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Keywords = flexible vibration suppression control

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23 pages, 3652 KB  
Article
Vibration Control of a Two-Link Manipulator Using a Reduced Model
by Amir Mohamad Kamalirad and Reza Fotouhi
Vibration 2025, 8(4), 58; https://doi.org/10.3390/vibration8040058 - 1 Oct 2025
Abstract
This research aims to actively suppress vibrations at the end-effector of a flexible manipulator. When configured in a locked state, the system behaves as a two-link manipulator subjected to disturbances on the first link. To analyze its behavior, Finite Element Analysis (FEA) is [...] Read more.
This research aims to actively suppress vibrations at the end-effector of a flexible manipulator. When configured in a locked state, the system behaves as a two-link manipulator subjected to disturbances on the first link. To analyze its behavior, Finite Element Analysis (FEA) is employed to extract the natural frequencies (eigenvalues) and corresponding mode shapes (eigenvectors) of a two-link, two-joint flexible manipulator (2L2JM). The obtained eigenvectors are transformed into uncoupled state-space equations using balanced realization and the Match-DC-Gain model reduction algorithm. An H-infinity controller is then designed and applied to both the full-order and reduced-order models of the manipulator. The objective of this study is to validate an analytical framework through FEA, demonstrating its applicability to complex manipulators with multiple joints and flexible links. Given that the full state-space representation typically results in high-dimensional matrices, model reduction enables effective vibration control with a minimal number of states. The derivation of the 2L2JM state space, its model reduction, and a subsequent control strategy have not been previously addressed in this manner. Simulation results showcasing vibration suppression of a cantilever beam are presented and benchmarked against two alternative modeling approaches. Full article
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29 pages, 2881 KB  
Article
Distributed Cooperative Control of Flexible Spacecraft Based on PDE-ODE Coupled Dynamics Model
by Kai Cao, Pan Sun, Zhitao Zhou, Fan Mo, Liguo Wang, Haiyang Li, Kaiheng Xiang and Shuang Li
Aerospace 2025, 12(9), 828; https://doi.org/10.3390/aerospace12090828 - 15 Sep 2025
Viewed by 220
Abstract
With the increasing application of smart-material-based actuators for vibration suppression in flexible spacecraft, there is a growing need for advanced control strategies suited to distributed-parameter systems. This paper proposes a distributed cooperative control (DCC) scheme to address phase inconsistencies in actuator outputs within [...] Read more.
With the increasing application of smart-material-based actuators for vibration suppression in flexible spacecraft, there is a growing need for advanced control strategies suited to distributed-parameter systems. This paper proposes a distributed cooperative control (DCC) scheme to address phase inconsistencies in actuator outputs within a decentralized control framework. The piezoelectric actuators embedded in flexible appendages are modeled as a multi-agent system that utilizes local information to improve coordination. A consensus-based cooperative controller is designed to synchronize actuator actions, with closed-loop stability rigorously established via Lyapunov’s direct method. The robustness of the controller is evaluated through Monte Carlo simulations under varying initial conditions. Comparative numerical results demonstrate that the proposed DCC achieves superior performance and energy efficiency over conventional decentralized control, along with inherent fault tolerance due to its distributed topology. Furthermore, the practical implementability of the approach is supported by discrete-time controller validation and automatic code generation, confirming its readiness for real-time embedded deployment. The study highlights the potential of DCC for enhancing vibration suppression in next-generation flexible spacecraft. Full article
(This article belongs to the Section Astronautics & Space Science)
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24 pages, 8109 KB  
Article
A Bidirectional Tuned Mass Damper for Flutter Suppression in Ultra-Large Offshore Wind Turbine Flexible Blades
by Weiliang Liao, Mingming Zhang, Jianjun Yang, Youhua Fan, Tianlun Du and Yanfei Deng
J. Mar. Sci. Eng. 2025, 13(9), 1776; https://doi.org/10.3390/jmse13091776 - 14 Sep 2025
Viewed by 253
Abstract
As onshore space resources become exhausted, the migration of wind turbines to offshore areas is an inevitable trend. The blades of offshore wind turbines are typically over 100 m long, and this increased nonlinearity in the blades escalates the risk of flutter. Addressing [...] Read more.
