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Search Results (925)

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Keywords = input and output stability

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17 pages, 1544 KB  
Article
Evaluation of Photovoltaic Generation Forecasting Using Model Output Statistics and Machine Learning
by Eun Ji Kim, Yong Han Jeon, Youn Cheol Park, Sung Seek Park and Seung Jin Oh
Energies 2026, 19(2), 486; https://doi.org/10.3390/en19020486 - 19 Jan 2026
Abstract
Accurate forecasting of photovoltaic (PV) power generation is essential for mitigating weather-induced variability and maintaining power-system stability. This study aims to improve PV power forecasting accuracy by enhancing the quality of numerical weather prediction (NWP) inputs rather than modifying forecasting model structures. Specifically, [...] Read more.
Accurate forecasting of photovoltaic (PV) power generation is essential for mitigating weather-induced variability and maintaining power-system stability. This study aims to improve PV power forecasting accuracy by enhancing the quality of numerical weather prediction (NWP) inputs rather than modifying forecasting model structures. Specifically, systematic errors in temperature, wind speed, and solar radiation data produced by the Unified Model–Local Data Assimilation and Prediction System (UM-LDAPS) are corrected using a Model Output Statistics (MOS) approach. A case study was conducted for a 20 kW rooftop PV system in Buan, South Korea, comparing forecasting performance before and after MOS application using a random forest-based PV forecasting model. The results show that MOS significantly improves meteorological input accuracy, reducing the root mean square error (RMSE) of temperature, wind speed, and solar radiation by 38.1–62.3%. Consequently, PV power forecasting errors were reduced by 70.0–78.7% across lead times of 1–6 h, 7–12 h, and 19–24 h. After MOS correction, the normalized mean absolute percentage error (nMAPE) remained consistently low at approximately 7–8%, indicating improved forecasting robustness across the evaluated lead-time ranges. In addition, an economic evaluation based on the Korean renewable energy forecast-settlement mechanism estimated an annual benefit of approximately 854 USD for the analyzed 20 kW PV system. A complementary valuation using an NREL-based framework yielded an annual benefit of approximately 296 USD. These results demonstrate that improving meteorological data quality through MOS enhances PV forecasting performance and provide measurable economic value. Full article
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13 pages, 2796 KB  
Article
Real-Time Implementation of Auto-Tuned PID Control in PMSM Drives
by Adile Akpunar Bozkurt
Machines 2026, 14(1), 100; https://doi.org/10.3390/machines14010100 - 15 Jan 2026
Viewed by 109
Abstract
Permanent magnet synchronous motors (PMSM) are widely favored in industry for their high efficiency, compact size, and robust performance. This study employs a model-based PID control approach for speed regulation of PMSM. In contrast to traditional PID approaches, this method addresses the inherent [...] Read more.
Permanent magnet synchronous motors (PMSM) are widely favored in industry for their high efficiency, compact size, and robust performance. This study employs a model-based PID control approach for speed regulation of PMSM. In contrast to traditional PID approaches, this method addresses the inherent nonlinearity of PMSM systems and tunes PID coefficients dynamically for fast multi-input and multi-output (MIMO) operations. Traditional PID controllers typically assume linear motor dynamics and determine a single set of coefficients, often through trial and error. However, the nonlinear dynamics of motor drives and variations in motor parameters often lead to instability, limiting the effectiveness of conventional PID controllers. The proposed auto-tuning PID controller adjusts its coefficients in real-time based on the system’s operational state. This method has been implemented in both simulation and experimental setups, with real-time execution facilitated by dSPACE DS1104. A comparative analysis with conventional PI control demonstrates the enhanced stability and adaptability of the proposed approach. Full article
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12 pages, 3547 KB  
Proceeding Paper
A Study on Fuzzy PID Controllers with a Parallel Structure for Electro-Hydraulic Servo System Control
by Georgi Mihalev, Stanimir Yordanov, Krasimir Ormandzhiev, Stefan Ivanov and Hristina Stoycheva
Eng. Proc. 2026, 122(1), 2; https://doi.org/10.3390/engproc2026122002 - 14 Jan 2026
Viewed by 129
Abstract
This paper presents the design of a fuzzy PID controller with a parallel structure for controlling an electro-hydraulic servo system. The main factors affecting control performance in electro-hydraulic systems are discussed in detail. The proposed fuzzy controller features a specific structure obtained through [...] Read more.
