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Keywords = nonsingular fast terminal sliding mode control

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20 pages, 8558 KB  
Article
Super-Twisting Algorithm-Based Sensorless Sliding-Mode Control for PMSM
by Shuanglong Wu, Shubin Chen, Xiaoxing Ye, Jiajun Rao, Yijie He, Xing Shu, Shaotao Chen, Caixia Lin and Long Qi
Electronics 2026, 15(12), 2650; https://doi.org/10.3390/electronics15122650 - 15 Jun 2026
Viewed by 156
Abstract
To address the issues of sluggish dynamic response, significant steady-state fluctuations, and poor disturbance rejection associated with traditional proportional–integral (PI) and conventional speed control methods, a novel sensorless sliding-mode speed control strategy for permanent magnet synchronous motors (PMSMs) based on the super-twisting algorithm [...] Read more.
To address the issues of sluggish dynamic response, significant steady-state fluctuations, and poor disturbance rejection associated with traditional proportional–integral (PI) and conventional speed control methods, a novel sensorless sliding-mode speed control strategy for permanent magnet synchronous motors (PMSMs) based on the super-twisting algorithm (STA) is proposed. First, an advanced sliding-mode speed controller is designed by integrating an integral nonsingular fast terminal sliding-mode surface with the STA, thereby enhancing the dynamic response and transient stability of the PMSM under speed variations. Subsequently, to mitigate inherent sliding-mode chattering, a novel load torque observer is developed. This observer continuously feeds forward real-time load estimates to the speed controller, which substantially improves the system’s robustness against external disturbances. Furthermore, to eliminate the reliance on mechanical sensors and ensure reliable operation across diverse scenarios, an improved sliding-mode observer (SMO) incorporating the STA is utilized to achieve more precise rotor position and speed estimation. Finally, an experimental platform is established to conduct comprehensive variable-speed and variable-load tests on the PMSM. Experimental results demonstrate that the proposed method improves the dynamic response and disturbance immunity of the PMSM by 58.33% and 71.75%, respectively, while reducing steady-state fluctuations by 33.33%. These results demonstrate the effectiveness of the proposed sensorless sliding-mode control strategy and show improved speed regulation performance for PMSM drives. Full article
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22 pages, 7796 KB  
Article
Sensorless Speed Control of PMSMs Based on an Improved Fast Power Reaching Law
by En Lu, Yufei Liu, Minghui Zhang and Jinyong Ju
Sensors 2026, 26(12), 3737; https://doi.org/10.3390/s26123737 - 11 Jun 2026
Viewed by 265
Abstract
Traditional permanent magnet synchronous motor (PMSM) control systems rely on mechanical position sensors for high-precision rotor position and speed information, which increases hardware complexity, raises system cost, reduces reliability, and limits adaptability to harsh environments. To overcome the above limitations, this paper proposes [...] Read more.
Traditional permanent magnet synchronous motor (PMSM) control systems rely on mechanical position sensors for high-precision rotor position and speed information, which increases hardware complexity, raises system cost, reduces reliability, and limits adaptability to harsh environments. To overcome the above limitations, this paper proposes a novel high-performance sensorless speed control strategy for PMSMs, which is constructed based on a non-singular terminal sliding mode observer (NTSMO) and a non-singular terminal sliding mode controller (NTSMC). First, an improved fast power reaching law (IFPRL) is proposed, which consists of a variable exponential reaching term and a power reaching term. Specifically, the gain of the exponential reaching term is dynamically adjusted by the absolute value of the sliding mode switching function, enabling the reaching law to operate in two different modes throughout the entire convergence process of the system state. Moreover, the introduction of scaling coefficient c compensates for the performance degradation caused by variations in the range of sliding mode surfaces (SMSs) in different systems. The proposed IFPRL not only effectively mitigates the inherent chattering issue, it also expedites the rate at which the system state converges to its SMS. On this basis, both the NTSMO for rotor position observation and the NTSMC for speed closed-loop control are designed by embedding the proposed IFPRL into the framework of non-singular terminal sliding mode control theory. Finally, the effectiveness of the proposed method is validated through numerical simulations and experimental tests. Experimental results demonstrate that the proposed IFPRL-based NTSMC + NTSMO scheme reduces the root mean square error (RMSE) of speed control by 2.7% relative to the traditional SMC + SMO method. The proposed method realizes reliable sensorless speed control for PMSMs and exhibits superior dynamic response, higher control accuracy, and stronger robustness against disturbances. Full article
(This article belongs to the Special Issue Novel Sensing Methods in Advanced Manufacturing Systems)
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43 pages, 15260 KB  
Article
Precision Docking of a Foldable Quadrotor on a Wheel-Legged Robot via CFNTSM with GFA-FEO and FiLM-SAC Deep Reinforcement Learning
by Qibin Gu and Zhenxing Sun
Drones 2026, 10(5), 378; https://doi.org/10.3390/drones10050378 - 14 May 2026
Viewed by 356
Abstract
Deploying unmanned aerial vehicles (UAVs) cooperatively with legged robots for disaster response and inspection requires autonomous docking on miniature walking platforms. This study addresses the problem of landing a foldable quadrotor onto the back of a trotting wheel-legged robot (300×180 [...] Read more.
