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16 pages, 2849 KB

Open AccessArticle

A Comparative Study on the Influence of Track and Conductor Rail Irregularity on Collector Shoe-Conductor Rail Interaction Dynamics

by Like Pan, Tong Xing, Wenrui Dai, Yan Xu and Weidong Zhu

Machines 2026, 14(5), 475; https://doi.org/10.3390/machines14050475 - 24 Apr 2026

Viewed by 257

Abstract

The dynamic characteristics of the collector shoe–conductor rail interaction directly affect the operational performance of metro systems. Although irregularities exist in both the track and the conductor rail, their relative influence on interaction dynamics has not been comprehensively compared. This study develops a [...] Read more.

The dynamic characteristics of the collector shoe–conductor rail interaction directly affect the operational performance of metro systems. Although irregularities exist in both the track and the conductor rail, their relative influence on interaction dynamics has not been comprehensively compared. This study develops a coupled train–track–shoe–rail dynamic model to investigate these effects. Specifically, the conductor rail is modeled using a localized approach based on the Arbitrary Lagrangian–Eulerian (ALE) method. This is integrated with a multibody collector shoe model and an existing train–track interaction model to form a comprehensive simulation framework. After validating the model, the impacts of track irregularity, conductor rail irregularity, and support spacing are analyzed and compared. The results demonstrate that while conductor rail irregularity is the primary driver of contact loss, standard track irregularity can also account for approximately 10% of the dynamic response variation. Consequently, both factors must be integrated into future studies of collector shoe–conductor rail dynamics. Full article

(This article belongs to the Special Issue Mastering Vibrations: The Latest Breakthroughs in Control for Mechanical Systems)

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19 pages, 5198 KB

Open AccessArticle

Time-Optimal and Collision-Free Trajectory Generation for Large Cranes with Load Sway and Tower Torsion Suppression

by Abdallah Farrage, Nur Azizah Amir, Hideki Takahashi, Shintaro Sasai, Hitoshi Sakurai, Masaki Okubo and Naoki Uchiyama

Machines 2026, 14(4), 430; https://doi.org/10.3390/machines14040430 - 11 Apr 2026

Viewed by 427

Abstract

Tower torsion in large cranes poses a significant challenge to achieving precise control of load motion, as it amplifies oscillations of the crane load during motion and after reaching a destination. Therefore, tower torsion should be incorporated into crane motion control strategies to [...] Read more.

Tower torsion in large cranes poses a significant challenge to achieving precise control of load motion, as it amplifies oscillations of the crane load during motion and after reaching a destination. Therefore, tower torsion should be incorporated into crane motion control strategies to improve load sway suppression and enhance overall operational stability. This study proposes a time-optimal trajectory generation method for large cranes with addressing tower torsion challenges and load swaying angles. The time-optimal trajectory is able to provide smooth motion with sufficient time while navigating around obstacles. The proposed approach integrates two distinct algorithms: the A* algorithm is employed to determine the shortest collision-free load path, and an optimization method that generates time-optimal trajectories along the A* path while considering the constraints of tower torsion and load sway angles. The desired trajectory is modeled using a polynomial function, ensuring practical motion for each crane joint. The proposed method’s effectiveness is validated both computationally and experimentally, demonstrating its capability to suppress load sway and tower torsion in the crane system without collision. Full article

(This article belongs to the Special Issue Mastering Vibrations: The Latest Breakthroughs in Control for Mechanical Systems)

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22 pages, 4091 KB

Open AccessArticle

3D Trajectory Tracking Based on Super-Twisting Observer and Non-Singular Terminal Sliding Mode Control for Underactuated Autonomous Underwater Vehicle

by Zehui Yuan, Long He, Ya Zhang, Shizhong Li, Chenrui Bai and Zhuoyan Qi

Machines 2026, 14(3), 354; https://doi.org/10.3390/machines14030354 - 21 Mar 2026

Viewed by 487

Abstract

This paper addresses the three-dimensional trajectory tracking problem for underactuated autonomous underwater vehicles subject to external disturbances and model uncertainties in complex ocean environments. A robust control method integrating backstepping dynamic surface control and non-singular terminal sliding mode is proposed. Firstly, based on [...] Read more.

