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22 pages, 4981 KB  
Article
Causal State-Space Reduced-Order Modeling of Sweeping Jet Actuators Using Internal Mixing-Chamber Dynamics
by Shafi Al Salman Romeo and Kursat Kara
Mathematics 2026, 14(10), 1694; https://doi.org/10.3390/math14101694 - 15 May 2026
Viewed by 183
Abstract
Sweeping jet (SWJ) actuators are widely used in active flow control, but explicitly resolving actuator-scale unsteadiness in full-configuration computational fluid dynamics (CFD) remains prohibitively expensive because of the small geometric scales and high-frequency oscillations involved. Existing reduced-order boundary-condition models constructed from exit-plane data [...] Read more.
Sweeping jet (SWJ) actuators are widely used in active flow control, but explicitly resolving actuator-scale unsteadiness in full-configuration computational fluid dynamics (CFD) remains prohibitively expensive because of the small geometric scales and high-frequency oscillations involved. Existing reduced-order boundary-condition models constructed from exit-plane data alone can reproduce the observed switching waveform, but they treat the actuator as an input–output black box and provide limited insight into the internal dynamics that generate the response. This work develops a causal state-space reduced-order modeling framework that links internal mixing-chamber dynamics to time-resolved exit-plane boundary conditions. Proper orthogonal decomposition (POD) is used to obtain a low-dimensional representation of the internal flow, and a data-driven linear evolution operator is identified in the reduced space by least-squares regression of successive snapshot pairs. A POD truncation rank of r=60 is selected from cumulative-energy and validation-error sensitivity analyses, capturing well above 99% of the fluctuation energy while lying within the converged performance regime. A corresponding reduced operator is identified for the exit plane, and spectral comparison reveals near-neutrally stable oscillatory modes in both regions. Using a ±1% relative frequency-matching tolerance, the dominant reduced-operator modes exhibit a 28.3% frequency overlap, providing operator-level evidence that exit-plane oscillations are dynamically linked to internal coherent structures. This correspondence is further supported by cross-spectral coherence analysis between representative internal and exit-plane probe signals, which shows strong coherence at dynamically relevant frequencies. A delayed causal output mapping is then formulated in which the internal reduced state drives the exit-plane response after an identified lag of 149 time steps, corresponding to 2.98×103 s. This delay provides a physically interpretable convective transport timescale from the mixing chamber to the actuator exit. Over the validation interval, the model maintains a mean relative L2 error below 0.02, with maximum normalized errors below 0.04 for most of the prediction horizon, and localized increases are confined to rapid jet-switching events. Field-level reconstructions of streamwise velocity and total pressure show that the model captures both phases of the jet-switching cycle, with errors concentrated primarily in high-gradient shear-layer regions. Compared with exit-only reduced-order models, the proposed internal-driven formulation improves amplitude and phase fidelity over extended prediction horizons. The resulting framework provides a compact, interpretable, operator-based representation of SWJ actuator dynamics suitable for use as a CFD-embeddable dynamic boundary condition. Full article
(This article belongs to the Special Issue Advanced Computational Fluid Dynamics and Applications)
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24 pages, 3883 KB  
Article
Research on FOPID Controller and CMOPSO Optimization for Prevention and Control of Oscillatory Instability at the PCC in a Hydro–Wind–Photovoltaic Grid-Connected System
by Bojin Tang, Weiwei Yao, Teng Yi, Rui Lv, Zhi Wang and Chaoshun Li
Electronics 2026, 15(10), 2104; https://doi.org/10.3390/electronics15102104 - 14 May 2026
Viewed by 117
Abstract
To address the key problems of low-frequency oscillation and insufficient regulation accuracy at the Point of Common Coupling (PCC) in hydro–wind–photovoltaic hybrid systems, which are caused by the randomness of wind and photovoltaic output, the water-hammer effect of hydropower units, and multi-source power [...] Read more.
