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Search Results (1,071)

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Keywords = proportional-integral-derivative (PID) controller

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25 pages, 13743 KB  
Article
Adaptive Fuzzy Feedforward Compensation for High-Precision X–Y Positioning Systems Driven by Stepper Motors
by Emmanuel García-Galvan, Antonio J. Cruz-Estrada, Eduardo Vincent-Islas, José R. Rivera-Ruiz, Edson E. Cruz-Miguel, Javier Calderón-Sánchez and José R. García-Martínez
Automation 2026, 7(4), 114; https://doi.org/10.3390/automation7040114 - 23 Jul 2026
Viewed by 141
Abstract
High-precision X–Y positioning systems driven by stepper motors are widely used in industrial automation, manufacturing, and scientific instrumentation. However, fixed feedforward–feedback controllers may degrade when operating conditions vary, particularly as step frequency changes and the risk of synchronism loss increases. This work proposes [...] Read more.
High-precision X–Y positioning systems driven by stepper motors are widely used in industrial automation, manufacturing, and scientific instrumentation. However, fixed feedforward–feedback controllers may degrade when operating conditions vary, particularly as step frequency changes and the risk of synchronism loss increases. This work proposes an adaptive fuzzy feedforward–feedback controller for stepper-motor-driven X–Y positioning systems. The controller uses a Takagi–Sugeno (T–S) fuzzy inference system to adjust the proportional, derivative, and feedforward actions according to the tracking error, step frequency, and an auxiliary error-based adaptation variable. The control law is integrated with the inverse kinematics of the platform to generate synchronized step-domain commands, and a practical synchronism-preservation condition is established. Experimental validation on a NEMA 17-based X–Y platform showed accurate trajectory tracking, with a steady-state error of approximately 1.6[μm] for a trapezoidal profile. For a multi-segment trajectory, the RMSE was 0.0749[mm] without load and 0.0760[mm] under a 7.5[kg] external load. Compared with a conventional PID controller, the proposed method reduced the RMSE from 0.1741[mm] to 0.0749[mm], while preserving motor synchronism. Full article
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10 pages, 1134 KB  
Article
Coordinated Feedback–Feedforward Control for Coupled Seat–Suspension Dynamics: A Ride Comfort Enhancement Strategy for In-Wheel-Motor Electric Vehicles
by Magdy Abdullah Eissa and Pingen Chen
World Electr. Veh. J. 2026, 17(7), 379; https://doi.org/10.3390/wevj17070379 - 22 Jul 2026
Viewed by 235
Abstract
Electric vehicles equipped with in-wheel motors provide packaging, controllability, and drivetrain-simplification advantages; however, the increase in wheel-side unsprung mass can intensify vibration transmission to the chassis, seat, and occupant. This paper presents a coordinated active seat and active suspension control strategy for an [...] Read more.
Electric vehicles equipped with in-wheel motors provide packaging, controllability, and drivetrain-simplification advantages; however, the increase in wheel-side unsprung mass can intensify vibration transmission to the chassis, seat, and occupant. This paper presents a coordinated active seat and active suspension control strategy for an integrated 8-DOF quarter-car model that includes an in-wheel motor, an active seat suspension, and a 4-DOF seated driver body model. The proposed controller combines a Harmony Search (HS)-optimized proportional–integral–derivative (PID) feedback baseline with a repeatable-disturbance feedforward compensation term. The HS-PID loop provides baseline transient attenuation, while the feedforward term compensates the repeatable component of the bump-induced disturbance transmitted through the coupled seat–vehicle system. The controller is evaluated against passive suspension, active-seat-only control, active-vehicle-suspension-only control, and an HS-PID baseline under repeated bump/shock excitation. The results show that coordinated actuation reduces occupant displacement and acceleration responses relative to the benchmark cases. The discussion explains the active-seat-only peak-acceleration amplification, the different magnitudes of displacement and acceleration improvements, and the practical implications of suspension stroke and actuator-force limits. The reported conclusions are therefore confined to the repeated bump/shock condition considered in this numerical study; broader ride-comfort generalization requires standardized whole-body vibration metrics, random-road validation, speed variation, parametric uncertainty analysis, and drivetrain energy evaluation. Full article
(This article belongs to the Section Vehicle Control and Management)
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26 pages, 7598 KB  
Article
Assist-As-Needed Backstepping Control of Lower-Limb Exoskeletons with Human Effort Estimation and Comparative Evaluation Against Sliding Mode and PID Controllers
by Mukhtar Fatihu Hamza, Abdulbasid Ismail Isa, Abdulrahman Alqahtani and Nizar Rokbani
Appl. Sci. 2026, 16(14), 7336; https://doi.org/10.3390/app16147336 - 22 Jul 2026
Viewed by 165
Abstract
In this paper, we propose an assist-as-needed (AAN) backstepping control scheme for a lower-limb exoskeleton with nonlinear dynamics and uncertain human–robot interactions. The main objective is to achieve a good trajectory tracking capability while adaptively controlling the assistance of the robot according to [...] Read more.
