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Keywords = sliding mode disturbance observer

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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 230
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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29 pages, 2512 KB  
Article
An Augmented Deep Koopman Operator-Based MPC for Steering Control of High-Speed Electric Tracked Vehicles
by Hao Zhong, Ming Zhuang, Weida Wang, Liuquan Yang, Chao Yang, Mingjun Zha and Xuelong Du
Vehicles 2026, 8(6), 132; https://doi.org/10.3390/vehicles8060132 - 11 Jun 2026
Viewed by 58
Abstract
With advances in electric drive technology, electric tracked vehicles (ETVs) have emerged as a promising solution for high-mobility ground vehicles. However, under high-speed steering conditions, the equivalent motor load inertia varies significantly, introducing strong nonlinear and time-varying characteristics into the ETV that may [...] Read more.
With advances in electric drive technology, electric tracked vehicles (ETVs) have emerged as a promising solution for high-mobility ground vehicles. However, under high-speed steering conditions, the equivalent motor load inertia varies significantly, introducing strong nonlinear and time-varying characteristics into the ETV that may induce lateral instability and even rollover. To address this issue, a novel augmented deep Koopman operator-based model predictive control (ADK-MPC) method is proposed. First, a high-order sliding-mode (HOSM) observer is designed to estimate the lumped load disturbances associated with the time-varying equivalent motor load inertia. Then, the estimated disturbances are introduced as an augmented state into the DK operator to construct a data-driven augmented model. The proposed model transforms the nonlinear dynamics into a lifted linear time-invariant representation in the augmented-state space while capturing the dominant nonlinear characteristics. Based on the ADK model, an ADK-MPC controller is developed to convert the nonlinear optimization problem into a quadratic programming problem, thereby improving steering stability and reducing computational complexity. Simulation results under steering conditions indicate that the proposed method achieves better yaw rate tracking and lower computational cost than nonlinear MPC. The yaw rate tracking error is reduced by 45.5%, while the average solving time is shortened by 11.7%. Full article
(This article belongs to the Special Issue Energy Management Strategy of Hybrid Electric Vehicles)
23 pages, 8880 KB  
Article
Load Frequency Control of Interconnected Multi-Area Power Systems: A Single-Phase Second-Order Observer Sliding Mode Control Design
by Cong-Thanh Pham, Thieu Quang Tri, Van Nguyen Ngoc Thanh, Hoai Duong Minh and Nguyen Minh Tam
Appl. Sci. 2026, 16(12), 5862; https://doi.org/10.3390/app16125862 - 10 Jun 2026
Viewed by 81
Abstract
The increasing integration of renewable energy sources into interconnected multi-area power systems (IMAPSs) has led to a significant reduction in synchronous inertia, making frequency regulation considerably more challenging. While existing studies have explored the use of integral sliding mode load frequency control (ISMLFC) [...] Read more.
The increasing integration of renewable energy sources into interconnected multi-area power systems (IMAPSs) has led to a significant reduction in synchronous inertia, making frequency regulation considerably more challenging. While existing studies have explored the use of integral sliding mode load frequency control (ISMLFC) schemes to stabilize area frequency and tie-line power flows in IMAPSs, these approaches predominantly rely on conventional two-phase sliding mode control. Such methods, however, have demonstrated notable limitations in maintaining the stability of IMAPSs under increasingly complex operating conditions. In addition, all the IMAPS state variables must be measured, which can cause difficulty in real IMAPS applications. Therefore, this study proposes a novel load frequency control (LFC) strategy that coordinates the single-phase sliding mode control and state observer methods to solve these above limitations. First, a dynamic IMAPS model with single phase sliding mode control based on state observer scheme is established under renewable resource uncertainties and load disturbances. Then, a novel linear matrix inequality (LMI) based on Lyapunov functional is constructed to analyze the stability of the IMAPS. Furthermore, the decentralized single-phase sliding mode load frequency control (DSPSMLFC) method is developed for the LFC of the ISMLFC. Finally, three testing scenarios are employed to verify the efficiency and advantage of the proposed DSPSMLFC approach in MATLAB/Simulink R2023a. The simulation results confirm that the proposed DSPSMLFC scheme can improve the LFC of the IMAPS under renewable resource uncertainties and load disturbances. Full article
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23 pages, 7670 KB  
Article
Practical Predefined-Time Fractional-Order Sliding Mode Control for Quadrotors with Variable Exponential Coefficients
by Zhenyong Luo, Yongping Li, Xinhan Li and Liting Zhu
Appl. Sci. 2026, 16(12), 5877; https://doi.org/10.3390/app16125877 - 10 Jun 2026
Viewed by 92
Abstract
This article addresses the trajectory tracking control problem for quadrotor unmanned aerial vehicles (UAVs) subject to complex external disturbances and parameter uncertainties. To balance disturbance rejection with control signal smoothness, a practical predefined-time control scheme incorporating variable exponent coefficients (VEC) is proposed. First, [...] Read more.
