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Keywords = torque estimation

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13 pages, 2256 KiB  
Article
Hybridization of ADM-Type Rail Service Cars for Enhanced Efficiency and Environmental Sustainability
by Ziyoda Mukhamedova, Ergash Asatov, Rustam Kuchkarbaev, Gulamova Madina and Dilbar Mukhamedova
World Electr. Veh. J. 2025, 16(5), 260; https://doi.org/10.3390/wevj16050260 - 6 May 2025
Abstract
The hybridization of ADM-Type Rail Service Cars aims to enhance energy efficiency, environmental sustainability, and cost-effectiveness within Uzbekistan’s railway network. Diesel-powered service cars currently contribute to high fuel consumption, elevated emissions, and costly maintenance, necessitating a transition to hybrid technology. This study introduces [...] Read more.
The hybridization of ADM-Type Rail Service Cars aims to enhance energy efficiency, environmental sustainability, and cost-effectiveness within Uzbekistan’s railway network. Diesel-powered service cars currently contribute to high fuel consumption, elevated emissions, and costly maintenance, necessitating a transition to hybrid technology. This study introduces an innovative “sequence of linear sets–torsion electric motor–wheel pairs” design, optimizing torque distribution and power efficiency for improved operational reliability. Through system modeling, performance simulations, and real-world field trials, the hybrid system demonstrates a 15% reduction in energy consumption, a 25% decrease in CO2 emissions, and up to 30% lower maintenance costs compared to conventional diesel models. Additionally, the hybrid technology enhances operational flexibility, allowing seamless functionality on both electrified and non-electrified railway lines. From an economic perspective, retrofitting existing service cars instead of full fleet replacement provides a cost-effective alternative, offering an estimated 10-year return on investment (ROI) through fuel savings and reduced downtime. This initiative directly supports Uzbekistan’s Green Development Strategy and railway modernization plans while holding significant commercialization potential in Central Asia and other regions with aging railway infrastructure. By addressing technical scalability, regulatory compliance, and economic feasibility, this study proposes a practical and timely hybrid retrofit solution for sustainable railway operations, aligning current industry needs with long-term environmental and financial benefits. Full article
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21 pages, 7333 KiB  
Article
Observer-Based Remote Conductivity Variable-Parameter Sliding Mode Control for Water–Fertilizer Integration Machines Using Recursive Least Squares Adaptive Estimation
by Peng Zhang, Zhigang Li, Xue Hu and Lixin Zhang
Appl. Sci. 2025, 15(9), 4993; https://doi.org/10.3390/app15094993 - 30 Apr 2025
Viewed by 76
Abstract
In remote conductivity control for water–fertilizer integration systems, challenges such as long-distance nonlinearities and variable parameters can lead to fertilization inaccuracies, including over-irrigation and uneven distribution, affecting both productivity and environmental sustainability. To mitigate these issues, this study proposes a variable-parameter sliding mode [...] Read more.
In remote conductivity control for water–fertilizer integration systems, challenges such as long-distance nonlinearities and variable parameters can lead to fertilization inaccuracies, including over-irrigation and uneven distribution, affecting both productivity and environmental sustainability. To mitigate these issues, this study proposes a variable-parameter sliding mode control (VSMC) strategy, combined with an adaptive observer based on Recursive Least Squares (RLS) to estimate system inertia and load torque in real time. This allows for dynamic adjustment of the sliding surface parameters, ensuring robust control even under varying operating conditions. Two parameter derivation approaches—analytical modeling and data-driven fitting—are evaluated. Field tests demonstrate that VSMC outperforms the Proportional–Integral (PI) and conventional sliding mode control (SMC) methods in maintaining target electrical conductivity (EC) levels. Specifically, for a target EC of 1.4 mS/cm, VSMC stabilizes the system to within 1.18–1.60 mS/cm in 95 s, with a 14.3% overshoot, well within agronomic tolerance. In regional irrigation trials, VSMC significantly improves fertilizer uniformity, reducing the standard deviation of potassium nitrate distribution from 2.14 (PI) to 0.59. The simulation and experimental results validate the effectiveness and robustness of the proposed method, highlighting its potential to enhance agronomic efficiency and reduce environmental impact. Full article
(This article belongs to the Collection Agriculture 4.0: From Precision Agriculture to Smart Agriculture)
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21 pages, 7985 KiB  
Article
Study on the Influence of Inertial Force on the Performance of Aerostatic Thrust Bearings
by Shuo Jia, Chenhui Jia and Yanhui Lu
Lubricants 2025, 13(5), 198; https://doi.org/10.3390/lubricants13050198 - 28 Apr 2025
Viewed by 188
Abstract
Firstly, the Reynolds equation considering gas inertia force is theoretically deduced in the cylindrical coordinate system, and then a mathematical model of aerostatic thrust bearing with three degrees of freedom (3-DOF) is constructed. Secondly, the Reynolds equation and velocity control equation are solved [...] Read more.