This paper presents the design of a fuzzy PID controller with a parallel structure for controlling an electro-hydraulic servo system. The main factors affecting control performance in electro-hydraulic systems are discussed in detail. The proposed fuzzy controller features a specific structure obtained through a coefficient transfer approach from a classical PID controller, enabling seamless integration of the fuzzy logic component and simplifying the tuning process. Relevant mathematical equations and dependencies are provided. The closed-loop system’s stability is analyzed using the BIBO (Bounded Input, Bounded Output) criterion. The designed controller is implemented in the MATLAB/Simulink 2019 environment and tested using a real-time measurement and control system. Graphical results are presented, illustrating the performance of the closed-loop system under step and sinusoidal reference signals. The obtained results confirm the qualities and proper tuning of the implemented controller. Full article
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20 pages, 1129 KB  
Article
Solving the Synthesis Problem Self-Organizing Control System in the Class of Elliptical Accidents Optics for Objects with One Input and One Output
by Maxot Rakhmetov, Ainagul Adiyeva, Balaussa Orazbayeva, Shynar Yelezhanova, Raigul Tuleuova and Raushan Moldasheva
Computation 2026, 14(1), 21; https://doi.org/10.3390/computation14010021 - 14 Jan 2026
Viewed by 112
Abstract
Nonlinear single-input single-output (SISO) systems operating under parametric uncertainty often exhibit bifurcations, multistability, and deterministic chaos, which significantly limit the effectiveness of classical linear, adaptive, and switching control methods. This paper proposes a novel synthesis framework for self-organizing control systems based on catastrophe [...] Read more.
Nonlinear single-input single-output (SISO) systems operating under parametric uncertainty often exhibit bifurcations, multistability, and deterministic chaos, which significantly limit the effectiveness of classical linear, adaptive, and switching control methods. This paper proposes a novel synthesis framework for self-organizing control systems based on catastrophe theory, specifically within the class of elliptic catastrophes. Unlike conventional approaches that stabilize a predefined system structure, the proposed method embeds the control law directly into a structurally stable catastrophe model, enabling autonomous bifurcation-driven transitions between stable equilibria. The synthesis procedure is formulated using a Lyapunov vector-function gradient–velocity method, which guarantees aperiodic robust stability under parametric uncertainty. The definiteness of the Lyapunov functions is established using Morse’s lemma, providing a rigorous stability foundation. To support practical implementation, a data-driven parameter tuning mechanism based on self-organizing maps (SOM) is integrated, allowing adaptive adjustment of controller coefficients while preserving Lyapunov stability conditions. Simulation results demonstrate suppression of chaotic regimes, smooth bifurcation-induced transitions between stable operating modes, and improved transient performance compared to benchmark adaptive control schemes. The proposed framework provides a structurally robust alternative for controlling nonlinear systems in uncertain and dynamically changing environments. Full article
(This article belongs to the Topic A Real-World Application of Chaos Theory)
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16 pages, 2197 KB  
Article
Machine Learning and Operator-Based Nonlinear Internal Model Control Design for Soft Robotic Finger Using Robust Right Coprime Factorization
by Zizhen An and Mingcong Deng
Appl. Sci. 2026, 16(2), 808; https://doi.org/10.3390/app16020808 - 13 Jan 2026
Viewed by 91
Abstract
Currently, machine learning (ML) methods provide a practical approach to model complex systems. Unlike purely analytical models, ML methods can describe the uncertainties (e.g., hysteresis, temperature effects) that are difficult to deal with, potentially yielding higher-precision dynamics by a learning plant given a [...] Read more.