In this paper, we propose an assist-as-needed (AAN) backstepping control scheme for a lower-limb exoskeleton with nonlinear dynamics and uncertain human–robot interactions. The main objective is to achieve a good trajectory tracking capability while adaptively controlling the assistance of the robot according to the user’s effort. The adopted dynamic model is nonlinear, which includes joint dynamics and external human interaction torque. This allows for the derivation of the tracking error formulation. The backstepping control law, formulated based on the filtered tracking error, ensures stable closed-loop performance with bounded tracking errors. We incorporate an AAN scaling framework based on estimated human effort to regulate the overall control torque as a convex combination of the nominal backstepping torque and the impedance-based assistance torque. The proposed controller was tested by numerical simulations and was compared with the sliding mode control (SMC) and the proportional–integral–derivative (PID) control. The overall root-mean-square tracking error for the proposed controller was 0.0962 rad, while for the SMC controller and PID controller, it was 0.0819 rad and 0.1246 rad, respectively. Moreover, the proposed controller reduced the peak human–robot interaction torque to 14.68 N·m compared to 15.36 N·m for SMC and 15.81 N·m for PID, adaptively controlling assistance based on the applied effort of the user. The assistance ratio went down from an average of 0.7988 in the low-effort condition to 0.6960 in the higher-effort condition, indicating effective adaptation while maintaining stable tracking performance. Although the PID controller achieved the lowest torque-variation index, the proposed controller achieved a more favorable trade-off among tracking accuracy, adaptive assistance, and acceptable torque smoothness. Finally, the proposed AAN backstepping controller achieved a practical trade-off between tracking accuracy, adaptive assistance, torque smoothness, and interaction safety, suggesting its potential in rehabilitation and assistive exoskeleton applications. Full article
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27 pages, 51084 KB  
Article
Load Frequency Regulation of Renewable-Integrated Power System Using Novel Fractional and Degree of Freedom-Based Controller with Real-Time Validation
by Kona Amarendra, Kiran Teeparthi, Murali Sariki, Yellapragada Venkata Pavan Kumar, Vinod Kumar D.M. and Rammohan Mallipeddi
Energies 2026, 19(14), 3401; https://doi.org/10.3390/en19143401 - 18 Jul 2026
Viewed by 234
Abstract
Microgrid integration introduces fast, stochastic disturbances that challenge frequency stability. This paper presents a two-degree-of-freedom fractional-order proportional tilt integral derivative plus one controller (2DOF-FOPTID+1) tuned with a Modified Walrus Optimization Algorithm (MWA) to mitigate frequency deviations while preserving tracking performance. The novelty lies [...] Read more.