Firstly, the Reynolds equation considering gas inertia force is theoretically deduced in the cylindrical coordinate system, and then a mathematical model of aerostatic thrust bearing with three degrees of freedom (3-DOF) is constructed. Secondly, the Reynolds equation and velocity control equation are solved by the finite difference method (FDM), and the characteristics of gas pressure and velocity distribution in the gas film under steady-state conditions are revealed. On this basis, in the single-factor analysis, the bearing capacity error and recovery torque error caused by the inertia force term are quantitatively analyzed. It is found that the bearing rotating speed has a significant influence on the inertial force error, and the bearing radius also has a certain influence on the inertial force error, while the initial clearance, gas supply pressure, and torsion angle have relatively little influence on the inertial force error. Finally, in the multi-factor analysis, the sample regression equation of relative error of bearing capacity and relative error of restoring torque is established by using the multiple regression analysis method. By comparing the estimated values with the simulation results, the validity of the constructed regression equation is verified. Full article
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20 pages, 4069 KiB  
Article
A New Approach to Field-Oriented Control That Substantially Improves the Efficiency of an Induction Motor with Speed Control
by Chung-Wuu Ding and Pi-Cheng Tung
Appl. Sci. 2025, 15(9), 4845; https://doi.org/10.3390/app15094845 - 27 Apr 2025
Viewed by 117
Abstract
Accurate estimation of the rotor flux angle remains a significant challenge when conventional direct or indirect field-oriented control (FOC) strategies are applied to induction motor drives. This paper proposes a novel method for determining the rotor flux angle under steady-state conditions using only [...] Read more.
Accurate estimation of the rotor flux angle remains a significant challenge when conventional direct or indirect field-oriented control (FOC) strategies are applied to induction motor drives. This paper proposes a novel method for determining the rotor flux angle under steady-state conditions using only stator voltage and current measurements. An adjustable steady-state detection mechanism is introduced and integrated into a phase-locked loop (PLL)-based indirect field-oriented framework to enable a smooth injection of the actual rotor flux angle into the control system. Both simulation and experimental results validate the effectiveness of the proposed method, demonstrating a significant reduction in stator current compared to conventional FOC approaches under identical load torque conditions. Full article
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14 pages, 5178 KiB  
Article
Non-Singular Fast Sliding Mode Control of Robot Manipulators Based on Integrated Dynamic Compensation
by Xinyi Wang, Xichang Liang, Shunjing Hu and Qianqian Xin
Actuators 2025, 14(5), 215; https://doi.org/10.3390/act14050215 - 26 Apr 2025
Viewed by 116
Abstract
In order to realize the problem of tracking control of the trajectory of robot manipulators under variable load conditions, this paper proposes a non-singular fast terminal sliding mode tracking control design for robot manipulators based on integrated dynamic compensation. First, in the model, [...] Read more.
In order to realize the problem of tracking control of the trajectory of robot manipulators under variable load conditions, this paper proposes a non-singular fast terminal sliding mode tracking control design for robot manipulators based on integrated dynamic compensation. First, in the model, the friction torque under the influence of speed is considered while combined with the joint torque estimation for integrated dynamic compensation. Second, a novel non-singular fast terminal sliding mode controller is proposed, which helps to overcome the singularity problem and has been analyzed for stability using the Lyapunov method. Finally, trajectory tracking experiments are conducted on an experimental platform and compared with the PID algorithm, demonstrating the superior control performance of the proposed algorithm. Full article
(This article belongs to the Section Actuators for Robotics)
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20 pages, 5242 KiB  
Article
Development of a Force Feedback Controller with a Speed Feedforward Compensator for a Cable-Driven Actuator
by Juan Fang, Michael Haldimann, Bardia Amiryavari and Robert Riener
Actuators 2025, 14(5), 214; https://doi.org/10.3390/act14050214 - 25 Apr 2025
Viewed by 140
Abstract
Cable-driven actuators (CDAs) are extensively used in the rehabilitation field because of advantages such as low moment of inertia, fast movement response, and intrinsic flexibility. Accurate control of cable force is essential for achieving precise movement control, especially when the movement is generated [...] Read more.