As onshore space resources become exhausted, the migration of wind turbines to offshore areas is an inevitable trend. The blades of offshore wind turbines are typically over 100 m long, and this increased nonlinearity in the blades escalates the risk of flutter. Addressing the flutter phenomenon in these ultra-long flexible blades, this research establishes a full-scale model (FSM) considering geometric and material nonlinearities to accurately characterize the nonlinear dynamic response. Compared to the equivalent beam model, the proposed FSM better lays a foundation for flutter suppression research. On this basis, a bidirectional TMD was innovatively applied to the wind turbine blade and compared against a unidirectional TMD. The results demonstrate that bidirectional TMD can enhance the flutter control rate of 15 MW blades to over 90%, significantly improving flutter characteristics. Compared to the original blade, the steady-state amplitude is reduced by up to 45.73%, markedly suppressing flutter levels. These findings provide theoretical and data support for subsequent studies on aeroelastic instability and flutter suppression in ultra-long flexible blades, offering significant engineering application value and potential for broader implementation. Full article
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20 pages, 3671 KB  
Article
Trajectory Control of Flexible Manipulators Using Forward and Inverse Models with Neural Networks
by Minoru Sasaki, Mizuki Takeda, Joseph Muguro and Waweru Njeri
Vibration 2025, 8(3), 48; https://doi.org/10.3390/vibration8030048 - 26 Aug 2025
Viewed by 480
Abstract
This study explores trajectory control in flexible manipulators using neural-network-based forward and inverse modeling. Unlike traditional approaches that enhance precision by increasing structural rigidity—often at the cost of added weight and energy consumption—this work focuses on lightweight flexible manipulators, which are more suitable [...] Read more.
This study explores trajectory control in flexible manipulators using neural-network-based forward and inverse modeling. Unlike traditional approaches that enhance precision by increasing structural rigidity—often at the cost of added weight and energy consumption—this work focuses on lightweight flexible manipulators, which are more suitable for aerospace and other weight-sensitive applications but introduce control complexities due to elastic deformations. To address these challenges, neural-network-based models are proposed for a two-link, three-degree-of-freedom (3-DOF) flexible manipulator. Simulation and experimental results show that incorporating system delay compensation into the training data significantly improves tracking accuracy. Nonetheless, difficulties remain in achieving smooth trajectory generation. The findings highlight the potential of neural networks in adaptive control and point to future opportunities for refining input–output modeling to better align theoretical developments with practical implementation. Full article
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18 pages, 5977 KB  
Article
Attenuation of the First-Cycle Peak Response to an Impulse Disturbance
by Abasiodiong Jackson, Simon Fletcher and Andrew Longstaff
Vibration 2025, 8(2), 33; https://doi.org/10.3390/vibration8020033 - 17 Jun 2025
Viewed by 972
Abstract
Traditional control strategies for vibration suppression primarily focus on reducing settling time. However, this approach may not adequately address situations where the initial peak response of the vibration poses a risk of damage. This paper presents a novel application of active disturbance rejection [...] Read more.
Traditional control strategies for vibration suppression primarily focus on reducing settling time. However, this approach may not adequately address situations where the initial peak response of the vibration poses a risk of damage. This paper presents a novel application of active disturbance rejection control (ADRC) for attenuating the first-cycle peak response of free vibration in flexible structures. Inspired by the sudden impact scenario of particle accelerator collimators, a smart beam was designed to investigate the percentage first-cycle peak attenuation (FCPA) achievable by the disturbance estimation-based controller, in comparison with a classical proportional–differential (PD) controller. This study examined the limitations of the controller in mitigating initial deviations caused by real-world factors, such as delay and noise, through experimental methods. Results indicate that the PD controller achieves a maximum attenuation of 18%, while the ADRC achieves 30% attenuation. Improving the collocation configuration of the smart beam further improves the ADRC attenuation to 46.5%. Experimental data was used to fine-tune the system model in a sensitivity analysis to determine the delay within the system. Additionally, a new tuning parameter, α, representing the ratio of the observer bandwidth to controller bandwidth, was introduced to investigate the impact of observer and controller gain choices. System noise was amplified by 20 to 30 times, depending on the α value, although no significant effect on the control of the beam was observed. Full article
(This article belongs to the Special Issue Vibration in 2025)
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24 pages, 1293 KB  
Article
Singular Perturbation Decoupling and Composite Control Scheme for Hydraulically Driven Flexible Robotic Arms
by Jianliang Xu, Zhen Sui and Xiaohua Wei
Processes 2025, 13(6), 1805; https://doi.org/10.3390/pr13061805 - 6 Jun 2025
Viewed by 611
Abstract
Hydraulically driven flexible robotic arms (HDFRAs) play an indispensable role in industrial precision operations such as aerospace assembly and nuclear waste handling, owing to their high power density and adaptability to complex environments. However, inherent mechanical flexibility-induced vibrations, hydraulic nonlinear dynamics, and electromechanical [...] Read more.