Microgrid integration introduces fast, stochastic disturbances that challenge frequency stability. This paper presents a two-degree-of-freedom fractional-order proportional tilt integral derivative plus one controller (2DOF-FOPTID+1) tuned with a Modified Walrus Optimization Algorithm (MWA) to mitigate frequency deviations while preserving tracking performance. The novelty lies in jointly deploying a 2DOF-FOPTID+1 structure for decoupled tracking and regulation, an MWA-based tuning strategy tailored for resilient frequency control, and the explicit use of aggregated electric vehicles as fast distributed storage to damp frequency and tie-line power excursions; hardware-in-the-loop validation using an OPAL-RT platform is included to demonstrate practical feasibility. The controller is evaluated under step and random load variations, and robustness is examined for ±25% parameter perturbations and stochastic renewable inputs. Compared with the strong baselines PID, FOPID, 2DOF-PID, and FOPTID, the proposed approach reduces settling time by up to 39.27% and lowers peak-to-peak frequency deviation by about 20.88% under these operating scenarios, indicating a practical and effective solution for enhancing frequency resilience in microgrid-integrated power systems. Full article
(This article belongs to the Section F1: Electrical Power System)
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24 pages, 12983 KB  
Review
Advances in FPGA-Based Laser Frequency Stabilization Techniques
by Zhilin Yan, Wenqiang Fan, Longjie Zhang, Wanxiao Gao, Cunwei Zhang, Jiaming Zhang, Tie Li, Yancheng Guo, Yulei Wang, Zhiwei Lu, Qiunan Yang and Zhenxu Bai
Micromachines 2026, 17(7), 838; https://doi.org/10.3390/mi17070838 - 14 Jul 2026
Viewed by 309
Abstract
Laser frequency stabilization underpins precision metrology, optical atomic clocks, quantum optics, and laser spectroscopy. In recent years, field-programmable gate arrays (FPGAs) have become attractive for this task because signal generation, phase-sensitive detection, digital filtering, feedback control, lock monitoring, and automatic re-locking can be [...] Read more.
Laser frequency stabilization underpins precision metrology, optical atomic clocks, quantum optics, and laser spectroscopy. In recent years, field-programmable gate arrays (FPGAs) have become attractive for this task because signal generation, phase-sensitive detection, digital filtering, feedback control, lock monitoring, and automatic re-locking can be integrated on compact and reconfigurable platforms. This review examines recent progress in FPGA-based laser frequency stabilization from four linked perspectives: stabilization principles, digital implementation, system architecture, and intelligent control. We first summarize representative error-signal generation methods, including Pound–Drever–Hall locking, saturation absorption spectroscopy, frequency modulation spectroscopy, and modulation transfer spectroscopy. We then discuss the FPGA functions that determine practical performance, such as data acquisition, direct digital synthesis, digital demodulation, proportional-integral-derivative (PID)/infinite impulse response (IIR) filtering, latency management, and lock-state monitoring. Mixed-signal, all-digital, distributed, and machine-learning-assisted systems are compared to show how bandwidth, latency, stability, integration, cost, and automation are balanced in different designs. This review closes by identifying remaining challenges in analog-to-digital converter/digital-to-analog converter (ADC/DAC) resolution, converter noise, loop latency, actuator bandwidth, long-term robustness, and algorithm portability, and by outlining future directions toward low-latency, software-defined, and intelligent stabilization platforms. Full article
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24 pages, 4512 KB  
Article
Optimization of the Controller Settings for the Mean Arterial Blood Pressure Regulation Using Pelican Optimization Approach
by Abhishek Jain, Mohammad Atif Siddiqui, Tirumalasetty Chiranjeevi and Łukasz Knypiński
Algorithms 2026, 19(7), 565; https://doi.org/10.3390/a19070565 - 9 Jul 2026
Viewed by 257
Abstract
This paper presents a unified comparative study of various controllers, including proportional–integral–derivative (PID), Fractional-Order PID (FOPID), Internal Model Control (IMC) controllers, and Tilt–Integral–Derivative (TID) controllers, for the regulation of mean arterial blood pressure (MABP). The controllers are optimally tuned by using a single [...] Read more.