Cable-driven actuators (CDAs) are extensively used in the rehabilitation field because of advantages such as low moment of inertia, fast movement response, and intrinsic flexibility. Accurate control of cable force is essential for achieving precise movement control, especially when the movement is generated by multiple CDAs. However, velocity-induced disturbances pose challenges to accurate force control during dynamic movements. Several strategies for direct force control have been investigated in the literature, but time-consuming tests are often required. The aim of this study was to develop a force feedback controller and a speed feedforward compensator for a CDA with a convenient experiment-based approach. The CDA consisted of a motor with a gearbox, a cable drum, and a force sensor. The transfer function between motor torque and cable force was estimated through an open-loop test. A PI force feedback controller was developed and evaluated in a static test. Subsequently, a dynamic test with a reference force of 100 N was conducted, during which the cable was pulled to move at different speeds. The relationship between the motor speed and the cable force was determined, which facilitated further development of a speed feedforward compensator. The controller and compensator were evaluated in dynamic tests at various speeds. Additionally, the system dynamics were simulated in MATLAB/Simulink. The static test showed that the PI force controller produced a mean force control error of 4.7 N, which was deemed very good force-tracking accuracy. The simulated force output was very similar to the experiment (RMSE error of 4.0 N). During the dynamic test, the PI force controller alone produced a force control error of 9.0 N. Inclusion of the speed feedforward compensator improved the force control accuracy, resulting in a mean error at various speeds of 5.6 N. The combined force feedback controller and speed feedforward compensator produced a satisfactory degree of accuracy in force control during dynamic tests of the CDA across varying speeds. Additionally, the accuracy level was comparable to that reported in the literature. The convenient experiment-based design of the force control strategy exhibits potential as a general control approach for CDAs, laying the solid foundation for precise movement control. Future work will include the integration of the speed compensator into better feedback algorithms for more accurate force control. Full article
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15 pages, 5685 KiB  
Article
Six-Wheeled Mobile Manipulator for Brush Cleaning in Difficult Areas: Stability Analysis and Grip Condition Estimation
by Giandomenico Di Massa, Stefano Pagano, Ernesto Rocca and Sergio Savino
Machines 2025, 13(5), 359; https://doi.org/10.3390/machines13050359 - 25 Apr 2025
Viewed by 192
Abstract
This paper aims to analyze a six-wheeled mobile manipulator as a solution for brush clearing difficult areas. To this end, a rover with a rocker–bogie suspension system, like those used for space explorations, is considered; the cutting head is moved by a robotic [...] Read more.
This paper aims to analyze a six-wheeled mobile manipulator as a solution for brush clearing difficult areas. To this end, a rover with a rocker–bogie suspension system, like those used for space explorations, is considered; the cutting head is moved by a robotic arm fixed to the rover so that it can reach areas to clean in front of the rover or on its sides. The change of the pose of the robotic arm shifts the centre of mass of the rover and, although the shift is not important, it can be used to improve stability, to overcome an obstacle, or to change the load distribution between the wheels to prevent the wheels from slipping or sinking. Some analyses of the interaction between the rover and robotic arm are reported in this paper. To prevent the rover from entering a low-grip area, the possibility of estimating the grip conditions of the terrain is considered, using the front wheels as tactile sensors. By keeping the rear wheels stationary and gradually increasing the torque on the front wheels, it is possible to evaluate the conditions under which slippage occurs. In case of poor grip, using the other drive wheels, the rover can reverse its direction and look for an alternative path. Full article
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15 pages, 6446 KiB  
Article
Speed Sensorless Motion Control Scheme for a Robotic Manipulator Under External Forces and Payload Changes
by Jorge Pacheco, David Cortés-Vega and Hussain Alazki
Actuators 2025, 14(5), 209; https://doi.org/10.3390/act14050209 - 24 Apr 2025
Viewed by 214
Abstract
This paper proposes the design of a speed sensorless robust discontinuous controller for the trajectory tracking problem of a 5-DOF robotic manipulator under payload changes and torque disturbances in the joints. The developed observer-based controller is capable of performing trajectory tracking, ensuring stability, [...] Read more.
