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Search Results (198)

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Keywords = fractional-order PID controller

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23 pages, 7019 KiB  
Article
An Enhanced Control of Grid-Connected Solid-Oxide Fuel Cell System Using Beluga Whale-Optimized Fractional-Order PID Control
by Moayed Mohamed, Ilyes Boulkaibet, Mohamed Ebeed and Ali M. El-Rifaie
Processes 2025, 13(7), 2044; https://doi.org/10.3390/pr13072044 - 27 Jun 2025
Viewed by 270
Abstract
Fuel cells (FCs) are widely used in various applications such as transportation, vehicles, and energy storage, as well as in commercial and residential buildings. The FC is connected to the grid via an inverter, which converts DC power to AC power for integration [...] Read more.
Fuel cells (FCs) are widely used in various applications such as transportation, vehicles, and energy storage, as well as in commercial and residential buildings. The FC is connected to the grid via an inverter, which converts DC power to AC power for integration with the AC grid. Thus, it is essential to adjust the gain of the inverter’s controllers to improve FC performance and the quality of the power generated by the FCs. In this work, a fractional-order PID (FOPID) controller is used to control an inverter where the FOPID’s gain settings are determined optimally to improve the performance of the current controller of the solid-oxide fuel cell (SOFC). The optimal parameters of the FOPID are obtained using a newly developed and efficient algorithm called beluga whale optimization (BWO). To highlight the efficiency of the proposed optimization approach, the obtained results are compared with particle swarm optimization (PSO) and the conventional active power controller (APC). The findings of this paper demonstrate that the SOFC achieves significantly superior performance when the FOPID controller is optimally tuned using BWO across all performance metrics related to the FC inverter. PSO also yields good results, ensuring smooth system operation and good performance. Based on the results, the output current from the SOFC using the BWO and PSO algorithms aligns well with the reference current, whereas the APC exhibits poor performance in tracking reference current changes in two cases. Specifically, the APC introduces a delay of approximately one second (0.5 to 0.6 s), resulting in poor control performance. This delay causes the system to deviate from the reference current control (RCC) by 10%, leading to poor performance. However, the proposed optimization algorithms effectively resolve this issue, offering a robust solution for enhanced current control. Full article
(This article belongs to the Section Process Control and Monitoring)
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36 pages, 6279 KiB  
Article
Eel and Grouper Optimization-Based Fuzzy FOPI-TIDμ-PIDA Controller for Frequency Management of Smart Microgrids Under the Impact of Communication Delays and Cyberattacks
by Kareem M. AboRas, Mohammed Hamdan Alshehri and Ashraf Ibrahim Megahed
Mathematics 2025, 13(13), 2040; https://doi.org/10.3390/math13132040 - 20 Jun 2025
Cited by 1 | Viewed by 438
Abstract
In a smart microgrid (SMG) system that deals with unpredictable loads and incorporates fluctuating solar and wind energy, it is crucial to have an efficient method for controlling frequency in order to balance the power between generation and load. In the last decade, [...] Read more.