Currently, machine learning (ML) methods provide a practical approach to model complex systems. Unlike purely analytical models, ML methods can describe the uncertainties (e.g., hysteresis, temperature effects) that are difficult to deal with, potentially yielding higher-precision dynamics by a learning plant given a high-volume dataset. However, employing learning plants that lack explicit mathematical representations in real-time control remains challenging, namely, the model can be conversely looked at as a mapping from input data to output, and it is difficult to represent the corresponding time relationships in real applications. Hence, an ML and operator-based nonlinear control design is proposed in this paper. In this new framework, the bounded input/output spaces of the learning plant are addressed rather than mathematical dynamic formulation, which is realized by robust right coprime factorization (RRCF). While the stabilized learning plant is explored by RRCF, the desired tracking performance is also considered by an operator-based nonlinear internal model control (IMC) design. Eventually, practical application on a soft robotic finger system is conducted, which indicates the better performance of using the controlled learning plant and the feasibility of the proposed framework. Full article
(This article belongs to the Special Issue New Topics on System Learning and Control and Its Applications)
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17 pages, 5916 KB  
Article
Three-Dimensional Shape Estimation of a Soft Finger Considering Contact States
by Naoyuki Matsuyama, Weiwei Wan and Kensuke Harada
Appl. Sci. 2026, 16(2), 717; https://doi.org/10.3390/app16020717 - 9 Jan 2026
Viewed by 178
Abstract
To achieve precise in-hand manipulation and feedback control using soft robotic fingers, it is essential to accurately measure their deformable structures. In particular, estimating the three-dimensional shape of a soft finger under contact conditions is a critical challenge, as the deformation state directly [...] Read more.
To achieve precise in-hand manipulation and feedback control using soft robotic fingers, it is essential to accurately measure their deformable structures. In particular, estimating the three-dimensional shape of a soft finger under contact conditions is a critical challenge, as the deformation state directly affects manipulation reliability. However, nonlinear deformations and occlusions arising from interactions with external objects make the estimation difficult. To address these issues, we propose a soft finger structure that integrates small magnets and magnetic sensors inside the body, enabling the acquisition of rich deformation information in both contact and non-contact states. The design provides a 15-dimensional time-series signal composed of motor angles, motor currents, and magnetic sensor outputs as inputs for shape estimation. Built on the sensing signals, we propose a mode-selection-based learning approach that outputs multiple candidate shapes and selects the correct one. The proposed network predicts the three-dimensional positions of four external markers attached to the finger, which serve as a proxy representation of the finger’s shape. The network is trained in a supervised manner using ground-truth marker positions measured by a motion capture system. The experimental results under both contact and non-contact conditions demonstrate that the proposed method achieves an average estimation error of approximately 4 mm, outperforming conventional one-shot regression models that output coordinates directly. The integration of magnetic sensing is demonstrated to be able to enable accurate recognition of contact states and significantly improve stability in shape estimation. Full article
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40 pages, 3919 KB  
Article
Robust Disturbance Reconstruction and Compensation for Nonlinear First-Order System
by Mikulas Huba, Pavol Bistak, Damir Vrancic and Miroslav Halas
Mathematics 2026, 14(2), 257; https://doi.org/10.3390/math14020257 - 9 Jan 2026
Viewed by 94
Abstract
The article discusses the control of nonlinear processes with first-order dominant dynamics, focusing on implementation using modern hardware available in various programmable devices and embedded systems. The first two approaches rely on linearization with an ultra-local process model, considering small changes of the [...] Read more.