This article addresses the trajectory tracking control problem for quadrotor unmanned aerial vehicles (UAVs) subject to complex external disturbances and parameter uncertainties. To balance disturbance rejection with control signal smoothness, a practical predefined-time control scheme incorporating variable exponent coefficients (VEC) is proposed. First, a variable exponent practical predefined-time disturbance observer (VEC-PPTDO) is designed to dynamically estimate and compensate for unknown aerodynamic disturbances. Additionally, a practical predefined-time fractional-order sliding mode control (VEC-PPTFOSMC) scheme is developed, which fuses fractional-order calculus with VEC reaching laws to accelerate convergence and mitigate high-frequency chattering. Based on Lyapunov stability theory, the practical predefined-time stability of the entire closed-loop system is rigorously proven. Finally, comparative simulations under severe stochastic disturbances validate the proposed framework. Quantitative results demonstrate that the proposed scheme achieves a steady-state convergence time of 0.95 s. Compared to the integer-order benchmarks, the proposed method reduces the convergence time by an average of 15.2%, while decreasing the root mean square error (RMSE) and integral absolute error (IAE) by an average of 13.4% and 14.5%, respectively. Consequently, the proposed architecture enhances the dynamic tracking precision, control efficiency, and operational robustness of the quadrotor system. Full article
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21 pages, 5869 KB  
Article
Adaptive Fractional-Order Sliding-Mode Control with Extended State Observer for Autonomous Underwater Vehicles Under Uncertain Disturbances
by Nanmu Hui, Changjin Dong, Baoju Wu, Binbin Tu, Yan Huo and Zehao Wang
Fractal Fract. 2026, 10(6), 398; https://doi.org/10.3390/fractalfract10060398 - 10 Jun 2026
Viewed by 96
Abstract
In this paper, a composite control framework integrating feedback linearization, an extended state observer, and an adaptive fractional-order sliding-mode controller is presented for autonomous underwater vehicles operating under uncertain hydrodynamics and external disturbances. The proposed algorithm, named adaptive fractional-order sliding-mode control with extended [...] Read more.
In this paper, a composite control framework integrating feedback linearization, an extended state observer, and an adaptive fractional-order sliding-mode controller is presented for autonomous underwater vehicles operating under uncertain hydrodynamics and external disturbances. The proposed algorithm, named adaptive fractional-order sliding-mode control with extended state observer, aims to enhance trajectory-tracking accuracy, disturbance rejection, and robustness against model uncertainties beyond what is offered by conventional active disturbance rejection control and integer-order sliding-mode control. First, a fractional-order sliding surface with an extended state observer is introduced to estimate and compensate lumped disturbances, where the fractional operator provides intrinsic filtering and memory effects to reduce chattering. Second, an adaptive exponential reaching law with smooth switching is formulated to overcome the trade-off between convergence speed and chattering, and a Levant differentiator is employed for sensorless velocity estimation. Finally, the uniform ultimate boundedness of the closed-loop system is proved via Lyapunov stability theory. Comparative simulation studies on step, sinusoidal, and circular trajectories under external disturbances, measurement noise, and 50% parametric uncertainties demonstrate that the proposed controller achieves zero overshoot, suppresses position fluctuations by 97%, and reduces root mean square tracking errors by 38–70% relative to conventional methods, confirming its superior performance. Full article
(This article belongs to the Special Issue Advances in Fractional-Order Control for Nonlinear Systems)
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25 pages, 22136 KB  
Article
Disturbance-Derivative-Driven Gain Scheduling for Adaptive Super-Twisting Sliding Mode Control of PMSM
by Yuying Ji, Qiang Xu, Qiang Gao, Hao Li and Runmin Hou
Machines 2026, 14(6), 670; https://doi.org/10.3390/machines14060670 - 9 Jun 2026
Viewed by 148
Abstract
This paper addresses a specific dynamic limitation in conventional adaptive super-twisting sliding mode control (ASTSMC) for permanent-magnet synchronous motor (PMSM) speed regulation: the reactive lag of gain adaptation. In standard ASTSMC, controller gains are adjusted based solely on the sliding variable, which grows [...] Read more.