In a smart microgrid (SMG) system that deals with unpredictable loads and incorporates fluctuating solar and wind energy, it is crucial to have an efficient method for controlling frequency in order to balance the power between generation and load. In the last decade, cyberattacks have become a growing menace, and SMG systems are commonly targeted by such attacks. This study proposes a framework for the frequency management of an SMG system using an innovative combination of a smart controller (i.e., the Fuzzy Logic Controller (FLC)) with three conventional cascaded controllers, including Fractional-Order PI (FOPI), Tilt Integral Fractional Derivative (TIDμ), and Proportional Integral Derivative Acceleration (PIDA). The recently released Eel and Grouper Optimization (EGO) algorithm is used to fine-tune the parameters of the proposed controller. This algorithm was inspired by how eels and groupers work together and find food in marine ecosystems. The Integral Time Squared Error (ITSE) of the frequency fluctuation (ΔF) around the nominal value is used as an objective function for the optimization process. A diesel engine generator (DEG), renewable sources such as wind turbine generators (WTGs), solar photovoltaics (PVs), and storage components such as flywheel energy storage systems (FESSs) and battery energy storage systems (BESSs) are all included in the SMG system. Additionally, electric vehicles (EVs) are also installed. In the beginning, the supremacy of the adopted EGO over the Gradient-Based Optimizer (GBO) and the Smell Agent Optimizer (SAO) can be witnessed by taking into consideration the optimization process of the recommended regulator’s parameters, in addition to the optimum design of the membership functions of the fuzzy logic controller by each of these distinct algorithms. The subsequent phase showcases the superiority of the proposed EGO-based FFOPI-TIDμ-PIDA structure compared to EGO-based conventional structures like PID and EGO-based intelligent structures such as Fuzzy PID (FPID) and Fuzzy PD-(1 + PI) (FPD-(1 + PI)); this is across diverse symmetry operating conditions and in the presence of various cyberattacks that result in a denial of service (DoS) and signal transmission delays. Based on the simulation results from the MATLAB/Simulink R2024b environment, the presented control methodology improves the dynamics of the SMG system by about 99.6% when compared to the other three control methodologies. The fitness function dropped to 0.00069 for the FFOPI-TIDμ-PIDA controller, which is about 200 times lower than the other controllers that were compared. Full article
(This article belongs to the Special Issue Mathematical Methods Applied in Power Systems, 2nd Edition)
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34 pages, 5161 KiB  
Article
Robust Adaptive Fractional-Order PID Controller Design for High-Power DC-DC Dual Active Bridge Converter Enhanced Using Multi-Agent Deep Deterministic Policy Gradient Algorithm for Electric Vehicles
by Seyyed Morteza Ghamari, Daryoush Habibi and Asma Aziz
Energies 2025, 18(12), 3046; https://doi.org/10.3390/en18123046 - 9 Jun 2025
Viewed by 635
Abstract
The Dual Active Bridge converter (DABC), known for its bidirectional power transfer capability and high efficiency, plays a crucial role in various applications, particularly in electric vehicles (EVs), where it facilitates energy storage, battery charging, and grid integration. The Dual Active Bridge Converter [...] Read more.
The Dual Active Bridge converter (DABC), known for its bidirectional power transfer capability and high efficiency, plays a crucial role in various applications, particularly in electric vehicles (EVs), where it facilitates energy storage, battery charging, and grid integration. The Dual Active Bridge Converter (DABC), when paired with a high-performance CLLC filter, is well-regarded for its ability to transfer power bidirectionally with high efficiency, making it valuable across a range of energy applications. While these features make the DABC highly efficient, they also complicate controller design due to nonlinear behavior, fast switching, and sensitivity to component variations. We have used a Fractional-order PID (FOPID) controller to benefit from the simple structure of classical PID controllers with lower complexity and improved flexibility because of additional filtering gains adopted in this method. However, for a FOPID controller to operate effectively under real-time conditions, its parameters must adapt continuously to changes in the system. To achieve this adaptability, a Multi-Agent Reinforcement Learning (MARL) approach is adopted, where each gain of the controller is tuned individually using the Deep Deterministic Policy Gradient (DDPG) algorithm. This structure enhances the controller’s ability to respond to external disturbances with greater robustness and adaptability. Meanwhile, finding the best initial gains in the RL structure can decrease the overall efficiency and tracking performance of the controller. To overcome this issue, Grey Wolf Optimization (GWO) algorithm is proposed to identify the most suitable initial gains for each agent, providing faster adaptation and consistent performance during the training process. The complete approach is tested using a Hardware-in-the-Loop (HIL) platform, where results confirm accurate voltage control and resilient dynamic behavior under practical conditions. In addition, the controller’s performance was validated under a battery management scenario where the DAB converter interacts with a nonlinear lithium-ion battery. The controller successfully regulated the State of Charge (SOC) through automated charging and discharging transitions, demonstrating its real-time adaptability for BMS-integrated EV systems. Consequently, the proposed MARL-FOPID controller reported better disturbance-rejection performance in different working cases compared to other conventional methods. Full article
(This article belongs to the Special Issue Power Electronics for Smart Grids: Present and Future Perspectives II)
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31 pages, 57273 KiB  
Article
A New Hybrid Framework for the MPPT of Solar PV Systems Under Partial Shaded Scenarios
by Rahul Bisht, Afzal Sikander, Anurag Sharma, Khalid Abidi, Muhammad Ramadan Saifuddin and Sze Sing Lee
Sustainability 2025, 17(12), 5285; https://doi.org/10.3390/su17125285 - 7 Jun 2025
Viewed by 428
Abstract
Nonlinear characteristics of solar photovoltaic (PV) and nonuniform surrounding conditions, including partial shading conditions (PSCs), are the major factors responsible for lower conversion efficiency in solar panels. One major condition is the cause of the multiple peaks and oscillation around the peak point [...] Read more.
