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Search Results (1,038)

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Keywords = sliding mode observer

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22 pages, 3101 KB  
Article
Model-Free Non-Singular Fast Terminal Sliding Mode Control Based on Agricultural Unmanned Aerial Vehicle Electrical Control System
by Mingyuan Hu, Longhui Qi, Changning Wei, Lei Zhang, Yaqing Gu, Bo Gao, Yang Liu and Dongjun Zhang
Symmetry 2026, 18(4), 678; https://doi.org/10.3390/sym18040678 (registering DOI) - 18 Apr 2026
Abstract
Permanent magnet synchronous motors (PMSMs) are widely used in agricultural unmanned aerial vehicle (UAV) electromechanical systems for their high efficiency and power density. While sliding mode control (SMC) offers robustness for PMSM drives, conventional designs face challenges like slow convergence, singularity, and chattering. [...] Read more.
Permanent magnet synchronous motors (PMSMs) are widely used in agricultural unmanned aerial vehicle (UAV) electromechanical systems for their high efficiency and power density. While sliding mode control (SMC) offers robustness for PMSM drives, conventional designs face challenges like slow convergence, singularity, and chattering. This paper proposes a model-free improved non-singular fast terminal SMC scheme with an improved adaptive super-twisting algorithm and a disturbance observer (MFINFTSMC-IADSTA-IFTSMO) for agricultural UAV applications. The designed sliding surface ensures fixed-time convergence without singularity, the adaptive reaching law reduces chattering, and the observer enables feedforward compensation of disturbances. Closed-loop stability is proven via Lyapunov theory. DSP-based experiments demonstrate that the proposed method outperforms existing SMC variants in dynamic response, steady-state accuracy, chattering suppression, and disturbance rejection. Specifically, the proposed method achieves a start-up convergence time of only 0.35 s, which is 56.25% shorter than that of the classic SMC-STA method, fully verifying its superior fast convergence performance. Full article
(This article belongs to the Special Issue Symmetry/Asymmetry in Control Theory)
15 pages, 1142 KB  
Article
Sliding Mode Coordinate Positioning-Based Friction Anomaly Monitoring of Multiple Wheelsets for Traction Drive System
by Shicai Yin, Mingyang Shang, Jinqiu Gao, Wanshun Zang, Chao Gong and Yaofei Han
Lubricants 2026, 14(4), 171; https://doi.org/10.3390/lubricants14040171 - 17 Apr 2026
Abstract
Accurately monitoring the wheelset–rail friction condition is crucial for ensuring the safety and operational efficiency of the traction drive system. However, the friction characteristics of wheelsets are easily influenced by factors such as ramp transitions and variable railway conditions in the complex environment. [...] Read more.
Accurately monitoring the wheelset–rail friction condition is crucial for ensuring the safety and operational efficiency of the traction drive system. However, the friction characteristics of wheelsets are easily influenced by factors such as ramp transitions and variable railway conditions in the complex environment. These factors significantly increase the difficulty of detecting friction anomalies and accurately locating faulty wheelsets in a timely manner. To address this issue, this paper proposes a sliding mode coordinate positioning–based friction anomaly monitoring scheme for multiple wheelsets in traction drive systems. First, a multi-sliding mode fusion-based friction characteristic observer is developed. Then, an friction coordinate analysis-based anomaly identification method is proposed. Finally, the proposed method is validated on a hardware-in-the-loop (HIL)-based experimental platform. Experimental results demonstrate that the proposed scheme can effectively detect friction anomalies and accurately locate abnormal wheelsets in multi-wheelset traction systems. Compared with traditional methods, the proposed scheme exhibits stronger robustness to varying railway conditions and does not require complex optimization mechanisms, making it suitable for practical on-board applications. Full article
23 pages, 4099 KB  
Article
Composite Control Strategy for PMSM Based on Non-Singular Terminal Sliding Mode Control and Angle-Domain Iterative Learning
by Longbao Liu, Gang Li, Benjian Ruan and Yongqiang Fan
Appl. Sci. 2026, 16(8), 3920; https://doi.org/10.3390/app16083920 - 17 Apr 2026
Abstract
To mitigate low-speed speed oscillations in permanent magnet synchronous motors (PMSMs) arising from the combined effects of rotor-position-related periodic disturbances and external perturbations, this paper develops a composite robust speed regulation scheme that integrates non-singular terminal sliding mode control (NTSMC) with angle-domain iterative [...] Read more.