Deploying unmanned aerial vehicles (UAVs) cooperatively with legged robots for disaster response and inspection requires autonomous docking on miniature walking platforms. This study addresses the problem of landing a foldable quadrotor onto the back of a trotting wheel-legged robot (300×180 mm) and subsequently taking off while carrying it as a payload. Four tightly coupled challenges distinguish this task from conventional mobile-platform landing: (i) an extremely small landing surface, (ii) gait-induced periodic vibrations at 2.5 Hz, (iii) continuous platform translation at 0.30.8 m/s, and (iv) surface docking that requires simultaneous position and attitude matching rather than mere point tracking. The proposed framework comprises four components: (1) a novel single-servo crank-rocker folding mechanism that reduces the folded body footprint by 48.5% and the maximum linear dimension from 590 mm to 309 mm (↓47.6%) compared with the prior dual-servo design; (2) a staged Continuous Fast Nonsingular Terminal Sliding Mode (CFNTSM) controller combined with a Gait-Frequency-Aware Finite-time Extended Observer (GFA-FEO); (3) a Feature-wise Linear Modulation Soft Actor-Critic (FiLM-SAC) residual reinforcement-learning policy conditioned on physical states and mission phase, with an adaptive trust weight λ(t); and (4) a payload-adaptive takeoff strategy with parameter hot-switching to handle the twofold mass increase. Extensive Monte Carlo simulations and ablation studies across three experiment groups demonstrate that the proposed hierarchical framework achieves sub-centimetre (<10 mm) position accuracy and <3° attitude matching on a walking platform. Quantitatively, the full method reduces docking RMSE by 42% relative to the model-based CFNTSM + GFA-FEO controller without residual RL (4.2 vs. 7.2 mm) and reduces post-lock takeoff RMSE by 63% through FEO hot-switching (16.2 vs. 44.2 mm). Full article
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17 pages, 9618 KB  
Article
Three-Switching-Surface Nonsingular Fast Terminal Sliding Mode Control for Two-Phase Buck Converters Powering DC Bus of Permanent Magnet Synchronous Motor Drives
by Jiaxin Xiong and Xinghe Fu
Electronics 2026, 15(10), 2024; https://doi.org/10.3390/electronics15102024 - 9 May 2026
Viewed by 250
Abstract
Aiming to improve the robustness of two-phase buck converters powering DC bus of permanent magnet synchronous motor drives, this article presents a novel voltage regulation scheme. The proposed scheme comprises a three-switching-surface nonsingular fast terminal sliding mode controller (TSS-NFTSMC) for output voltage regulation [...] Read more.