Nonlinear characteristics of solar photovoltaic (PV) and nonuniform surrounding conditions, including partial shading conditions (PSCs), are the major factors responsible for lower conversion efficiency in solar panels. One major condition is the cause of the multiple peaks and oscillation around the peak point leading to power losses. Therefore, this study proposes a novel hybrid framework based on an artificial neural network (ANN) and fractional order PID (FOPID) controller, where new algorithms are employed to train the ANN model and to tune the FOPID controller. The primary aim is to maintain the computed power close to its true peak power while mitigating persistent oscillations in the face of continuously varying surrounding conditions. Firstly, a modified shuffled frog leap algorithm (MSFLA) was employed to train the feed-forward ANN model using real-world solar PV data with the aim of generating a reference solar PV peak voltage. Subsequently, the parameters of the FOPID controller were tuned through the application of the Sanitized Teacher–Learning-Based Optimization (s-TLBO) algorithm, with a specific focus on achieving maximum power point tracking (MPPT). The robustness of the proposed hybrid framework was assessed using two different types (monocrystalline and polycrystalline) of solar panels exposed to varying levels of irradiance. Additionally, the framework’s performance was rigorously tested under cloudy conditions and in the presence of various partial shading scenarios. Furthermore, the adaptability of the proposed framework to different solar panel array configurations was evaluated. This work’s findings reveal that the proposed hybrid framework consistently achieves maximum power point with minimal oscillation, surpassing the performance of recently published works across various critical performance metrics, including the MPPefficiency, relative error (RE), mean squared error (MSE), and tracking speed. Full article
(This article belongs to the Section Energy Sustainability)
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27 pages, 17572 KiB  
Article
Optimal Design of a Fractional Order PIDD2 Controller for an AVR System Using Hybrid Black-Winged Kite Algorithm
by Fei Dai, Tianli Ma and Song Gao
Electronics 2025, 14(12), 2315; https://doi.org/10.3390/electronics14122315 - 6 Jun 2025
Viewed by 362
Abstract
This study addresses the optimization of control performance for automatic voltage regulator systems by proposing a fractional-order PIDD2 (FOPIDD2) controller design method based on the hybrid Black-winged Kite Algorithm (BWOA). To overcome the challenges of complex parameter tuning and adaptability [...] Read more.