Hydraulically driven flexible robotic arms (HDFRAs) play an indispensable role in industrial precision operations such as aerospace assembly and nuclear waste handling, owing to their high power density and adaptability to complex environments. However, inherent mechanical flexibility-induced vibrations, hydraulic nonlinear dynamics, and electromechanical coupling effects lead to multi-timescale control challenges, severely limiting high-precision trajectory tracking performance. The present study introduces a novel hierarchical control framework employing dual-timescale perturbation analysis, which effectively addresses the constraints inherent in conventional single-timescale control approaches. First, the system is decoupled into three subsystems via dual perturbation parameters: a second-order rigid-body motion subsystem (SRS), a second-order flexible vibration subsystem (SFS), and a first-order hydraulic dynamic subsystem (FHS). For SRS/SFS, an adaptive fast terminal sliding mode active disturbance rejection controller (AFTSM-ADRC) is designed, featuring a dual-bandwidth extended state observer (BESO) to estimate parameter perturbations and unmodeled dynamics in real time. A novel reaching law with power-rate hybrid characteristics is developed to suppress sliding mode chattering while ensuring rapid convergence. For FHS, a sliding mode observer-integrated sliding mode coordinated controller (SMO-ISMCC) is proposed, achieving high-precision suppression of hydraulic pressure fluctuations through feedforward compensation of disturbance estimation and feedback integration of tracking errors. The globally asymptotically stable property of the composite system has been formally verified through systematic Lyapunov-based analysis. Through comprehensive simulations, the developed methodology demonstrates significant improvements over conventional ADRC and PID controllers, including (1) joint tracking precision reaching 104 rad level under nominal conditions and (2) over 40% attenuation of current oscillations when subjected to stochastic disturbances. These results validate its superiority in dynamic decoupling and strong disturbance rejection. Full article
(This article belongs to the Special Issue Modelling and Optimizing Process in Industry 4.0)
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28 pages, 6914 KB  
Article
Guided Reinforcement Learning with Twin Delayed Deep Deterministic Policy Gradient for a Rotary Flexible-Link System
by Carlos Saldaña Enderica, José Ramon Llata and Carlos Torre-Ferrero
Robotics 2025, 14(6), 76; https://doi.org/10.3390/robotics14060076 - 31 May 2025
Viewed by 1841
Abstract
This study proposes a robust methodology for vibration suppression and trajectory tracking in rotary flexible-link systems by leveraging guided reinforcement learning (GRL). The approach integrates the twin delayed deep deterministic policy gradient (TD3) algorithm with a linear quadratic regulator (LQR) acting as a [...] Read more.
This study proposes a robust methodology for vibration suppression and trajectory tracking in rotary flexible-link systems by leveraging guided reinforcement learning (GRL). The approach integrates the twin delayed deep deterministic policy gradient (TD3) algorithm with a linear quadratic regulator (LQR) acting as a guiding controller during training. Flexible-link mechanisms common in advanced robotics and aerospace systems exhibit oscillatory behavior that complicates precise control. To address this, the system is first identified using experimental input-output data from a Quanser® virtual plant, generating an accurate state-space representation suitable for simulation-based policy learning. The hybrid control strategy enhances sample efficiency and accelerates convergence by incorporating LQR-generated trajectories during TD3 training. Internally, the TD3 agent benefits from architectural features such as twin critics, delayed policy updates, and target action smoothing, which collectively improve learning stability and reduce overestimation bias. Comparative results show that the guided TD3 controller achieves superior performance in terms of vibration damping, transient response, and robustness, when compared to conventional LQR, fuzzy logic, neural networks, and GA-LQR approaches. Although the controller was validated using a high-fidelity digital twin, it has not yet been deployed on the physical plant. Future work will focus on real-time implementation and structural robustness testing under parameter uncertainty. Overall, this research demonstrates that guided reinforcement learning can yield stable and interpretable policies that comply with classical control criteria, offering a scalable and generalizable framework for intelligent control of flexible mechanical systems. Full article
(This article belongs to the Section Industrial Robots and Automation)
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16 pages, 3753 KB  
Article
Control of Active Suspension Systems Based on Mechanical Wave Concepts
by Hossein Habibi
Actuators 2025, 14(5), 230; https://doi.org/10.3390/act14050230 - 5 May 2025
Cited by 1 | Viewed by 1504
Abstract
Wave-based control (WBC) offers a relatively novel approach to the challenge of controlling flexible mechanisms by treating the interaction between actuator and system as the launch and absorption of mechanical waves. WBC is a robust approach but has been unexplored in active suspension [...] Read more.