This paper addresses the three-dimensional trajectory tracking problem for underactuated autonomous underwater vehicles subject to external disturbances and model uncertainties in complex ocean environments. A robust control method integrating backstepping dynamic surface control and non-singular terminal sliding mode is proposed. Firstly, based on the kinematic and dynamic models of autonomous underwater vehicle, virtual velocity commands are constructed via backstepping approach to stabilize the position and attitude errors. To circumvent the “differential explosion” problem inherent in conventional backstepping control caused by repeated differentiations of virtual control variables, first-order low-pass filters are introduced to construct dynamic surface control, yielding smooth derivatives of virtual velocity commands. Secondly, to enhance convergence rate and robustness, a non-singular terminal sliding surface is designed at the dynamic level, and a terminal reaching law is formulated to achieve finite-time convergence of velocity tracking errors. Furthermore, to compensate for external disturbances and unmodeled dynamics, a disturbance observer based on the super-twisting algorithm is developed, enabling finite-time high-precision estimation of lumped disturbances, with the estimation results incorporated into the control law for feedforward compensation. Finally, comparative simulations are conducted under two typical disturbance scenarios. The results demonstrate that the proposed method achieves instantaneous disturbance estimation (reducing convergence time from 3 s to near zero), significantly smoother control inputs, and superior tracking accuracy with RMSE as low as 0.6788 m and MAE as low as 0.1468 m, reducing errors by up to 30.6% compared to baseline methods. Full article

(This article belongs to the Special Issue Mastering Vibrations: The Latest Breakthroughs in Control for Mechanical Systems)

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35 pages, 7094 KB

Open AccessArticle

Beyond Linear Limits: Advanced Nonlinear Suspensions for Enhanced Vibration Control

by Farhad S. Samani, Amirali Mehrabian, Antonio Zippo and Francesco Pellicano

Machines 2026, 14(2), 209; https://doi.org/10.3390/machines14020209 - 10 Feb 2026

Viewed by 711

Abstract

The vehicle suspensions have the primary task of attenuating the forces coming from the road surface. The performance is directly linked to the stiffness of the suspension system. Traditional suspensions, composed of linear elements, effectively damp high frequencies but perform poorly at low [...] Read more.

The vehicle suspensions have the primary task of attenuating the forces coming from the road surface. The performance is directly linked to the stiffness of the suspension system. Traditional suspensions, composed of linear elements, effectively damp high frequencies but perform poorly at low frequencies. In this regard, non-linear suspensions, characterized by a non-linear force–displacement relationship, have been introduced. These types of suspensions achieve this characteristic by combining elements with positive stiffness with elements with negative stiffness, resulting in an equivalent system with quasi-zero stiffness (QZS) around the equilibrium. The performance of the QZS suspension system is analyzed here using the Multibody Dynamics software MSC Adams^® (2022.2). Static characteristics, transmissibility, and isolation performance are investigated through dynamic tests based on road profiles according to ISO 8608 regulations generated using MATLAB^® (R2022b). The proposed quasi-zero stiffness suspension demonstrates an improvement of approximately 19% in vibration attenuation compared to a conventional suspension system under realistic road excitations. Full article

(This article belongs to the Special Issue Mastering Vibrations: The Latest Breakthroughs in Control for Mechanical Systems)

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19 pages, 2794 KB

Open AccessArticle

Second-Order Nonsingular Terminal Sliding Mode Control for Tracking and Stabilization of Cart–Inverted Pendulum

by Hiep Dai Le and Tamara Nestorović

Machines 2026, 14(1), 111; https://doi.org/10.3390/machines14010111 - 18 Jan 2026

Viewed by 393

Abstract

A second-order nonsingular terminal sliding mode control (SONTSMC) is proposed to solve the stabilization and tracking problems of an inverted pendulum. Although, a first-order sliding mode controller with the integral of the cart position can eliminate the offset in the cart position caused [...] Read more.

