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Keywords = nonlinear systems

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22 pages, 2865 KB  
Article
Theoretical Analysis of IGAO-Fuzzy PID Fault-Tolerant Control and Performance Optimization for Electro-Hydraulic Active Suspensions Under Internal Leakage Faults
by Haiwu Zheng, Hao Xiong, Dingxuan Zhao, Yufei Zhao, Yinying Ren, Yao Xiao and Yi Han
Actuators 2026, 15(3), 149; https://doi.org/10.3390/act15030149 (registering DOI) - 4 Mar 2026
Abstract
To address performance degradation and control instability in electro-hydraulic servo active suspension systems due to internal leakage faults arising from wear and aging of hydraulic components, this paper proposes an innovative fuzzy PID fault-tolerant controller based on the Improved Giant Armadillo Optimization (IGAO) [...] Read more.
To address performance degradation and control instability in electro-hydraulic servo active suspension systems due to internal leakage faults arising from wear and aging of hydraulic components, this paper proposes an innovative fuzzy PID fault-tolerant controller based on the Improved Giant Armadillo Optimization (IGAO) algorithm. Specifically, to overcome the limitations of the standard Giant Armadillo Optimization (GAO), which is prone to local optima and exhibits poor convergence performance when handling multi-constraint parameter optimization problems, this study introduces a nonlinear dynamic inertia weight mechanism and a random reflection strategy for out-of-bounds particles to improve the original algorithm’s performance. These enhancements significantly enhance its ability to balance global exploration and local exploitation. Furthermore, this research develops a comprehensive performance evaluation fitness function by quantifying key performance indicators such as body acceleration, suspension dynamic deflection, and tire dynamic load. A quarter-car model incorporating an internal leakage fault was established as a simulation validation platform to demonstrate the reliability of the proposed method. Simulation results indicate that under various road excitation conditions, the proposed IGAO algorithm can rapidly and stably converge to superior parameters for the fuzzy PID controller. Compared to the Particle Swarm Optimization (PSO) and standard GAO algorithm, the control system optimized by IGAO not only significantly more effectively suppresses body vibration and reduces shock amplitude but also exhibits stronger dynamic recovery performance and control robustness under varying degrees of internal leakage faults. This research provides a robust control approach for addressing internal parameter uncertainties in hydraulic systems and offers a new approach to theoretical modeling for enhancing the reliability of design and fault-tolerant control capabilities of active suspension systems. Full article
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29 pages, 1583 KB  
Article
Sideslip Angle Estimation for Electric Vehicles Based on Adaptive Weight Fusion: Collaborative Optimization of Robust Observer and Kalman Filter
by Xi Chen, Kanghui Cheng, Te Chen, Guowei Dou, Xinlong Cheng and Xiaoyu Wang
Algorithms 2026, 19(3), 189; https://doi.org/10.3390/a19030189 (registering DOI) - 3 Mar 2026
Abstract
Accurate estimation of vehicle sideslip angle is vital for the stability and safety of four-wheel independent drive electric vehicles (4WIDEVs), but it faces challenges, including model uncertainties caused by tire yaw stiffness variations and system delays. This paper proposes a novel adaptive fusion [...] Read more.
Accurate estimation of vehicle sideslip angle is vital for the stability and safety of four-wheel independent drive electric vehicles (4WIDEVs), but it faces challenges, including model uncertainties caused by tire yaw stiffness variations and system delays. This paper proposes a novel adaptive fusion strategy that combines the dynamic robust observer (DRO) and the improved adaptive square-root unscented Kalman filter (ASUKF). The DRO is designed based on a two-degrees-of-freedom vehicle model and ensures stability through linear matrix inequalities (LMIs), effectively handling parameter uncertainties and time delays; the ASUKF utilizes a three-degrees-of-freedom model and the magic formula tire model, combined with Sage–Husa adaptive filtering, to address the nonlinear tire dynamics. The key innovation of this paper is the introduction of a fuzzy-rule-based adaptive weighting mechanism that dynamically adjusts the fusion weights of the DRO and ASUKF in real time, thereby exploiting their complementary advantages under uncertainty and nonlinear conditions. The simulation and experimental validations demonstrate that this method significantly improves estimation accuracy, reducing the estimation error of vehicle sideslip angle by an average of 9.36%, and maintains robust performance and dynamic adaptability in various conditions, providing a reliable solution for the real-time state estimation of intelligent electric vehicles. Full article
31 pages, 695 KB  
Article
A Novel Fractional-Order Scheme for Non-linear Problems with Applications in Optimization
by Mudassir Shams, Nasreen Kausar and Pourya Pourhejazy
Math. Comput. Appl. 2026, 31(2), 40; https://doi.org/10.3390/mca31020040 - 3 Mar 2026
Abstract
The existing methods for solving non-linear equations encounter convergence issues and computing constraints, especially when used in fractional-order or complex non-linear problems. This study develops a higher-order fractional technique for solving non-linear equations based on the Caputo fractional derivative. The proposed method uses [...] Read more.