To address the key problems of low-frequency oscillation and insufficient regulation accuracy at the Point of Common Coupling (PCC) in hydro–wind–photovoltaic hybrid systems, which are caused by the randomness of wind and photovoltaic output, the water-hammer effect of hydropower units, and multi-source power coupling, a joint control strategy based on Fractional-Order Proportional Integral Derivative (FOPID) and Co-evolutionary Multi-objective Particle Swarm Optimization (CMOPSO) is proposed. First, a small-signal transfer function model of the system covering photovoltaic inverters, doubly fed induction generators (DFIGs), hydropower units and voltage-source converter-based high-voltage direct current (VSC-HVDC) converter stations is established to accurately characterize the water-hammer effect and multi-source dynamic coupling characteristics. Second, a Caputo-type FOPID controller is designed. Compared with traditional integer-order controllers with limited tuning flexibility, the FOPID controller utilizes its five degrees of freedom to address specific multi-source coupling challenges. This precisely compensates for the non-minimum phase lag caused by the water-hammer effect in hydropower units via the fractional derivative link, and effectively smooths the impact of stochastic wind–solar fluctuations on PCC voltage through the memory characteristics of the fractional integral link. This multi-parameter regulation mechanism prevents a trade-off between response speed and overshoot suppression, achieving effective decoupling of complex multi-source dynamic interactions. Third, a dual-objective optimization framework with the Integral of Time-weighted Absolute Error (ITAE) and Oscillatory Disturbance Risk Index (ODRI) as the objectives is constructed. The multi-population co-evolution mechanism of the CMOPSO algorithm is adopted to solve the Pareto-optimal solution set, realizing the coordinated optimization of dynamic response accuracy and oscillation instability risk. Finally, comparative simulations are carried out on the Simulink platform with traditional PI/FOPI controllers and optimization algorithms such as Multi-objective Particle Swarm Optimization based on the Decomposition/Simple Indicator-Based Evolutionary Algorithm (MPSOD/SIBEA). The results show that the proposed strategy can effectively suppress low-frequency oscillations in the range of 0~30 Hz. Compared with the traditional PI controller, the PCC voltage overshoot is reduced by more than 40%, the oscillation decay time is shortened by 33%, the ITAE and ODRI indices are decreased by 12.58% and 2.47%, respectively, and the stability of DC bus voltage is significantly improved. Its robustness and comprehensive control performance are superior to existing methods, providing an efficient and stable control scheme for power electronics-dominated complex new energy grid-connected systems. Full article
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27 pages, 26393 KB  
Article
Oil Production Forecasting Under Asymmetric Temporal Dynamics Using Signature-Weighted Kolmogorov–Arnold Network
by Zhidan Yang, Chaoran Zhang, Jiaqi Bian, Jian Zou and Zhong Chen
Symmetry 2026, 18(5), 818; https://doi.org/10.3390/sym18050818 (registering DOI) - 9 May 2026
Viewed by 158
Abstract
Accurate production forecasting of oil wells is of great significance for reservoir management, production optimization, and investment decisions. However, complex subsurface dynamics and sudden operational interventions frequently break the temporal symmetry of production sequences, generating highly asymmetric data distributions. Standard deep sequence architectures [...] Read more.
Accurate production forecasting of oil wells is of great significance for reservoir management, production optimization, and investment decisions. However, complex subsurface dynamics and sudden operational interventions frequently break the temporal symmetry of production sequences, generating highly asymmetric data distributions. Standard deep sequence architectures often suffer from severe phase lag and limited adaptability when modeling such asymmetric regime transitions. To resolve these bottlenecks, we introduce the Signature-Weighted Kolmogorov–Arnold Network with Gated Recurrent Units (SigKAN-GRU). The architecture replaces static node activations with adaptive edge–spline mappings, enabling robust approximation of asymmetric nonlinearities. Path signatures compress high-order asymmetric temporal trajectories into invariant geometric features, a learnable gating kernel filters critical variations, and a final GRU layer enforces explicit sequential memory. This integration bridges long-term depletion trends with abrupt asymmetrical perturbations while maintaining structurally controlled complexity and an interpretable decomposition of nonlinear response and temporal weighting. Validated on two real-world wells with contrasting data characteristics, SigKAN-GRU consistently minimizes absolute error metrics and phase distortions against prevailing baselines. In addition, event-sensitive evaluations further confirm its reliability in peak regions and abrupt shock intervals. The resulting framework translates erratic historical data into robust deterministic forecasts, offering a rigorous quantitative tool for field-level reservoir optimization. Full article
(This article belongs to the Section Computer)
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27 pages, 9150 KB  
Article
Physics-Driven Hybrid Framework for Vehicle State Estimation Using Residual Learning and Adaptive UKF
by Peng Zhou, Yanbin Zhou, Xi Sun, Ziming Li, Mingpu Liu and Ping Han
Appl. Sci. 2026, 16(9), 4230; https://doi.org/10.3390/app16094230 - 26 Apr 2026
Viewed by 260
Abstract
Accurate estimation of vehicle sideslip angle and lateral velocity is essential for the stability control of Advanced Driver Assistance Systems (ADASs). Traditional physics-based observers often exhibit dynamic response distortions under stability-limit conditions due to unmodeled tire relaxation effects, while data-driven methods lack physical [...] Read more.