To mitigate low-speed speed oscillations in permanent magnet synchronous motors (PMSMs) arising from the combined effects of rotor-position-related periodic disturbances and external perturbations, this paper develops a composite robust speed regulation scheme that integrates non-singular terminal sliding mode control (NTSMC) with angle-domain iterative learning control (ILC). First, a non-singular terminal sliding mode speed controller is established to remove the singularity inherent in conventional terminal sliding mode formulations while preserving finite-time error convergence. To further improve robustness and reduce chattering, an enhanced generalized super-twisting reaching law incorporating a continuous saturation function is introduced. Second, to compensate for periodic disturbances associated with rotor position, an angle-domain ILC law is constructed to iteratively learn the periodic speed-tracking error, thereby suppressing low-speed speed ripple. Meanwhile, an extended state observer (ESO) is incorporated to estimate aperiodic disturbances online, enabling coordinated rejection of disturbances with different temporal characteristics. Experimental results demonstrate that the proposed composite strategy effectively weakens the dominant harmonic components in speed fluctuation and enhances low-speed operational smoothness, confirming the effectiveness of the developed method. Full article
(This article belongs to the Section Electrical, Electronics and Communications Engineering)
24 pages, 942 KB  
Article
Enhanced Wind Energy Integration and Grid Stability via Adaptive Nonlinear Control with Advanced Energy Management
by Nabil ElAadouli, Adil Mansouri, Abdelmounime El Magri, Rachid Lajouad, Ilyass El Myasse and Karim El Mezdi
Energies 2026, 19(8), 1941; https://doi.org/10.3390/en19081941 - 17 Apr 2026
Abstract
This paper proposes an advanced wind energy conversion and management framework for improving grid integration and mitigating frequency and power fluctuations caused by wind intermittency. The studied system combines a permanent magnet synchronous generator (PMSG), a unidirectional Vienna rectifier on the machine side, [...] Read more.
This paper proposes an advanced wind energy conversion and management framework for improving grid integration and mitigating frequency and power fluctuations caused by wind intermittency. The studied system combines a permanent magnet synchronous generator (PMSG), a unidirectional Vienna rectifier on the machine side, a Li-ion battery energy storage system, and a bidirectional Vienna rectifier on the grid side. The main scientific challenge addressed in this work is to ensure efficient wind power extraction, secure battery charging/discharging operation, and stable power exchange with the grid under variable operating conditions. To this end, a comprehensive nonlinear state-space model of the overall system is first established. Then, nonlinear controllers based on integral sliding mode principles are developed to guarantee rotor-speed tracking, DC-bus voltage regulation, battery charging current limitation, and active/reactive power control. In addition, an adaptive observer is designed to estimate the battery open-circuit voltage and support the supervision of the state of charge. An energy management strategy is further proposed to coordinate the operating modes according to grid conditions and battery constraints. Simulation results demonstrate that the proposed approach effectively smooths wind power fluctuations, improves grid support capability, and enhances the overall dynamic performance of the wind energy conversion system. Full article
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21 pages, 1718 KB  
Article
Anti-Disturbance Trajectory Tracking Control for Quadrotor UAVs Based on Radial Basis Function Neural Network and Integral Terminal Sliding Mode Control
by Xizhao Zhang and Shaohua Niu
Mathematics 2026, 14(8), 1332; https://doi.org/10.3390/math14081332 - 15 Apr 2026
Viewed by 145
Abstract
Quadrotor unmanned aerial vehicles (UAVs) operating in complex and dynamic environments, especially when subjected to unknown disturbances such as wind, can experience significant degradation in the stability of trajectory tracking control. Current research on UAV control has proposed algorithms that exhibit good disturbance [...] Read more.