This paper presents a unified comparative study of various controllers, including proportional–integral–derivative (PID), Fractional-Order PID (FOPID), Internal Model Control (IMC) controllers, and Tilt–Integral–Derivative (TID) controllers, for the regulation of mean arterial blood pressure (MABP). The controllers are optimally tuned by using a single metaheuristic approach, namely the Pelican Optimization Algorithm (POA), ensuring a fair and consistent comparison. The POA optimizes the objective function using standard error indices (ITAE, IAE, and ISE) along with transient characteristics. The aforementioned controllers are then evaluated under varying patient conditions for different patient categories, including sensitive, nominal, and insensitive, and their performance is systematically compared with one another and with the reported methods from the existing literature. The simulation results demonstrate that IMC offers fast settling with minimal overshoot, FOPID improves robustness through fractional dynamics, and the TID controller provides the smoothest transient response and disturbance rejection across all patient categories. The results confirm the effectiveness of advanced control strategies over conventional PID and highlight the potential of POA-tuned TID control for reliable and patient-specific MABP regulation in critical care applications. Full article
(This article belongs to the Special Issue Algorithmic Approaches to Control Theory and System Modeling)
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28 pages, 10549 KB  
Article
State Machine Model of the Operation Control of a Differential- Drive Mobile Robot
by Lluís Ribas-Xirgo
Electronics 2026, 15(14), 2993; https://doi.org/10.3390/electronics15142993 - 8 Jul 2026
Viewed by 307
Abstract
Existing robotic control frameworks often rely on complex hierarchical state machines or middleware infrastructures, which may be unsuitable for resource-constrained embedded systems and difficult to map directly to low-level code. This work presents a complete state-machine model for the reactive control layer of [...] Read more.
Existing robotic control frameworks often rely on complex hierarchical state machines or middleware infrastructures, which may be unsuitable for resource-constrained embedded systems and difficult to map directly to low-level code. This work presents a complete state-machine model for the reactive control layer of a differential-drive mobile robot. Although mobile-robot controllers often exhibit considerable complexity—particularly at lower levels, where numerous hardware-dependent operations occur—this work shows that a network of concurrent state machines provides a clear and lightweight method for specifying and implementing control behavior. The proposed approach decomposes the reactive controller into two concurrent extended finite-state machines (CEFSMs) responsible for locomotion and lidar operation, connected through simple and predictable protocols. This structure enables a direct mapping from model diagrams to procedural code in languages such as C++ and Lua. The method has been used extensively in an undergraduate Embedded Systems course since 2011, supporting both physical robots (Arduino-based) and their digital twins in CoppeliaSim. We also introduce a discrete control strategy that approximates continuous behavior and incorporates a simplified proportional–integral–derivative (PID) controller for pose correction. The approach reduces development effort, increases model clarity, and yields reusable code across hardware and simulation platforms. Quantitative evaluation shows that the proposed PID-based control strategy can improve positioning accuracy by up to an order of magnitude compared to a baseline on–off controller, without increasing the computational cost. In addition, the control cycle time has been significantly reduced (from 31 ms to 12 ms) in order to ensure a stable execution period; this, in turn, results in a more predictable controller output and improved trajectory consistency. Full article
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15 pages, 5562 KB  
Article
Model Predictive Control of a Multi-Effect Evaporator for Robust Discharge Concentration Regulation in Biomanufacturing
by Wangsoo Kim, Wonseok Lee, Chanhun Park, Joon Young Jung, Sangmin Park, Ho-Yeon Lee, Jay Yun and Jun-Woo Kim
Processes 2026, 14(14), 2229; https://doi.org/10.3390/pr14142229 - 8 Jul 2026
Viewed by 287
Abstract
Multi-effect evaporators are widely used in biomanufacturing to create concentrates of fermentation-derived products prior to or during crystallization, where the discharge concentration directly governs crystal product quality. However, bioprocess feed streams are subject to large and irregular disturbances arising from batch-to-batch fermentation variability [...] Read more.