The existing methods for solving non-linear equations encounter convergence issues and computing constraints, especially when used in fractional-order or complex non-linear problems. This study develops a higher-order fractional technique for solving non-linear equations based on the Caputo fractional derivative. The proposed method uses a fractional framework to improve local convergence and stability while ensuring high efficiency in every iteration step. Local convergence analysis using generalized Taylor series expansion reveals that the order of the new fractional scheme for solving non-linear equations is 5¢ + 1, where  ¢ ∈ (0,1] represents the Caputo fractional order, determining the memory depth of the Caputo fractional derivative. The performance of the method is further investigated using a variety of non-linear problems from engineering optimization and applied sciences, such as engineering control systems, computational chemistry, thermodynamics models, and operations research, such as inventory optimization. Analyzing the key performance metrics, such as dynamical analysis, percentage convergence, residual error, and computation time, confirms the advantages of the developed method over the state-of-the-art. This study provides a solid framework for higher-order fractional iterative approaches, paving the way for advanced applications of non-linear problems. Full article
26 pages, 366 KB  
Article
Nonlinear Sequential Caputo Fractional Differential Systems: Existence and Hyers–Ulam Stability Under Coupled Mixed Boundary Constraints
by Manigandan Murugesan, Saud Fahad Aldosary and Hami Gündoğdu
Fractal Fract. 2026, 10(3), 165; https://doi.org/10.3390/fractalfract10030165 - 3 Mar 2026
Abstract
In this paper, we study a nonlinear system of sequential Caputo fractional differential equations equipped with coupled mixed multi-point boundary conditions. In particular, the boundary conditions involve the values of the unknown functions at the endpoints expressed as linear combinations of their values [...] Read more.
In this paper, we study a nonlinear system of sequential Caputo fractional differential equations equipped with coupled mixed multi-point boundary conditions. In particular, the boundary conditions involve the values of the unknown functions at the endpoints expressed as linear combinations of their values at several interior points, forming a closed system of relations. The existence of solutions is established by applying the Leray–Schauder alternative, while uniqueness is proved using Banach’s contraction principle. In addition, we investigate the Hyers–Ulam stability of the proposed system. Several examples are included to demonstrate the applicability of the theoretical results. Some special cases of the general problem are also discussed. Full article
28 pages, 1084 KB  
Article
Modeling and Performance Analysis of a Solar Energy and Above-Ground Biogas Digester Complementary Coupling Energy Supply System
by Lei Fang, Miao Luo, Ting Xu and Xiaofei Zhen
Energies 2026, 19(5), 1267; https://doi.org/10.3390/en19051267 (registering DOI) - 3 Mar 2026
Abstract
Rural households in cold regions still rely heavily on coal for cooking and domestic hot water, while single renewable energy sources suffer from intermittency and limited system-level assessment. This study proposes a solar–biogas complementary energy supply system integrating evacuated-tube solar collectors, an above-ground [...] Read more.