Accurate estimation of vehicle sideslip angle and lateral velocity is essential for the stability control of Advanced Driver Assistance Systems (ADASs). Traditional physics-based observers often exhibit dynamic response distortions under stability-limit conditions due to unmodeled tire relaxation effects, while data-driven methods lack physical interpretability. This paper proposes a Physics-Driven Hybrid Estimation Framework (PD-HEF) to bridge this gap. First, a nonlinear nominal model is constructed as a physical skeleton, and dynamic residual equations are derived to define learning targets. Second, a Spatio-Temporal Feature Coupled Residual Network is designed to capture time-domain phase lag and compensate for spatial nonlinear deviations. Furthermore, a hybrid unscented Kalman filter is developed to inject predicted residuals into the sigma-point evolution. A Dual-Layer Adaptive Mechanism is also introduced to regulate trust weights based on innovation statistics. Joint simulations demonstrate that the proposed framework reduces the root mean square error by over 60% compared to traditional observers while satisfying real-time constraints. Full article
(This article belongs to the Section Mechanical Engineering)
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18 pages, 2986 KB  
Article
A Compact Closed-Form Dynamic Hysteresis Model for Energy-Loss Prediction in Power Magnetic Components
by Yingjie Tang, Chayma Guemri and Matthew Franchek
Energies 2026, 19(9), 2078; https://doi.org/10.3390/en19092078 - 24 Apr 2026
Viewed by 300
Abstract
Magnetic hysteresis strongly influences energy dissipation and efficiency in power magnetic components under time-varying excitation. This work proposes a compact dynamic hysteresis model using a Hammerstein structure, consisting of a closed-form arctangent static operator followed by a first-order relaxation dynamic stage. The formulation [...] Read more.
Magnetic hysteresis strongly influences energy dissipation and efficiency in power magnetic components under time-varying excitation. This work proposes a compact dynamic hysteresis model using a Hammerstein structure, consisting of a closed-form arctangent static operator followed by a first-order relaxation dynamic stage. The formulation enables direct datasheet-based parameterization and avoids iterative differential solvers or distributed hysteron representations, resulting in low calibration effort and computational cost. The static hysteresis behavior is characterized using four static parameters directly identified from manufacturer B-H datasheets, while dynamic effects are captured using two global calibration parameters derived from datasheet loss curves. This formulation enables accurate reconstruction of major and minor hysteresis loops, while introducing frequency-dependent phase lag and dynamic loop opening. Model performance is evaluated under diverse excitations, including sinusoidal, amplitude-modulated, FORC and chirp signals, showing waveform deviations below 7.2% peak-to-peak NRMSE relative to classical hysteresis models. Energy-loss predictions are validated against manufacturer datasheet curves for ferrite material 3C90 across multiple frequencies, yielding a root-mean-square relative error of 8.3% with 89% of operating points within ±20% deviation. The proposed model provides a datasheet-driven framework for hysteresis and energy-loss prediction in power magnetic components. Full article
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24 pages, 2467 KB  
Article
Comparative Development of Machine Learning Models for Short-Term Indoor CO2 Forecasting Using Low-Cost IoT Sensors: A Case Study in a University Smart Laboratory
by Zhanel Baigarayeva, Assiya Boltaboyeva, Zhuldyz Kalpeyeva, Raissa Uskenbayeva, Maksat Turmakhan, Adilet Kakharov, Aizhan Anartayeva and Aiman Moldagulova
Algorithms 2026, 19(5), 328; https://doi.org/10.3390/a19050328 - 24 Apr 2026
Viewed by 377
Abstract
Unlike reactive systems, mechanical ventilation controlled by CO2 concentration operates at a target efficiency that dynamically increases whenever the target CO2 level is exceeded. This approach eliminates the typical ‘dead-time’ and prevents air quality degradation by ensuring the system adjusts its [...] Read more.