Multi-effect evaporators are widely used in biomanufacturing to create concentrates of fermentation-derived products prior to or during crystallization, where the discharge concentration directly governs crystal product quality. However, bioprocess feed streams are subject to large and irregular disturbances arising from batch-to-batch fermentation variability and cell separation operations, making stable concentration control essential. In this study, a dynamic differential-algebraic model of a three-effect evaporator was developed, in which product composition evolves according to mass balance ordinary differential equations, while vapor and concentrate flows are determined algebraically from energy balances. Using this model, the discharge concentration was controlled against a representative feed composition disturbance scenario by comparing proportional–integral–derivative (PID) control with model predictive control (MPC). The PID controller failed to suppress the disturbance and exhibited sustained oscillations due to the large structural time delay and composition-dependent nonlinearity of the cascaded process. In contrast, the terminal-cost MPC predicted future behavior from the process model and compensated for disturbances preemptively, maintaining the discharge concentration almost exactly at its set point. The integrated absolute error decreased from 0.3872 for PID to 0.00145 for MPC with a 99.6% improvement. These results demonstrate that MPC enables robust product quality control in disturbance-rich biomanufacturing processes. Full article
(This article belongs to the Section Biological Processes and Systems)
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14 pages, 3528 KB  
Article
Simulation Study on Navigation Control of Microrobots in Vascular Blind Zone Environments
by Liangtian Li, Shuangquan Wen and Junfeng Xiong
Micro 2026, 6(3), 49; https://doi.org/10.3390/micro6030049 - 2 Jul 2026
Viewed by 281
Abstract
Magnetically actuated microrobots have exhibited broad application prospects in biomedical fields. To advance their clinical application, extensive research has attempted to enhance the navigation robustness of microrobots in the body. In the vascular environment, microrobots are easily obscured by blood cells and disturbed [...] Read more.
Magnetically actuated microrobots have exhibited broad application prospects in biomedical fields. To advance their clinical application, extensive research has attempted to enhance the navigation robustness of microrobots in the body. In the vascular environment, microrobots are easily obscured by blood cells and disturbed by fluid flow, leading to the failure of external sensors and the formation of navigation blind zones. However, most existing navigation methods are based on ideal environment assumptions and struggle to address the challenges posed by navigation blind zones. The study proposes a navigation framework integrating Extended Kalman Filter (EKF) and a Proportional–Integral–Derivative (PID) controller. The EKF fuses sensor measurements and the microrobot kinematic model to sustain continuous state estimation when sensors fail inside blind zones. The simulation results show that this navigation framework achieves pixel-level positioning accuracy under ideal conditions and a 100% navigation success rate. In the presence of blind zone interference, this navigation framework can effectively suppress the divergence of position errors and significantly improve navigation robustness. The study proposes a theoretical framework for microrobot navigation in vascular blind zones. Further physical prototype experiments are required to verify its practical performance. Full article
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42 pages, 2119 KB  
Review
Path Tracking Control and Algorithm Transplantation for Agricultural Robots: A Review and Prospect
by Shuai Yu, Lixing Liu, Xin Yang, Jianping Li, Pengfei Wang and Hongjie Liu
Agriculture 2026, 16(13), 1432; https://doi.org/10.3390/agriculture16131432 - 30 Jun 2026
Viewed by 262
Abstract
Path tracking control and algorithm portability for agricultural robots serve as the core technological foundation for achieving precision and automation in farming operations, playing a critical role in ensuring food security and enhancing production efficiency. This paper systematically reviews recent technological advancements in [...] Read more.