Rural households in cold regions still rely heavily on coal for cooking and domestic hot water, while single renewable energy sources suffer from intermittency and limited system-level assessment. This study proposes a solar–biogas complementary energy supply system integrating evacuated-tube solar collectors, an above-ground anaerobic digester, thermal storage, and biogas utilization for rural residential applications in Minqin, Northwest China. A dynamic system-wide model was developed by coupling TRNSYS with nonlinear representations of anaerobic fermentation and biogas boilers, enabling hour-by-hour simulation of energy production, conversion, storage, and consumption. Field measurements were used for validation, and the root mean square deviation between simulated and measured temperatures and gas production remained below 10%. During the heating season, the solar subsystem supplied 10% of the digester heating demand and 90% of the domestic hot-water load, while the biogas subsystem contributed 9.29% and 90.71%, respectively. The system delivered 4728.96 MJ of heat against a seasonal demand of 4636.22 MJ, fully meeting user requirements. A comprehensive 3E (energy–environment–economic) assessment shows that, compared with traditional rural energy supply modes, the proposed system reduces CO2 and NOx emissions by 65.85% and 98.13%, respectively, and demonstrates favorable economics with a benefit–cost ratio of 2.41 and a discounted payback period of 3.27 years. The proposed modeling and evaluation framework provides a replicable solution for clean energy substitution and circular waste utilization in rural areas. Full article
(This article belongs to the Topic Advanced Bioenergy and Biofuel Technologies)
21 pages, 3026 KB  
Article
PID Tuning for Micro Screw Pumps Based on an Improved Spider Wasp Algorithm
by Zhuanzhe Zhao, Deao Shen, Yongming Liu, Zhibo Liu and Huichuang Luo
Electronics 2026, 15(5), 1061; https://doi.org/10.3390/electronics15051061 - 3 Mar 2026
Abstract
To address the issues of large overshoot, slow response, poor stability, and suboptimal control performance of traditional PID algorithms caused by the nonlinear relationship between the rotational speed and output flow rate of micro screw pump motors, this study proposes a PID parameter [...] Read more.
To address the issues of large overshoot, slow response, poor stability, and suboptimal control performance of traditional PID algorithms caused by the nonlinear relationship between the rotational speed and output flow rate of micro screw pump motors, this study proposes a PID parameter optimization method based on an improved spider wasp optimizer algorithm. First, this method incorporates the Tent chaotic mapping into the Spider Wasp Optimizer algorithm (SWO) to enhance initial population diversity, integrates differential evolution strategies to accelerate convergence, and employs Levy flight to boost local search capabilities, thereby balancing global exploration with local exploitation. Subsequently, comparative validation using 12 benchmark functions demonstrates that the improved algorithm (ISWO) outperforms SWO, PSO, SA, GOOSE, and CPO across metrics including mean, standard deviation, and Wilcoxon rank-sum test. Finally, integrating ISWO with PID control yields ISWO-PID, applied to a screw pump model. Simulation results demonstrate superior optimization efficiency and control performance: runtime was reduced by over 60% compared to benchmark algorithms, with enhanced system robustness and adaptability. Full article
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16 pages, 6076 KB  
Article
Joint Nonlinear Trellis-Coded Precoding and Noise-Weighted Viterbi Decoding for Robust High-Speed MISO Underwater Visible Light Communication
by Yunlong Pan, Jiabin Ye, Yunkai Wang, Zhe Feng, Xinyi Liu, Zengyi Xu, Fujie Li, Chao Shen and Nan Chi
Photonics 2026, 13(3), 248; https://doi.org/10.3390/photonics13030248 - 3 Mar 2026
Abstract
In this paper, we propose a robust multi-input single-output (MISO) underwater visible light communication (UVLC) system. By integrating NLTCP and NW-Viterbi decoding, the system effectively alleviates nonlinear distortions and stochastic power fluctuations. NLTCP is employed to achieve probabilistic shaping by generating a non-uniformly [...] Read more.