This study addresses the optimization of control performance for automatic voltage regulator systems by proposing a fractional-order PIDD2 (FOPIDD2) controller design method based on the hybrid Black-winged Kite Algorithm (BWOA). To overcome the challenges of complex parameter tuning and adaptability to high-dimensional nonlinear optimization in PID controllers, the BWOA integrates the precise search mechanism of the Black-winged Kite Algorithm (BKA) with the spiral encircling strategy of the Whale Optimization Algorithm (WOA). By dividing high-fitness individuals into subgroups for parallel optimization, combined with an elitism preservation mechanism and Levy flight perturbation, the BWOA effectively balances global exploration and local exploitation capabilities, preventing premature convergence. Furthermore, a multi-factor objective function is adopted to optimize the six parameters of the FOPIDD2 controller. Numerical simulations in MATLAB evaluate the controller’s performance across multiple dimensions, including transient response, frequency-domain stability, trajectory tracking, parameter uncertainty, and disturbance rejection, with comparisons to other recent controllers. Simulation results demonstrate that the BWOA-FOPIDD2 controller achieves superior performance in most metrics. Therefore, the proposed method provides an efficient hybrid optimization framework for AVR system controller design. Full article
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35 pages, 24700 KiB  
Article
Optimizing Load Frequency Control of Multi-Area Power Renewable and Thermal Systems Using Advanced Proportional–Integral–Derivative Controllers and Catch Fish Algorithm
by Saleh A. Alnefaie, Abdulaziz Alkuhayli and Abdullah M. Al-Shaalan
Fractal Fract. 2025, 9(6), 355; https://doi.org/10.3390/fractalfract9060355 - 29 May 2025
Viewed by 578
Abstract
Renewable energy sources (RESs) are increasingly combined into the power system due to market liberalization and environmental and economic benefits, but their weather-dependent variability causes power production and demand mismatches, leading to issues like frequency and regional power transmission fluctuations. To maintain synchronization [...] Read more.
Renewable energy sources (RESs) are increasingly combined into the power system due to market liberalization and environmental and economic benefits, but their weather-dependent variability causes power production and demand mismatches, leading to issues like frequency and regional power transmission fluctuations. To maintain synchronization in power systems, frequency must remain constant; disruptions in the proper balance of production and load might produce frequency variations, risking serious issues. Therefore, a mechanism known as load frequency control (LFC) or automated generation control (AGC) is needed to keep the frequency and tie-line power within predefined stable limits. In this study, advanced proportional–integral–derivative PID controllers such as fractional-order PID (FOPID), cascaded PI(PDN), and PI(1+DD) for LFC in a two-area power system integrated with RES are optimized using the catch fish optimization algorithm (CFA). The controllers’ optimal gains are attained through using the integral absolute error (IAE) and ITAE objective functions. The performance of LFC with CFA-tuned PID, PI, cascaded PI(PDN), and FOPID, PI(1+DD) controllers is compared to other optimization techniques, including sine cosine algorithm (SCA), particle swarm optimization (PSO), brown bear algorithm (BBA), and grey wolf optimization (GWO), in a two-area power system combined with RESs under various conditions. Additionally, by contrasting the performance of the PID, PI, cascaded PI(PDN), and FOPID, PI(1+DD) controllers, the efficiency of the CFA is confirmed. Additionally, a sensitivity analysis that considers simultaneous modifications of the frequency bias coefficient (B) and speed regulation (R) within a range of ±25% validates the efficacy and dependability of the suggested CFA-tuned PI(1+DD). In the complex dynamics of a two-area interconnected power system, the results show how robust the suggested CFA-tuned PI(1+DD) control strategy is and how well it can stabilize variations in load frequency and tie-line power with a noticeably shorter settling time. Finally, the results of the simulation show that CFA performs better than the GWO, BBA, SCA, and PSO strategies. Full article
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17 pages, 3425 KiB  
Article
Research on Fractional-Order Control of Anchor Drilling Machine Optimized by Intelligent Algorithms
by Jingkai Li, Jun Zhang, Jiaquan Xie, Wei Shi and Jianzhong Zhao
Appl. Sci. 2025, 15(10), 5656; https://doi.org/10.3390/app15105656 - 19 May 2025
Viewed by 418
Abstract
Anchor–bolt support operations are lengthy and conducted under harsh conditions, restricting the efficiency and safety of roadway excavation. To address these challenges, we developed an integrated solution combining mechanical structure optimization with control algorithms. Specifically, we designed a novel automated drilling system equipped [...] Read more.