Unlike reactive systems, mechanical ventilation controlled by CO2 concentration operates at a target efficiency that dynamically increases whenever the target CO2 level is exceeded. This approach eliminates the typical ‘dead-time’ and prevents air quality degradation by ensuring the system adjusts its performance immediately in response to concentration changes. In this work, the study focuses on the development and evaluation of data-driven predictive models for near-term indoor CO2 forecasting that can be integrated into pre-occupancy ventilation strategies, rather than designing a complete control scheme. Experimental data were collected over four months in a 48 m2 smart laboratory configured as an open-plan office, where a heterogeneous IoT sensing architecture logged synchronized time-series measurements of CO2 and microclimate variables (temperature, relative humidity, PM2.5, TVOCs), together with acoustic noise levels and appliance-level energy consumption used as indirect occupancy-related signals. Raw telemetry was transformed into a 22-feature state vector using a structured feature engineering method incorporating z-score standardization, cyclic time encodings, multi-horizon CO2 lags, rolling statistics, momentum features, and non-linear interactions to represent temporal autocorrelation and daily periodicity. The study benchmarks multiple regression paradigms, including simple baselines and ensemble methods, and found that an automated multi-level stacked ensemble achieved the highest predictive fidelity for short-term forecasting, with an Mean Absolute Error (MAE) of 32.97 ppm across an observed CO2 range of 403–2305 ppm, representing improvements of approximately 24% and 43% over Linear Regression and K-Nearest Neighbors (KNN), respectively. Temporal diagnostics showed strong phase alignment with observed CO2 rises during occupancy transitions and statistically reliable prediction intervals. Five-fold walk-forward cross-validation confirmed the temporal stability of these results, with top models achieving consistent R2 values of 0.93–0.95 across Folds 2–5. These results demonstrate that, within a single-room university laboratory setting, historical sensor data from low-cost IoT devices can support accurate short-term CO2 forecasting, providing a predictive layer that could support future proactive ventilation scheduling aimed at reducing CO2 lag at the start of occupancy while avoiding unnecessary ventilation runtime. Generalization to other building types and occupancy profiles requires further validation. Full article
(This article belongs to the Special Issue Emerging Trends in Distributed AI for Smart Environments)
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27 pages, 6278 KB  
Article
Obstacle Avoidance Trajectory Planning and ESO-MPC Tracking Control for a 6-DOF Manipulator in Constrained Environments
by Qiushi Hu, Kelong Zhao, Heng Li, Zhirong Wang and Lei Li
Machines 2026, 14(4), 442; https://doi.org/10.3390/machines14040442 - 16 Apr 2026
Viewed by 440
Abstract
To address the challenges of constrained grid-like compartments, a motion framework integrating adaptive obstacle avoidance planning and active disturbance rejection control is proposed. First, an Adaptive Rapidly exploring Random Tree Star (Adaptive RRT*) algorithm based on multi-source state feedback is developed. Scaled-down model [...] Read more.
To address the challenges of constrained grid-like compartments, a motion framework integrating adaptive obstacle avoidance planning and active disturbance rejection control is proposed. First, an Adaptive Rapidly exploring Random Tree Star (Adaptive RRT*) algorithm based on multi-source state feedback is developed. Scaled-down model simulations show that, compared to conventional algorithms, its path length (374.28 mm), planning time (0.30 s), and node count (50.83) are reduced by at least 29.5%, 64.7%, and 28.6%, respectively, achieving a 100% planning success rate. Next, a control scheme based on Extended State Observer–Model Predictive Control (ESO-MPC) is designed. Simulations indicate that under nominal conditions, tracking errors are reduced by 5.78–84.35% compared to traditional MPC. Under a 20% link mass perturbation, the scheme effectively eliminates phase lag. Under complex scenarios involving parameter perturbation and a 0.6 N·m step torque disturbance, the tracking error reduction ranges from 25.27% to 87.59%, exhibiting excellent disturbance rejection robustness. Physical experiments conducted on a scaled-down experimental platform further verify that the maximum tracking errors of the manipulator end-effector along the x, y, and z axes under ESO-MPC are 0.88 mm, 0.85 mm, and 0.89 mm, respectively, significantly outperforming the 2.41 mm, 2.39 mm, and 2.47 mm observed with MPC. Finally, obstacle avoidance and trajectory-tracking simulations of an industrial manipulator in a full-scale ship compartment environment validate the engineering feasibility of the proposed framework. Full article
(This article belongs to the Special Issue Design, Control and Application of Precision Robots)
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36 pages, 431 KB  
Article
Predicting the Volatility of Cryptocurrencies’ Returns Using High-Frequency Data: A Comparative Analysis of GARCH, EGARCH, IGARCH, GJR-GARCH, LRE, and HAR Models
by Abdulrahman Alsamaani and Huda Aldhahi
Int. J. Financial Stud. 2026, 14(4), 90; https://doi.org/10.3390/ijfs14040090 - 3 Apr 2026
Cited by 1 | Viewed by 2188
Abstract
This study provides a comprehensive evaluation of six volatility forecasting models applied to twelve dominant and less dominant cryptocurrencies across multiple time horizons using high-frequency intraday data. The exponential generalized autoregressive conditional heteroskedastic (EGARCH), integrated GARCH (IGARCH), standard GARCH, GJR-GARCH, lagged realized volatility [...] Read more.