Quadrotor unmanned aerial vehicles (UAVs) operating in complex and dynamic environments, especially when subjected to unknown disturbances such as wind, can experience significant degradation in the stability of trajectory tracking control. Current research on UAV control has proposed algorithms that exhibit good disturbance rejection capabilities for small and weak disturbances, but their effectiveness decreases significantly as the disturbance magnitude increases. To address this issue, this paper proposes a hybrid control strategy that combines a Radial Basis Function Neural Network (RBFNN) with Integral Terminal Sliding Mode Control (ITSMC). The RBFNN is designed as an online disturbance observer, capable of estimating and compensating external disturbance forces and torques in real time, with an adaptive weight law. The ITSMC utilizes an integral term to eliminate steady-state errors and a terminal sliding mode term to achieve finite-time convergence of tracking errors. Simulation results demonstrate that the proposed controller maintains high-precision trajectory tracking and attitude control performance under various disturbance conditions, exhibiting strong robustness and anti-disturbance capability, and outperforms other controllers in overall performance. Full article
(This article belongs to the Section E2: Control Theory and Mechanics)
21 pages, 1542 KB  
Article
Adaptive Sliding Mode Control for PMSM Drives with High-Order Disturbance Compensation
by Bingmin Ji, Xin Mu, Lingbo Kong and Mingzhe Yang
Sensors 2026, 26(8), 2402; https://doi.org/10.3390/s26082402 - 14 Apr 2026
Viewed by 225
Abstract
To enhance the dynamic response and robustness of permanent magnet synchronous motor (PMSM) speed regulation under load disturbances, this study proposes a composite control strategy that integrates a novel sliding mode control based on an adaptive reaching law (NSMC) with a high-order disturbance [...] Read more.
To enhance the dynamic response and robustness of permanent magnet synchronous motor (PMSM) speed regulation under load disturbances, this study proposes a composite control strategy that integrates a novel sliding mode control based on an adaptive reaching law (NSMC) with a high-order disturbance observer (HDOB). First, an adaptive reaching law is designed to accelerate the convergence process when the system state is far from the sliding surface, while an adaptive saturation function (ASF) is introduced to smooth switching actions and reduce chattering near the sliding surface. Subsequently, a high-order disturbance observer is developed to estimate the lumped disturbance and its variation in real time, with the estimated disturbance being fed forward to the output of the speed-loop controller to enhance disturbance rejection capability. The effectiveness of the proposed method is validated through simulations and real-time experiments on a Hall-sensor-based PMSM drive platform. Experimental results show that, at a reference speed of 600 r/min, the proposed NSMC reduces settling time by 43.1% compared with conventional sliding mode control, while virtually eliminating overshoot. Under sudden load application and removal, the proposed NSMC + HDOB reduces the maximum speed deviation by 38.3% and 57.2%, respectively, compared with SMC + HDOB. These results indicate that the proposed strategy achieves faster speed tracking, smaller speed fluctuations, and enhanced robustness against load disturbances, offering an effective solution for high-performance PMSM drive systems. Full article
(This article belongs to the Section Electronic Sensors)
20 pages, 3668 KB  
Article
Research on a Sliding Mode Self-Disturbance-Rejection Control Strategy for Three-Phase Interleaved Buck Converters
by Shihao Xing, Yang Cui, Cheng Liu and Ke Liu
Energies 2026, 19(8), 1846; https://doi.org/10.3390/en19081846 - 9 Apr 2026
Viewed by 285
Abstract
To address the issues of slow dynamic response and poor disturbance rejection in three-phase interleaved parallel buck converters under disturbance conditions such as voltage or load transients, an improved sliding mode auto-disturbance rejection control (SM-ADRC) strategy is proposed. Firstly, the traditional ADRC algorithm [...] Read more.