Aiming to improve the robustness of two-phase buck converters powering DC bus of permanent magnet synchronous motor drives, this article presents a novel voltage regulation scheme. The proposed scheme comprises a three-switching-surface nonsingular fast terminal sliding mode controller (TSS-NFTSMC) for output voltage regulation and a current balancing controller to equalize the inductor currents. Due to the fast terminal sliding mode surface, the output voltage error converges more rapidly both when far from zero and when approaching zero. The phase plane is split into four regions by three independent switching surfaces. Based on the region where the sliding variable resides, the TSS-NFTSMC can directly decide the number of enabled high-side switches, which helps suppress internal disturbances effectively. The stability and convergence of the presented control system are verified via Lyapunov stability analysis. The convergence property of TSS-NFTSMC is independent of the current controller. Both simulation and experimental results demonstrate that the proposed control strategy achieves satisfactory dynamic response and strong disturbance rejection capability. Full article
(This article belongs to the Section Power Electronics)
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24 pages, 3169 KB  
Article
Non-Singular Fast Terminal Sliding Mode Control Based Trajectory Tracking Control of Cable-Driven Manipulators Subject to Lumped Mismatched Uncertainties
by Tran Buu Thach Nguyen, Hoai Vu Anh Truong and Kyoung Kwan Ahn
Mathematics 2026, 14(10), 1602; https://doi.org/10.3390/math14101602 - 8 May 2026
Viewed by 296
Abstract
Cable-driven manipulators have emerged as a compelling alternative to traditional manipulators (driven by either electrical, hydraulic, or pneumatic motors), especially for operations in constrained and complex environments. Despite offering many advantages, they still pose significant control challenges. Therefore, this paper presents a novel [...] Read more.
Cable-driven manipulators have emerged as a compelling alternative to traditional manipulators (driven by either electrical, hydraulic, or pneumatic motors), especially for operations in constrained and complex environments. Despite offering many advantages, they still pose significant control challenges. Therefore, this paper presents a novel position tracking control framework for an n-DOF cable-driven manipulator subject to lumped mismatched uncertainties arising from unknown dynamic errors and external disturbances. The proposed approach is built upon non-singular fast terminal sliding mode control (NFTSMC), which provides robustness, high-precision tracking, fast finite-time convergence, chattering-free torque input, and complete elimination of singularity issues. To further enhance control performance, an extended state observer (ESO) is incorporated to accurately estimate unmeasured states and suppress lumped uncertainties. The stability of the closed-loop system under the proposed method is rigorously proven by the Lyapunov theorem. Finally, the superiority of the proposed method over existing controllers is demonstrated by comparative simulations to highlight its potential for practical implementation in complex robotic environments. Full article
(This article belongs to the Special Issue Mathematics Methods of Robotics and Intelligent Systems)
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13 pages, 22772 KB  
Article
Vision Inertial Stabilized Platform-Based Finite-Time Target Tracking Control for Multi-Rotor UAVs
by Jing Zhang, Zhiyong Yang, Wenwu Zhu and Jian Xiao
Actuators 2026, 15(5), 261; https://doi.org/10.3390/act15050261 - 2 May 2026
Viewed by 332
Abstract
This paper proposes a finite-time target tracking control for multi-rotor unmanned aerial vehicles (UAVs) based on a vision-inertial-stabilized platform. To address the challenge of stable and accurate moving target tracking, the sliding mode control (SMC) technique is used to overcome limitations of conventional [...] Read more.
This paper proposes a finite-time target tracking control for multi-rotor unmanned aerial vehicles (UAVs) based on a vision-inertial-stabilized platform. To address the challenge of stable and accurate moving target tracking, the sliding mode control (SMC) technique is used to overcome limitations of conventional control algorithms, such as poor robustness and slow convergence speed. First, by computing the pixel deviation between the target and the image center, a kinematic model of the tracking target is established. Then, by introducing homogeneous system theory into the sliding mode surface design, a non-singular fast integral terminal sliding mode control (NFITSMC) is designed for target tracking via regulating the rotational angular acceleration of dual actuators in the vision inertial stabilized platform, thereby driving the pixel deviation to converge to zero in a finite time. Strict theoretical analysis is given to prove the finite-time stability and robustness of the closed-loop control system. Furthermore, simulation results demonstrate that the proposed method maintains higher tracking accuracy than SMC, ISMC, and TSMC. Full article
(This article belongs to the Special Issue Advanced Learning and Intelligent Control Algorithms for Robots)
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21 pages, 2720 KB  
Article
Adaptive Neural Barrier Function-Based Fast Terminal Sliding Mode Control for Bionic Aerial Manipulators in Canopy Sampling
by Xiaohu Chen, Li Ding, Wenfeng Wu and Hongtao Wu
Aerospace 2026, 13(4), 392; https://doi.org/10.3390/aerospace13040392 - 21 Apr 2026
Viewed by 375
Abstract
This paper proposes a novel adaptive sliding mode control strategy for bionic aerial manipulators performing canopy-sampling tasks. Specifically, an adaptive neural barrier function-based fast terminal sliding mode control (BFASMC-NN) scheme is developed to address the joint-space trajectory tracking problem by integrating fast continuous [...] Read more.
