Search Results (96)

Fractional-order calculus (FOC) has gained significant attention in electric vehicle (EV) energy storage and management systems, as it provides enhanced modeling and analysis capabilities compared to traditional integer-order approaches. This review presents a comprehensive survey of recent advancements in the application of FOC to EV energy storage systems, including lithium-ion batteries (LIBs), supercapacitors (SCs), and fuel cells (FCs), as well as their integration within energy management systems (EMS). The review focuses on developments in electrochemical, equivalent circuit, and data-driven models formulated in the fractional-order domain, which improve the representation of nonlinear, memory-dependent, and multi-scale dynamics of energy storage devices. It also discusses the benefits and limitations of current FOC-based models, identifies open challenges such as computational feasibility and parameter identification, and outlines future research directions. Overall, the findings indicate that FOC offers a robust framework with significant potential to advance next-generation EV energy storage and management systems. Full article

Supercapacitors (SCs) are emerging as a dependable energy storage technology in industrial applications, valued for their high power output and exceptional longevity. In high-power applications, SCs are not used as single cells but are configured in a series–parallel combination to form a bank. Accurate state-of-charge estimation is essential for effective energy management in power systems employing SC banks. This work presents a novel state estimation approach for SC banks. First, a dynamic model of an SC bank is derived by applying a fractional-order Thévenin equivalent circuit to a single-cell SC. Then, an observability analysis is conducted, which reveals that the system is empirically weakly observable. This is the fundamental challenge for state-of-the-art observers to robustly perform state estimation. To address this challenge, an implicitly regularized observer is developed based on generalized parameter estimation techniques. The performance of the proposed observer is benchmarked against a fractional-order extended Kalman filter using experimental data. The results demonstrate that incorporating a regularization law into the observer dynamics effectively mitigates observability limitations, offering a robust solution for the SC bank state estimation. Full article

This paper presents a novel four-dimensional autonomous conservative model characterized by an infinite set of equilibrium points and an unusual algebraic structure in which all eigenvalues of the Jacobian matrix are zero. The linearization of the proposed model implies that classical stability analysis is inadequate, as only the center manifolds are obtained. Consequently, the stability of the system is investigated through both analytical and numerical methods using Lyapunov functions and numerical simulations. The proposed model exhibits rich dynamics, including hyperchaotic behavior, which is characterized using the Lyapunov exponents, bifurcation diagrams, sensitivity analysis, attractor projections, and Poincaré map. Moreover, in this paper, we explore the model with fractional-order derivatives, demonstrating that the fractional dynamics fundamentally change the geometrical structure of the attractors and significantly change the system stability. The Grünwald–Letnikov formulation is used for modeling, while numerical integration is performed using the Caputo operator to capture the memory effects inherent in fractional models. Finally, an analog electronic circuit realization is provided to experimentally validate the theoretical and numerical findings. Full article

This paper presents three novel sufficient and necessary conditions for the admissibility of singular fractional-order systems (FOSs), a stabilization criterion, and a solution algorithm. The strict linear matrix inequality (LMI) stability criterion for integer-order systems is generalized to singular FOSs by using column-full rank matrices. This admissibility criterion does not involve complex variables and is different from all previous results, filling a gap in this area. Based on the LMIs in the generalized condition, the improved criterion utilizes a variable substitution technique to reduce the number of matrix variables to be solved from one pair to one, reflecting the admissibility more essentially. This improved result simplifies the programming process compared to the traditional approach that requires two matrix variables. To complete the state feedback controller design, the system matrices in the generalized admissibility criterion are decoupled, but bilinear constraints still occur in the stabilization criterion. For this case, where a feasible solution cannot be found using the MATLAB LMI toolbox, a branch-and-bound algorithm (BBA) is designed to solve it. Finally, the validity of these criteria and the BBA is verified by three examples, including a real circuit model. Full article