This study provides a comprehensive evaluation of six volatility forecasting models applied to twelve dominant and less dominant cryptocurrencies across multiple time horizons using high-frequency intraday data. The exponential generalized autoregressive conditional heteroskedastic (EGARCH), integrated GARCH (IGARCH), standard GARCH, GJR-GARCH, lagged realized volatility (LRE), and heterogeneous autoregressive (HAR) models are systematically compared using 5 min computed return data from September 2018 to September 2020. Our analysis encompasses three forecast horizons (1-day, 7-day, and 30-day) to assess model performance under varying temporal constraints. Through univariate Mincer–Zarnowitz regressions, encompassing tests, and out-of-sample evaluation using root mean squared error (RMSE) and quasi-likelihood loss (QLIKE) functions, we identify significant performance heterogeneity across models and cryptocurrencies. The HAR model exhibits stronger predictive accuracy at short horizons, while EGARCH exhibits relatively stronger performance at longer horizons, although overall explanatory power declines as forecast horizon increases. Importantly, no single model consistently provides optimal forecasts across all cryptocurrencies. Consistent with prior evidence suggesting model performance varies across assets. Encompassing regressions reveal that combining HAR with EGARCH specifications significantly enhances explanatory power across all temporal frames. Out-of-sample Diebold–Mariano tests indicate that HAR generates the lowest forecast errors for most cryptocurrencies, though EGARCH performs exceptionally well for high-market-capitalization assets. These findings provide regime-conditional insights into horizon- and asset-specific volatility dynamics during the pre-institutionalization phase of cryptocurrency markets. The study contributes to emerging literature by incorporating less-dominant cryptocurrencies and offering robust empirical evidence on the asymmetric and persistent volatility characteristics unique to digital asset markets. These findings should be interpreted within the context of the 2018–2020 sample period, representing a pre-institutionalized phase of cryptocurrency markets, and may not fully generalize to structurally different market regimes characterized by increased institutional participation and regulatory development. Full article
28 pages, 4302 KB  
Article
Short-Term Photovoltaic Power Forecasting Based on CNN–LSTM–Attention Mechanism
by Mingze Lei, Tao Chen, Yao Xiao, Caixia Yang, Worawat Sa-Ngiamvibool, Supannika Wattana and Buncha Wattana
Energies 2026, 19(7), 1747; https://doi.org/10.3390/en19071747 - 2 Apr 2026
Viewed by 670
Abstract
Accurate short-term photovoltaic (PV) power forecasting is crucial for maintaining grid stability. However, existing hybrid deep learning models suffer from inherent limitations owing to static feature-weighting mechanisms, often displaying significant phase lag and peak clipping under severe meteorological fluctuations. To address this, in [...] Read more.
Accurate short-term photovoltaic (PV) power forecasting is crucial for maintaining grid stability. However, existing hybrid deep learning models suffer from inherent limitations owing to static feature-weighting mechanisms, often displaying significant phase lag and peak clipping under severe meteorological fluctuations. To address this, in this study, we adopt a hybrid CNN–LSTM–Attention forecasting framework incorporating an SE-based attention strategy. Field validation at a 150 kW PV power plant in Ningxia, China, demonstrated that the adopted model achieved a Root Mean Square Error (RMSE) convergence of 2.157 kW. Notably, this represented a 41.92% reduction in error compared to the standard LSTM benchmark and a further 16.46% improvement over the suboptimal CNN-LSTM baseline, explicitly confirming the specific contribution of the SE-based attention mechanism. Moreover, multi-weather evaluations and ablation studies confirm the framework’s robustness. Dynamic Time Warping (DTW) and Diebold–Mariano (DM) tests establish its statistical superiority and the reduction in phase lag against baselines. Residual analysis reveals a leptokurtic distribution with white noise properties, confirming the reduction in systematic bias. Consequently, this high-fidelity tracking allows precise minute-level ramping detection and decreases spinning reserve demands in practical power dispatch. Full article
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30 pages, 3234 KB  
Article
Modeling and Optimization of an Automatic Temperature Control System for the Catalytic Cracking Process
by Yury Ilyushin, Alexander Vitalevich Martirosyan, Mir-Amal Asadulagi and Tatyana Kukharova
Modelling 2026, 7(2), 68; https://doi.org/10.3390/modelling7020068 - 30 Mar 2026
Cited by 2 | Viewed by 741
Abstract
Modern oil refining is faced with the need to maximize raw material processing in the face of fierce competition and environmental requirements. Therefore, the fluid catalytic cracking (FCC) process, key to the production of high-octane gasoline, requires special attention to automation efficiency. Maintaining [...] Read more.