Path tracking control and algorithm portability for agricultural robots serve as the core technological foundation for achieving precision and automation in farming operations, playing a critical role in ensuring food security and enhancing production efficiency. This paper systematically reviews recent technological advancements in the field. It first elucidates the fundamental theories and technical components of path tracking control, providing detailed analyses of the characteristics and limitations of traditional methods such as Proportional-Integral-Derivative (PID) control, model predictive control (MPC), sliding-mode control (SMC), and the Stanley algorithm. Subsequently, it focuses on innovations in intelligent technologies, exploring the integration trends of adaptive control and intelligent learning algorithms, with particular emphasis on the combined applications of reinforcement learning, deep learning, and intelligent control methodologies. The paper clarifies the significance of algorithm portability and summarizes the current applications and performance differences among various algorithms. The study concludes that traditional methods demonstrate stability and reliability in structured scenarios, while advanced intelligent approaches exhibit stronger adaptability in complex environments, albeit facing challenges such as data dependency and real-time deployment requirements. Future technological developments will prioritize deep integration of multiple technologies and the unified achievement of both safety and real-time performance. Full article
(This article belongs to the Section Agricultural Technology)
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33 pages, 13728 KB  
Article
Trajectory Tracking Control of Autonomous Underwater Vehicles Using GP-Based Model Predictive Control
by Yuankui Wang, Zhiwei Sun, Xiange Tian, Yuhang Jia, Hao Li, Bohan Wang, Dahai Zhang and Peng Qian
Drones 2026, 10(7), 498; https://doi.org/10.3390/drones10070498 - 30 Jun 2026
Viewed by 243
Abstract
In this paper, a Gaussian process-based model predictive control (GP-MPC) method is proposed, which aims to enhance the trajectory tracking performance of autonomous underwater vehicles (AUVs). This method can compensate for internal errors and external disturbances based on a limited amount of data. [...] Read more.
In this paper, a Gaussian process-based model predictive control (GP-MPC) method is proposed, which aims to enhance the trajectory tracking performance of autonomous underwater vehicles (AUVs). This method can compensate for internal errors and external disturbances based on a limited amount of data. Firstly, numerical models of the AUV are presented. Then, the offline GP-MPC algorithm and online GP-MPC algorithm are presented and described. Meanwhile, the current disturbances and initial errors are also considered. The circular trajectory, L-shaped steering trajectory, and lemniscate trajectory are tracked to evaluate the trajectory tracking performances of different algorithms. Compared with proportional–integral–derivative (PID) and nominal MPC algorithms, the GP-MPC algorithms show reduced root mean square error (over 40%) and reduced maximum error (over 40%) in both position and yaw angle when performing different trajectory tracking tasks. Finally, real-time pool experiments are conducted to validate the implementation feasibility of the GP-corrected MPC framework on a physical AUV under surface three-degrees-of-freedom motion, while the online GP-MPC is evaluated through numerical simulations. Full article
(This article belongs to the Special Issue Advances in Autonomous Underwater Drones: 2nd Edition)
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25 pages, 5475 KB  
Article
Robust Frequency Regulation of Hybrid Wind–PV Thermal Power Systems via Adaptive Fractional-Order PID Control
by Yevgeniy Muralev, Dinmukhambet Baimbetov, Samal Syrlybekkyzy, Mohamed Salem, Ali Bughneda and Khalid Yahya
Energies 2026, 19(13), 3076; https://doi.org/10.3390/en19133076 - 29 Jun 2026
Viewed by 354
Abstract
As modern electrical grids increasingly incorporate renewable generation—specifically from wind and solar–thermal installations—they face heightened volatility and operational complexities, which severely complicate load frequency regulation. While fractional-order proportional-integral-derivative (FOPID) controllers are commonly employed for this purpose, their conventional formulations rely on fixed fractional [...] Read more.