In this paper, we propose a robust multi-input single-output (MISO) underwater visible light communication (UVLC) system. By integrating NLTCP and NW-Viterbi decoding, the system effectively alleviates nonlinear distortions and stochastic power fluctuations. NLTCP is employed to achieve probabilistic shaping by generating a non-uniformly distributed constellation, which effectively suppresses the occurrence of high-amplitude symbols to mitigate device nonlinearity. To further optimize power allocation, a MISO architecture is utilized to distribute the signal load and reduce the power burden on individual devices. Moreover, the NW-Viterbi decoder incorporates a noise-aware weighting mechanism to optimize the decision metric, thereby enhancing decoding reliability in response to signal-dependent power fluctuations and noise variations in the underwater channel. Experimental results confirm that at an aggregate data rate of 5.8 Gbps, the proposed scheme achieves a significant Q-factor gain of 0.92 dB compared to the traditional PAM4 scheme, alongside a 90.76% enlargement in the effective operating dynamic range. This approach offers a computationally efficient yet effective solution to nonlinearity and power jitter, demonstrating significant potential for practical underwater deployments. Full article
(This article belongs to the Special Issue Progress and Prospects in Visible Light Communications)
25 pages, 2213 KB  
Article
Adaptive Subsidy Policies for Shore Power Promotion: An Integrated Game Theory–System Dynamics Approach
by Huilin Lin and Lei Dai
Mathematics 2026, 14(5), 860; https://doi.org/10.3390/math14050860 (registering DOI) - 3 Mar 2026
Abstract
Shore power (SP) is a critical solution for decarbonizing maritime transport, yet its adoption is hindered by the “high investment, low utilization” paradox, driven by high initial costs and misaligned incentives between ports and ships. While government subsidies are essential, traditional static policy [...] Read more.
Shore power (SP) is a critical solution for decarbonizing maritime transport, yet its adoption is hindered by the “high investment, low utilization” paradox, driven by high initial costs and misaligned incentives between ports and ships. While government subsidies are essential, traditional static policy designs often fail to adapt to the complex, non-linear dynamics of technology diffusion. To address this, the study proposes a dynamic evaluation framework combining System Dynamics (SD) with Evolutionary Game Theory (EGT), embedding a Rolling Horizon Optimization algorithm. Using Shanghai Port as a case study, simulation results demonstrate that optimal subsidies are highly state-dependent. Specifically, effective promotion requires prioritizing ship-side incentives during the early start-up phase, followed by facilities subsidies supporting the coordinated evolution of both ships and berths, and finally a market-driven exit. Furthermore, the proposed dynamic strategy demonstrates superior robustness against oil price volatility and demand shocks compared to static policies, while strictly complying with fiscal budget caps. This framework provides a foundation for the adaptive management of green port infrastructure, facilitating the advancement of energy-saving and environmental protection initiatives within the maritime industry. Additionally, it contributes to the forecasting and evaluation of the policy outcomes of green technology adoption. Full article
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18 pages, 4743 KB  
Article
Reinforcement Learning-Based Super-Twisting Sliding Mode Control for Maglev Guidance System
by Junqi Xu, Wenshuo Wang, Chen Chen, Lijun Rong, Wen Ji and Zijian Guo
Actuators 2026, 15(3), 147; https://doi.org/10.3390/act15030147 - 3 Mar 2026
Abstract
The high-speed Electromagnetic Suspension (EMS) maglev guidance system exhibits inherent characteristics of strong nonlinearity, parameter time-variation, and complex external disturbances. To further optimize and improve the control performance of the guidance system for high-speed maglev trains, a novel intelligent control strategy that integrates [...] Read more.
The high-speed Electromagnetic Suspension (EMS) maglev guidance system exhibits inherent characteristics of strong nonlinearity, parameter time-variation, and complex external disturbances. To further optimize and improve the control performance of the guidance system for high-speed maglev trains, a novel intelligent control strategy that integrates the Deep Deterministic Policy Gradient (DDPG) algorithm with Super-Twisting Sliding Mode Control (STSMC) is proposed. Focusing on a single-ended guidance unit with differential control of dual electromagnets, an STSMC controller is first designed based on a cascaded control framework. To overcome the limitation of offline parameter tuning in dynamic operational conditions, a reinforcement learning optimization framework employing DDPG is introduced. A multi-objective hybrid reward function is formulated, incorporating error convergence, sliding mode stability, and chattering suppression, thereby realizing the online self-tuning of core STSMC parameters via real-time interaction between the agent and the environment. Numerical simulations under typical disturbance conditions verify that the proposed DDPG-STSMC controller significantly reduces the amplitude of guidance gap variation and accelerates dynamic recovery compared to conventional PID control. Its superior performance in disturbance rejection, control accuracy, and operational adaptability is validated. This study, conducted through high-fidelity numerical simulations based on actual system parameters, provides a robust theoretical foundation for subsequent hardware-in-the-loop (HIL) experimentation. Full article
(This article belongs to the Special Issue Advanced Theory and Application of Magnetic Actuators—3rd Edition)
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20 pages, 4993 KB  
Article
Dual-System Interactive Performance Optimization Strategy for Single-Winding Consequent-Pole Bearingless Permanent Magnet Synchronous Motors
by Ye Yuan, Jun Zhang, Yongjiang Zhang, Fan Yang, Yizhou Hua, Yichen Liu and Qingguo Sun
Energies 2026, 19(5), 1261; https://doi.org/10.3390/en19051261 - 3 Mar 2026
Abstract
In the single-winding consequent-pole bearingless permanent magnet synchronous motor (SW-CP-BPMSM), the torque and suspension systems utilize a shared winding configuration. This structure significantly intensifies inter-system coupling. Furthermore, the presence of non-linear and strongly coupled relationships among structural parameters, combined with inherent coupling and [...] Read more.