The article discusses the control of nonlinear processes with first-order dominant dynamics, focusing on implementation using modern hardware available in various programmable devices and embedded systems. The first two approaches rely on linearization with an ultra-local process model, considering small changes of the process input and output around a fixed operating point, which can be adjusted through gain scheduling with the setpoint variable. This model is used to configure either the historically established automatic reset controller (ARC) or a stabilizing proportional (P) controller enhanced by an inversion-based disturbance observer (DOB). This solution can be interpreted as an application of modern control theory (MCT), as DOB-based control (DOBC) or as advanced disturbance rejection control (ADRC). Alternatively, they can be viewed as a special case of automatic offset control (AOC) based on two types of linear process models. In the third design method, setpoint tracking by exact linearization (EL) is extended with a nonlinear DOB designed using the inverse of the nonlinear process dynamics (EEL). The fourth approach augments EL-based tracking with a DOB derived from the transfer functions of nonlinear processes (NTF). An illustrative example involving the control of a liquid reservoir with a variable cross-section clarifies motivation for the definition of (linear) local and ultra-local process models as well as their advantages in designing robust control that accounts for process uncertainties. Thus, the speed, homogeneity, and shape of transient responses, the ability to reconstruct disturbances, control signal saturation, and measurement noise attenuation are evaluated according to the assumptions specified in the controller design. The novelty of the paper lies in presenting a unifying perspective on several seemingly different control options under the impact of measurement noise. By explaining their essence, advantages, and disadvantages, it provides a foundation for controlling more complex time-delayed systems. The paper emphasizes that certain aspects of controller design, often overlooked in traditional linearization procedures, can significantly improve closed-loop properties. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
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24 pages, 7136 KB  
Article
Extended Kalman Filter-Enhanced LQR for Balance Control of Wheeled Bipedal Robots
by Renyi Zhou, Yisheng Guan, Tie Zhang, Shouyan Chen, Jingfu Zheng and Xingyu Zhou
Machines 2026, 14(1), 77; https://doi.org/10.3390/machines14010077 - 8 Jan 2026
Viewed by 170
Abstract
With the rapid development of mobile robotics, wheeled bipedal robots, which combine the terrain adaptability of legged robots with the high mobility of wheeled systems, have attracted increasing research attention. To address the balance control problem during both standing and locomotion while reducing [...] Read more.
With the rapid development of mobile robotics, wheeled bipedal robots, which combine the terrain adaptability of legged robots with the high mobility of wheeled systems, have attracted increasing research attention. To address the balance control problem during both standing and locomotion while reducing the influence of noise on control performance, this paper proposes a balance control framework based on a Linear Quadratic Regulator integrated with an Extended Kalman Filter (KLQR). Specifically, a baseline LQR controller is designed using the robot’s dynamic model, where the control input is generated in the form of wheel-hub motor torques. To mitigate measurement noise and suppress oscillatory behavior, an Extended Kalman Filter is applied to smooth the LQR torque output, which is then used as the final control command. Filtering experiments demonstrate that, compared with median filtering and other baseline methods, the proposed EKF-based approach significantly reduces high-frequency torque fluctuations. In particular, the peak-to-peak torque variation is reduced by more than 60%, and large-amplitude torque spikes observed in the baseline LQR controller are effectively eliminated, resulting in continuous and smooth torque output. Static balance experiments show that the proposed KLQR algorithm reduces the pitch-angle oscillation amplitude from approximately ±0.03 rad to ±0.01 rad, corresponding to an oscillation reduction of about threefold. The estimated RMS value of the pitch angle is reduced from approximately 0.010 rad to 0.003 rad, indicating improved convergence and steady-state stability. Furthermore, experiments involving constant-speed straight-line locomotion and turning indicate that the KLQR algorithm maintains stable motion with velocity fluctuations limited to within ±0.05 m/s. The lateral displacement deviation during locomotion remains below 0.02 m, and no abrupt acceleration or deceleration is observed throughout the experiments. Overall, the results demonstrate that applying Extended Kalman filtering to smooth the control torque effectively improves the smoothness and stability of LQR-based balance control for wheeled bipedal robots. Full article
(This article belongs to the Section Robotics, Mechatronics and Intelligent Machines)
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12 pages, 5306 KB  
Article
Key Noise Evaluation of Analog Front-End in Microradian-Level Phasemeter for Space Gravitational Wave Detection
by Ke Xue, Tao Yu and Hongyu Long
Symmetry 2026, 18(1), 93; https://doi.org/10.3390/sym18010093 - 4 Jan 2026
Viewed by 185
Abstract
For microradian-level phasemeters aimed at space-based gravitational wave detection, the analog front-end circuitry plays a critical role in determining the system’s phase noise. This paper focuses on the symmetric differential structure-based operational amplifier analog front-end between the Quadrant Photodiode output and the high-resolution [...] Read more.