As modern electrical grids increasingly incorporate renewable generation—specifically from wind and solar–thermal installations—they face heightened volatility and operational complexities, which severely complicate load frequency regulation. While fractional-order proportional-integral-derivative (FOPID) controllers are commonly employed for this purpose, their conventional formulations rely on fixed fractional parameters that cannot adapt to fluctuating network conditions. To address this limitation, the present study develops an adaptive FOPID (AFOPID) control architecture capable of real-time adjustment of fractional orders, thereby enhancing regulatory effectiveness. The Coot Optimization Algorithm (COA) is utilized to optimally determine the operational parameters of all controllers under investigation. The proposed strategy is validated on a simulated hybrid power system comprising wind generation, solar–thermal units, and physical nonlinearities including governor dead band and generation rate constraints. A comparative analysis is conducted across four distinct operating scenarios, benchmarking the COA-tuned AFOPID against conventional PI, PID, and standard FOPID controllers. Quantitative results demonstrate that the proposed COA-AFOPID configuration achieves superior performance, with improvements in settling time up to 46.06% and reductions in ITAE index up to 89.89% compared to traditional methods. These findings confirm the enhanced stability and robustness of the proposed approach for frequency regulation in sustainable energy networks. Full article
(This article belongs to the Special Issue Energy Systems: Optimization, Modeling, and Simulation)
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42 pages, 14758 KB  
Article
A Reinforcement Learning Autopilot for Fixed-Wing UAVs with Windowed Violation Summaries and Bounded Reward Reweighting
by Yan Kang, Tingwei Ji, Fangfang Xie, Chenglou Liu and Zihao Yuan
Drones 2026, 10(7), 489; https://doi.org/10.3390/drones10070489 - 26 Jun 2026
Viewed by 267
Abstract
Gain-scheduled and cascaded proportional–integral–derivative (PID) autopilots remain common practical baselines for fixed-wing unmanned aerial vehicles (UAVs), but training one shared learned controller for heading, altitude, and true airspeed across several maneuvers remains difficult. We study this problem under a strict reach-then-hold benchmark in [...] Read more.
Gain-scheduled and cascaded proportional–integral–derivative (PID) autopilots remain common practical baselines for fixed-wing unmanned aerial vehicles (UAVs), but training one shared learned controller for heading, altitude, and true airspeed across several maneuvers remains difficult. We study this problem under a strict reach-then-hold benchmark in which all the active channels must enter prescribed green bands and remain there for a terminal hold window. The proposed training recipe combines proximal policy optimization (PPO) with a tri-band maneuver-tracking reward and an outer bounded reward reweighting (BDR) step that updates the base reward weights from recent violation summaries under a Kullback–Leibler (KL) gate. In the JSBSim F-16 six-degree-of-freedom dynamics model, used here as a challenging surrogate benchmark for fixed-wing UAV autopilot learning, the learned controller transfers across a fixed five-lesson sequence, reaches strict success rates of 0.966 on turn and 0.921 on climb, and issues substantially smaller executed-command updates than the shared fixed-gain PID reference used here. Under the reported lesson sequence and step budget, fixed-weight PPO and a reweighting-only variant stall under the same envelopes, while speed remains the main bottleneck for both controllers. We further report exploratory long-horizon tracking, difficult-command stress checks, and an added command-filtered nonlinear dynamic-surface-control (CF-DSC) reference without retraining the learned policy. The CF-DSC results confirm that advanced non-reinforcement-learning (non-RL) controllers can be strong reference methods; therefore, within this reported simulator setup, BDR should be read as a practical and inspectable reward-scheduling heuristic for shared triad tracking rather than as a proof of superiority over all classical, nonlinear, or model-based controllers. Full article
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20 pages, 1384 KB  
Article
A Comparative Analysis of Sliding Mode Control, Feedback Linearization, and Proportional Integral Derivative Control in a Two-Tank System Using a High-Gain Observer
by Yohannes Lisanewerk Mulualem, Yeabisra Wubishet Engda, Tewodros Asfaw Gebretsadik, Gang Gyoo Jin, Yung Deug Son and Jongkap Ahn
Mathematics 2026, 14(13), 2272; https://doi.org/10.3390/math14132272 - 26 Jun 2026
Viewed by 305
Abstract
Maintaining precise liquid levels in interconnected tank systems is a critical requirement in many industrial processes; however, achieving reliable control remains challenging due to inherent nonlinearities and external disturbances. This paper presents a comparative analysis of three control strategies—sliding mode control (SMC), feedback [...] Read more.