This paper addresses a specific dynamic limitation in conventional adaptive super-twisting sliding mode control (ASTSMC) for permanent-magnet synchronous motor (PMSM) speed regulation: the reactive lag of gain adaptation. In standard ASTSMC, controller gains are adjusted based solely on the sliding variable, which grows only after a disturbance has already induced a tracking error. This reactive behavior may produce a non-negligible transient speed droop during abrupt load variations. To alleviate this limitation, a proactive gain-scheduled ASTSMC (PDG-ASTSMC) strategy is proposed. A second-order nonlinear extended state observer (NESO) is employed to estimate the lumped disturbance and to extract its time derivative d^˙l. This disturbance-derivative signal is incorporated into the gain adaptation law to increase the controller gains during the incipient phase of a load change, before significant speed error accumulates. Stability analysis based on a composite Lyapunov function establishes uniformly ultimately bounded convergence of the closed-loop system, and a quantitative relationship between the proactive index and transient droop reduction is derived. Experimental validation on a 1.42 kW PMSM platform shows that, compared with conventional reactive ASTSMC, the proposed PDG-ASTSMC reduces transient speed droop by over 17% (from 10.5 rpm to 8.7 rpm) and shortens load recovery time by approximately 69% (from 140 ms to 44 ms), without increasing steady-state chattering or current ripple. Full article
(This article belongs to the Section Electrical Machines and Drives)
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20 pages, 3900 KB  
Article
Improved Terminal Integral Sliding Mode Adaptive Disturbance Rejection Control Method for UAV SPMSM
by Mingyuan Hu, Huaimiao Zhu, Changning Wei, Lei Zhang, Haoran Wei, Yaqing Gu, Bo Gao, Yaohua Ma and Dongjun Zhang
Machines 2026, 14(6), 667; https://doi.org/10.3390/machines14060667 - 8 Jun 2026
Viewed by 102
Abstract
High-performance control of surface-mounted permanent magnet synchronous motors (SPMSMs) is critical for unmanned aerial vehicle (UAV) rotor servo systems, which demand fast dynamic response, high steady-state accuracy, and strong robustness against complex disturbances. However, conventional sliding mode control (SMC) methods often suffer from [...] Read more.