This paper proposes a novel adaptive sliding mode control strategy for bionic aerial manipulators performing canopy-sampling tasks. Specifically, an adaptive neural barrier function-based fast terminal sliding mode control (BFASMC-NN) scheme is developed to address the joint-space trajectory tracking problem by integrating fast continuous nonsingular terminal sliding mode control (FNTSMC), neural networks (NNs), and barrier functions (BFs). The aerial manipulator is modeled as a rootless system, and its kinematic and dynamic characteristics are analyzed separately. Radial basis function neural networks (RBF-NNs) are introduced to approximate lumped disturbances, while BFs are incorporated to mitigate the effects of joint input saturation. Meanwhile, FNTSMC is employed to guarantee finite-time convergence of the system states. The stability of the closed-loop system is rigorously proven based on Lyapunov stability theory. Two simulation studies are conducted to validate the proposed method, and the results demonstrate that it achieves stronger disturbance rejection capability, faster convergence, and higher tracking accuracy than existing approaches. Full article
(This article belongs to the Special Issue New Perspective on Flight Guidance, Control and Dynamics)
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22 pages, 4182 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 - 18 Apr 2026
Viewed by 308
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)
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36 pages, 7620 KB  
Article
Unified Modulation Matrix-Based Shared Control for Teleoperated Multi-Robot Formation and Obstacle Avoidance
by Ruidong Chen, Zhuoyue Zhang, Zhiyao Zhang, Jinyan Li and Haochen Zhang
Sensors 2026, 26(8), 2387; https://doi.org/10.3390/s26082387 - 13 Apr 2026
Viewed by 662
Abstract
Multi-omnidirectional mobile robot formations offer significant advantages for applications in unstructured environments. However, under constraints such as limited field of view and high operator cognitive load, existing teleoperation frameworks struggle to guarantee formation safety and stability. In this study, a bilateral shared control [...] Read more.
Multi-omnidirectional mobile robot formations offer significant advantages for applications in unstructured environments. However, under constraints such as limited field of view and high operator cognitive load, existing teleoperation frameworks struggle to guarantee formation safety and stability. In this study, a bilateral shared control framework for multi-robot formation that integrates intent perception and vortex-field modulation is proposed. First, an Intent-Mediated Asymmetric Vortex Modulation (IM-AVM) strategy is developed, where the operator’s micro-intentions are mapped to determine the topological orientation of a vortex field. By constructing a dynamic asymmetric modulation matrix, saddle points in the potential field are geometrically eliminated, enabling deadlock-free obstacle avoidance while maintaining a rigid formation. Second, a multi-dimensional perception-based dynamic authority arbitration and topological deadlock escape mechanism is constructed, facilitating a seamless transition from assisted deadlock to autonomous escape. Finally, a formation coordination system based on anisotropic flow field modulation and adaptive sliding mode control is designed. Rigid formation constraints are transformed into a tangential safe flow field, and robust tracking is subsequently achieved through an Adaptive Nonsingular Fast Terminal Sliding Mode Controller (ANFTSMC). Theoretical analysis and experimental results demonstrate that the proposed framework achieves collision-free navigation for the formation in simulated environments. Full article
(This article belongs to the Section Sensors and Robotics)
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25 pages, 2828 KB  
Article
Adaptive Nonsingular Fast Terminal Sliding Mode Control for Space Robot Based on Wavelet Neural Network Under Lumped Uncertainties
by Junwei Mei, Yawei Zheng, Haiping Ai, Feilong Xiong, An Zhu and Xiaodong Fu
Aerospace 2026, 13(4), 334; https://doi.org/10.3390/aerospace13040334 - 2 Apr 2026
Viewed by 440
Abstract
This paper proposes an adaptive wavelet neural network nonsingular fast terminal sliding mode control strategy based on a finite-time framework for a space robot system under external disturbances and model uncertainties. Firstly, the dynamic model of space robot is established based on the [...] Read more.
