FPGA Implementation of the Fractional Order Integrator/Differentiator: Two Approaches and Applications

Tolba, Mohamed F.; Said, Lobna A.; Madian, Ahmed H.; Radwan, Ahmed G.

doi:10.1109/tcsi.2018.2885013

Cited by 61 publications

(38 citation statements)

References 24 publications

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“…Many interesting solutions of two-port interconnections have been presented as parts of various fractional-order controllers [10][11][12][13][14][15][16][17][18]. Many of them are using standard topologies based on OA [10,11] because of their simplicity.…”

Section: Sum Of Reconfigurable Filtering Responsesmentioning

confidence: 99%

“…Many of them are using standard topologies based on OA [10,11] because of their simplicity. Some approaches target on extensive and complex design, based on field programmable analog arrays (FPAAs) [12] and field programmable gate arrays (FPGAs) [16], [17] because of their programmability. Moreover, FPGA represents a digital-only solution of the design.…”

Section: Sum Of Reconfigurable Filtering Responsesmentioning

confidence: 99%

“…Moreover, FPGA represents a digital-only solution of the design. It allows the integration of highly complex topologies [12,16,17], but certain latency and delay of processing may occur in some cases. However, a significant drawback of these concepts is the necessity of software development and also quite high costs in comparison to a simple analog solution.…”

Section: Sum Of Reconfigurable Filtering Responsesmentioning

confidence: 99%

“…Frequency responses influenced by the fractional-order behavior of used components are studied more frequently in recent years [1]. Many works in this field focus on novel solutions of integral and derivative two-ports (for example [2][3][4][5][6][7][8][9]), proportional integral and derivative controllers (for example [10][11][12][13][14][15][16][17][18] and so-called bilinear two ports [8,9,[19][20][21] serving for various purposes. Two ports, known as integrators and differentiators, have started to be interesting for designers of fractional-order systems, and especially for proportional, integral and derivative controllers (PIDs).…”

Section: Introductionmentioning

confidence: 99%

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Integer-and Fractional-Order Integral and Derivative Two-Port Summations: Practical Design Considerations

et al. 2019

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This paper targets on the design and analysis of specific types of transfer functions obtained by the summing operation of integer-order and fractional-order two-port responses. Various operations provided by fractional-order, two-terminal devices have been studied recently. However, this topic needs to be further studied, and the topologies need to be analyzed in order to extend the state of the art. The studied topology utilizes the passive solution of a constant-phase element (with order equal to 0.5) implemented by parallel resistor–capacitor circuit (RC) sections operating as a fractional-order two-port. The integer-order part is implemented by operational amplifier-based lossless integrators and differentiators in branches with electronically adjustable gain, useful for time constant tuning. Four possible cases of the fractional-order and integer-order two-port interconnections are analyzed analytically, by PSpice simulations and also experimentally in the frequency range between 10 Hz and 1 MHz. Standard discrete active components are used in this design for laboratory verification. Practical recommendations for construction and also particular solutions overcoming possible issues with instability and DC offsets are also given. Experimental and simulated results are in good agreement with theory.

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Section: Sum Of Reconfigurable Filtering Responsesmentioning

confidence: 99%

Section: Sum Of Reconfigurable Filtering Responsesmentioning

confidence: 99%

Section: Sum Of Reconfigurable Filtering Responsesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Integer-and Fractional-Order Integral and Derivative Two-Port Summations: Practical Design Considerations

et al. 2019

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“…In this paper, we only study the CMPS of FOCCS theoretically but do not study hardware implementation. Recently, there are many papers considering the implementation of the fractional-order operator and fractional-order synchronization scheme [40][41][42][43], which provide good research ideas for the implementation of the CMPS proposed in this paper. Therefore, we will further investigate the hardware implementation of the CMPS of FOCCS in future work.…”

Section: Remarkmentioning

confidence: 99%

Synchronization of Fractional-Order Complex Chaotic Systems Based on Observers

Xia

Jiang

2019

Entropy

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By designing a state observer, a new type of synchronization named complex modified projective synchronization is investigated in a class of nonlinear fractional-order complex chaotic systems. Combining stability results of the fractional-order systems and the pole placement method, this paper proves the stability of fractional-order error systems and realizes complex modified projective synchronization. This method is so effective that it can be applied in engineering. Additionally, the proposed synchronization strategy is suitable for all fractional-order chaotic systems, including fractional-order hyper-chaotic systems. Finally, two numerical examples are studied to show the correctness of this new synchronization strategy.

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Design method and implementation of the fractional‐order inductor and its application in series‐resonance circuit

Hao

Wang

2022

Circuit Theory & Apps

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Summary By using the fractional‐order medium constitutive relations and Maxwell equations, the modeling and theoretical analysis of the fractional‐order inductor (FOI) is investigated in this study. The general formulations of the magnetic property model of FOI core material are derived. This paper proposes a generalized approach to design and implement a single‐component FOI and constructs the independent fractional‐order circuit element in Matlab/Simulink based on the fractional calculus Grünwald–Letnikov (GL) definition. The electrical and magnetic performance of the FOI are characterized in both frequency and time domain by simulation and experimentation. All results show that it is effective to use the proposed method and design guidance to construct the FOI. Furthermore, the results from the application of FOI in the fractional‐order RLλC series‐resonance circuit show that the order has an effect on the characteristics and frequency properties of it.

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FPGA Implementation of the Fractional Order Integrator/Differentiator: Two Approaches and Applications

Cited by 61 publications

References 24 publications

Integer-and Fractional-Order Integral and Derivative Two-Port Summations: Practical Design Considerations

Integer-and Fractional-Order Integral and Derivative Two-Port Summations: Practical Design Considerations

Synchronization of Fractional-Order Complex Chaotic Systems Based on Observers

Design method and implementation of the fractional‐order inductor and its application in series‐resonance circuit

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