To address the issues of slow dynamic response and poor disturbance rejection in three-phase interleaved parallel buck converters under disturbance conditions such as voltage or load transients, an improved sliding mode auto-disturbance rejection control (SM-ADRC) strategy is proposed. Firstly, the traditional ADRC algorithm suffers from reduced disturbance observation accuracy in the extended state observer (ESO) due to discontinuous switching of the nonlinear function at segment boundaries. To address this, a novel nonlinear function is designed using an interpolation fitting method. Concurrently, an improved ESO is constructed based on deviation-control principles, utilising the deviation between each state variable and its observed value. Secondly, an enhanced state error feedback law combines an improved exponential approach law with an integral sliding mode surface, thereby enhancing the control system’s robustness. Finally, simulation comparisons of output voltage fluctuations and power response speeds under various operating conditions validate the superiority and feasibility of the proposed SM-ADRC strategy over both the conventional ADRC strategy and PI control strategy. Full article
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21 pages, 8757 KB  
Article
A Study on Control System Design for Tugboat-Assisted Vessel Berthing Under Tugboat Failure
by Jung-Suk Park, Young-Bok Kim and Thinh Huynh
Actuators 2026, 15(4), 211; https://doi.org/10.3390/act15040211 - 8 Apr 2026
Viewed by 240
Abstract
This paper investigates the controllability of vessel berthing systems assisted by multiple tugboats under actuator faults or failures. In such interconnected systems, a failure of an individual tugboat can potentially compromise the berthing operation, or even lead to the collapse of the entire [...] Read more.
This paper investigates the controllability of vessel berthing systems assisted by multiple tugboats under actuator faults or failures. In such interconnected systems, a failure of an individual tugboat can potentially compromise the berthing operation, or even lead to the collapse of the entire system. To address this challenge, the dynamic model of the multi-tug-assisted vessel system is first derived, followed by a controllability analysis under various fault scenarios to identify tolerable fault configurations. Then, a robust controller is proposed, integrating an adaptive disturbance observer with finite-time sliding mode control. This design ensures effective rejection of maritime environmental disturbances, practical finite-time stability, and bounded trajectory tracking errors. To accommodate different fault conditions, a switching control allocation strategy is developed to redistribute control efforts among the remaining healthy tugboats, thereby maintaining system reliability and efficiency. Simulation results under various faulty conditions demonstrate the effectiveness and robustness of the proposed control approach. Full article
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17 pages, 10033 KB  
Article
Prescribed Performance Attitude-Tracking Control for Rigid Satellite Under External Disturbance
by Chunyu Zhang, Ting Wang, Min Wan and Tao Li
Sensors 2026, 26(7), 2189; https://doi.org/10.3390/s26072189 - 1 Apr 2026
Viewed by 354
Abstract
This paper addresses the attitude control problem for a rigid satellite and proposes an anti-disturbance prescribed performance control (PPC) scheme, aiming to achieve accurate attitude tracking while guaranteeing tracking performance under external disturbances. First, a prescribed-time disturbance observer (PTDO) is developed to achieve [...] Read more.
This paper addresses the attitude control problem for a rigid satellite and proposes an anti-disturbance prescribed performance control (PPC) scheme, aiming to achieve accurate attitude tracking while guaranteeing tracking performance under external disturbances. First, a prescribed-time disturbance observer (PTDO) is developed to achieve the precise and rapid estimation of external disturbances within a prescribed time. Second, an appointed-time performance function (ATPF) is introduced, based on which an asymmetric performance boundary is constructed to ensure convergence within the appointed time. Subsequently, by enforcing the constructed sliding-mode error to satisfy prescribed performance constraint, the desired tracking performance of the satellite attitude system is achieved. Third, according to Lyapunov stability theory, it is proven that the disturbance estimation error and the unconstrained error in the attitude system are uniformly ultimately bounded, thereby enabling the achievement of the desired control performance. Finally, the effectiveness of the proposed control strategy is verified via numerical simulations. Full article
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23 pages, 3524 KB  
Article
Nonlinear Disturbance Observer-Based Cooperative Control of Multi-Hydraulic Robotic Arms with Digital Twin Validation
by Bo Gao, Yuliang Lin and Liangsong Huang
Electronics 2026, 15(7), 1472; https://doi.org/10.3390/electronics15071472 - 1 Apr 2026
Viewed by 278
Abstract
This paper presents a finite-time uniformly ultimately bounded (FTUUB) cooperative control strategy based on a nonlinear disturbance observer (NDOB) for high-precision collaborative control of multi-hydraulic robotic arm systems operating under unknown disturbances and model uncertainties in confined scenarios such as coal silo cleaning. [...] Read more.