This paper proposes an adaptive wavelet neural network nonsingular fast terminal sliding mode control strategy based on a finite-time framework for a space robot system under external disturbances and model uncertainties. Firstly, the dynamic model of space robot is established based on the second Lagrange equation. Unlike sliding mode control, which converges asymptotically, terminal sliding mode control (TSMC) has been proposed to ensure finite-time convergence for a space robot system. Based on the aforementioned TSMC framework, the fast terminal sliding mode control (FTSMC) is proposed to enhance system convergence rate. However, TSMC exhibits a singularity issue attributed to the presence of negative fractional order. To avoid this issue, a nonsingular fast terminal sliding mode controller (NFTSMC) has been proposed. The controller is designed to integrate linear and nonlinear terms into a novel nonsingular fast terminal sliding mode surface. The method achieves fast finite-time convergence concurrently with improved robustness, while effectively avoiding singularities. To compensate for external disturbances and model uncertainties in the space robot system, this paper proposes the combination of wavelet neural network (WNN) for the real-time estimation of lumped uncertainties. Network parameters are dynamically adjusted via an adaptive law to mitigate chattering effectively and enhance trajectory tracking precision. Utilizing Lyapunov stability theory and numerical simulations, the space robot system’s stability is rigorously proven and the controller effectiveness is validated. Compared with the traditional NFTSMC, the proposed control strategy reduces the convergence time by 20.74%. In the case of trajectory tracking comparison, the root mean square error (RMSE) improves by 35.85%, the mean tracking error improves by 63.29%, the integral of absolute error (IAE) improves by 29.37%, and the integral of time-weighted absolute error (ITAE) improves by 93.06%. Additionally, a comparative simulation with RBFNN is included in this paper. Compared with RBFNN, the proposed control strategy reduces input torque energy consumption by 77.36% and improves control smoothness by 87.03%, quantitatively demonstrating the effectiveness of the proposed control strategy. Full article
(This article belongs to the Special Issue Space Navigation and Control Technologies (2nd Edition))
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25 pages, 6419 KB  
Article
Improved ARBF Sliding Mode Tension Control for a Carbon Fiber Diagonal Weaving Loom with a Hyperbolic Tangent Disturbance Observer
by Guowei Xu, Lipeng Fang, Wei Liu and Jian Liu
Symmetry 2026, 18(3), 433; https://doi.org/10.3390/sym18030433 - 1 Mar 2026
Viewed by 449
Abstract
The tension control of carbon fiber diagonal weaving looms is severely affected by the coupling between structured friction and unstructured disturbances, leading to strong nonlinearities and time-varying uncertainties. To overcome the chattering and model-dependency issues inherent in traditional sliding mode control, a nonlinear [...] Read more.
The tension control of carbon fiber diagonal weaving looms is severely affected by the coupling between structured friction and unstructured disturbances, leading to strong nonlinearities and time-varying uncertainties. To overcome the chattering and model-dependency issues inherent in traditional sliding mode control, a nonlinear dynamic model incorporating the Stribeck friction term was established. An Improved Adaptive Radial Basis Function-based Nonsingular Fast Terminal Sliding Mode Control (I-ARBF-NFTSMC) framework was then proposed. The framework adopts a divide-and-conquer composite compensation mechanism, in which a smooth Hyperbolic Tanh Fixed-Time Disturbance Observer (Tanh-FTDO) estimates external disturbances and suppresses chattering, and an Improved Adaptive Radial Basis Function (I-ARBF) neural network approximates and compensates internal nonlinear friction. Simulation results show that, compared with the conventional Fixed-Time Extended State Observer-based method (FESO-NFTSMC), the proposed controller achieves higher disturbance-estimation accuracy and tracking performance under sinusoidal, triangular, and composite disturbances. In composite-disturbance conditions, the steady-state mean-squared error is reduced by about 60%, the maximum tracking error decreases from 0.08787 N to 0.01965 N, and the settling time shortens by approximately 25.2%, while effectively mitigating high-frequency chattering. The proposed strategy achieves fast finite-time convergence with enhanced smoothness and robustness, providing a real-time executable solution for high-precision tension control in complex nonlinear weaving processes. Full article
(This article belongs to the Special Issue Symmetry and Nonlinear Control: Theory and Application)
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21 pages, 41229 KB  
Article
Research on a Sensorless Control Strategy for Permanent Magnet Synchronous Motors Based on Non-Singular Fast Terminal Sliding Mode Theory
by Min Ge, Guozhong Yao, Te Pu and Zhengjiang Wang
Appl. Sci. 2026, 16(4), 1767; https://doi.org/10.3390/app16041767 - 11 Feb 2026
Viewed by 606
Abstract
This study introduces a sensorless control approach for permanent magnet synchronous motors (PMSMs) that employs an Improved Non-Singular Fast Terminal Sliding Mode Controller (IMNFTSMC) and an Improved Non-Singular Fast Terminal Sliding Mode Observer (IMNFTSMO). The IMNFTSMC employs a novel hybrid reaching law and [...] Read more.