In the single-winding consequent-pole bearingless permanent magnet synchronous motor (SW-CP-BPMSM), the torque and suspension systems utilize a shared winding configuration. This structure significantly intensifies inter-system coupling. Furthermore, the presence of non-linear and strongly coupled relationships among structural parameters, combined with inherent coupling and conflicts between optimization objectives, makes the unified optimization of key performance indicators for both the torque and suspension systems a substantial challenge. To address these issues, this paper proposes a dual-system interactive optimization strategy based on the classification of sensitive variables. First, the strategy employs the Sobol method to conduct a global sensitivity analysis. By defining dual-system coupled sensitive parameters and single-system sensitive parameters, the method achieves dimensionality reduction through parameter classification. Subsequently, Response Surface Methodology (RSM) and Back Propagation (BP) neural network surrogate models are constructed for the suspension and torque systems, respectively. A progressive optimization process—comprising single-system optimization followed by dual-system interactive optimization—is then performed on the single-system and dual-system sensitive variables to determine the final optimal parameters. Finally, a comparative simulation analysis of the key performance indicators for both the torque and suspension systems before and after optimization is conducted. The results validate the feasibility and effectiveness of the proposed optimization strategy. Full article
(This article belongs to the Collection State-of-the-Art of Electrical Power and Energy System in China)
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17 pages, 3614 KB  
Article
Adaptive Cooperative Control of Dual-Arm Robots Using RBF-ADP with Event-Triggering Mechanism
by Yuanwei Dai
Symmetry 2026, 18(3), 437; https://doi.org/10.3390/sym18030437 - 3 Mar 2026
Abstract
High-precision cooperative control of dual-arm manipulators faces significant challenges arising from complex dynamic coupling, parametric uncertainties, and external disturbances. Furthermore, in networked control scenarios, communication bandwidth and computational resources are inevitably constrained. To address these issues, this paper proposes a novel composite control [...] Read more.
High-precision cooperative control of dual-arm manipulators faces significant challenges arising from complex dynamic coupling, parametric uncertainties, and external disturbances. Furthermore, in networked control scenarios, communication bandwidth and computational resources are inevitably constrained. To address these issues, this paper proposes a novel composite control framework that integrates adaptive dynamic programming (ADP) with active disturbance rejection control (ADRC) under a static event-triggering mechanism (SETM). First, to handle model uncertainties and external perturbations, a smooth nonlinear extended state observer (ESO) based on continuous fractional-power functions is developed. This observer guarantees finite-time convergence of the disturbance estimation without inducing the high-frequency chattering inherent in conventional sliding-mode observers. Second, leveraging the disturbance-compensated dynamics, a radial basis function (RBF) neural network-based ADP controller is designed to learn the optimal control policy online, thereby minimizing a quadratic performance index without requiring accurate model knowledge. Third, to improve resource utilization, a static event-triggering strategy is introduced to schedule control updates based on the system state and tracking error. Extensive simulation studies on a 3-DoF dual-arm system demonstrate that the proposed scheme achieves superior trajectory tracking accuracy and disturbance robustness while significantly reducing the communication frequency compared to time-triggered approaches. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry and Autonomous Robotics)
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17 pages, 1240 KB  
Article
Enhancing the Resilience of Distributed Energy Storage on Smart Highways: A System Dynamics Approach for Dynamic Maintenance Decision-Making
by Xiaochun Peng and Yanqun Yang
Energies 2026, 19(5), 1259; https://doi.org/10.3390/en19051259 - 3 Mar 2026
Abstract
The resilience of Intelligent Transportation Systems (ITSs) heavily relies on distributed Battery Energy Storage Systems (BESSs) deployed in harsh, unattended highway environments. Traditional maintenance strategies often fail to account for the dynamic feedback between battery aging, environmental stress, and maintenance response latency. This [...] Read more.