Modern oil refining is faced with the need to maximize raw material processing in the face of fierce competition and environmental requirements. Therefore, the fluid catalytic cracking (FCC) process, key to the production of high-octane gasoline, requires special attention to automation efficiency. Maintaining optimal reactor temperature is a complex scientific and technical challenge, the solution to which directly impacts the yield of target products and the service life of the catalyst. Existing automatic control systems often fail to cope with process transients, nonlinearities, and time delays, making the search for new control approaches highly relevant. The scientific significance of this study lies in the system analysis and quantitative comparison of the effectiveness of classical control laws (P, PI, PID) applied to a plant with a delay. For the first time, a rigorous comparative analysis of tuning methods—analytical (based on phase margin specifications) and automated (using the PID Tuner tool in MATLAB Simulink R2024b)—is performed for a plant characterized as a second-order system with time delay, formed by the series connection of two first-order lag elements with transport delay. The results contribute to automatic control theory by clearly demonstrating the limitations of the proportional controller and the insufficient speed of the integral controller, as well as confirming the hypothesis that a PID law is necessary to achieve a balance between accuracy and response speed under inertia conditions. The practical significance of the work is confirmed by the development of an optimized automatic temperature control system. Using the PID Tuner tool, we achieved critical industrial performance indicators: zero static error, minimal control time (44 s), and acceptable overshoot (9.6%). The system’s robustness (maintaining stability with changes in plant parameters by 30–40%) and its invariance to the main disturbance (catalyst temperature fluctuations), confirmed during simulation, guarantee the viability of the proposed solution under real-world production conditions. Implementation of such a controller will minimize deviations from the process conditions, leading to increased yield of light petroleum products and an extended service life of the expensive catalyst, providing direct economic benefits. Full article
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22 pages, 4990 KB  
Article
Parametric Optimization of Sensible Thermocline Packed Bed Thermal Energy Storage Systems: A Computation Fluid Dynamics Study
by Lahcen El-Mahaouchi, Mourad Yessef, Hamza El Hafdaoui, Jouhayna Bouanani, Saad A. Alqahtani, Z. M. S. El-Barbary and Ahmed Lagrioui
Sustainability 2026, 18(7), 3333; https://doi.org/10.3390/su18073333 - 30 Mar 2026
Viewed by 418
Abstract
Mathematical and numerical models for Packed Bed Thermal Energy Storage (PBTES) systems are essential to predict the different parameters that influence their thermodynamic behavior and then optimize their performance and efficiency. In this research paper, an industrial-scale sensible thermocline Packed Bed Thermal Energy [...] Read more.
Mathematical and numerical models for Packed Bed Thermal Energy Storage (PBTES) systems are essential to predict the different parameters that influence their thermodynamic behavior and then optimize their performance and efficiency. In this research paper, an industrial-scale sensible thermocline Packed Bed Thermal Energy Storage system (9.17 m high and 4.72 m in diameter) was modeled and simulated during the heat charging process, based on FEM, CFD one-dimensional, and two-phase analysis. The model rigorously couples the Local Thermal Non-Equilibrium (LTNE) energy formulation with Darcy–Forchheimer hydrodynamics. The developed model was verified and validated using experimental data from the literature. The model was in close agreement with the experiment, with a global mean relative error of 3.62%. The two-dimensional velocity and temperature fields were presented to describe flow and temperature distributions in the hybrid medium (free and porous). The effect of varying flow rates (8–15 kg/s), porosities (0.35–0.55), and particle diameters (5–20 cm) on the thermal behavior of the heat storage system, temperature fields for solid and fluid, thermocline behavior, and charge efficiency were evaluated and presented. The simulation results demonstrate that the system achieves a high charge efficiency of 92.3% at a nominal charging rate of 15 kg/s. Increasing mass flow rate accelerates charging but widens the thermocline thickness and thermal stratification. Furthermore, increasing the porosity from 0.35 to 0.55 reduced charging time, decreased the temperature difference between the HTF and the storage medium by 10 °C, and increased the final heat charging efficiency by 8%. On the contrary, an increase in particle size from 5 to 20 cm leads to a slower rise in temperature within the solid phase, creating an important LTNE lag of ≈34 °C, thereby reducing the final heat charge efficiency by 16%, and prolonging the time required to charge the tank. Full article
(This article belongs to the Section Energy Sustainability)
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24 pages, 5962 KB  
Article
Power Reconstruction and Quantitative Analysis of Photovoltaic Cluster Fluctuation Characteristics Considering Cloud Movement Time Lag
by Gangui Yan, Jianshu Li, Aolan Xing and Weian Kong
Electronics 2026, 15(6), 1172; https://doi.org/10.3390/electronics15061172 - 11 Mar 2026
Viewed by 343
Abstract
The power fluctuation of large-scale photovoltaic (PV) clusters is significantly affected by cloud movement. Aiming at the engineering reality that meteorological observation data are generally lacking for most power stations in wide-area PV clusters, as well as the problem that existing models overfit [...] Read more.