Next-generation smart sensing devices necessitate on-chip integration of power-efficient reference circuits. The latters are required to provide other circuit blocks with highly reliable bias signals, even in the presence of temperature shifts and supply voltage disturbances, while draining a small fraction of the overall power budget. In particular, it is especially challenging to design current references with enhanced robustness and efficiency; hence, thorough exploration of novel architectures and design approaches is needed for this type of circuits. In this work, we propose a novel CMOS-only current reference, achieving temperature compensation by exploiting geometry dependences of the threshold voltage (specifically, the reverse short-channel effect and the narrow-channel effect). This allows reaching first-order temperature compensation within a single current reference core. Implemented in 0.18 µm CMOS, a version of the proposed current reference designed to deliver 141 nA (with 377 nW of total power consumption) achieved an average temperature coefficient equal to 194 ppm/°C (from −20 °C to 80 °C) and an average line sensitivity of −0.017%/V across post-layout statistical Monte Carlo simulations. Based on such findings, the newly proposed design methodology stands out as a noteworthy solution to design robust current references for power-constrained mixed-signal systems-on-chip. Full article

The high-fidelity lithium-ion battery (LIB) models are crucial for realizing an accurate state estimation in battery management systems (BMSs). Recently, the fractional-order equivalent circuit models (FOMs), as a frequency-domain modeling approach, offer distinct advantages for constructing high-precision battery models in field of electric vehicles. However, the quantitative evaluations and adaptability of these models under different driving cycle datasets are still lacking and challenging. For this reason, comparative evaluations of different FOMs using a novel drive cycle dataset of a battery was carried out in this paper. First, three typical FOMs were initially established and the particle swarm optimization algorithm was then employed to identify model parameters. Complementarily, the efficiency and accuracy of the offline identification for three typical FOMs are also discussed. Subsequently, the terminal voltages of these different FOMs were investigated and evaluated under dynamic operating conditions. Results demonstrate that the FOM-W model exhibits the highest superiority in simulation accuracy, achieving a mean absolute error (MAE) of 9.2 mV and root mean square error (RMSE) of 19.1 mV under Highway Fuel Economy Test conditions. Finally, the accuracy verification of the FOM-W model under two other different dynamic operating conditions has also been thoroughly investigated, and it could still maintain a RMSE and MAE below 21 mV, which indicates its strong adaptability and generalization compared with other FOMs. Conclusions drawn from this paper can further guide the selection of battery models to achieve reliable state estimations of BMS. Full article

Fractional-order four-wing (FO 4-wing) systems are of significant importance due to their complex dynamics and wide-ranging applications in secure communications, encryption, and nonlinear circuit design, making their control and stabilization a critical area of study. In this research, a novel model-free finite-time flexible sliding mode control (FTF-SMC) strategy is developed for the stabilization of a particular category of hyperchaotic FO 4-wing systems, which are subject to unknown uncertainties and input saturation constraints. The proposed approach leverages fractional-order Lyapunov stability theory to design a flexible sliding mode controller capable of effectively addressing the chaotic dynamics of FO 4-wing systems and ensuring finite-time convergence. Initially, a dynamic sliding surface is formulated to accommodate system variations. Following this, a robust model-free control law is designed to counteract uncertainties and input saturation effects. The finite-time stability of both the sliding surface and the control scheme is rigorously proven. The control strategy eliminates the need for explicit system models by exploiting the norm-bounded characteristics of chaotic system states. To optimize the parameters of the model-free FTF-SMC, a deep reinforcement learning framework based on the adaptive dynamic programming (ADP) algorithm is employed. The ADP agent utilizes two neural networks (NNs)—action NN and critic NN—aiming to obtain the optimal policy by maximizing a predefined reward function. This ensures that the sliding motion satisfies the reachability condition within a finite time frame. The effectiveness of the proposed methodology is validated through comprehensive simulations, numerical case studies, and comparative analyses. Full article