A second-order nonsingular terminal sliding mode control (SONTSMC) is proposed to solve the stabilization and tracking problems of an inverted pendulum. Although, a first-order sliding mode controller with the integral of the cart position can eliminate the offset in the cart position caused by incorrect calibration of the pendulum angle while balancing the pendulum at the upright equilibrium position, its control precision and chattering reduction can be improved by using a higher-order sliding mode controller. Therefore, the SONTSMC is designed by combining nonsingular sliding mode control and first-order sliding mode control to construct a second-order sliding mode controller that enhances tracking accuracy and reduces the chattering problems associated with sliding mode control. The performance of the proposed control is compared with that of the linear quadratic regulator sliding mode control (LQRSMC) and the integral linear quadratic regulator sliding mode control (ILQRSMC) for CIP’s stabilization and tracking. The results indicate that SONTSMC significantly increases the control performance of CIP while efficiently utilizing control energy. Full article

(This article belongs to the Special Issue Mastering Vibrations: The Latest Breakthroughs in Control for Mechanical Systems)

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26 pages, 7959 KB

Open AccessArticle

Effect of Boundary Conditions on Vibration Characteristics of a Sandwich Plate with Viscoelastic Periodic Cores

by Zhiwei Guo, Meiping Sheng and Kai Zhang

Machines 2025, 13(9), 863; https://doi.org/10.3390/machines13090863 - 17 Sep 2025

Cited by 1 | Viewed by 936

Abstract

The effects of boundary conditions on the vibration characteristics of a sandwich plate with viscoelastic periodic cores were examined. The tangential, vertical, transverse, and torsional springs were utilized to restrict the sandwich plate’s edge in order to model a general boundary condition, bringing [...] Read more.

The effects of boundary conditions on the vibration characteristics of a sandwich plate with viscoelastic periodic cores were examined. The tangential, vertical, transverse, and torsional springs were utilized to restrict the sandwich plate’s edge in order to model a general boundary condition, bringing the benefit that the conventional free, clamped, and simply supported boundary conditions became special cases in the proposed model as these spring constants took extreme values. A theoretical model was established to calculate the forced response and band structure of the periodic sandwich plate, providing computational support for evaluating its vibration characteristics. The correctness of the theoretical model was also validated by the finite element method. The results show that the boundary spring stiffness has a significant effect on the band-gap frequencies and band-gap width of the periodic sandwich plate. Increasing the boundary spring stiffness contributes to achieving broader band gaps. In addition, the band-gap frequencies and band-gap width are more sensitive to transverse spring stiffness than the tangential, vertical, and torsional spring stiffnesses. Therefore, changing transverse spring stiffness is more effective for adjusting the band gap property. This study may provide helpful guidance on vibration and noise reduction design in engineering. Full article

(This article belongs to the Special Issue Mastering Vibrations: The Latest Breakthroughs in Control for Mechanical Systems)

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30 pages, 6045 KB

Open AccessArticle

An Optimized Active Compensation Control Framework for High-Speed Railway Pantograph via Imitation-Guided Deep Reinforcement Learning

by Zhun Han, Qingsheng Feng, Wangyang Liu, Yuqi Liu, Hangtao Yang, Hong Li, Mingxia Xu and Shuai Xiao

Machines 2025, 13(9), 769; https://doi.org/10.3390/machines13090769 - 28 Aug 2025

Cited by 1 | Viewed by 1413

Abstract

Extreme pantograph–catenary contact force (PCCF) oscillations pose a serious challenge to the stable coupling between pantograph and catenary in high-speed railway systems. This paper introduces an active compensation control framework CPO-LQR-BC-SAC, which combines optimized Linear Quadratic Regulator (LQR) baseline control with behavior cloning [...] Read more.