Wave-based control (WBC) offers a relatively novel approach to the challenge of controlling flexible mechanisms by treating the interaction between actuator and system as the launch and absorption of mechanical waves. WBC is a robust approach but has been unexplored in active suspension systems to date. This study adapts WBC to a quarter-car suspension model. Having embedded an actuator as the active element of a car suspension, a novel but simple ‘force impedance’ adaptation of WBC is introduced and implemented for effective vibration control. Testing with various input signals (pulse, sinusoidal, and random profile) highlights the active system’s significant ride comfort and rapid vibration suppression with zero steady-state error. Compared to two other models—one employing an ideal skyhook strategy and the other a passive suspension—the active system utilizing WBC outperforms across many criteria. The active controller achieves over 38% superior ride comfort compared to the skyhook model for a pulse road input. This is accomplished while adhering to WBC principles: relying solely on actuator-interface measurements, simplicity, cost-effectiveness, with no need for detailed system models, extensive sensors, or deep system knowledge. Full article
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17 pages, 4148 KB  
Article
Optimal Control Based on Reinforcement Learning for Flexible High-Rise Buildings with Time-Varying Actuator Failures and Asymmetric State Constraints
by Min Li and Rui Xie
Buildings 2025, 15(6), 841; https://doi.org/10.3390/buildings15060841 - 7 Mar 2025
Cited by 2 | Viewed by 806
Abstract
This study centers on the vibration suppression of high-rise building systems under extreme conditions, exploring a reinforcement learning (RL)-based vibration control strategy for flexible building systems with time-varying faults and asymmetric state constraints. A mathematical model precisely depicting the dynamic characteristics of flexible [...] Read more.
This study centers on the vibration suppression of high-rise building systems under extreme conditions, exploring a reinforcement learning (RL)-based vibration control strategy for flexible building systems with time-varying faults and asymmetric state constraints. A mathematical model precisely depicting the dynamic characteristics of flexible high-rise buildings, considering the time-varying nature of actuator faults, is initially established. Subsequently, a reinforcement learning-based controller is devised to counteract the negative impacts of faults on system performance. By introducing a time-varying asymmetric Lyapunov function, system state constraints are ensured, safeguarding system stability and security. The stability of the closed-loop system is rigorously proven using the Lyapunov stability theory, guaranteeing stable vibration suppression performance even in the presence of faults. The simulation results indicate that the proposed reinforcement learning vibration control method can effectively reduce the vibration response of flexible high-rise buildings when facing time-varying actuator faults. This demonstrates its remarkable robustness and adaptability, presenting a novel and effective solution for vibration control in real-world flexible high-rise buildings. Full article
(This article belongs to the Section Building Structures)
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23 pages, 37944 KB  
Article
Residual Vibration Reduction in Flexible Systems Based on Trapezoidal Velocity Profiles
by Xining Cui, Yi Fang and Chaochen Gu
Appl. Sci. 2025, 15(4), 1791; https://doi.org/10.3390/app15041791 - 10 Feb 2025
Viewed by 1262
Abstract
Industrial parts are increasingly being designed to be more lightweight in modern manufacturing for energy saving and material cost reduction. However, the high-speed motion of flexible systems tends to excite severe residual vibrations that result in positioning accuracy degradation and loss of productivity. [...] Read more.