High-performance control of surface-mounted permanent magnet synchronous motors (SPMSMs) is critical for unmanned aerial vehicle (UAV) rotor servo systems, which demand fast dynamic response, high steady-state accuracy, and strong robustness against complex disturbances. However, conventional sliding mode control (SMC) methods often suffer from inherent issues like integral windup, persistent chattering, and sensitivity to parameter variations, limiting their effectiveness in such challenging applications. To address these limitations, this paper proposes a novel composite control strategy. The method integrates an improved terminal integral sliding mode controller (ITISMC) with an adaptive super-twisting reaching law (ADSTA) and a terminal integral sliding mode observer (TISMO). The key innovations include: (1) a redesigned sliding surface incorporating a smooth nonlinear function to suppress chattering and a variable-gain integral term to mitigate integral windup; (2) an adaptive reaching law that dynamically adjusts its gains based on the system state to balance convergence speed and chattering suppression; and (3) a disturbance observer that provides real-time estimation and feedforward compensation of total disturbances, significantly enhancing robustness. The proposed ITISMC-ADSTA-TISMO strategy was implemented and validated on a TMS320F28379D DSP-based experimental platform. Comparative results demonstrate its superiority over benchmark methods (e.g., SMC-STA). Key achievements include a rapid no-load startup time of 0.45 s, high steady-state precision with speed fluctuations suppressed to only 3 rpm, and superior disturbance rejection capability under sudden load changes, sinusoidal disturbances, and parameter perturbations. The method also yields favorable q-axis current response. These results confirm that the proposed strategy offers a high-performance, practical solution for advanced UAV servo control systems. Full article
(This article belongs to the Section Electrical Machines and Drives)
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30 pages, 10049 KB  
Article
Three-Dimensional Integrated Guidance and Control Design with Terminal Angle and Attitude Angle Constraints
by Qi Wang, Zhe Hu, Tianyi Wang, Shusen Yuan, Lei Zhang and Wenjun Yi
Aerospace 2026, 13(6), 534; https://doi.org/10.3390/aerospace13060534 - 8 Jun 2026
Viewed by 98
Abstract
To address the limitations of existing sliding mode-based integrated guidance and control (IGC) schemes, such as chattering, input saturation, and insufficient robustness, this paper proposes a three-dimensional IGC design method incorporating both terminal angle and attitude angle constraints. First, a control-oriented six-degrees-of-freedom model [...] Read more.
To address the limitations of existing sliding mode-based integrated guidance and control (IGC) schemes, such as chattering, input saturation, and insufficient robustness, this paper proposes a three-dimensional IGC design method incorporating both terminal angle and attitude angle constraints. First, a control-oriented six-degrees-of-freedom model is established based on three-dimensional relative motion and vehicle dynamics, and the control objectives for maneuvering target interception under multiple constraints are clarified. Subsequently, a finite-time terminal sliding mode guidance law based on time-to-go (TGO) is integrated with dynamic surface control to construct the IGC framework. In this design, command filters are introduced to overcome the “explosion of complexity”, while amplitude saturation functions are employed to constrain system states and control inputs. Meanwhile, a generalized super-twisting extended state observer (GSTESO) is incorporated to estimate and compensate for lumped uncertainties in the system. Finally, by combining Lyapunov stability theory with an integral barrier Lyapunov (IBL) function, it is proven that the closed-loop system is uniformly ultimately bounded and satisfies the terminal angle constraints. Comparative simulations under multiple disturbance scenarios demonstrate that the proposed method meets the accuracy requirements in terms of miss distance and LOS angle error. Moreover, it alleviates high-frequency chattering and prevents control-input saturation, showing improved robustness and disturbance rejection capability compared with the baseline methods. Therefore, the proposed approach provides a valuable reference for engineering applications of three-dimensional IGC in maneuvering target interception. Full article
(This article belongs to the Section Aeronautics)
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12 pages, 2493 KB  
Proceeding Paper
Enhanced Harmonic Mitigation and Reactive Power Support in Photovoltaic-Connected Power Filters Using a Robust Control Approach
by Julius Omorodion Uwagboe and Akshay Kumar Saha
Eng. Proc. 2026, 140(1), 59; https://doi.org/10.3390/engproc2026140059 - 5 Jun 2026
Viewed by 145
Abstract
The increasing integration of photovoltaic (PV) systems and nonlinear loads intensifies harmonic distortion and reactive power imbalance in modern power networks. Conventional shunt active power filters (SAPFs) often employ control strategies that perform poorly under uncertain and dynamic grid conditions. This paper develops [...] Read more.
