Analog Implementation of Fractional-Order Elements and Their Applications

With advancements in the theory of fractional calculus and also with widespread engineering application of fractional-order systems, analog implementation of fractional-order integrators and differentiators have received considerable attention. This is due to the fact that this powerful mathematical tool allows us to describe and model a real-world phenomenon more accurately than via classical “integer” methods. Moreover, their additional degree of freedom allows researchers to design accurate and more robust systems that would be impractical or impossible to implement with conventional capacitors. Throughout this thesis, a wide range of problems associated with analog circuit design of fractional-order systems are covered: passive component optimization of resistive-capacitive and resistive-inductive type fractional-order elements, realization of active fractional-order capacitors (FOCs), analog implementation of fractional-order integrators, robust fractional-order proportional-integral control design, investigation of different materials for FOC fabrication having ultra-wide frequency band, low phase error, possible low- and high-frequency realization of fractional-order oscillators in analog domain, mathematical and experimental study of solid-state FOCs in series-, parallel- and interconnected circuit networks. Consequently, the proposed approaches in this thesis are important considerations in beyond the future studies of fractional dynamic systems

Bearing/Incipient/Open Phase Fault Detection and Diagnosis of Multi-Phase Induction Motor Drives Equipped By GBDTI2HO Technique

In this paper, a hybrid system is performed with fault detection and diagnosis on multi-phase induction motor (IM). The proposed method is hybrid of integrated Harris Hawk optimization (IHHO) and gradient boosting decision trees (GBDT) thus called the GBDTI2HO method. Here, additional operators are included in this paper to improve HHO’s search behaviour namely crossover and mutation. Distorted waveforms are generated by different frequency patterns to indicate the time domain frequency as an assessment of failure. For this signal representation, the discrete wavelet transformation (DWT) is suggested. It extracts the characteristics and forwards them to IHHO technique to form the possible data sets. After the generation of the data set, GBDT classifies the ways of failure reached as winding of stator in multi-phase IM. The implementation of the proposed system is compared with existing systems, such as ANN, S-Transform and GBDT. The proposed method is executed on MATLAB/Simulink work platform to demonstrate the successfulness of proposed system, statistical measures are determined, as precision, sensitivity and specificity, mean median and standard deviation. For demonstrating the successfulness of proposed system, statistical measures are determined as precision, sensitivity, specificity, mean median as well as standard deviation. In 50 trails the proposed method, 0.98 for accuracy, 0.96 for specificity, 1.60 for recall as well as 0.97 for precision. In 100 trail the proposed method, 0.96 for accuracy, 0.93 for specificity, 0.87 for recall as well as 0.99 for precision

Design of a Fractional Order Low-pass Filter Using a Differential Voltage Current Conveyor, Journal of Telecommunications and Information Technology, 2023, nr 2

In this paper, an active implementation of a differential voltage current conveyor (DVCC) based on a low-pass filter operating in the fractional order domain is presented. The transfer function for a fractional order system is dependent on the rational approximation of sα. Different methods used for calculating the rational approximation, including Carlson, Elkhazalil, and curve fitting, are evaluated here. Finally, to validate the theoretical results, a fractional order Butterworth filter is simulated in the Pspice environment using the 0.5 micrometer CMOS technology with an R-C network-based fractional order capacitor. Additionally, using the Monte Carlo analysis, the impact of current and voltage faults on DVCC response is investigated. It has been inferred that realization with a wider bandwidth is possible

HYBRID APPROXIMATION METHOD FOR TIME RESPONSE IMPROVEMENT OF CFE BASED APPROXIMATE FRACTIONAL ORDER DERIVATIVE MODELS BY USING GRADIENT DESCENT ALGORITHM

Due to its high computational complexity, fractional order (FO) derivative operators have been widely implemented by using rational transfer function approximation methods. Since these methods commonly utilize frequency domain approximation techniques, their time responses may not be prominent for time-domain solutions. Therefore, time response improvements for the approximate FO derivative models can contribute to real-world performance of FO applications. Recent works address the hybrid use of popular frequency-domain approximation methods and time-domain approximation methods to deal with time response performance problems. In this context, this study presents a hybrid approach that implements Continued Fraction Expansion (CFE) method as frequency domain approximation and applies the gradient descent optimization (GDO) for step response improvement of the CFE-based approximate model of FO derivative operators. It was observed that GDO can fine-tune coefficients of CFE-based rational transfer function models, and this hybrid use can significantly improve step and impulse responses of CFE-based approximate models of derivative operators. Besides, we demonstrate analog circuit realization of this optimized transfer function model of the FO derivative element according to the sum of low pass active filters in Multisim and Matlab simulation environments. Performance improvements of hybrid CFE-GDO approximation method were demonstrated in comparison with the stand-alone CFE method