Industrial parts are increasingly being designed to be more lightweight in modern manufacturing for energy saving and material cost reduction. However, the high-speed motion of flexible systems tends to excite severe residual vibrations that result in positioning accuracy degradation and loss of productivity. This study proposes a closed-form trajectory optimization method for vibration suppression based on trapezoidal velocity profiles, which are most widely used in industrial robots and machines. First, the formulation and minimum time solution under actuator limits of the motion profile are defined. Then, the relationship between the trajectory parameters and the vibration response is investigated. It is shown that residual vibration can be eliminated by properly tuning the acceleration/deceleration switching times according to the natural frequency. Based on the derived vibration suppression conditions, a tuning procedure for time parameters compliant with actuator limits is established to generate fast and precise movement. A main advantage of the proposed method is easy implementation for general machines without requiring extra computational resources or modification to the control system. The effectiveness and practicality of the proposed approach are verified through experiments conducted on a robot. The experimental results show that the optimized trajectory achieves superior residual vibration reduction performance. Full article
(This article belongs to the Special Issue Motion Control for Robots and Automation)
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15 pages, 15889 KB  
Article
Slewing and Active Vibration Control of a Flexible Single-Link Manipulator
by Dae W. Kim, Moon K. Kwak, Soo-Min Kim and Brian F. Feeny
Actuators 2025, 14(2), 43; https://doi.org/10.3390/act14020043 - 22 Jan 2025
Cited by 1 | Viewed by 1129
Abstract
This study focuses on the slewing and vibration suppression of flexible single-link manipulators. While extensive research has been conducted on such systems, few studies have experimentally validated their theoretical models. To address this gap, an experimental setup is developed, connecting the flexible link [...] Read more.
This study focuses on the slewing and vibration suppression of flexible single-link manipulators. While extensive research has been conducted on such systems, few studies have experimentally validated their theoretical models. To address this gap, an experimental setup is developed, connecting the flexible link to a zero-backlash worm gear and further attaching it to the rotor shaft of the AC servomotor. The worm gear’s characteristics isolate the link’s vibrations from the rotor’s angular motion, enabling independent design of the vibration controller and slewing control. This approach facilitates simultaneous accurate trajectory tracking and vibration suppression. An active vibration control algorithm is implemented based on an accurate dynamic model. This research encompasses dynamic modeling, slewing control, and vibration control for the system. Theoretical predictions are compared with experimental results to validate both the theoretical model and the proposed vibration control algorithm. Full article
(This article belongs to the Special Issue Nonlinear Active Vibration Control)
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23 pages, 7359 KB  
Article
Distributed Passivity-Based Control for Multiple Space Manipulators Holding Flexible Beams
by Ti Chen, Yue Cao, Mingyan Xie, Shihao Ni, Enchang Zhai and Zhengtao Wei
Actuators 2025, 14(1), 20; https://doi.org/10.3390/act14010020 - 8 Jan 2025
Cited by 1 | Viewed by 1229
Abstract
This paper proposes a distributed passivity-based control scheme for the consensus and vibration suppression of multiple space manipulators holding flexible beams. A space manipulator holding a flexible beam is essentially a rigid–flexible underactuated system. The bending deformation of the flexible beam is discretized [...] Read more.
This paper proposes a distributed passivity-based control scheme for the consensus and vibration suppression of multiple space manipulators holding flexible beams. A space manipulator holding a flexible beam is essentially a rigid–flexible underactuated system. The bending deformation of the flexible beam is discretized by employing the assumed modes method. Based on Lagrange’s equations of the second kind, the dynamics model of each manipulator holding a flexible beam is established. By connecting such underactuated systems with the auxiliary Euler–Lagrange systems, a distributed passivity-based controller is designed under undirected communication graphs. To suppress flexible vibration effectively, a distributed controller with the feedback of the velocity of deflection at the free end of the flexible beam is proposed to achieve the manipulator synchronization and vibration suppression simultaneously. The stability of the proposed controller is analyzed with LaSalle’s invariance principle. Numerical simulations and experiments are conducted to show the effectiveness of the designed controllers. Full article
(This article belongs to the Special Issue Dynamics and Control of Aerospace Systems)
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20 pages, 20108 KB  
Article
Physics-Informed Neural Network-Based Input Shaping for Vibration Suppression of Flexible Single-Link Robots
by Tingfeng Li and Tengfei Xiao
Actuators 2025, 14(1), 14; https://doi.org/10.3390/act14010014 - 5 Jan 2025
Cited by 2 | Viewed by 2177
Abstract
The vibration suppression of flexible robotic arms is challenging due to their nonlinear spatiotemporal dynamics. This paper presents a novel physics-informed neural network (PINN)-based input-shaping method for the vibration suppression problem. Through a two-phase training process of a neural network based on a [...] Read more.