This paper presents a finite-time uniformly ultimately bounded (FTUUB) cooperative control strategy based on a nonlinear disturbance observer (NDOB) for high-precision collaborative control of multi-hydraulic robotic arm systems operating under unknown disturbances and model uncertainties in confined scenarios such as coal silo cleaning. The proposed approach simplifies control design by lumping various uncertainties into a total disturbance, which is estimated and compensated in real time by the NDOB. Building upon this, a finite-time convergent sliding mode controller is developed, wherein the disturbance compensation is inherently embedded, ensuring that both position and velocity tracking errors converge to a small neighborhood of zero within a finite time. A master–slave distributed control architecture is adopted, with the agent communication topology characterized by graph theory. To mitigate the chattering inherent in traditional sliding mode control, a smooth hyperbolic tangent function is employed to construct the sliding surface. Rigorous Lyapunov stability analysis demonstrates that the closed-loop system achieves uniform ultimate boundedness within a finite time. Comprehensive simulation experiments, including a digital twin-based visualization in a virtual coal silo environment, validate the superior performance of the proposed method in terms of tracking accuracy, convergence speed, disturbance rejection, and control smoothness. Full article
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26 pages, 9433 KB  
Article
CCRNATSM Control for Quadrotor Trajectory Tracking Under Coupled Wind–Rain Disturbances
by Fei Xie, Zhiling Peng, Honghui Fan, Jie Duan, Shuwen Zhao, Xiaoyu Guo and Jiani Zhao
Symmetry 2026, 18(4), 590; https://doi.org/10.3390/sym18040590 - 30 Mar 2026
Viewed by 235
Abstract
Despite the widespread deployment of quadrotor unmanned aerial vehicles (UAVs), ensuring their flight stability under asymmetric environmental disturbances, such as concurrent wind and rain, remains a significant challenge. To address the trajectory tracking problem under these severe conditions, this paper proposes a Composite [...] Read more.
Despite the widespread deployment of quadrotor unmanned aerial vehicles (UAVs), ensuring their flight stability under asymmetric environmental disturbances, such as concurrent wind and rain, remains a significant challenge. To address the trajectory tracking problem under these severe conditions, this paper proposes a Composite Continuous Rapid Nonsingular Adaptive Terminal Sliding Mode (CCRNATSM) control strategy. First, a composite dynamic model is developed, integrating wind aerodynamics with rain impact characteristics to accurately simulate realistic flight environments. A High-Order Sliding Mode Observer (HOSMO) is then employed for the real-time, accurate estimation of these lumped disturbances. Subsequently, this observer is integrated with an adaptive control law to ensure rapid and precise system stabilization. Comparative simulations conducted under strong disturbance conditions demonstrate that the proposed method exhibits superior performance over existing strategies, reducing roll angle deviation by 75% and shortening the recovery time to 1.5 s. Ultimately, this control strategy significantly enhances the robustness and safety of quadrotor UAVs operating in harsh, asymmetric environments. Full article
(This article belongs to the Section Engineering and Materials)
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32 pages, 1792 KB  
Article
A Hybrid Systems Framework for Electric Vehicle Adoption: Microfoundations, Networks, and Filippov Dynamics
by Pascal Stiefenhofer and Jing Qian
Complexities 2026, 2(2), 8; https://doi.org/10.3390/complexities2020008 - 29 Mar 2026
Viewed by 223
Abstract
Electric vehicle(EV) diffusion exhibits nonlinear, path-dependent dynamics shaped by interacting economic, technological, and social constraints. This paper develops a unified hybrid systems framework that captures these complexities by integrating microfounded household choice, capacity-constrained firm behavior, local network spillovers, and multi-level policy intervention within [...] Read more.