Maintaining precise liquid levels in interconnected tank systems is a critical requirement in many industrial processes; however, achieving reliable control remains challenging due to inherent nonlinearities and external disturbances. This paper presents a comparative analysis of three control strategies—sliding mode control (SMC), feedback linearization (FL), and proportional–integral–derivative (PID) control—applied to a nonlinear two-tank system. To address the practical limitation of unmeasured system states, a high-gain observer (HGO) is integrated into the control architecture to reconstruct unmeasured water levels. In addition, the controller and observer parameters are optimized using a hybrid genetic algorithm to balance tracking precision and control effort. Simulation results demonstrate that, although all three methods achieve acceptable setpoint tracking performance, the SMC-HGO configuration exhibits superior robustness. Specifically, it outperforms FL and PID in rejecting external disturbances and maintaining stability under significant parameter variations, such as changes in discharge coefficients. Full article
(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems, 3rd Edition)
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39 pages, 7637 KB  
Article
Design and Implementation of an Industry 4.0 Oriented Robotic Cell Through the Integration of the ABB IRB 14000 Robot and Optimized PID Control of a Conveyor Belt
by Ricardo Balcazar, José de Jesús Rubio, Mario Alberto Hernandez, Jaime Pacheco, Alejandro Zacarías, Eduardo Orozco, Enrique Garcia, Genaro Ochoa, Ricardo Rodriguez-Figueroa and Roberto Morales-Montaño
Appl. Sci. 2026, 16(13), 6318; https://doi.org/10.3390/app16136318 - 23 Jun 2026
Viewed by 512
Abstract
This work addresses the design and implementation of an automated system for the handling and transportation of parts, integrating speed sensors, an optimized PID controller, an HMI interface, and an industrial robotic system. The speed sensors, powered by 5 V DC, enable continuous [...] Read more.
This work addresses the design and implementation of an automated system for the handling and transportation of parts, integrating speed sensors, an optimized PID controller, an HMI interface, and an industrial robotic system. The speed sensors, powered by 5 V DC, enable continuous measurement of the conveyor belt’s speed and direction of rotation, providing the feedback signal required for the control loop. The core element of the system is the implementation of a PID controller applied to a direct current motor responsible for driving the conveyor belt. This controller regulates the motor speed by analyzing the error between the reference speed and the measured speed, using proportional, integral, and derivative actions to improve system stability, reduce steady-state error, and minimize oscillations. The application of PID control makes it possible to achieve an appropriate dynamic response, ensuring accuracy and reliability in the transportation process. System monitoring and operation are carried out through a human–machine interface (HMI) developed in LOGO Web Editor, which communicates with the PLC (LOGO V8) to visualize and control the status of the conveyor belt, sensors, and control elements in real time. This interface facilitates interaction between the operator and the system, allowing both virtual and physical operation. In addition, RAPID programming is used to control the IRB 14000 industrial robot, enabling the reading of PLC signals and the execution of coordinated trajectories between both arms. The operating sequence includes picking up a part with the left arm, placing it on the conveyor belt, and, after detection by sensors and PLC control, subsequent manipulation by the right arm to a specific point. Finally, both arms return to their original position, ensuring synchronized and collision-free operation. Lastly, this work integrates scientific knowledge related to the modeling, analysis, and control of dynamic systems, particularly in the implementation of closed-loop PID control optimized using genetic algorithms. This control is applied directly to an embedded system through the use of an Arduino board as the processing and control platform. Likewise, technological knowledge associated with industrial automation, PLC programming, HMI development, and industrial robotics is incorporated. The convergence of these scientific and technological approaches results in a comprehensive and compelling project that demonstrates the practical application of theoretical concepts in a functional automated system representative of real industrial environments. Full article
(This article belongs to the Special Issue Advances in Industrial Robotics and Control Systems)
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