Fractional-order Circuit Model Research Articles

Passive Synthesis of Fractional Order Immittance of Three-Element-Kind

For the actual circuit with fractional order characteristics, the fractional order circuit model is more concise and precise than the classical circuit model. So studying the synthesis of fractional order immittance is of great significance. This paper investigates the passive synthesis method of the three-element-kind fractional order immittance function. It means designing a network with three kinds of passive fractional-order elements that exhibit a specific impedance function. This paper proposes a variable substitution method to solve this problem. The method consists of three steps: The first step of the process is to establish the correspondence between the fractional order and lossy reactance. This way, the fractional order immittance function is transformed into an integer order immittance function. Then the Brune procedure realizes the immittance function as a network with lossy reactance. Finally, a fractional order network is obtained by replacing the lossy reactance with the corresponding fractional reactance. A simulation example and an experiment are also given for verification. This method applies to all three-element-kind network impedance functions that meet the passive condition.

State of Charge Estimation of Supercapacitor Under Different Temperatures Using Particle Filter Algorithm Based on Fractional-Order Model

With the rise of new energy vehicles, supercapacitors (SCs) have been used as energy storage components for new energy vehicles due to their high-power density and good low-temperature performance. Accurate modeling and state of charge estimation of SC can ensure the safe operation of new energy vehicles. In order to explore the low-temperature performance of supercapacitors, this paper proposes a dual ZARC fractional-order circuit model to simulate the dynamic characteristics of SC. Using adaptive genetic algorithm for SC parameter identification, the model terminal voltage error is less than 6.5 mV. In addition, the SOC of SC at different temperatures and working conditions is estimated by using the fractional-order particle filter (FOPF) method and compared with the fractional-order extended Kalman filter (FOEKF). The experimental results show that the FOPF method has high estimation accuracy and robustness. Under the temperature of minus 40 °C, the maximum mean absolute error and maximum root-mean-square deviation of SOC estimation under different working conditions are less than 2%, showing good low-temperature performance.

Oscillators Based on Fractional-Order Memory Elements

This paper deals with the new oscillator structures that contain new elements, so-called memory elements, known as memristor, meminductor, and memcapacitor. Such circuits can exhibit oscillations as well as chaotic behavior. New mathematical models of fractional-order elements and whole oscillator circuits are proposed as well. An illustrative example to demonstrate the oscillations and the chaotic behavior through the numerical solution of the fractional-order circuit model is provided.

Plant stem tissue modeling and parameter identification using metaheuristic optimization algorithms

Bio-impedance non-invasive measurement techniques usage is rapidly increasing in the agriculture industry. These measured impedance variations reflect tacit biochemical and biophysical changes of living and non-living tissues. Bio-impedance circuit modeling is an effective solution used in biology and medicine to fit the measured impedance. This paper proposes two new fractional-order bio-impedance plant stem models. These new models are compared with three commonly used bio-impedance fractional-order circuit models in plant modeling (Cole, Double Cole, and Fractional-order Double-shell). The two proposed models represent the characterization of the biological cellular morphology of the plant stem. Experiments are conducted on two samples of three different medical plant species from the family Lamiaceae, and each sample is measured at two inter-electrode spacing distances. Bio-impedance measurements are done using an electrochemical station (SP150) in the range of 100 Hz to 100 kHz. All employed models are compared by fitting the measured data to verify the efficiency of the proposed models in modeling the plant stem tissue. The proposed models give the best results in all inter-electrode spacing distances. Four different metaheuristic optimization algorithms are used in the fitting process to extract all models parameter and find the best optimization algorithm in the bio-impedance problems.

DC-AC hybrid rapid heating method for lithium-ion batteries at high state of charge operated from low temperatures

Alternating current (AC) preheating strategy for lithium ion batteries (LiBs) at high state of charge (SOC) is prone to exceeding their voltage limit and risking their health. To address these problems, DC-AC hybrid rapid heating method is proposed to preheat LiBs at high SOC operated from low temperatures. In the proposed method, a fractional order circuit model is adopted to derive a total impedance of a LiB which is used to calculate the optimal excitation parameters of a DC-AC preheating at different conditions. Experimental results demonstrate that the proposed strategy can preheat a LiB from −20 °C to 10.02 °C within 443s and a series-connected LiB pack from −19.26 °C to 10.97 °C within 395s at an average heat generation rate of 4.07 °C/min and 4.6 °C/min, respectively. No appreciable capacity fade for the LiB is observed after the proposed method is used to preheat LiBs after 210 cycles.