Anchor–bolt support operations are lengthy and conducted under harsh conditions, restricting the efficiency and safety of roadway excavation. To address these challenges, we developed an integrated solution combining mechanical structure optimization with control algorithms. Specifically, we designed a novel automated drilling system equipped with a robotic manipulator and an anchor–bolt magazine to handle modular hollow self-drilling anchor bolts, enabling automated support operations. To achieve precise docking in unmanned conditions, we employed an inner-loop fractional-order proportional–integral–derivative (FOPID) controller optimized by an improved particle swarm optimization (ILPSO) algorithm. Additionally, robust control based on H∞ control theory was introduced to ensure reliable system performance under disturbances and model uncertainties. Simulation results indicate that the ILPSO-tuned FOPID controller significantly outperforms conventional controllers in dynamic response accuracy; frequency–domain analysis further confirms that the H∞ control approach enhances system stability. Collectively, these results provide a theoretical basis for advancing automated mining technologies. Full article
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21 pages, 3304 KiB  
Article
Personalised Fractional-Order Autotuner for the Maintenance Phase of Anaesthesia Using Sine-Tests
by Marcian D. Mihai, Isabela R. Birs, Nicoleta E. Badau, Erwin T. Hegedus, Amani Ynineb and Cristina I. Muresan
Fractal Fract. 2025, 9(5), 317; https://doi.org/10.3390/fractalfract9050317 - 15 May 2025
Viewed by 317
Abstract
The research field of clinical practice has experienced a substantial increase in the integration of information technology and control engineering, which includes the management of medication administration for general anaesthesia. The invasive nature of input signals is the reason why autotuning methods are [...] Read more.
The research field of clinical practice has experienced a substantial increase in the integration of information technology and control engineering, which includes the management of medication administration for general anaesthesia. The invasive nature of input signals is the reason why autotuning methods are not widely used in this research field. This study proposes a non-invasive method using small-amplitude sine tests to estimate patient parameters, which allows the design of a personalised controller using an autotuning principle. The primary objective is to regulate the Bispectral Index through the administration of Propofol during the maintenance phase of anaesthesia, using a personalised fractional-order PID. This work aims to demonstrate the effectiveness of personalised control, which is facilitated by the proposed sine-based method. The closed-loop simulation results demonstrate the efficiency of the proposed approach. Full article
(This article belongs to the Special Issue Fractional Mathematical Modelling: Theory, Methods and Applications)
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30 pages, 13188 KiB  
Article
Research on Sensorless Control System of Permanent Magnet Synchronous Motor Based on Improved Fuzzy Super Twisted Sliding Mode Observer
by Haoran Jiang, Xiaodong Lv, Xiaoqi Fan and Guangming Zhang
Electronics 2025, 14(9), 1900; https://doi.org/10.3390/electronics14091900 - 7 May 2025
Viewed by 493
Abstract
In order to achieve precise vector control of permanent magnet synchronous motors and maintain reliability during operation, it is necessary to obtain more accurate rotor position and rotor angular velocity. However, the installation of sensors can lead to increased motor volume and cost, [...] Read more.