The power fluctuation of large-scale photovoltaic (PV) clusters is significantly affected by cloud movement. Aiming at the engineering reality that meteorological observation data are generally lacking for most power stations in wide-area PV clusters, as well as the problem that existing models overfit second-order high-frequency noise such as microscopic cloud deformation, this paper proposes a disturbance reconstruction and smoothing effect quantification method for PV clusters focusing on the first-order dominant meteorological component. First, a clear-sky model is introduced as a deterministic trend filter to extract the purely random disturbance sequence that induces grid-connection risks from the measured output power. Second, the dimensionality reduction modeling concept of “macro-advection dominance and microscopic deformation filtering” is established: the PV cluster is finely partitioned by fusing Dynamic Time Warping (DTW) and geographical distance, and a cross-space inversion of the macro-cloud velocity vector is realized, driven by pure power data using the Time-Lagged Cross-Correlation (TLCC) algorithm, thus constructing a disturbance power generation model that accounts for the phase misalignment of power output. Independent verification based on measured data in Jilin Province shows that the 95% confidence interval of the power reconstructed only by the first-order advection characteristics can cover 90.2% of the measured fluctuations, and the reconstruction error of the fluctuation standard deviation—an indicator that determines the system reserve demand—is merely 5.9%. This verifies that the macro-cloud displacement is the absolute dominant factor governing the extreme fluctuations of PV clusters. Finally, a normalized Smoothing Factor (SF) characterizing the “reserve capacity release ratio” is constructed, and combined with its statistical indicators, it is used to quantitatively evaluate the smoothing benefits provided by different spatial layout schemes. Under data-constrained conditions, the method proposed in this paper verifies the engineering rationality that microscopic meteorological noise can be safely neglected at the macro-PV cluster scale, providing a reliable quantitative basis for the safe grid expansion and peak-shaving energy storage capacity sizing of high-proportion PV bases. Full article
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22 pages, 4485 KB  
Article
Design and Validation of a Real-Time FPGA-Based PID Control System for Angular Positioning in Servo-Hydraulic Actuators
by Ersin Tural and Rıza Emre Ergün
Machines 2026, 14(3), 315; https://doi.org/10.3390/machines14030315 - 10 Mar 2026
Viewed by 946
Abstract
Electro-hydraulic servo systems (EHSS) are widely used in industrial applications due to their high power-to-weight ratio; however, their nonlinear dynamics pose significant challenges for precise position control. This study proposes and validates a real-time Proportional–Integral–Derivative (PID) control system implemented on a Field Programmable [...] Read more.
Electro-hydraulic servo systems (EHSS) are widely used in industrial applications due to their high power-to-weight ratio; however, their nonlinear dynamics pose significant challenges for precise position control. This study proposes and validates a real-time Proportional–Integral–Derivative (PID) control system implemented on a Field Programmable Gate Array (FPGA) platform for the angular positioning of a servo-hydraulic actuator. The control algorithm is deployed on an embedded system to achieve high-speed execution independent of host processing. The controller gains were tuned using system identification techniques based on step response analysis. The system’s performance was experimentally assessed under both step inputs and sinusoidal trajectories. Experimental results demonstrated that the proposed controller achieved a rise time of 0.06 s and a steady-state error within ±1° for small step inputs. Furthermore, frequency domain analysis via Bode diagrams validated the system’s dynamic bandwidth, showing exceptional tracking capabilities at 10 Hz excitation with a negligible phase lag of −0.71°. These findings confirm that an FPGA-based PID control architecture effectively overcomes hydraulic nonlinearities, providing a robust and precise solution for real-time motion control compared to traditional methods. Full article
(This article belongs to the Section Automation and Control Systems)
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35 pages, 941 KB  
Article
Bioenergy from Maize Silage by Anaerobic Digestion: Batch Kinetics in Relation to Biochemical Composition
by Krzysztof Pilarski, Agnieszka A. Pilarska, Michał B. Pietrzak and Bartłomiej Igliński
Energies 2026, 19(4), 1105; https://doi.org/10.3390/en19041105 - 22 Feb 2026
Cited by 1 | Viewed by 850
Abstract
Maize silage can play a key role in policies aimed at stabilising local energy systems, as it constitutes a critical renewable feedstock for European biogas plants. By providing a dense and predictable source of chemical energy, it supports balance and reliability in the [...] Read more.