The vibration suppression of flexible robotic arms is challenging due to their nonlinear spatiotemporal dynamics. This paper presents a novel physics-informed neural network (PINN)-based input-shaping method for the vibration suppression problem. Through a two-phase training process of a neural network based on a loss function that follows both the physical model constraints and the vibration modal conditions, we identify optimal input-shaping parameters to minimize residual vibration. With the use of powerful computational resources to handle multimode information about the vibration, the PINN-based approach outperforms traditional input-shaping methods in terms of computational efficiency and performance. Extensive simulations are carried out to validate the effectiveness of the method and highlight its potential for complex control tasks in flexible robotic systems. Full article
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23 pages, 8708 KB  
Article
Development of a Passive Vibration Damping Structure for Large Solar Arrays Using a Superelastic Shape Memory Alloy with Multi-Layered Viscous Lamination
by Gi-Seong Woo, Jae-Hyeon Park, Sung-Woo Park and Hyun-Ung Oh
Aerospace 2025, 12(1), 29; https://doi.org/10.3390/aerospace12010029 - 2 Jan 2025
Cited by 2 | Viewed by 1299
Abstract
In the space environment, the elastic vibrations of satellite solar panels are caused by various factors that disturb satellite missions. Therefore, we propose a multi-layered high-damping yoke structure based on a passive control method. To optimize the proposed yoke structure, we performed a [...] Read more.
In the space environment, the elastic vibrations of satellite solar panels are caused by various factors that disturb satellite missions. Therefore, we propose a multi-layered high-damping yoke structure based on a passive control method. To optimize the proposed yoke structure, we performed a free vibration test on various multi-layered blade specimens and designed a yoke structure with the maximum damping performance based on the test results. This high-damping yoke structure was mounted on a dummy solar panel with flexible mode (0.79 Hz) and basic characteristic tests were performed to validate the effectiveness of the solar panel vibration suppression. The test results demonstrated that the proposed multi-layered high-damping yoke is effective in suppressing the vibrations of the first and second modes. In addition, a thermal vacuum test was performed to investigate the delamination between multi-layered structures, and the test results proved the applicability of the proposed yoke structure in an actual space environment. Full article
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12 pages, 2029 KB  
Communication
Neural Network Adaptive Inverse Control of Flexible Joint Space Manipulator Considering the Influence of Gravity
by Shaoqing Li, Lingcong Meng, Kai Fang and Fucai Liu
Sensors 2024, 24(21), 6942; https://doi.org/10.3390/s24216942 - 29 Oct 2024
Cited by 1 | Viewed by 925
Abstract
With the aim of correcting the problem of trajectory tracking control of a flexible joint space manipulator in environments with different gravity, a neural network adaptive inverse control algorithm based on singular perturbation theory is proposed to resist the disturbance caused by system [...] Read more.
With the aim of correcting the problem of trajectory tracking control of a flexible joint space manipulator in environments with different gravity, a neural network adaptive inverse control algorithm based on singular perturbation theory is proposed to resist the disturbance caused by system uncertainty. Firstly, the dynamic model of a flexible joint space manipulator with the influence of gravity is established, and then the system is divided into a fast subsystem and a slow subsystem using singular perturbation theory. The velocity feedback control rate is designed for the fast subsystem to suppress the elastic vibration caused by the joint flexibility. For the slow subsystem, the uncertain term and known term are separated by the inverse control algorithm, where the uncertain term is approximated online by the RBF neural network, and the robust control rate is designed to compensate for the approximation error. The simulation results show that the control method can not only effectively reduce the high-frequency vibration caused by the flexible joint but also resist the system disturbance so that a good track control effect is achieved. Full article
(This article belongs to the Section Sensors and Robotics)
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