In order to achieve precise vector control of permanent magnet synchronous motors and maintain reliability during operation, it is necessary to obtain more accurate rotor position and rotor angular velocity. However, the installation of sensors can lead to increased motor volume and cost, so it is necessary to use sensorless estimation of rotor position and angular velocity. The switching function of traditional sliding mode observers is a discontinuous sign function, which can lead to serious chattering problems and phase lag problems caused by low-pass filters. Therefore, this article proposes an improved fuzzy hyper spiral sliding mode observer based on the traditional sliding mode observer. Firstly, the observer takes the current as the observation object and uses the difference between the actual current and the observed current and its derivative as the fuzzy input. The sliding mode gain is used as the fuzzy output to tune the parameters of the sliding mode gain. Secondly, in response to the chattering problem caused by traditional sliding mode control methods, the hyper spiral algorithm is adopted and a sin (arctan(nx)) nonlinear function is introduced instead of the sign function as the switching function to achieve switch continuous sliding mode control, thereby suppressing the system’s chattering. Finally, the rotor position information is extracted through an orthogonal normalized phase-locked loop to improve observation accuracy. For time-varying nonlinear permanent magnet synchronous motor control systems, fractional order PID can improve the control accuracy of the system and adjust the dynamic performance of the system more quickly compared to traditional PID control algorithms. Therefore, fractional order PID is used instead of traditional PID controllers. By comparing simulation experiments with traditional sliding mode observers and fuzzy improved adaptive sliding mode observers, it was proven that the improved fuzzy super spiral sliding mode observer can effectively suppress chattering and extract rotor position with higher accuracy, a faster response rate, and better dynamic performance. This provides a new approach for the sensorless control strategy of permanent magnet synchronous motors. Full article
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19 pages, 2109 KiB  
Article
Robust Frequency Regulation Management System in a Renewable Hybrid Energy Network with Integrated Storage Solutions
by Subhranshu Sekhar Pati, Umamani Subudhi and Sivkumar Mishra
Electricity 2025, 6(2), 22; https://doi.org/10.3390/electricity6020022 - 1 May 2025
Viewed by 918
Abstract
The rapid proliferation of renewable energy sources (RESs) has significantly reduced system inertia, thereby intensifying stability challenges in modern power grids. To address these issues, this study proposes a comprehensive approach to improve the grid stability concerning RESs and load disturbances. The methodology [...] Read more.
The rapid proliferation of renewable energy sources (RESs) has significantly reduced system inertia, thereby intensifying stability challenges in modern power grids. To address these issues, this study proposes a comprehensive approach to improve the grid stability concerning RESs and load disturbances. The methodology integrates controlled energy storage systems, including ultra-capacitors (UC), superconducting magnetic energy storage (SMES), and battery storage, alongside a robust frequency regulation management system (FRMS). Central to this strategy is the implementation of a novel controller which combines a constant with proportional–integral–derivative (PID) and modified fractional-order (MFO) control, forming 1+MFOPID controller. The controller parameters are optimized using a novel formulation of an improved objective function that incorporates both frequency and time domain characteristics to achieve superior performance. The efficacy of the proposed controller is validated by comparing its performance with conventional PID and fractional-order PID controllers. System stability is further analyzed using eigenvector analysis. Additionally, this study evaluates the performance of various energy storage systems and their individual contributions to frequency regulation, with a particular emphasis on the synergistic benefits of battery storage in conjunction with other storages. Finally, sensitivity analysis is conducted to assess the impact of parameter uncertainties in the system design, reinforcing the robustness of the proposed approach. Full article
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21 pages, 4499 KiB  
Article
Mechanism Modeling and Analysis of Fractional-Order Synchronous Generator
by Junhua Xu, Zheng Gong, Xiaocong Li, Songqin Tang, Chunwei Wang and Yue Lan
Fractal Fract. 2025, 9(4), 244; https://doi.org/10.3390/fractalfract9040244 - 12 Apr 2025
Viewed by 305
Abstract
This paper investigates the fractional-order characteristics of the stator and rotor windings of a synchronous generator. Utilizing mechanism-based modeling methodology, it pioneers the derivation of the fractional-order voltage equations for a synchronous generator across both the three-phase stationary coordinate system (A, B, C) [...] Read more.