The dielectric relaxation behavior of polymeric materials is critical to their performance in electronic, insulating, and energy storage applications. This study presents an electrical fractional model (EFM) based on fractional calculus and the complex electric modulus ($M^{*}\mathit{=}{M}^{\prime }\mathit{+}i{M}^{″}$) formalism to simultaneously describe two key relaxation phenomena: $\alpha$-relaxation and interfacial polarization (Maxwell–Wagner–Sillars effect). The model incorporates fractional elements (cap-resistors) into a modified Debye equivalent circuit to capture polymer dynamics and energy dissipation. Fractional differential equations are derived, with fractional orders taking values between 0 and 1; the frequency and temperature responses are analyzed using Fourier transform. Two temperature-dependent behaviors are considered: the Matsuoka model, applied to $\alpha$-relaxation near the glass transition, and an Arrhenius-type equation, used to describe interfacial polarization associated with thermally activated charge transport. The proposed model is validated using literature data for amorphous polymers, polyetherimide (PEI), polyvinyl chloride (PVC), and polyvinyl butyral (PVB), successfully fitting dielectric spectra and extracting meaningful physical parameters. The results demonstrate that the EFM is a robust and versatile tool for modeling complex dielectric relaxation in polymeric systems, offering improved interpretability over classical integer-order models. This approach enhances understanding of coupled relaxation mechanisms and may support the design of advanced polymer-based materials with tailored dielectric properties. Full article

The present work proposes a novel fractional-order multifunction filter topology in current-mode (CM), which is designed based on the Modified Current Feedback Operational Amplifier (MCFOA). The proposed design simultaneously generates fractional-order low-pass (FO-LPF), high-pass (FO-HPF), and band-pass (FO-BPF) outputs while utilizing an optimized set of essential active and passive elements, thereby ensuring simplicity, cost efficiency, and compatibility with integrated circuits (ICs). The fractional-order feature allows precise control over the transition slope between the passband and the stopband, enhancing design flexibility. PSpice simulations validated the filter’s theoretical performance, confirming a 1 kHz cut-off frequency, making it suitable for VLF applications such as military communication and submarine navigation. Monte Carlo analyses demonstrate robustness against parameter variations, while a low THD, a wide dynamic range, and low power consumption highlight its efficiency for high-precision, low-power applications. This work offers a practical and adaptable approach to fractional-order circuit design, with significant potential in communication, control, and biomedical systems. Full article

This study examines how the effective dielectric characteristics of the human torso affect the carrier-link-margin (CLM) and data-link-margin (DLM) of a biocompatible gelatin-encapsulated implantable medical device (IMD) that consists of a small implantable antenna, battery, printed circuit board (PCB), camera, and sensor operating at 2.5 GHz. The specific absorption rate (SAR) and the radio frequency (RF) link performances of the IMD are tested for ±20% changes in reference to the mean values of the effective relative permittivity, ɛ_eff, and the effective conductivity, σ_eff, of the human body model. An artificial neural network (ANN) with two inputs (ɛ_eff, σ_eff) and five outputs (SAR_1 g, SAR_10 g, fractional bandwidth, CLM, and DLM) is trained by 80% of the total scenarios and tested by 20% of them in order to provide reliable dependent analyses. The highest changes in 1 g SAR value, 10 g SAR value, fractional bandwidth, CLM, and DLM at a 4 m distance for 100 Kbps are 63%, 41.6%, 17.97%, 26.79%, and 5.89%, respectively, when compared to the reference effective electrical properties of the homogeneous human body model. This work is the first to accurately depend on the electrical analyses of the human body for the link margins of an implantable antenna system. Furthermore, the work’s uniqueness is distinguished by the application of the CLM and DLM principles in the sphere of IMD communication. Full article

This article investigates non-fragile synchronization control and circuit implementation for incommensurate fractional-order (IFO) chaotic neural networks with parameter uncertainties. In this paper, we explore three aspects of the research challenges, i.e., theoretical limitations of uncertain IFO systems, the fragility of the synchronization controller, and the lack of circuit implementation. First, we establish an IFO chaotic neural network model incorporating parametric uncertainties, extending beyond conventional commensurate-order architectures. Second, a novel, non-fragile state-error feedback controller is designed. Through the formulation of FO Lyapunov functions and the application of inequality scaling techniques, sufficient conditions for asymptotic synchronization of master–slave systems are rigorously derived via the multi-order fractional comparison principle. Third, an analog circuit implementation scheme utilizing FO impedance units is developed to experimentally validate synchronization efficacy and accurately replicate the system’s dynamic behavior. Numerical simulations and circuit experiments substantiate the theoretical findings, demonstrating both robustness against parameter perturbations and the feasibility of circuit realization. Full article