Extreme pantograph–catenary contact force (PCCF) oscillations pose a serious challenge to the stable coupling between pantograph and catenary in high-speed railway systems. This paper introduces an active compensation control framework CPO-LQR-BC-SAC, which combines optimized Linear Quadratic Regulator (LQR) baseline control with behavior cloning (BC) and Soft Actor-Critic (SAC) deep reinforcement learning. First, the Crowned Porcupine Optimization algorithm (CPO) is used to offline tune the LQR weighting matrix, producing a high-performance CPO-LQR controller that significantly reduces PCCF fluctuation. Next, a dual model-based offline control law provides “expert” adjustments that further suppress extreme contact force values. Observing that superimposing these offline-tuned actions onto real-time CPO-LQR outputs yields further suppression gains, we developed the BC-SAC compensatory controller to provide corrective control actions. In this scheme, expert actions guide the SAC policy via a behavior cloning loss term in its loss function, and a decaying imitation weight ensures a balance between imitation and exploration. Simulation results demonstrate that, compared to both CPO-LQR and the idealized offline control law, the proposed CPO-LQR-BC-SAC framework achieves over 77% reduction in PCCF standard deviation and exhibits the ability to generalize across different pantograph types, confirming its effectiveness and robustness as a practical solution for mitigating extreme PCCF oscillations. Full article

(This article belongs to the Special Issue Mastering Vibrations: The Latest Breakthroughs in Control for Mechanical Systems)

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16 pages, 2924 KB

Open AccessArticle

Design Technique on Speed Control Combined with an Inertial Element for Vibration Suppression

by Guoguang Zhang, Shuntai Xie, Peng Hou and Xiaoguang Wang

Machines 2025, 13(7), 573; https://doi.org/10.3390/machines13070573 - 1 Jul 2025

Cited by 1 | Viewed by 828

Abstract

The suppression of mechanical resonance stands as the most crucial issue in enhancing system performance. In this study, based on a speed control system, the mechanisms of vibration suppression both with and without a first-order inertial element are analyzed and compared, and a [...] Read more.

The suppression of mechanical resonance stands as the most crucial issue in enhancing system performance. In this study, based on a speed control system, the mechanisms of vibration suppression both with and without a first-order inertial element are analyzed and compared, and a pole assignment method featuring an identical radius is put forward. Through an optimized design of pole assignment, the constraint conditions, control parameters, and applicable boundary of the first-order inertial element are explicitly derived in an analytical form. These derived results possess clear design significance and are very convenient for practical use. It is demonstrated that speed control with the first-order inertial element can effectively improve the underdamping performance. The proposed control method and the constrained optimization design of pole assignment are validated through experiments. Full article

(This article belongs to the Special Issue Mastering Vibrations: The Latest Breakthroughs in Control for Mechanical Systems)

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18 pages, 2053 KB

Open AccessArticle

Optimization of Hybrid Machining of Nomex Honeycomb Structures: Effect of the CZ10 Tool and Ultrasonic Vibrations on the Cutting Process

by Oussama Beldi, Tarik Zarrouk, Ahmed Abbadi, Mohammed Nouari, Jamal-Eddine Salhi, Mohammed Abbadi and Mohamed Barboucha

Machines 2025, 13(6), 515; https://doi.org/10.3390/machines13060515 - 13 Jun 2025

Cited by 1 | Viewed by 1081

Abstract

Machining Nomex honeycomb composite structures is crucial for manufacturing components that meet stringent industry requirements. However, the complex characteristics of this material require specialized machining techniques to avoid defects, ensure optimal surface quality, and preserve the integrity of the cutting tool. Thus, hybrid [...] Read more.