This paper investigates the fractional-order characteristics of the stator and rotor windings of a synchronous generator. Utilizing mechanism-based modeling methodology, it pioneers the derivation of the fractional-order voltage equations for a synchronous generator across both the three-phase stationary coordinate system (A, B, C) and the synchronous rotating coordinate system (d, q, 0). Through simplifying assumptions and rigorous derivations, a 2 + α (α ∈ (0, 2)) order synchronous generator model is formulated. This paper develops a digital simulation model of a fractional-order single-machine infinite bus system and analyzes the impact of the order α on the synchronous generator system’s dynamic performance through disturbance simulation experiments. Experimental results demonstrate that under conventional disturbances, increasing α from 0.8 to 1.2 reduces the system oscillation period and frequency while enhancing mechanical oscillation suppression, whereas decreasing α to 0.8 accelerates the generator terminal voltage response, lowers electromagnetic power overshoot, and improves excitation control effectiveness. Full article
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24 pages, 5721 KiB  
Article
Design, Tuning, and Experimental Validation of Switched Fractional-Order PID Controllers for an Inverted Pendulum System
by Matias Fernández-Jorquera, Marco Zepeda-Rabanal, Norelys Aguila-Camacho and Lisbel Bárzaga-Martell
Fractal Fract. 2025, 9(4), 234; https://doi.org/10.3390/fractalfract9040234 - 8 Apr 2025
Viewed by 461
Abstract
Stabilizing inverted pendulum systems remains a challenging and open control problem due to their inherent instability and relevance in a wide range of real-world applications, including robotics and aerospace systems. While PID and fractional-order PID (FOPID) controllers offer distinct advantages, they individually suffer [...] Read more.
Stabilizing inverted pendulum systems remains a challenging and open control problem due to their inherent instability and relevance in a wide range of real-world applications, including robotics and aerospace systems. While PID and fractional-order PID (FOPID) controllers offer distinct advantages, they individually suffer from trade-offs between performance and control energy. This paper presents the design, implementation, and experimental validation of a switched SW FOPID-PID controller for the stabilization of an inverted pendulum (InvP) system, aiming to achieve an improved balance between system performance and control energy used. The controller was tuned offline using particle swarm optimization (PSO) and a mathematical model of the system for simulation. Additional PID and FOPID controllers were also designed, tuned and validated for comparison purposes. Their performance was assessed through key indicators, including ITAE, ISI, settling time, peak values, and variance and compared against a manufacturer-provided PID controller. The experimental results demonstrated that all three designed controllers outperformed the manufacturer’s PID under nominal conditions. The SW FOPID-PID controller achieved the best overall performance, balancing control energy efficiency and response quality. Under external disturbances, the FOPID and SW FOPID-PID controllers exhibited superior robustness, with the switched controller being the most effective, responding quickly to disturbances while minimizing positional and angular errors. Still, this research is limited to a specific plant and switching strategy; thus, further validation on other systems and switching criteria is necessary to generalize these findings. Full article
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39 pages, 29772 KiB  
Article
Improving Vehicle Dynamics: A Fractional-Order PIλDμ Control Approach to Active Suspension Systems
by Zongjun Yin, Chenyang Cui, Ru Wang, Rong Su and Xuegang Ma
Machines 2025, 13(4), 271; https://doi.org/10.3390/machines13040271 - 25 Mar 2025
Viewed by 499
Abstract
This paper presents a comprehensive vehicle model featuring an active suspension system integrated with semi-active seat and engine mounting controls. The time-domain stochastic excitation of the four tires was modeled using the filtered white noise method, and the required road excitation was simulated [...] Read more.