This paper proposes the design of a speed sensorless robust discontinuous controller for the trajectory tracking problem of a 5-DOF robotic manipulator under payload changes and torque disturbances in the joints. The developed observer-based controller is capable of performing trajectory tracking, ensuring stability, fast error convergence and speed sensorless operation. In order to avoid joint speed measurement, an estimation scheme based on a differentiation algorithm is implemented to estimate it. Simulation tests developed in MATLAB/Simulink are presented to show the high performance of the proposed scheme for two different trajectories with the model of the CRS Catalyst-5 by Thermo Electron®, Burlington, ON, Canada. Full article
(This article belongs to the Section Control Systems)
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16 pages, 8791 KiB  
Article
Assessing the Meshing for Windage Power Loss Simulations of an Orthogonal Face Gear
by Tiberiu-Daniel Pau, Zoltan-Iosif Korka, Dorian Nedelcu and Corneliu Hrimiuc
Machines 2025, 13(5), 341; https://doi.org/10.3390/machines13050341 - 22 Apr 2025
Viewed by 149
Abstract
In the current energy landscape, efficiency is a critical topic. Therefore, even in the case of geared transmissions, it is essential to predict and calculate power losses as accurately as possible from the design phase. There are mainly three categories of losses in [...] Read more.
In the current energy landscape, efficiency is a critical topic. Therefore, even in the case of geared transmissions, it is essential to predict and calculate power losses as accurately as possible from the design phase. There are mainly three categories of losses in a gear unit: friction—the power losses due to the contact between teeth in rotation on the one hand and the seals with the spindles on the other hand; churning—the power losses generated by the air–lubricant mixture compression around teeth roots during rotation; and windage—the power losses due to the teeth aerodynamic trail in the air–lubricant mixture. While the first two categories of losses are intensively studied in the literature, the papers focusing on windage power losses are less representative. An estimation of windage power losses can be performed by numerical simulation, and the accuracy of the results depends on the mesh density and the available computing power. The present study discusses the influence of meshing on the windage torque of an orthogonal face gear immersed in air and compares numerical results generated by SolidWorks 2025 Flow Simulation software with experimental data measured on a test rig. Full article
(This article belongs to the Special Issue Dynamics and Lubrication of Gears)
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21 pages, 18629 KiB  
Article
High-Precision Control of Control Moment Gyroscope Gimbal Servo Systems via a Proportional–Integral–Resonant Controller and Noise Reduction Extended Disturbance Observer
by Zhihao Lu and Zhong Wu
Actuators 2025, 14(4), 196; https://doi.org/10.3390/act14040196 - 18 Apr 2025
Viewed by 257
Abstract
Speed control accuracy of gimbal servo systems for control moment gyroscopes (CMGs) is crucial for spacecraft attitude control. However, multiple disturbances from internal and external factors severely degrade the speed control accuracy of gimbal servo systems. To suppress the effects of these complex [...] Read more.
Speed control accuracy of gimbal servo systems for control moment gyroscopes (CMGs) is crucial for spacecraft attitude control. However, multiple disturbances from internal and external factors severely degrade the speed control accuracy of gimbal servo systems. To suppress the effects of these complex disturbances on speed control accuracy, a control method based on a proportional–integral–resonant (PIR) controller and a noise reduction extended disturbance observer (NREDO) is proposed in this paper. First, the disturbance dynamic model of an (n+1)th-order NREDO is derived. The integral of the virtual measurement of the lumped disturbance is an augmented state in the model. NREDO states are updated by using the estimation error of the augmented state. The NREDO significantly enhances the measurement noise suppression performance compared with an EDO. Second, a resonant controller is introduced to suppress the high-frequency rotor dynamic imbalance torque. The PIR controller is composed of a resonant controller in parallel with a PI controller. Numerical simulation and experimental results demonstrate the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue New Control Schemes for Actuators—2nd Edition)
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15 pages, 4545 KiB  
Article
Research on Environmental Adaptability of Force–Position Hybrid Control for Quadruped Robots Based on Model Predictive Control
by Yuquan Xue, Liming Wang, Bi He, Yonghui Zhao, Yang Wang and Longmei Li
Electronics 2025, 14(8), 1604; https://doi.org/10.3390/electronics14081604 - 16 Apr 2025
Viewed by 218
Abstract
This study proposes a force–position hybrid control method for quadruped robots based on the Model Predictive Control (MPC) algorithm, aiming to address the challenges of stability and adaptability in complex terrain environments. Traditional control methods for quadruped robots are often based on simplified [...] Read more.
