating region. The results given in this study verify the validity and effectiveness of the proposed control technique. © 2022 Elsevier Inc. All rights reserved.
Adsorption as an Emerging Technology and Its New Advances of Eco-Friendly Characteristics: Isotherm, Kinetic, and Thermodynamic Analysis
Water contamination with paints causes a colour agent to the water that negatively affects the environment, organisms, and humans. Different physicochemical processes are applied for wastewater treatment; however, they have many drawbacks such as high cost, generating toxic waste, and non-effective at low concentrations. Adsorption is considered a promising technique for pollutant removal from polluted wastewater. Commercial activated carbon, nano-materials, and natural biological materials are used as adsorbents in adsorption. This chapter focuses on discussing the adsorption process, the factors affecting the adsorption, different adsorption materials, and the isothermal, kinetic, and thermodynamic models. © 2023 selection and editorial matter, Irene Samy Fahim and Lobna A. Said; individual chapters, the contributors.
Applied Techniques for Wastewater Treatment: Physicochemical and Biological Methods
Polluted water is one of the significant challenges facing the world nowadays, especially with the noticed water shortage recorded in the last period. Different treatment methods, physicochemical and biological, were presented for pollutant removal from polluted wastewater. This review discusses the treatment methods starting from the biological part to help reduction of organics, which are solids that appear in the wastewater. After that, the physicochemical techniques will be discussed as a second part of the treatment process to minimize the heavy metal, dyes, and other pollutants. Additionally, filtration techniques and advanced treatment processes will be discussed as the final steps in the water treatment systems and how they were used to finally sterilize the water after the treatment processes. © 2023 selection and editorial matter, Irene Samy Fahim and Lobna A. Said; individual chapters, the contributors.
Modeling woody plant tissue using different fractional-order circuits
This chapter presents results on the most suitable bio-impedance circuits for modeling woody plants. The modified double-shell, the modified triple Cole-Cole, and the traditional wood circuit models are compared for fitting experimentally measured data. Consequently, a modified circuit model is proposed. This model gives the best results for all interelectrode spacing distances when compared to the other circuits. All impedance data have been measured using the research-grade SP150 electrochemical station in the frequency range 0.1 Hz to 200 kHz. The fitting is done using the Zfit of the impedance analyzer SP150. © 2022 Elsevier Inc. All rights reserved.
Biologically Inspired Optimization Algorithms for Fractional-Order Bioimpedance Models Parameters Extraction
This chapter introduces optimization algorithms for parameter extractions of three fractional-order circuits that model bioimpedance. The Cole-impedance model is investigated; it is considered one of the most commonly used models providing the best fit with the measured data. Two new models are introduced: the fractional Hayden model and the fractional-order double-shell model. Both models are the generalization of their integer-order counterpart. These fractional-order models provide an improved description of observed bioimpedance behavior. New metaheuristic optimization algorithms for extracting the impedance parameters of these models are investigated. The proposed algorithms inspired by nature are known as the Flower Pollination Algorithm, the Grey Wolf Optimizer, the Moth-flame Optimizer, the Whale Optimization Algorithm, and the Grasshopper Optimization Algorithm. These algorithms are tested over sets of simulated and experimental data. Their results are compared with a conventional fitting algorithm (the nonlinear least square) in aspects of speed, accuracy, and precision. © 2018 Elsevier Inc. All rights reserved.
Fractional-order oscillators based on a single Op-Amp
This chapter introduces a family of fractional-order oscillators based on a single operational amplifier (Op-Amp) with two fractional-order capacitors. Twelve different fractional-order oscillator circuits are investigated where the state matrix, oscillation frequency, and oscillation condition for each circuit are presented. The phase difference between the two oscillatory outputs is deduced in terms of the fractional-order parameters. The fractional-order parameter enhances the oscillator performance by providing an extra degree-of-freedom. Also, the resulting circuits provide independent controllability for the phase difference and the oscillation frequency. Numerical simulations using MATLAB® are performed to study the effect of the fractional-order parameters on the circuit response. Moreover, PSpice simulations are performed on different cases using two different fractional-order capacitors. Selected cases are verified experimentally to confirm the theoretical findings. © 2022 Elsevier Inc. All rights reserved.
On the Approximation of Fractional-Order Circuit Design
Despite the complex nature of fractional calculus, it is still fairly possible to reduce this complexity by using integer-order approximation. Each integer-order approximation has its own trade-offs from the complexity, sensitivity, and accuracy points of view. In this chapter, two different fractional-order electronic circuits are studied: the Wien oscillator and the CCII-based KHN filter with two different fractional elements of orders ? and ?. The investigation is concerned with changes in the response of these two circuits under two approximations: Oustaloup and Matsuda. A detailed review of each approximation technique is provided as well as its design procedure. Oscillator and filter responses are simulated using MATLAB. Foster-I realization is used to implement the approximated Wien oscillator and filter transfer functions as circuits in order to simulate them in PSpice. The responses are compared to the exact solution to investigate which achieves the lowest error. For oscillators, the comparison is based on oscillation condition and oscillation frequency while for filters, the focus is on filter fundamental frequencies. This is a big issue in filter design: maximum or minimum frequency, right phase frequency, and half-power frequency. © 2018 Elsevier Inc. All rights reserved.