Maize silage can play a key role in policies aimed at stabilising local energy systems, as it constitutes a critical renewable feedstock for European biogas plants. By providing a dense and predictable source of chemical energy, it supports balance and reliability in the agricultural energy sector. To convert this potential into stable energy production, operators require kinetic models that translate routine silage quality indicators into concrete guidance for digester operation and control. Therefore, the aim of this article was to evaluate the batch kinetics of anaerobic digestion (AD) of maize silage and to select an adequate model for describing biochemical methane potential (BMP) profiles and associated energy recovery in the context of start-up, organic loading rate (OLR), hydraulic retention time (HRT) and feedstock preparation. Ten batches of silage (A–J) were examined, covering a realistic range of pH, electrical conductivity (EC), dry and volatile solids, ash, protein–fat–fibre fractions, fibre composition (NDF, ADF and ADL), derived fractions (hemicellulose, cellulose, and residual organic matter (OM)), C/N ratio and macro-/micronutrient profiles, including trace elements relevant to methanogenesis (Ni, Co, Mo, and Se). BMP tests were carried out in batch mode, and the resulting curves were fitted using the modified Gompertz and a first-order kinetic model. Methane yields of approx. 100–120 m3 CH4/Mg fresh matter (FM) and 336–402 m3 CH4/Mg volatile solids (VS), with CH4 contents of 52–57% v/v, were typical for energy-grade maize silage. Kinetic and energetic behaviours were governed mainly by residual OM and hemicellulose (shortening the lag phase and increasing the maximum methane production rate), the ADL/cellulose ratio (controlling the slower hydrolytic tail), EC and Na/Cl/S (extending the lag phase), and C/N together with Ni/Co/Mo/Se (stabilising methanogenesis). The modified Gompertz model reproduced BMP curves with a pronounced lag phase and asymmetry more accurately (lower error and better information criterion values), and its parameters directly support start-up design, OLR ramp-up and energetic performance optimisation in bioenergy reactors. The novelty of this work lies in combining batch BMP tests, comparative kinetic modelling and detailed silage characterisation to establish quantitative links between kinetic parameters and routine maize silage quality indicators that are directly relevant for biogas plant operation and renewable energy production. Full article
(This article belongs to the Section A4: Bio-Energy)
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Article
Generalized Proportional–Integral–Derivative Interpretation of a Class of Improved Two-Degree-of-Freedom Controllers
by Wenfei Yu, Ping Lin, Shang Jiang and Xu Fang
Sensors 2026, 26(2), 466; https://doi.org/10.3390/s26020466 - 10 Jan 2026
Viewed by 593
Abstract
In the framework of the traditional active disturbance rejection controller (ADRC), the state error feedback utilizes estimated values from the extended state observer, which may introduce phase lag. Therefore, academic researchers have proposed a modified version called the improved linear ADRC that employs [...] Read more.
In the framework of the traditional active disturbance rejection controller (ADRC), the state error feedback utilizes estimated values from the extended state observer, which may introduce phase lag. Therefore, academic researchers have proposed a modified version called the improved linear ADRC that employs output values from the plant for state error feedback except the output value from the extended state observer. However, there is limited literature exploring the relationship between traditional linear ADRC and improved linear ADRC. To address this gap, this article establishes mathmatical relationship between traditional linear ADRC and improved linear ADRC from the generalized PID control perspective, highlighting their distinctions in the frequency domain. Compared to the traditional ADRC, the improved ADRC incorporates differential terms and offers a novel approach to realize the generalized PID control via generalized PID interpretation. And to be more specific, the improved ADRC is a new way to realize the generalized PID control by three tuned parameters, and the number of parameters of the improved ADRC is fewer than that of the generalized PID control. From the time domain, numerical simulation results demonstrate that improved ADRC exhibits superior control performance by eliminating overshoot during set value tracking processes compared to the traditional ADRC. From the disturbance rejection simulations in direct current to direct current converter (DCDC), the improved ADRC can achieve better disturbance rejection performance than the traditional ADRC. The DC bus voltage drop values of the traditional ADRC are 55.8 V and 32 V; thus, the biggest voltage drop is 55.8 V, which is 7.44 times the the improved ADRC. The voltage rise of improved ADRC can be neglected compared to the voltage rise of the traditional ADRC. From the tracking performance perspective, the time to fully reach the reference value of the traditional ADRC is about 0.3 s, and the time to fully reach the reference value of the improved ADRC is about 0.15 s. Full article
(This article belongs to the Collection Sensors and Intelligent Control Systems)
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