This study proposes a force–position hybrid control method for quadruped robots based on the Model Predictive Control (MPC) algorithm, aiming to address the challenges of stability and adaptability in complex terrain environments. Traditional control methods for quadruped robots are often based on simplified models, neglecting the impact of complex terrains and unstructured environments on control performance. To enhance the real-world performance of quadruped robots, this paper employs the MPC algorithm to integrate force and position control to achieve precise force–position hybrid regulation. By transforming foot-end forces into joint torques and optimizing them using kinematic inverse solutions, the robot’s stability and motion accuracy in challenging terrains is further enhanced. In this study, a Kalman filter-based state estimation method is adopted to estimate the robot’s state in real time, enabling closed-loop control through the MPC framework, combined with kinematic inverse solutions for hybrid control. The experimental results demonstrate that the proposed MPC algorithm significantly improves the robot’s adaptability and control accuracy across various terrains. In particular, it exhibits superior performance and robustness in multi-contact and uneven terrain scenarios. This research provides a novel approach for deploying quadruped robots in dynamic and complex environments and offers strong support for further optimization of motion control strategies. Full article
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22 pages, 12731 KiB  
Article
New Fault-Tolerant Sensorless Control of FPFTPM Motor Based on Hybrid Adaptive Robust Observation for Electric Agricultural Equipment Applications
by Zifeng Pei, Li Zhang, Haijun Fu and Yucheng Wang
Energies 2025, 18(8), 1962; https://doi.org/10.3390/en18081962 - 11 Apr 2025
Viewed by 163
Abstract
This paper proposes a hybrid adaptive robust observation (HARO)-based sensorless control strategy of a five-phase fault-tolerant permanent-magnet (FPFTPM) motor for electric agricultural equipment applications under various operating conditions, including fault conditions. Regarding fault-tolerant sensorless control, the existing studies usually treat fault-tolerant control and [...] Read more.
This paper proposes a hybrid adaptive robust observation (HARO)-based sensorless control strategy of a five-phase fault-tolerant permanent-magnet (FPFTPM) motor for electric agricultural equipment applications under various operating conditions, including fault conditions. Regarding fault-tolerant sensorless control, the existing studies usually treat fault-tolerant control and sensorless control as two independent units rather than a unified system, which makes the algorithm complex. In addition, under the traditional fault-tolerant algorithm, the system needs to switch after diagnosis when the fault occurs, which leads to a degraded sensorless control performance. Hence, this paper proposes a fault-tolerant sensorless control strategy that can achieve the whole speed range without fault-tolerant switching. At zero/low speed, a disturbance adaptive controller (DAC) architecture is developed by treating phase faults as system disturbances, where robust controllers and extended state observer (ESO) collaboratively suppress speed and position errors. At medium/high speeds, this paper provides a steady-healthy SMO, which combines the enhanced observer and universal phase-locked loop (PLL) without phase compensation. With above designs, the proposed strategy can significantly improve the estimated accuracy of rotor position under normal conditions and fault circumstances, while simplifying the complexity of the fault-tolerant sensorless algorithm. Furthermore, the proposed strategy is verified based on the experimental platform of the FPFTPM motor drive system. The experimental results show that compared with the traditional method, the torque ripple and position error are reduced by nearly 20% and 60%, respectively, at zero-low speed and medium-high speed, and the torque ripple is reduced by 55% during fault operation, which verifies the robustness and effectiveness of the proposed method. Full article
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21 pages, 8674 KiB  
Article
Improved Estimation Procedure of Cage-Induction-Motor-Equivalent Circuit Parameters Based on Two-Stage PSO Algorithm
by Jovan Vukašinović, Saša Štatkić, Nebojša Arsić, Nebojša Mitrović, Bojan Perović and Andrijana Jovanović
Energies 2025, 18(8), 1952; https://doi.org/10.3390/en18081952 - 11 Apr 2025
Viewed by 198
Abstract
This paper analyzes errors in the estimation of induction-motor-equivalent circuit parameters using an improved combined two-stage Particle Swarm Optimization (PSO) method. The proposed method accounts for variations in rotor parameters based on both linear and square root speed approximations, as well as two [...] Read more.