The resilience of Intelligent Transportation Systems (ITSs) heavily relies on distributed Battery Energy Storage Systems (BESSs) deployed in harsh, unattended highway environments. Traditional maintenance strategies often fail to account for the dynamic feedback between battery aging, environmental stress, and maintenance response latency. This study proposes a system dynamics (SD) framework to evaluate and optimize the resilience of these critical power infrastructures. By modeling the nonlinear interactions among sensor data, controller logic, and remote discharge terminals, we simulate the system’s dynamic behavior over a 36-month lifecycle. The results reveal a critical “scalability threshold”: when battery pack quantity exceeds 40 units, the system’s self-healing time increases disproportionately, degrading resilience. Furthermore, the study identifies 384 V as the optimal “Resilience Topology Voltage”, offering the fastest recovery speed by balancing thermal stability with consistency management efficiency. These findings provide theoretical guidelines for configuring BESS capacity and optimizing remote maintenance protocols to ensure uninterrupted highway operations. Full article
(This article belongs to the Section D: Energy Storage and Application)
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26 pages, 461 KB  
Article
Driving Mechanisms and Configuration Paths of High-Quality Development for High-Speed Rail Enterprises: A Complex Adaptive System Perspective and TOE Framework Analysis
by Fang Yuan, Jiale Shang, Xiaodong Qiu, Xiaoming Yang and Yufan Song
Systems 2026, 14(3), 271; https://doi.org/10.3390/systems14030271 - 3 Mar 2026
Abstract
By expanding the Technology–Organization–Environment (TOE) framework to match the Complex Adaptive System (CAS) characteristics of high-speed rail (HSR) enterprises, this study adopts fuzzy-set Qualitative Comparative Analysis (fsQCA) and Necessary Condition Analysis (NCA) to investigate the driving mechanisms and configuration paths of high-quality development [...] Read more.
By expanding the Technology–Organization–Environment (TOE) framework to match the Complex Adaptive System (CAS) characteristics of high-speed rail (HSR) enterprises, this study adopts fuzzy-set Qualitative Comparative Analysis (fsQCA) and Necessary Condition Analysis (NCA) to investigate the driving mechanisms and configuration paths of high-quality development (HQD). Using data from 137 listed Chinese HSR concept companies during 2018–2023, the results reveal that HSR enterprises operate as CAS, where HQD emerges from the synergistic interaction of technology, organization, and environment subsystems rather than isolated factor contributions. Four equivalent configuration paths to HQD are identified, categorized into three models: Technology-Dominant, Dual-Driven Technology + Environment, and Multi-Collaborative Technology + Organization + Environment. Policy support is a necessary condition for system evolution, digital intelligence empowerment serves as the core “order parameter” driving subsystem adaptation, and high-quality human resources act as the key coordinating element for inter-subsystem coupling. The degree of subsystem synergy has a significant positive correlation with HQD levels. This study enriches the application of CAS theory in the transportation equipment manufacturing industry, expands the TOE framework’s analytical boundary from linear dimension division to systematic synergy, and provides theoretical insights for understanding the nonlinear, emergent mechanisms of HSR enterprise HQD. It also offers practical references for governments to optimize policy supply and for enterprises to enhance adaptive capacity. Full article
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25 pages, 3227 KB  
Article
Research and Development of Intelligent Control Systems for High-Frequency Ozone Generators
by Askar Abdykadyrov, Dina Ermanova, Maxat Mamadiyarov, Seidulla Abdullayev, Nurzhigit Smailov and Nurlan Kystaubayev
J. Sens. Actuator Netw. 2026, 15(2), 26; https://doi.org/10.3390/jsan15020026 - 3 Mar 2026
Abstract
This paper presents the development and investigation of an intelligent control system for a high-frequency ozone generator integrated into an IoT-based and telecommunication environment. A cyber-physical nonlinear mathematical model combining the electrical, thermal, gas-dynamic, and chemical subsystems of the ozone generation process is [...] Read more.