Machining Nomex honeycomb composite structures is crucial for manufacturing components that meet stringent industry requirements. However, the complex characteristics of this material require specialized machining techniques to avoid defects, ensure optimal surface quality, and preserve the integrity of the cutting tool. Thus, hybrid ultrasonic-vibration-assisted machining (HUSVAM) technology, using a CZ10 combined cutting tool, was introduced to overcome these limitations. To this end, a 3D numerical model based on the finite element method, developed using Abaqus/Explicit 2017 software, allows us to simulate the interaction between the cutting tool and the thin walls of the structure to be machined. The objective of this study was to validate a numerical model through experimental tests while quantifying the impact of critical machining parameters, including the rotation speed and tilt angle, on process performance, in terms of surface finish, tool wear, cutting force components and chip size. The numerical results demonstrated that HUSVAM technology allows for a significant reduction in the cutting force components, with a decrease of between 12% and 35%. Furthermore, this technology improves cutting quality by limiting the deformation and tearing of cell walls, while extending tool life through a significant reduction in wear. These improvements thus contribute to a substantial optimization of the overall efficiency of the machining process. Full article

(This article belongs to the Special Issue Mastering Vibrations: The Latest Breakthroughs in Control for Mechanical Systems)

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19 pages, 1077 KB

Open AccessArticle

Integral Linear Quadratic Regulator Sliding Mode Control for Inverted Pendulum Actuated by Stepper Motor

by Hiep Dai Le and Tamara Nestorović

Machines 2025, 13(5), 405; https://doi.org/10.3390/machines13050405 - 12 May 2025

Cited by 4 | Viewed by 1469

Abstract

Stabilization and tracking problems for cart inverted pendulums under disturbances and uncertainties have posed significant challenges for control engineers. While various controllers have been designed for an inverted pendulum, they often overlook the calibration error of the pendulum angle in practical implementations, which [...] Read more.

Stabilization and tracking problems for cart inverted pendulums under disturbances and uncertainties have posed significant challenges for control engineers. While various controllers have been designed for an inverted pendulum, they often overlook the calibration error of the pendulum angle in practical implementations, which degrades the control performance. Incorrect calibration of the pendulum angle in upright equilibrium position generates an offset of cart position errors. To solve this problem, an augmented model comprising integral cart position errors was first constructed. Afterwards, a sliding mode control was designed for this system based on a linear quadratic controller, to facilitate implementation. Additionally, a stepper motor was employed in the inverted pendulum to enhance the control performance and widen applicability in industrial settings. The effectiveness and performance of the proposed controller were validated by means of experimental studies, focusing on stabilization control and tracking control of a cart inverted pendulum actuated by a stepper motor. Full article

(This article belongs to the Special Issue Mastering Vibrations: The Latest Breakthroughs in Control for Mechanical Systems)

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Review

Jump to: Research

38 pages, 5185 KB

Open AccessReview

Review of Agricultural Machinery Seat Semi-Active Suspension Systems for Ride Comfort

by Xiaoliang Chen, Zhelu Wang, Haoyou Shi, Nannan Jiang, Sixia Zhao, Yiqing Qiu and Qing Liu

Machines 2025, 13(3), 246; https://doi.org/10.3390/machines13030246 - 18 Mar 2025

Cited by 12 | Viewed by 4255

Abstract

This paper systematically reviews research progress in semi-active suspension systems for agricultural machinery seats, focusing on key technologies and methods to enhance ride comfort. First, through an analysis of the comfort evaluation indicators and constraints of seat suspension systems, the current applications of [...] Read more.

This paper systematically reviews research progress in semi-active suspension systems for agricultural machinery seats, focusing on key technologies and methods to enhance ride comfort. First, through an analysis of the comfort evaluation indicators and constraints of seat suspension systems, the current applications of variable stiffness and damping components, as well as semi-active control technologies, are outlined. Second, a comparative analysis of single control methods (such as PID control, fuzzy control, and sliding mode control) and composite control methods (such as fuzzy PID control, intelligent algorithm-based integrated control, and fuzzy sliding mode control) is conducted, with control mechanisms explained using principle block diagrams. Furthermore, key technical challenges in current research are summarized, including dynamic characteristic optimization design, adaptability to complex operating environments, and the robustness of control algorithms. Further research could explore the refinement of composite control strategies, the integrated application of intelligent materials, and the development of intelligent vibration damping technologies. This paper provides theoretical references for the optimization design and engineering practice of agricultural machinery suspension systems. Full article

(This article belongs to the Special Issue Mastering Vibrations: The Latest Breakthroughs in Control for Mechanical Systems)

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