This paper analyzes errors in the estimation of induction-motor-equivalent circuit parameters using an improved combined two-stage Particle Swarm Optimization (PSO) method. The proposed method accounts for variations in rotor parameters based on both linear and square root speed approximations, as well as two different approaches for the stator and rotor leakage reactance ratios. The first approach assumes that the starting rotor leakage reactance is equal to the stator leakage reactance, while the second considers them as distinct. Improvement of the algorithm consists of increasing the accuracy of the approximations of parameter changes on the rotor. Thanks to more accurate determination of the initial rotor parameters, both approximations provide better results in parameter estimation. The analysis involved sixteen induction motors with four different power ratings and four different pole numbers. The analysis aimed to assess the impact of these approximations and assumptions on equivalent circuit parameter estimation errors. The estimated torque-speed characteristics closely matched the manufacturer’s reference data, including starting, maximum, and full-load torques. The deviation of the estimated torque-speed characteristics from the reference characteristics, within a defined speed range, is defined as the mean absolute percentage error. Based on the obtained results, the mean absolute percentage error is complex and depends on rotor parameter speed approximations, stator and rotor leakage reactance ratios, and the full power of the induction motor. Full article
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14 pages, 3111 KiB  
Article
A Method of Estimating an Object’s Parameters Based on Simplication with Momentum for a Manipulator
by Jaeyoung Jang and Jong Hyeon Park
Appl. Sci. 2025, 15(7), 3989; https://doi.org/10.3390/app15073989 - 4 Apr 2025
Viewed by 209
Abstract
For a manipulator to estimate an object’s inertial parameters—such as mass, center of mass position, and elements of the inertia tensor—it must grasp one side of the object and generate motion while utilizing the resulting forces and torques at its end-effector for estimation. [...] Read more.
For a manipulator to estimate an object’s inertial parameters—such as mass, center of mass position, and elements of the inertia tensor—it must grasp one side of the object and generate motion while utilizing the resulting forces and torques at its end-effector for estimation. In most previous studies, the estimation motion has involved high acceleration, resulting in larger motion trajectories and increased inertial forces. A larger trajectory raises the risk of collisions, while greater inertial forces could potentially damage the object. This paper introduces an innovative approach that simplifies the dynamic model using momentum, enabling accurate parameter estimation with minimal motion in robotic manipulation. Simulations are conducted to estimate key inertial parameters of the target object, including mass, center of mass position, and elements of the inertia tensor. The robotic manipulator securely grasps one side of the object and induces controlled motions to facilitate the estimation process. A comparative analysis with previously established estimation methods demonstrates that the proposed approach achieves accurate results with significantly smaller motions than prior techniques. The maximum acceleration reduction rates are 95% in linear motion and 98% in angular motion, respectively. Full article
(This article belongs to the Section Robotics and Automation)
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25 pages, 6180 KiB  
Article
Recursive PID-NT Estimation-Based Second-Order SMC Strategy for Knee Exoskeleton Robots: A Focus on Uncertainty Mitigation
by Vahid Behnamgol, Mohamad Asadi, Sumeet S. Aphale and Behnaz Sohani
Electronics 2025, 14(7), 1455; https://doi.org/10.3390/electronics14071455 - 3 Apr 2025
Viewed by 289
Abstract
This study introduces a modified second-order super-twisting sliding mode control algorithm designed to enhance the precision and robustness of knee exoskeleton robots by incorporating advanced uncertainty mitigation techniques. The key contribution of this research is the development of an efficient estimation mechanism capable [...] Read more.
This study introduces a modified second-order super-twisting sliding mode control algorithm designed to enhance the precision and robustness of knee exoskeleton robots by incorporating advanced uncertainty mitigation techniques. The key contribution of this research is the development of an efficient estimation mechanism capable of accurately identifying model parameter uncertainties and patients’ unwanted action torques disturbance within a finite time horizon, thereby improving overall system performance. The proposed control framework ensures smooth and precise control signal dynamics while effectively suppressing chattering effects, a common drawback in conventional sliding mode control methodologies. The theoretical foundation of the algorithm is rigorously established through the formulation of a PID non-singular terminal sliding variable, which ensures finite time stability in the sliding phase and a comprehensive Lyapunov-based stability analysis assuming that the upper bound of the uncertainty and its derivative are known in the reaching phase, which collectively guarantee the system’s robustness and reliability. Through simulations, the efficacy of the proposed control system is evaluated in its ability to track diverse desired knee angles, demonstrate robustness against disturbances, such as those caused by the patient’s foot reaction, and handle a 20% uncertainty in the model parameters. Additionally, the system’s effectiveness is assessed by three individuals with varying parameters. Notably, the controller gains remain consistent across all scenarios. This research constitutes a significant advancement in the domain of knee exoskeleton control, offering a more reliable and precise methodology for addressing model uncertainties. Full article
(This article belongs to the Special Issue Advancements in Robotics: Perception, Manipulation, and Interaction)
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