For microradian-level phasemeters aimed at space-based gravitational wave detection, the analog front-end circuitry plays a critical role in determining the system’s phase noise. This paper focuses on the symmetric differential structure-based operational amplifier analog front-end between the Quadrant Photodiode output and the high-resolution ADC input. An equivalent additive noise model is established, and the mechanism of noise conversion into phase noise is derived. The noise performance within the target 5–25 MHz band is evaluated through LTspice simulations and experimental verification. Experimental results show that, after suppressing sampling timing jitter with a 37.5 MHz pilot tone, the noise contribution of the front-end analog circuit to the phasemeter system is significantly better than the phase measurement noise requirement of 2π μrad/Hz1/2 in the 0.1 mHz–1 Hz band for space-based gravitational wave detection. Compared with a transformer-based front-end, the differential amplifier solution exhibits significant advantages in low-frequency noise suppression and signal stability. Further analysis using the digital phase-locked loop closed-loop transfer function confirms that the noise amplitude is proportional to phase noise and inversely proportional to signal amplitude, providing a theoretical basis for analog front-end circuit optimization and system-level noise budgeting. The results offer a reliable reference for the design of high-precision phasemeters and the engineering implementation of space-based gravitational wave detection missions. Full article
(This article belongs to the Section Physics)
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19 pages, 6650 KB  
Article
Scalable Relay Switching Platform for Automated Multi-Point Resistance Measurements
by Edoardo Boretti, Kostiantyn Torokhtii, Enrico Silva and Andrea Alimenti
Instruments 2026, 10(1), 3; https://doi.org/10.3390/instruments10010003 - 31 Dec 2025
Viewed by 317
Abstract
In both research and industrial settings, it is often necessary to expand the input/output channels of measurement instruments using relay-based multiplexer boards. In research activities in particular, the need for a highly flexible and easily configurable solution frequently leads to the development of [...] Read more.
In both research and industrial settings, it is often necessary to expand the input/output channels of measurement instruments using relay-based multiplexer boards. In research activities in particular, the need for a highly flexible and easily configurable solution frequently leads to the development of customized systems. To address this challenge, we developed a system optimized for automated direct current (DC) measurements. The result is based on a 4×4 switching platform that simplifies measurement procedures that require instrument routing. The platform is based on a custom-designed circuit board controlled by a microcontroller. We selected bistable relays to guarantee contact stability after switching. We finally developed a system architecture that allows for straightforward expansion and scalability by connecting multiple platforms. We share both the hardware design source files and the firmware source code on GitHub with the open-source community. This work presents the design and development of the proposed system, followed by the performance evaluation. Finally, we present a test of our designed system applied to a specific case study: the DC analysis of complex resistive networks through multi-point resistance measurements using only a single voltmeter and current source. Full article
(This article belongs to the Section Sensing Technologies and Precision Measurement)
19 pages, 6390 KB  
Article
Design of a Bandgap Reference with a High PSRR and Strong Load-Driving Capability
by Meng Li, Lei Guo, Bin Liu, Lin Qi, Binghui He, Yu Cao and Jian Ren
Micromachines 2026, 17(1), 50; https://doi.org/10.3390/mi17010050 - 30 Dec 2025
Viewed by 349
Abstract
This paper introduces an enhanced bandgap reference (BGR) design, addressing the shortcomings of traditional circuits, such as significant temperature drift, limited power-supply rejection, and inadequate load-driving capacity. The proposed design incorporates a symmetric folded common-emitter–common-base BJT amplifier with MOS-assisted biasing, employed in the [...] Read more.