The increasing integration of photovoltaic (PV) systems and nonlinear loads intensifies harmonic distortion and reactive power imbalance in modern power networks. Conventional shunt active power filters (SAPFs) often employ control strategies that perform poorly under uncertain and dynamic grid conditions. This paper develops a hybrid sliding mode control with disturbance observer (SMC+DOB) technique for a PV-integrated SAPF to achieve effective harmonic mitigation, reactive power compensation, and enhanced system robustness. The study models the PV-SAPF system in MATLAB/Simulink (R2025b), where the SMC ensures robust current tracking, while the DOB estimates and suppresses unknown disturbances in real-time. The controller’s performance is evaluated under varying nonlinear and reactive load conditions, as per IEEE 519-2014 standards. Simulation results show that the proposed SMC+DOB scheme reduces total harmonic distortion (THD) by 96.7%—from 31.45% to 1.05%—while maintaining DC-link voltage stability and unity power factor. The integrated control architecture enhances the dynamic performance of SAPF, providing superior harmonic suppression, fast transient recovery, and improved grid stability for PV-connected systems. Full article
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19 pages, 2930 KB  
Article
Capacitor-Energy-Based Super-Twisting Sliding Mode Control for Flywheel Energy Storage System DC-Bus Voltage in DC Microgrid
by Le Luan, Zhong Xu, Jun Xiong and Qingshen Xu
Energies 2026, 19(11), 2680; https://doi.org/10.3390/en19112680 - 2 Jun 2026
Viewed by 147
Abstract
To address the DC-link voltage control issue in flywheel energy storage systems (FESSs), a DC-link voltage control strategy using a capacitor-energy-based super-twisting sliding mode controller (CE-STSMC), integrated with a disturbance observer, is proposed in this article. First, an exponential term is incorporated into [...] Read more.
To address the DC-link voltage control issue in flywheel energy storage systems (FESSs), a DC-link voltage control strategy using a capacitor-energy-based super-twisting sliding mode controller (CE-STSMC), integrated with a disturbance observer, is proposed in this article. First, an exponential term is incorporated into the STSMC algorithm to enhance its convergence rate. Then, the improved STSMC is employed as the voltage-loop controller to mitigate the insufficient anti-disturbance capability of conventional control methods. To improve the system robustness, a nonlinear disturbance observer (NDOB) is developed to estimate the load power. The estimated disturbance is further feedforward-compensated into the improved STSMC controller. Finally, experiments are carried out on a 2.2 kW FESS prototype under DC-link voltage step and sudden load-change conditions, which demonstrates the effectiveness and superiority of the proposed control strategy. Full article
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20 pages, 27262 KB  
Article
Co-Optimized Target Perception and Disturbance Estimation for Unmanned Surface Vessels
by Yiqi Shi, Xiang Liu, Yueying Wang and Weidong Zhang
J. Mar. Sci. Eng. 2026, 14(11), 1023; https://doi.org/10.3390/jmse14111023 - 30 May 2026
Viewed by 179
Abstract
Unmanned surface vessels (USVs) equipped with onboard vision are increasingly used in environmental monitoring, search and rescue, and autonomous navigation. However, conventional USV autonomy systems often adopt a decoupled design in which target perception and disturbance estimation are developed independently. Such systems may [...] Read more.
Unmanned surface vessels (USVs) equipped with onboard vision are increasingly used in environmental monitoring, search and rescue, and autonomous navigation. However, conventional USV autonomy systems often adopt a decoupled design in which target perception and disturbance estimation are developed independently. Such systems may suffer performance degradation when visual observations become unreliable under water-surface reflections, illumination variations, or partial occlusions, while the disturbance observer still depends on manually tuned parameters under time-varying environmental disturbances. To address these issues, this paper proposes a three-stage co-optimized target perception and disturbance estimation framework for USVs. First, a lightweight hybrid convolutional neural network (CNN)–Transformer perception module is developed to extract robust vessel features under challenging water-surface visual conditions. Second, a reinforcement learning (RL)-driven mechanism is used to adaptively tune a higher-order sliding mode observer (HOSMO) for disturbance estimation. Third, a confidence-guided perception-observer co-optimization strategy is formulated, in which visual confidence is used to regulate observer adaptation and reduce estimation divergence during temporary perception degradation. Simulation and outdoor lake experiments demonstrate that the proposed framework improves visual matching accuracy, observer convergence, and estimation stability compared with conventional decoupled methods. The outdoor lake experiments provide initial real-world validation under natural illumination variations and mild water-surface disturbances, while further open-water and multi-vessel validation is planned for future work. Full article
(This article belongs to the Section Ocean Engineering)
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27 pages, 5867 KB  
Article
Fixed-Time Adaptive Sliding Mode Disturbance Observer-Based Nonsingular Fixed-Time Terminal Sliding Mode Control for Uncertain Space Robot with External Disturbance
by Yanzhe Yang, Zhiping Chen, An Zhu, Xiaodong Fu and Haiping Ai
Aerospace 2026, 13(6), 509; https://doi.org/10.3390/aerospace13060509 - 30 May 2026
Viewed by 164
Abstract
In this paper, a nonsingular fixed-time terminal sliding mode control (NFTSMC) strategy based on a fixed-time adaptive sliding mode disturbance observer (FASMDOB) is proposed for a space robot in the presence of dynamic uncertainties and external disturbance. Firstly, based on fixed-time theory, a [...] Read more.