Fractional-Order Bio-Impedance Modeling for Interdisciplinary Applications: A Review

Bio-impedance circuit modeling is a popular and effective non-invasive technique used in medicine and biology to fit the measured spectral impedance data of living or non-living tissues. The variations in impedance magnitude and/or phase at different frequencies reflect implicit biophysical and biochemical changes. Bio-impedance is also used for sensing environmental changes and its use in the agriculture industry is rapidly increasing. In this paper, we review and compare among the fractional-order circuit models that best fit bio-impedance data and the different methods for identifying the parameters of these circuits. Four different vegetables species (Carrot, Tomato, Zucchini, Cucumber) in three different conditions (fresh, frozen, and heated) are used to demonstrate the differences among these models.

An Improved Fractional-Order Circuit Model for Voltammetric Taste Sensor System With Infused Tea as Analyte

This paper presents a fractional-order equivalent circuit to better model the voltammetric sensor response in comparison with some existing fractional circuits generally used to model various electrochemical phenomena. The true behaviour of an electrochemical process is often described by a fractional-order model (FOM). Here, we propose a fractional-order circuit to model the current response of the voltammetric taste sensor system for black tea liquor. This current is due to the electrochemical reactions that occur when a voltage pulse is applied across the electrodes. So far, the change in model order to a fraction has not been considered in a circuit model of taste measurement systems. Therefore, this work estimates the equivalent circuit in the fractional-order domain to obtain a more pragmatic model of such a system. The methodology selects the most suitable fractional-order transfer function (FOTF) structure, optimally estimates the model parameters, and decomposes the FOTF into a fractional-order equivalent circuit. The effect of concentration of tea samples on the parameters values and the significance of electrodes towards potential discrimination of samples is also investigated. The estimation of such circuits without direct measurement of complex impedance is the main advantage of the approach.

Small-Signal Fractional-Order Model of PN Junction Long-Base Diode

Most models of PN junction diode are mathematical models rather than circuit models, and there is a necessary trade-off between model versatility and accuracy. The small-signal fractional-order circuit model of PN junction long-base diode based upon the device’s physical operating principles and fractional-order vector fitting is obtained. This model consists of fractional elements and traditional elements; at the same time, the conventional diffusion model, that is two-element diode model, is included as a special one. In particular, only two model parameters, inverse saturation current and minority carrier lifetime of the PN junction diode, need to be extracted for formulating fractional-order model. And it is proved that the simulation effect is perfect by comparing the normalized admittances of different diode models. So the efficiency and accuracy of the model can be greatly improved compared with the high-speed dynamic model of PN junction diode. The presented equivalent model is shown to be capable of reproducing the frequency-dependent characteristics of PN junction long-base diode, and it can be applied to different small-signal circuit environments. Finally, experiment of junction diode can also validate the efficiency of the small-signal fractional model.

Aging investigation of an echelon internal heating method on a three-electrode lithium ion cell at low temperatures

Abstract An echelon internal heating method based on alternating current has exhibited many advantages of high heat generation rate and thermal uniformity for fast battery heating at low temperatures. However, inappropriate parameter settings for the echelon internal heating method are prone to risk battery health due to side reactions. To address this problem, a three-electrode cell is fabricated to investigate the effect of the echelon internal heating method on cell health at low temperatures. A fractional order circuit model is used to determine the optimal current amplitude and frequency of alternating current at different temperatures for preheating the cell. After many cycles of preheating the cell, capacity calibration results and incremental capacity curves show no apparent detrimental effect of the proposed heating method on cell health.