This paper presents the development and investigation of an intelligent control system for a high-frequency ozone generator integrated into an IoT-based and telecommunication environment. A cyber-physical nonlinear mathematical model combining the electrical, thermal, gas-dynamic, and chemical subsystems of the ozone generation process is proposed. The model was implemented in discrete-time form and experimentally validated using the corona–discharge-based high-frequency ozonator ETRO-02. The deviation between simulation and experimental results did not exceed 5.3% for settling time, 6.7% for overshoot, 1.6% for steady-state ozone concentration, and 0.9% for gas temperature, confirming the adequacy of the proposed model. Based on this model, a hierarchical two-level intelligent control architecture is synthesized, consisting of a fast local control loop with a cycle time of 1–5 ms and a supervisory monitoring layer. The proposed adaptive state-feedback control law with online gain adjustment ensures stable real-time operation under nonlinear dynamics, ±20% parameter variations, network delays of 1–10 ms, and packet loss probabilities of up to 5%. As a result, the settling time is reduced from 420 ms to 160 ms, the overshoot from 12.5% to 3.1%, and the steady-state error from 6.5% to 1.6%, while the specific energy consumption decreases from 11.8 to 6.2 Wh/m3. The obtained results demonstrate that the integration of a cyber-physical model with a millisecond-level intelligent control system significantly improves the dynamic performance, robustness, and energy efficiency of high-frequency ozone generators compared to classical control and monitoring-oriented IoT systems. Unlike cloud-centric IoT monitoring architectures that operate at second-level update cycles, the proposed system closes the control loop locally at the millisecond scale, enabling stabilization of fast nonlinear electro-plasma dynamics. The results demonstrate that edge-intelligent adaptive control significantly enhances both dynamic performance and energy efficiency, confirming the feasibility of millisecond-level cyber-physical regulation for industrial ozone generation systems. Full article
(This article belongs to the Section Big Data, Computing and Artificial Intelligence)
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15 pages, 4435 KB  
Article
A Monolithic U-Shaped Rotor with Quasi-Zero Stiffness for Piezoelectric Ultrasonic Motors
by Jintao Wu and Huafeng Li
Symmetry 2026, 18(3), 436; https://doi.org/10.3390/sym18030436 - 3 Mar 2026
Abstract
Traveling wave ultrasonic motors (TWUMs) are critical components in precision systems, yet their performance is susceptible to degradation under dynamic disturbances in harsh operating environments. This paper presents a monolithic U-shaped rotor designed to intrinsically achieve quasi-zero stiffness (QZS). Unlike conventional QZS systems [...] Read more.
Traveling wave ultrasonic motors (TWUMs) are critical components in precision systems, yet their performance is susceptible to degradation under dynamic disturbances in harsh operating environments. This paper presents a monolithic U-shaped rotor designed to intrinsically achieve quasi-zero stiffness (QZS). Unlike conventional QZS systems that rely on assembling discrete positive and negative stiffness elements, the proposed design generates the target mechanical characteristic through the tailored nonlinear response of a unified U-shaped structure, thereby improving preload stability. Through exploring the critical parameters of the rotor cross-section, the finite element method (FEM) is employed to optimize the geometry configuration and characterize the mechanical performances. The simulation results show the QZS behavior demonstrating a stable force plateau of 320 ± 10 N across a 0.7 mm displacement range. A maximum von Mises stress of 788 MPa is obtained, well within the material’s safety margin, thereby ensuring the structural integrity. Experimental tests validate the effectiveness of the proposed design. This compact, monolithic U-shaped rotor provides a robust and reliable QZS solution, demonstrating significant potential for enhancing the stability of TWUMs in applications prone to harsh environments such as wide-range temperature fluctuations, thermal cycling conditions, and shock environments. Full article
(This article belongs to the Section Engineering and Materials)
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