Fractional-order Systems and PID Controllers

Bingi, Kishore; Ibrahim, Rosdiazli; Karsiti, Mohd Noh; Hassan, Sabo Miya; Harindran, Vivekananda Rajah

doi:10.1007/978-3-030-33934-0

Cited by 47 publications

(18 citation statements)

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“…The curve-fitting-based methods perform transfer-function estimation and are based on the following steps [7,11,12]: (a) Obtain the frequency-response data of the mother function within the desired frequency range using MATLAB freqresp function, then raise the obtained response to the power α for deriving the final response, (b) Obtain the data of the final response using the MATLAB function frd, (c) Choose the desired value of the approximation order (which will be the order of the derived approximate integer-order transfer function).…”

Section: Approximation Of Power-law Filters' Functionsmentioning

confidence: 99%

“…The approximation of the power-law filter function H(s) can be conducted in the following way: the frequency responses of (2a) and (2b) are initially obtained, and, afterward, they are approximated through appropriate magnitude and phase curve-fitting-based techniques [11,12]. The obtained functions have the form of rational integer-order transfer functions, which can be realized using multi-feedback structures, cascade connection, or sum of the intermediate filter functions.…”

Section: Introductionmentioning

confidence: 99%

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Electronically Controlled Power-Law Filters Realizations

et al. 2022

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A generalized structure that is capable of implementing power-law filters derived from 1st and 2nd-order mother filter functions is presented in this work. This is achieved thanks to the employment of Operational Transconductance Amplifiers (OTAs) as active elements, because of the electronic tuning capability of their transconductance parameter. Appropriate design examples are provided and the performance of the introduced structure is evaluated through simulation results using the Cadence Integrated Circuits (IC) design suite and Metal Oxide Semiconductor (MOS) transistors models available from the Austria Mikro Systeme (AMS) 0.35 μm Complementary Metal Oxide Semiconductor (CMOS) process.

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Section: Approximation Of Power-law Filters' Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Electronically Controlled Power-Law Filters Realizations

et al. 2022

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“…Note that for these parameters, ( 38) is equal to (30), but this is not always the case. The magnitude and phase responses in the frequency domain of the rational transfer function are depicted in Figure 3a,c and the error for each case is shown in Figure 3b,d, respectively.…”

Section: Continued Fraction Expansion Approximationmentioning

confidence: 99%

“…This approximation method was reported in [29,30], which is based on obtaining the frequency response data of s α into a set of logarithmically spaced frequencies given as w = [w l , w 2 , w 3 . .…”

Section: Curve-fitting Approximationmentioning

confidence: 99%

Rational Approximations of Arbitrary Order: A Survey

et al. 2021

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This paper deals with the study and analysis of several rational approximations to approach the behavior of arbitrary-order differentiators and integrators in the frequency domain. From the Riemann–Liouville, Grünwald–Letnikov and Caputo basic definitions of arbitrary-order calculus until the reviewed approximation methods, each of them is coded in a Maple 18 environment and their behaviors are compared. For each approximation method, an application example is explained in detail. The advantages and disadvantages of each approximation method are discussed. Afterwards, two model order reduction methods are applied to each rational approximation and assist a posteriori during the synthesis process using analog electronic design or reconfigurable hardware. Examples for each reduction method are discussed, showing the drawbacks and benefits. To wrap up, this survey is very useful for beginners to get started quickly and learn arbitrary-order calculus and then to select and tune the best approximation method for a specific application in the frequency domain. Once the approximation method is selected and the rational transfer function is generated, the order can be reduced by applying a model order reduction method, with the target of facilitating the electronic synthesis.

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“…Non-integer order signal processing has received significant research interest in the following fields [1][2][3][4][5][6]. The first field is electrical engineering, for implementing filters and oscillators [5,[7][8][9][10][11][12][13][14][15], chaotic systems [16], sensor systems [17], and control systems [2,[18][19][20][21]. This originates from the fact that both filters and oscillators offer additional degrees of freedom due to the non-integer order, which opens the door for scaling the characteristic frequencies of the filters/oscillators, as well as for precisely controlling the gradient of the transition from the pass-band to the stop-band.…”

Section: Introductionmentioning

confidence: 99%

Versatile Field-Programmable Analog Array Realizations of Power-Law Filters

2022

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A structure suitable for implementing power-law low-pass and high-pass filter transfer functions is presented in this work. Through the utilization of a field-programmable analog array device, full programmability of the characteristics of the intermediate stages, as is required for realizing the rational integer-order transfer function that approximates the corresponding power-law function, was achieved, making the structure versatile. In addition, a comparison between power-law and fractional-order filters regarding the effect of the non-integer order was performed. The presented design examples are fully supported by experimental results.

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Fractional-order Systems and PID Controllers

Cited by 47 publications

References 0 publications

Electronically Controlled Power-Law Filters Realizations

Electronically Controlled Power-Law Filters Realizations

Rational Approximations of Arbitrary Order: A Survey

Versatile Field-Programmable Analog Array Realizations of Power-Law Filters

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