Rates and Effects of Local Minima on Fractional-Order Circuit Model Parameters Extracted from Supercapacitor Discharging Using Least Squares Optimization

Optimization routines are widely used to numerically determine a set of model parameters that best fit collected experimental data. One recent application of these methods is to extract the fractional-order circuit model parameters that accurately characterize the transient behavior of discharging supercapacitors. However, the variability that these methods introduce to the extracted model parameters must be understood to determine if changes in model parameters are artifacts of the optimization routine or are representative of physical changes in the device under study. In this work, the variability of supercapacitor fractional-order model parameters is quantified when extracted using a nonlinear least squares optimization applied to simulated data (with 0.1–3% noise) and experimental data of their discharging behavior. These results indicate that the local minima problem occurs at a rate of $$<1\%$$ for this application, though this problem can be overcome using at least 10 independent executions of the solver to each dataset. The variability of the model parameters using 1000 executions of the solver with 1 and 10 iterates is quantified for both simulated and experimental data, with the 10 iterates showing at least an order of magnitude reduction in the range of returned parameters.

Finite-Time Control of Uncertain Fractional-Order Positive Impulsive Switched Systems with Mode-Dependent Average Dwell Time

This paper is concerned with the problem of finite-time control of uncertain fractional-order positive impulsive switched systems (UFOPISS) via mode-dependent average dwell time (MDADT). The uncertainties refer to interval and polytopic uncertainties. Firstly, the proof of the positivity of UFOPISS is given. By constructing linear copositive Lyapunov functions, the finite-time stability (FTS) of autonomous system with MDADT is studied. Then, state feedback controllers are designed to guarantee the FTS of the resulting closed-loop system with interval and polytopic uncertainties, respectively. All presented conditions can be easily solved by linear programming. Finally, a fractional-order circuit model is employed to illustrate the effectiveness of the proposed method.

Fractional-order circuit models of the human body impedance for compliance tests against contact currents

Compliance tests against contact currents presently require the usage of equivalent circuit networks aimed to reproduce the human body impedance in the frequency range 0–110MHz. The IEC 60990 standard specifies an equivalent network that is valid up to 1MHz, while a recent work from the authors has extended the validity of the IEC network up to 110MHz. However, a number of 11 integer-order lumped elements was employed in the latter case. In this study, an equivalent network based on fractional-order circuit models is proposed in order to reduce the number of elements needed to fit the human body impedance. Moreover, the fitting of the mixed curve defined as the lowest impedance between the IEC network and the extended one is for the first time considered to provide a more protective compliance network in the whole frequency range.

Nonlinear Fractional-Order Estimator with Guaranteed Robustness and Stability for Lithium-Ion Batteries

This paper proposes a new estimator design algorithm for state-of-charge (SoC) indication of lithium-ion batteries. A fractional-order model-based nonlinear estimator is first framed including a Luenberger term and a sliding mode term. The estimator gains are designed by Lyapunov's direct method, providing a guarantee for stability and robustness of the error system under certain assumptions. This generic estimation algorithm is then applied to lithium-ion batteries. A fractional-order circuit model is adopted to predict battery dynamic behaviours. Assumptions based on which the estimation algorithm is developed are justified and remarked. Experiments corresponding to electric vehicle applications are conducted to parameterize the battery model and demonstrate the estimation performance. It shows that the proposed approach is able to estimate SoC with errors less than 0.03 in the presence of initial deviation and persistent noise. Furthermore, the benefits of using the proposed estimator relative to other estimators are calculated over different cycles and conditions.

A Fractional Order Circuit Model of the PT

This paper presents a new digital potential transformer (PT) model. Due to the effect of hysteresis and saturation phenomenon, the magnetization curve of iron core has a strong nonlinear. From the perspective of hysteresis effect of iron core, this article presents a PT core model using the theory of fractional calculus, then propose a new PT circuit model. The model simulates the nonlinear part of iron core using the fractional order expressions and can reflect the feature of saturation. Finally it shows the correctness and validity of the model through the theoretical analysis and simulation results.

A Survey of Fractional-Order Circuit Models for Biology and Biomedicine

In this survey, we present many of the fractional- order circuit models used in biomedicine and biology to fit experimentally collected impedance data. An overview of the different methods used to extract the impedance parameters from collected datasets are also presented. Applications of fractional order circuit models for modelling human tissue, plant physiology, respiratory systems, and tissue-electrode interfaces are presented to highlight the significance of these models and their potential for further research. This survey is of a tutorial nature intended as an introduction to fractional-order circuit models and to consolidate the many models reported across literature.