This paper presents a circuit design methodology for the analog realization of time-varying fractional-order chaotic systems. While most existing studies implement such systems by switching between two or more constant fractional orders, these approaches become impractical when the fractional order changes smoothly over time. To overcome this limitation, the proposed method introduces a transfer function approximation specifically designed for variable fractional-order integrators. The formulation relies on a linear and time-invariant definition of the fractional-order operator, ensuring compatibility with Laplace-domain analysis. Under the condition that the fractional-order function is Laplace-transformable and its Bode plot slope lies between $-20$ dB/decade and 0 dB/decade, the system is realized using op-amps and standard RC components. The Grünwald–Letnikov method is employed for numerical calculation of phase portraits, which are then compared with simulation and experimental results. The strong agreement among these results confirms the effectiveness of the proposed method. Full article

The current research study presents a comprehensive analysis of the local discontinuous Galerkin (LDG) method for solving multi-order fractional differential equations (FDEs), with an emphasis on circuit modeling applications. We investigated the existence, uniqueness, and numerical stability of LDG-based discretized formulation, leveraging the Liouville–Caputo fractional derivative and upwind numerical fluxes to discretize governing equations while preserving stability. The method was validated through benchmark test cases, including comparisons with analytical solutions and established numerical techniques (e.g., Gegenbauer wavelets and Dickson collocation). The results demonstrate that the LDG method achieves high-accuracy solutions (e.g., with a relatively large time step size) and reduced computational costs, which are attributed to its element-wise formulation. These findings position LDG as a promising tool for complex scientific and engineering applications, particularly in modeling fractional-order systems such as RL, RLC circuits, and other electrical circuit equations. Full article

Half-bridge converter series microgrid (HBCS-MG) is susceptible to a variety of uncertainties and disturbances during operation, and therefore, the use of the traditional integer-order models cannot accurately reflect the effects of environmental variations on internal components of the off-grid system, such as converters, filters, and loads, including factors like time delays, memory effects, and multi-scale coupling. The fractional-order control method is better equipped to deal with these disturbances, thereby enhancing the robustness and stability of the system. In the off-grid state, a fractional-order PI (FOPI) controller is employed for double-closed-loop control, and the load voltage feedforward control is utilized to offset the impact of load voltage fluctuations on the system. A new simplified equivalent circuit calculation method for the fractional-order inductor is proposed, and a complete fractional mathematical model of the system in the dq rotating coordinate system is established to obtain the transfer function between the load voltage and the input voltage. Furthermore, the impact of the fractional-order variation of the FOPI controllers and the fractional elements on system performance in the frequency domain and time domain is described in detail. The simulation results are compared with the theoretical analysis to demonstrate the accuracy of the mathematical model. The overshoot of the load voltage at the switching instant of 0.7 s is reduced by 4.2% compared with the integer-order PI controller, which proves that the fractional-order controller can improve the system control accuracy. Full article

Open-circuit (OC) faults in power converters are common issues in motor drive systems, significantly affecting the safe and stable operation of the system. Conventional models can accurately diagnose faults under a single operating condition. However, when conditions change, these models may fail to recognize new fault features, resulting in a decrease in diagnosis accuracy. To address this challenge, this paper proposes a lifelong learning-enabled fractional order-convolutional encoder model for open-circuit fault diagnosis of power converters under multi-conditions. Firstly, the model automatically extracts and identifies fault signal features using the convolutional module and the encoder module, respectively. Subsequently, the model’s iterative computational process is optimized by learning historical gradient information through fractional order, and enhancing the model’s ability to capture the long-term dependencies inherent in fault signals. Finally, a multilevel lifelong learning framework has been established to enable the model to continuously learn the fault features of power converter under multi-conditions, thereby avoiding catastrophic forgetting that can occur when the model learns different tasks. The proposed model effectively addresses the challenge of low fault diagnosis accuracy that occurs when the operating conditions of the power converter change, achieving a diagnosis accuracy of 96.89% across 85 fault categories under multi-conditions. Full article