This paper introduces an enhanced bandgap reference (BGR) design, addressing the shortcomings of traditional circuits, such as significant temperature drift, limited power-supply rejection, and inadequate load-driving capacity. The proposed design incorporates a symmetric folded common-emitter–common-base BJT amplifier with MOS-assisted biasing, employed in the proposed BGR, enforcing branch voltage symmetry to effectively suppress intrinsic offset caused by structural mismatch. By reducing the amplifier input offset, the circuit achieves improved reference voltage stability, a lower temperature coefficient (TC), and an enhanced power-supply rejection ratio (PSRR). Additionally, a negative-feedback adaptive current-adjustment driver is implemented to dynamically adjust the output current in response to real-time load changes. This method bolsters the load-driving capability and maintains a stable reference output across varying load conditions. The circuit was simulated using a 0.18 μm BCD process, revealing that with a 3.3 V supply voltage, the BGR produces a stable output voltage of 2.5 V, with a TC of 2.372×106 °C−1. The simulated PSRR is −114.2 dB at DC and −62.07 dB at 1 kHz. Moreover, under a 3.3 V supply, sweeping the load capacitance from 0.1 μF to 100 μF demonstrates that the reference voltage remains consistently regulated at 2.5 V, confirming its excellent load tolerance and output stability. Full article
(This article belongs to the Section D1: Semiconductor Devices)
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22 pages, 1077 KB  
Article
Agricultural Price Fluctuations and Sectoral Performance: A Long-Term Structural Analytical Perspective Across Europe
by Anca Antoaneta Vărzaru
Agriculture 2026, 16(1), 80; https://doi.org/10.3390/agriculture16010080 - 29 Dec 2025
Viewed by 258
Abstract
The European agricultural sector has increasingly faced volatility in input and output prices, raising concerns about income stability and long-term performance. This study examines the relationship between agricultural price dynamics and sectoral performance across European countries from 2006 to 2024, with a particular [...] Read more.
The European agricultural sector has increasingly faced volatility in input and output prices, raising concerns about income stability and long-term performance. This study examines the relationship between agricultural price dynamics and sectoral performance across European countries from 2006 to 2024, with a particular focus on countries’ capacity to translate price movements into economic outcomes. Using Eurostat data, the analysis combines factor analysis to construct latent price and performance indicators, structural equation modeling to assess the structural association between price dynamics and real factor income and gross value added, and cluster analysis to identify cross-country heterogeneity. The results reveal a positive and statistically significant association between favorable price dynamics and agricultural performance at the aggregate level. Beyond this general relationship, the findings point to pronounced asymmetries across European agricultural systems. While some countries consistently convert favorable price dynamics into higher income and value creation, others remain structurally constrained and benefit less from similar market conditions. These differences give rise to identifiable groups of relative “winners” and “losers” within the EU agricultural market. The results indicate that price dynamics alone are insufficient to explain convergence in agricultural performance and that structural capacity plays a critical role in shaping outcomes. From a policy perspective, the study highlights the need for differentiated agricultural and regional policy approaches to strengthen resilience and reduce persistent structural disparities across European agriculture. Full article
(This article belongs to the Special Issue Price and Trade Dynamics in Agricultural Commodity Markets)
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33 pages, 8912 KB  
Article
Modified P-ECMS for Fuel Cell Commercial Vehicles Based on SSA-LSTM Vehicle Speed Prediction and Integration of Future Speed Trends into Dynamic Equivalent Factor Regulation
by Yiming Wu, Weiguang Zheng and Jirong Qin
Sustainability 2026, 18(1), 306; https://doi.org/10.3390/su18010306 - 28 Dec 2025
Viewed by 291
Abstract
Fuel cell commercial vehicles are widely used in commercial transport for their high efficiency and long range. However, in mixed operating scenarios, their energy economy and fuel cell operational stability cannot be fully balanced. Traditional strategies lack adaptability in mixed operating scenarios. Therefore, [...] Read more.