Electric vehicle(EV) diffusion exhibits nonlinear, path-dependent dynamics shaped by interacting economic, technological, and social constraints. This paper develops a unified hybrid systems framework that captures these complexities by integrating microfounded household choice, capacity-constrained firm behavior, local network spillovers, and multi-level policy intervention within a Filippov differential-inclusion structure. Households face heterogeneous preferences, liquidity limits, and network-mediated moral and informational influences; firms invest irreversibly under learning-by-doing and profitability thresholds; and national and local governments implement distinct financial and infrastructure policies subject to budget constraints. The resulting aggregate adoption dynamics feature endogenous switching, sliding modes at economic bottlenecks, network-amplified tipping, and hysteresis arising from irreversible investment. We establish conditions for the existence of Filippov solutions, derive network-dependent tipping thresholds, characterize sliding regimes at capacity and liquidity constraints, and show how network structure magnifies hysteresis and shapes the effectiveness of local versus national policy. Optimal-control analysis further demonstrates that national subsidies follow bang–bang patterns and that network-targeted local interventions minimize the fiscal cost of achieving regional tipping. Beyond theoretical characterization, the framework is structurally calibrated to match the order-of-magnitude effects reported in leading empirical and simulation-based studies, including network diffusion models, agent-based simulations, bass-type specifications, and fuel-price shock analyses. The hybrid formulation reproduces short-run percentage-point subsidy effects, long-run forecast dispersion under alternative network assumptions, and policy-induced equilibrium shifts observed in the applied literature while providing a unified geometric interpretation of these heterogeneous results through explicit basin boundaries and regime switching. The framework provides a complex systems perspective on sustainable mobility transitions and clarifies why identical national policies can generate asynchronous regional outcomes. These results offer theoretical foundations for designing coordinated, cost-effective, and network-aware EV transition strategies. Full article
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27 pages, 4264 KB  
Article
A Fast Integral Terminal Sliding Mode Buck Converter with a Fixed-Time Observer for Solar-Powered Livestock Smart Collars
by Shiming Zhang, Haochen Ouyang, Shengqiang Shi, Guichang Fang, Zhen Wang, Xinnan Du and Boyan Huang
Agriculture 2026, 16(7), 746; https://doi.org/10.3390/agriculture16070746 - 27 Mar 2026
Viewed by 420
Abstract
Fully maintenance-free smart collars for range cattle, sheep and deer must survive years of uncontrolled grazing under highly variable shade and motion conditions. This paper presents an ultra-low-power buck converter governed by a fast integral terminal sliding mode controller (FITSMC) with a fixed-time [...] Read more.
Fully maintenance-free smart collars for range cattle, sheep and deer must survive years of uncontrolled grazing under highly variable shade and motion conditions. This paper presents an ultra-low-power buck converter governed by a fast integral terminal sliding mode controller (FITSMC) with a fixed-time observer. A new reaching law retains the initial sliding manifold and a negative-power term maintains the constant switching gain to preserve robustness near the surface while attenuating chattering without widening the bandwidth. The fixed-time observer estimates the irradiance and load changes and provides a feed-forward correction, tightening the output regulation regardless of initial conditions. Load step tests with moderate resistance swings showed the proposed method recovers noticeably faster and exhibits slightly lower overshoot than a recent method based on a two-phase power reaching law, while visible inductor current spikes are also suppressed. Simulations under daily grazing profiles confirmed tight output regulation adequate for microwatt data logging and periodic long-range (LoRa) bursts. The sleep mode quiescent current remained in the 9 microamps range, eliminating the need for manual recharge across multi-season field deployments. By integrating robust power electronics with collar-grade solar harvesting, the circuit offers a truly maintenance-free energy path for untethered livestock wearables and supports sustainable precision agriculture. Full article
(This article belongs to the Section Artificial Intelligence and Digital Agriculture)
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28 pages, 11377 KB  
Article
Extended State Observer-Assisted Fast Adaptive Extremum-Seeking Searching Interval Type-2 Fuzzy PID Control of Permanent Magnet Synchronous Motors for Speed Ripple Mitigation at Low-Speed Operation
by Fuat Kılıç
Appl. Sci. 2026, 16(6), 3093; https://doi.org/10.3390/app16063093 - 23 Mar 2026
Viewed by 268
Abstract
Permanent magnet synchronous motors (PMSMs) are utilized in demanding conditions and applications requiring precision and accuracy, such as servo systems. Especially at low speeds, the effects of cogging torque, current measurement and offset errors, improper controller gains, mechanical resonance, and torque fluctuations caused [...] Read more.