In this paper, a nonsingular fixed-time terminal sliding mode control (NFTSMC) strategy based on a fixed-time adaptive sliding mode disturbance observer (FASMDOB) is proposed for a space robot in the presence of dynamic uncertainties and external disturbance. Firstly, based on fixed-time theory, a novel FASMDOB is designed to mitigate the impacts of the lumped disturbance including dynamic uncertainties and external disturbance, improving the robustness of the control system and utilizing an adaptive technique to reduce chattering. Additionally, compared to finite-time disturbance observers (FTDOB), FASMDOB converges estimation errors to zero within a fixed time, regardless of the information about the initial states of the system. Next, a nonsingular fixed-time terminal sliding mode (NFTSM) surface is developed for the following control system design. By replacing the high-order fractional term with a piecewise function, the singularity problem in conventional terminal sliding mode control is effectively avoided. Combining FASMDOB and NFTSM surface, a FASMDOB-based NFTSMC strategy is developed, which guarantees the fixed-time convergence of the sliding mode surface and tracking errors. Notably, the proposed NFTSMC method utilizes the arctangent function to construct the reaching law, improving the performance of the control system. Lastly, based on Lyapunov theory, the fixed-time stability of the proposed control system is rigorously proven. With several comparative simulations being conducted, the feasibility and effectiveness of the proposed FASMDOB-based NFTSMC strategy are verified and highlighted. Full article
(This article belongs to the Special Issue Advanced Spacecraft/Satellite Technologies (2nd Edition))
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17 pages, 3495 KB  
Article
Active Disturbance Rejection-Based Tracking Control of Robotic Manipulators Under a Universal Symmetry Constraint Framework
by Zhihan Shi, Chen Zhang and Guangming Zhang
Symmetry 2026, 18(6), 919; https://doi.org/10.3390/sym18060919 - 27 May 2026
Cited by 1 | Viewed by 148 | Correction
Abstract
This paper addresses the tracking control problem of robotic manipulators under a universal symmetry constraint framework in the presence of lumped uncertainties and external disturbances. Unlike conventional constrained control schemes that treat tracking error bounds and state bounds separately, the proposed method explicitly [...] Read more.