This study introduces a sensorless control approach for permanent magnet synchronous motors (PMSMs) that employs an Improved Non-Singular Fast Terminal Sliding Mode Controller (IMNFTSMC) and an Improved Non-Singular Fast Terminal Sliding Mode Observer (IMNFTSMO). The IMNFTSMC employs a novel hybrid reaching law and a continuous piecewise square root switching function to achieve faster convergence and effective chattering reduction over the conventional Sliding Mode Controller (SMC). This design successfully replaces two critical components: the discontinuous constant velocity term (a key component of the traditional SMC reaching law that is a primary source of control chattering in PMSM torque regulation) and the high-gain exponential term (which tends to induce overshoot during transient speed adjustments and degrade steady-state control precision). In the IMNFTSMO, a hybrid approach combining linear and non-singular terminal sliding modes eliminates phase lag associated with low-pass filtering in traditional sliding mode observers, improving rotor position and speed estimation accuracy. Stability of both IMNFTSMC and IMNFTSMO is rigorously proven using Lyapunov stability theory.Validation through extensive simulations and hardware experiments, including challenging zero-speed start, speed stepping, and load disturbance tests, confirms the proposed strategy provides improved dynamic response, effective anti-disturbance capability, and high accuracy for rotor position and speed estimation compared to established benchmark methods, demonstrating its feasibility for mid-to-low speed sensorless PMSM drives. Full article
(This article belongs to the Special Issue Power Electronics and Motor Control)
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21 pages, 5199 KB  
Article
Real-Time Trajectory Replanning and Tracking Control of Cable-Driven Continuum Robots in Uncertain Environments
by Yanan Qin and Qi Chen
Actuators 2026, 15(2), 83; https://doi.org/10.3390/act15020083 - 1 Feb 2026
Viewed by 646
Abstract
To address trajectory tracking of cable-driven continuum robots (CDCRs) in the presence of obstacles, this paper proposes an integrated control framework that combines online trajectory replanning, obstacle avoidance, and tracking control. The control system consists of two modules. The first is a trajectory [...] Read more.
To address trajectory tracking of cable-driven continuum robots (CDCRs) in the presence of obstacles, this paper proposes an integrated control framework that combines online trajectory replanning, obstacle avoidance, and tracking control. The control system consists of two modules. The first is a trajectory replanning controller developed on an improved model predictive control (IMPC) framework. The second is a trajectory-tracking controller that integrates an adaptive disturbance observer with a fast non-singular terminal sliding mode control (ADO-FNTSMC) strategy. The IMPC trajectory replanning controller updates the trajectory of the CDCRs to avoid collisions with obstacles. In the ADO-FNTSMC strategy, the adaptive disturbance observer (ADO) compensates for uncertain dynamic factors, including parametric uncertainties, unmodeled dynamics, and external disturbances, thereby enhancing the system’s robustness and improving trajectory tracking accuracy. Meanwhile, the fast non-singular terminal sliding mode control (FNTSMC) guarantees fast, stable, and accurate trajectory tracking. The average tracking errors for IMPC-ADO-FNTSMC, MPC-FNTSMC, and MPC-SMC are 1.185 cm, 1.540 cm, and 1.855 cm, with corresponding standard deviations of 0.035 cm, 0.057 cm, and 0.078 cm in the experimental results. Compared with MPC-FNTSMC and MPC-SMC, the IMPC-ADO-FNTSMC controller reduces average tracking errors by 29.96% and 56.54%. Simulation and experimental results demonstrate that the designed two-module controller (IMPC-ADO-FNTSMC) achieves fast, stable, and accurate trajectory tracking in the presence of obstacles and uncertain dynamic conditions. Full article
(This article belongs to the Section Control Systems)
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20 pages, 2503 KB  
Article
Disturbance Observer-Based Terminal Sliding Mode Control Approach for Virtual Coupling Train Set
by Zhiyu He, Ning Xu, Kun Liang, Zhiwei Cao, Xiaoyu Zhao and Zhao Sheng
Appl. Sci. 2026, 16(2), 887; https://doi.org/10.3390/app16020887 - 15 Jan 2026
Viewed by 418
Abstract
To enhance line capacity in high-speed railways without new infrastructure, virtual coupling train sets (VCTSs) enable reduced inter-train distances via real-time communication and cooperative control. However, unknown disturbances and model uncertainties challenge VCTS performance, often causing chattering, slow convergence, and poor disturbance rejection. [...] Read more.