Fuel cell commercial vehicles are widely used in commercial transport for their high efficiency and long range. However, in mixed operating scenarios, their energy economy and fuel cell operational stability cannot be fully balanced. Traditional strategies lack adaptability in mixed operating scenarios. Therefore, based on the equivalent factor regulation formula of the Adaptive Equivalent Hydrogen Consumption Minimization Strategy (A-ECMS) and the improved Sparrow Search Algorithm-Long Short-Term Memory (SSA-LSTM) hybrid model, short-term speed prediction and three-stage speed interval division are embedded into the equivalent factor regulation logic. A dynamic equivalent factor regulation strategy integrating SOC deviation is constructed, and an improved Predictive Equivalent Hydrogen Consumption Minimization Strategy (P-ECMS) is finally derived. The SSA-LSTM algorithm is optimized via constrained hyperparameter tuning for short-term speed prediction. A time-decay weighting mechanism enhances recent speed data weight, with weighted results as inputs to boost accuracy. Moving Average Residual Correction (MARC) is used to verify the speed prediction model accuracy and correct residuals. Multi-scenario tests show that the SSA-LSTM model outperforms the Gated Recurrent Unit (GRU) model in prediction accuracy and generalization ability, providing reliable data support for segmented regulation. With battery SOC deviation and the SSA-LSTM-predicted speed trend as core inputs, combined with three-stage speed interval division, A-ECMS’s equivalent factor regulation formula is improved. The model adopts a segmented dynamic regulation logic to integrate dual factors into equivalent factor adjustment, and it reasonably adjusts the energy output ratio of fuel cells and power batteries according to speed intervals and operating condition changes. In scenarios with significant speed fluctuations and frequent operating condition transitions, power shocks are mitigated by the power battery’s peak-shaving and valley-filling function. Simulation results for C-WTVC and NREL2VAIL show that, compared with traditional A-ECMS, the improved P-ECMS has notable energy benefits, with equivalent hydrogen consumption reduced by 3.41% and 5.48%, respectively. The fuel cell’s state is significantly improved, with its high-efficiency share reaching 63%. The output power curve is smoother, start–stop losses are reduced, and the fuel cell’s service life is extended, balancing the energy economy and component durability. Full article
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47 pages, 4007 KB  
Article
Fuzzy Model-Based Predictive Control Applied to Wastewater Treatment Plants Represented by the BSM1 Benchmark
by Pedro M. Vallejo LLamas and Pastora I. Vega Cruz
Appl. Sci. 2026, 16(1), 272; https://doi.org/10.3390/app16010272 - 26 Dec 2025
Viewed by 199
Abstract
The control of wastewater treatment plants (WWTPs) is an ecologically, economically, and socially important objective. In the case of plants using activated sludge (ASP) processes, their control presents a significant challenge due to the complexity of the dynamics of these processes (a consequence [...] Read more.