This paper addresses the tracking control problem of robotic manipulators under a universal symmetry constraint framework in the presence of lumped uncertainties and external disturbances. Unlike conventional constrained control schemes that treat tracking error bounds and state bounds separately, the proposed method explicitly exploits the symmetric structure of the prescribed constraints and formulates both tracking error constraints and full-state constraints in a unified manner. Based on the Euler–Lagrange dynamics of robotic manipulators, a universal symmetry constraint transformation is introduced to convert the original constrained system into an equivalent unconstrained form while preserving the intrinsic symmetry of the admissible sets. To enhance robustness against uncertainties and disturbances, a sliding-mode extended state observer is designed to estimate the total disturbance online. Meanwhile, a tracking differentiator is incorporated into the recursive design to avoid repeated differentiation of virtual control signals. On this basis, a disturbance-compensated backstepping controller is developed for the transformed manipulator system. It is shown that all closed-loop signals remain bounded, the prescribed symmetric tracking error and state constraints are never violated, and the tracking error converges asymptotically when the observer and differentiator errors vanish asymptotically. Simulation results obtained from a robotic manipulator verify the effectiveness of the proposed control strategy. Full article
(This article belongs to the Section Mathematics)
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18 pages, 5030 KB  
Article
Virtual State Coupled Sliding Mode Control: An Energy Exchange Approach with Tunable Performance Trade-Off
by Jialong Wang, Jianli Wang, Jiaxin Jing, Canyang Zhao and Lei Zhang
Sensors 2026, 26(11), 3381; https://doi.org/10.3390/s26113381 - 26 May 2026
Viewed by 318
Abstract
Traditional sliding mode control (SMC) lacks an active mechanism for redistributing energy among state channels during transient convergence, resulting in a rigid trade-off between response speed, overshoot suppression, and energy efficiency. This paper proposes a virtual state coupled SMC method that introduces a [...] Read more.
Traditional sliding mode control (SMC) lacks an active mechanism for redistributing energy among state channels during transient convergence, resulting in a rigid trade-off between response speed, overshoot suppression, and energy efficiency. This paper proposes a virtual state coupled SMC method that introduces a dynamic virtual state with bilinear product coupling x1x2 into the sliding surface. Unlike conventional virtual states that serve as static linear combinations or observer-based estimates, the proposed virtual state evolves dynamically and establishes an active energy exchange channel between the real and virtual state dynamics. Linearization and Lyapunov-based analyses prove local asymptotic stability of the closed-loop system. The coupling strength γ is shown to be decoupled from the linearized local eigenvalues and thus governs the energy–performance trade-off independently, while the condition c>γ/4 guarantees a non-vanishing domain of attraction. Simulations demonstrate that the proposed method achieves up to 53.2% control energy reduction under disturbance-free conditions compared with conventional SMC. Under persistent high-frequency disturbances, increasing γ reduces oscillations by 54.2% at a controllable energy cost of 45.7%. Systematic parameter selection guidelines are provided, and Monte Carlo simulations (500 trials, ±30% parameter perturbations) confirm 100% convergence. The proposed method offers an independently adjustable energy–performance trade-off mechanism suitable for sensor-based motion systems with stringent transient and energy requirements. Full article
(This article belongs to the Section Sensors and Robotics)
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35 pages, 4849 KB  
Article
Adaptive Control Strategy for a Single-Inverter Dual-PMSM System Under Load Disturbance
by Siling Wang and Dongsheng Li
Electronics 2026, 15(11), 2302; https://doi.org/10.3390/electronics15112302 - 26 May 2026
Viewed by 253
Abstract
To address the speed oscillation and stability degradation caused by load imbalance in a single−inverter dual−permanent magnet synchronous motor (PMSM) parallel system, this paper proposes an adaptive control strategy based on a sliding mode observer. The proposed method preserves the hardware simplicity of [...] Read more.
To address the speed oscillation and stability degradation caused by load imbalance in a single−inverter dual−permanent magnet synchronous motor (PMSM) parallel system, this paper proposes an adaptive control strategy based on a sliding mode observer. The proposed method preserves the hardware simplicity of the single−inverter topology while improving control performance under load disturbances. First, a sliding mode observer is designed to estimate the load torque difference between the two motors in real time, thereby enabling dynamic perception of load variations. Then, an adaptive controller is introduced to switch the control mode according to the estimated load imbalance. When the load difference is small, master−slave vector control without fixed role distinction is adopted. When the load difference exceeds a predefined threshold, an improved finite−set model predictive torque control (FCS−MPTC) is activated. In the predictive control mode, unnecessary full−time predictive optimization is avoided and a d−axis current suppression term is incorporated into the cost function to improve current waveform quality. Simulation results show that the proposed strategy reduces speed overshoot during load transients and improves the three−phase current waveform compared with conventional predictive torque control. Therefore, the proposed method provides an effective control solution for single−inverter dual−motor drive systems under load disturbance. Full article
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