Permanent magnet synchronous motors (PMSMs) are utilized in demanding conditions and applications requiring precision and accuracy, such as servo systems. Especially at low speeds, the effects of cogging torque, current measurement and offset errors, improper controller gains, mechanical resonance, and torque fluctuations caused by load torque and flux result in fluctuations at various frequencies in the motor output speed. This study, motivated by two factors, proposes an extended state observer (ESO)-based multivariable fast response extremum-seeking (FESC) interval type-2 fuzzy PID (IT2FPID) controller to improve dynamic response and reduce speed ripple at low speeds in situations where all these negative factors could arise. This approach enables the real-time adaptation of parameters to counteract the decline in controller performance caused by the nonlinear characteristics of PMSMs and parameter fluctuations while also optimizing disturbance rejection in the speed response under varying operating conditions and existing speed ripple. The experimental results from the prototype setup validate that the proposed control mechanism is functional, valid, and precise in diminishing speed ripples during low-speed operations. The simulation and test outcomes of the control scheme show that speed noise at low speeds is reduced from 26% to 3% compared to traditional proportional-integral (PI) controller and supertwisting (STW) sliding mode controller (SMC) responses and that the scheme exhibits a 16–23% reduction in undershoot amplitude and faster recovery in the presence of load torque variations. Full article
(This article belongs to the Special Issue Fuzzy Control Systems and Decision-Making)
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22 pages, 4091 KB  
Article
3D Trajectory Tracking Based on Super-Twisting Observer and Non-Singular Terminal Sliding Mode Control for Underactuated Autonomous Underwater Vehicle
by Zehui Yuan, Long He, Ya Zhang, Shizhong Li, Chenrui Bai and Zhuoyan Qi
Machines 2026, 14(3), 354; https://doi.org/10.3390/machines14030354 - 21 Mar 2026
Viewed by 357
Abstract
This paper addresses the three-dimensional trajectory tracking problem for underactuated autonomous underwater vehicles subject to external disturbances and model uncertainties in complex ocean environments. A robust control method integrating backstepping dynamic surface control and non-singular terminal sliding mode is proposed. Firstly, based on [...] Read more.
This paper addresses the three-dimensional trajectory tracking problem for underactuated autonomous underwater vehicles subject to external disturbances and model uncertainties in complex ocean environments. A robust control method integrating backstepping dynamic surface control and non-singular terminal sliding mode is proposed. Firstly, based on the kinematic and dynamic models of autonomous underwater vehicle, virtual velocity commands are constructed via backstepping approach to stabilize the position and attitude errors. To circumvent the “differential explosion” problem inherent in conventional backstepping control caused by repeated differentiations of virtual control variables, first-order low-pass filters are introduced to construct dynamic surface control, yielding smooth derivatives of virtual velocity commands. Secondly, to enhance convergence rate and robustness, a non-singular terminal sliding surface is designed at the dynamic level, and a terminal reaching law is formulated to achieve finite-time convergence of velocity tracking errors. Furthermore, to compensate for external disturbances and unmodeled dynamics, a disturbance observer based on the super-twisting algorithm is developed, enabling finite-time high-precision estimation of lumped disturbances, with the estimation results incorporated into the control law for feedforward compensation. Finally, comparative simulations are conducted under two typical disturbance scenarios. The results demonstrate that the proposed method achieves instantaneous disturbance estimation (reducing convergence time from 3 s to near zero), significantly smoother control inputs, and superior tracking accuracy with RMSE as low as 0.6788 m and MAE as low as 0.1468 m, reducing errors by up to 30.6% compared to baseline methods. Full article
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