The control of wastewater treatment plants (WWTPs) is an ecologically, economically, and socially important objective. In the case of plants using activated sludge (ASP) processes, their control presents a significant challenge due to the complexity of the dynamics of these processes (a consequence of their biological nature). To objectively evaluate control strategies, standardized benchmark simulation models (BSMs) are used. This article tests the feasibility and evaluates the performance, in a simulation environment, of a specific fuzzy model-based predictive control strategy, called FMBPC/CLP, applied to the BSM1 reference model. In each iteration, this strategy first uses an FMBPC-type algorithm, which determines the basic control action (based on a fuzzy model and applying functional predictive control) that guarantees the local stability of the closed-loop system. Then, a second predictive control algorithm, called closed-loop predictive control (CLP-MPC), calculates a compensating term that is added to the basic control law and ensures compliance with constraints in the control action. In the simulation experiments carried out, the plant structure described in the BSM1 benchmark (reactor divided into five tanks, followed by a settling tank) was maintained, but the default control configuration was modified. The alternative control configuration designed for the BSM1 test bench includes two control loops: one to regulate the oxygen concentration in compartment 5 of the reactor (maintaining the PI algorithm of the default control configuration) and another loop to regulate the nitrate concentration (nitrate and nitrite) in tank 2 and, simultaneously, the ammonia concentration in tank 5, using the alternative FMBPC/CLP strategy. This control hybrid configuration was tested and evaluated considering values of the influent (dry, rainy, and stormy weather), and performance measurement criteria, both standardized in the BSM1 platform. The base model of the plant to be controlled, necessary for the FMBPC strategy, is obtained by prior fuzzy identification, from open-loop input and output data. The identification is achieved with the help of a software tool that uses mathematical clustering methods (based on the Gustafson–Kessel algorithm) that allow for the extraction of fuzzy models of the Takagi–Sugeno type from the numerical input–output data of a given plant. The FMBPC strategy is potentially appropriate for the control of complex, changing or unknown systems and this article demonstrates that this strategy is viable, with satisfactory performance, and that it can even be competitive when compared with more traditional control strategies. Full article
(This article belongs to the Special Issue AI in Wastewater Treatment)
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27 pages, 3076 KB  
Article
Machine Learning and SHAP-Based Prediction of Tip Velocity Around Spur Dikes Using a Small-Scale Experimental Dataset
by Nadir Murtaza, Zeeshan Akbar, Raid Alrowais, Sohail Iqbal, Ghufran Ahmed Pasha, Mohammed Alquraish and Muhammad Tariq Bashir
Water 2026, 18(1), 26; https://doi.org/10.3390/w18010026 - 21 Dec 2025
Viewed by 421
Abstract
River-training structures such as spur dikes are frequently used in the field of river engineering, which play a critical role in flow regulation and stabilization of the riverbank. However, previous studies lack a precise prediction of factors inducing scour and turbulence phenomena, such [...] Read more.
River-training structures such as spur dikes are frequently used in the field of river engineering, which play a critical role in flow regulation and stabilization of the riverbank. However, previous studies lack a precise prediction of factors inducing scour and turbulence phenomena, such as tip velocity, for optimal design of the spur dikes. This study addresses a key gap in previous research by predicting tip velocity around spur dikes using advanced and interpretable machine learning models while simultaneously evaluating the influence of key geometric and hydraulic parameters. For this purpose, the current study utilized advanced artificial intelligence (AI) techniques like Gaussian Process Regression (GPR), Categorical Boosting (CatBoost), Random Forest (RF), and Extreme Gradient Boosting (XGBoost), optimized with Particle Swarm Optimization (PSO), to predict tip velocity in the vicinity of the spur dike. In this paper, a small dataset of 69 laboratory-scale experimental trials was collected; therefore, the chosen AI models were selected for their ability to handle such limited data points. In this study, the input parameters included Froude number (Fr), separation length to spur dike length ratio (L/l), and incidence angle (β), while the output parameter was tip velocity. The selected four AI models were trained on 70%, 15%, and 15% of the data for the training, testing, and validation phases, respectively. SHapley Additive exPlanations (SHAP) analysis was used to observe the influence of the critical parameters on the tip velocity. The results demonstrated the superior performance of GPR, followed by the CatBoost model, compared to other models. GPR and CatBoost show greater values of coefficient of determination (R2) (GPR R2 = 0.972 and CatBoost R2 = 0.970) and lower values of root mean square error (RMSE) (GPR RMSE = 0.0107 and CatBoost RMSE = 0.0236). The result of the heatmap and SHAP analysis indicated a greater influence of Fr and L/l and a lower impact of β on the tip velocity. The results of this study recommend the utilization of GPR and CatBoost for precise and robust performance of the hydrodynamic phenomenon around the spur dikes, supporting scour mitigation strategies in river engineering. Full article
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