This paper presents a comprehensive vehicle model featuring an active suspension system integrated with semi-active seat and engine mounting controls. The time-domain stochastic excitation of the four tires was modeled using the filtered white noise method, and the required road excitation was simulated using MATLAB software R2022b. Four comprehensive performance indices, including engine dynamic displacement, vehicle body acceleration, suspension dynamic deflection, and tire dynamic displacement, were selected and made dimensionless by the performance indices of a passive suspension under the same working conditions to construct the fitness function. A fractional-order PIλDμ (FOPID) controller was proposed, and its structural parameters were optimized using a gray wolf optimization algorithm. Furthermore, the optimized FOPID controller was evaluated under five road conditions, and its performance was compared with integer-order PID control and passive suspensions. The results demonstrate that the FOPID controller effectively improves the smoothness of the vehicle by reducing engine mounting deflection, vehicle body acceleration, suspension deflection, and tire displacement. Moreover, the simulation results indicate that, compared to the passive suspension, the FOPID-controlled suspension achieves an average optimization of over 42% in the root mean square (RMS) of body acceleration under random road conditions, with an average optimization of more than 38% for suspension deflection, 4.3% for engine mounting deflection, and 2.5% for tire displacement. In comparison to the integer-order PID-controlled suspension, the FOPID-controlled suspension demonstrates an average improvement of 28% in the RMS of acceleration and a 2.1% improvement in suspension deflection under random road conditions. However, the engine mounting deflection and tire displacement are reduced by 0.05% and 0.3%, respectively. FOPID control has better performance in vehicle acceleration control but shows asymmetrical effects on tire dynamic deflection. Full article
(This article belongs to the Special Issue Advances in Vehicle Suspension System Optimization and Control)
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16 pages, 2967 KiB  
Article
Applying a Gain Scheduled Fractional Order Proportional Integral and Derivative Controller to a Quadratic Buck Converter
by German Ardul Munoz Hernandez, Jose Fermi Guerrero-Castellanos and Rafael Antonio Acosta-Rodriguez
Fractal Fract. 2025, 9(3), 160; https://doi.org/10.3390/fractalfract9030160 - 5 Mar 2025
Cited by 1 | Viewed by 591
Abstract
This work presents a fractional order Proportional Integral and Derivative controller with adaptation characteristics in the control parameters depending on the required output, gain scheduling fractional order PID (GS-FO-PID). The fractional order PID is applied to the voltage control of a DC–DC buck [...] Read more.
This work presents a fractional order Proportional Integral and Derivative controller with adaptation characteristics in the control parameters depending on the required output, gain scheduling fractional order PID (GS-FO-PID). The fractional order PID is applied to the voltage control of a DC–DC buck quadratic converter (QBC). The DC–DC buck quadratic converter is designed to operate at 12 V, although in the simulation tests, the output voltage ranges from 5 to 36 V. The performance of the GS-FO-PID is compared with the one from a classic PID. The GS-FO-PID presents better performance when the reference voltage is changed. In the same way, the behavior of the converter with the reference fixed to 12 V output is analyzed with load changes; for this case, the amplitude value of the ripple when the converter is driven by the GS-FO-PID almost has no variation. Full article
(This article belongs to the Special Issue Applications of Fractional-Order Systems to Automatic Control)
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17 pages, 4470 KiB  
Article
Scene-Adaptive Loader Trajectory Planning and Tracking Control
by Yingnan Li, Wenwen Dong, Tianhao Zheng, Yakun Wang and Xuefei Li
Sensors 2025, 25(4), 1135; https://doi.org/10.3390/s25041135 - 13 Feb 2025
Cited by 2 | Viewed by 746
Abstract
Wheel loaders play a crucial role in daily production and transportation. With the rapid development of intelligence in passenger vehicles, freeing loader operators from high-risk and repetitive tasks has become a pressing issue. This paper presents a novel and efficient path planning and [...] Read more.
Wheel loaders play a crucial role in daily production and transportation. With the rapid development of intelligence in passenger vehicles, freeing loader operators from high-risk and repetitive tasks has become a pressing issue. This paper presents a novel and efficient path planning and tracking framework tailored to the unique body structure and specific operating environment of loaders. We improve the Hybrid A* search algorithm based on the operational characteristics of loaders and integrate it with dynamically updated grid maps to enable the autonomous planning of loader operating paths in unstructured environments, meeting the efficiency requirements of production. Additionally, to address the challenge of poor trajectory tracking control accuracy caused by hydraulic articulated steering, we propose a new loader trajectory tracking controller based on the idea of hierarchical control. We use an extended state observer to compensate for unknown disturbances in the steering execution layer and employ fuzzy fractional-order PID to handle the nonlinearity of loaders. Field experiments using the proposed approach demonstrate that loaders can autonomously and in real-time complete tasks in dynamically changing operating scenarios. Full article
(This article belongs to the Section Physical Sensors)
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