To enhance line capacity in high-speed railways without new infrastructure, virtual coupling train sets (VCTSs) enable reduced inter-train distances via real-time communication and cooperative control. However, unknown disturbances and model uncertainties challenge VCTS performance, often causing chattering, slow convergence, and poor disturbance rejection. This paper proposes a novel finite-time extended state observer-based nonsingular terminal sliding mode (FTESO-NTSM) control strategy. The method integrates a nonsingular terminal sliding mode surface with a hyperbolic tangent-based reaching law to ensure fast convergence and chattering suppression, while a finite-time extended state observer estimates and compensates for lumped disturbances in real time. Lyapunov analysis rigorously proves finite-time stability. Numerical simulations under different initial statuses are conducted to validate the effectiveness of the proposed method. The results show that the maximum observation error achieves 0.0087 kN. The speed chattering magnitudes reach 0.00087 km/h, 0.0017 km/h, 0.0026 km/h, and 0.0034 km/h for the leading train and three followers, respectively. Furthermore, the convergence time of the followers is 56 s, 130 s, and 76 s, respectively. The results highlight that the proposed method can significantly improve line capacity and transportation efficiency. Full article
(This article belongs to the Special Issue Advances in Intelligent Transportation and Its Applications)
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18 pages, 3663 KB  
Article
Trajectory Tracking Control of a Six-Axis Robotic Manipulator Based on an Extended Kalman Filter-Based State Observer
by Jianxuan Liu, Tao Chen, Zhen Dou, Xiaojuan Li and Xiangjun Zou
Machines 2026, 14(1), 78; https://doi.org/10.3390/machines14010078 - 8 Jan 2026
Cited by 1 | Viewed by 909
Abstract
To achieve high-precision trajectory tracking for multi-joint robotic manipulators in the presence of model uncertainties, external disturbances, and strong coupling effects, this paper proposes a nonsingular fast terminal sliding mode control (NFTSMC) scheme incorporating an extended Kalman filter-based disturbance observer. First, the Kalman [...] Read more.
To achieve high-precision trajectory tracking for multi-joint robotic manipulators in the presence of model uncertainties, external disturbances, and strong coupling effects, this paper proposes a nonsingular fast terminal sliding mode control (NFTSMC) scheme incorporating an extended Kalman filter-based disturbance observer. First, the Kalman filter is combined with an extended state observer to perform the real-time observation of both internal and external disturbances in the system, accurately estimating system uncertainty and external disturbances. This approach reduces noise interference while significantly improving the correction accuracy of position and tracking errors. Second, an improved nonsingular fast terminal sliding mode controller with an optimized convergence law is introduced to ensure stability during the tracking process, effectively mitigate oscillation phenomena, and accelerate the system’s convergence speed. Finally, the convergence of the proposed method is analyzed by constructing an appropriate Lyapunov function. Simulation and experimental results strongly validate the superior performance of the proposed control strategy, demonstrating that the system can achieve high-precision trajectory tracking under the complex coupled effects of a six-axis robotic manipulator, and exhibits significant advantages in terms of accuracy and robustness. Full article
(This article belongs to the Special Issue Sensing to Cognition: The Evolution of Robotic Vision)
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