Search Results (945)

This study presents a qualitative analysis of the fractional coupled nonlinear Schrödinger equation (FCNSE) to obtain its complete set of solutions. An appropriate wave transformation is applied to reduce the FCNSE to a fourth-order dynamical system. Due to its non-Hamiltonian nature, this system poses significant analytical challenges. To overcome this complexity, the dynamical behavior is examined within a specific phase–space subspace, where the system simplifies to a two-dimensional, single-degree-of-freedom Hamiltonian system. The qualitative theory of planar dynamical systems is then employed to characterize the corresponding phase portraits. Bifurcation analysis identifies the physical parameter conditions that give rise to super-periodic, periodic, and solitary wave solutions. These solutions are derived analytically and illustrated graphically to highlight the influence of the fractional derivative order on their spatial and temporal evolution. Furthermore, when an external generalized periodic force is introduced, the model exhibits quasi-periodic behavior followed by chaotic dynamics. Both configurations are depicted through 3D and 2D phase portraits in addition to the time-series graphs. The presence of chaos is quantitatively verified by calculating the Lyapunov exponents. Numerical simulations demonstrate that the system’s behavior is highly sensitive to variations in the frequency and amplitude of the external force. Full article

Environmental vibrations may affect the functional use of engineering structures and even lead to disastrous consequences. Vibration suppression and energy harvesting based on Nonlinear Energy Sink (NES) and the piezoelectric effect have gained significant attention in recent years. The harvested electrical energy can supply power to the structural health monitoring sensor device. In this work, the electromechanical-coupled governing equations of the primary structure coupled with the series-connected 2-degree-of-freedom NES (2-DOF NES) integrated by a piezoelectric energy harvester are derived. The absorption and dissipation performances of the system under varying transient excitation intensities are investigated. Additionally, the targeted energy transfer mechanism between the primary structure and the two NESs oscillators is investigated using the wavelet analysis. The reduced slow flow of the dynamical system is explored through the complex-variable averaging method, and the primary factors for triggering the target energy transfer phenomenon are revealed. Furthermore, a comparison is made between the vibration suppression performance of the single-degree-of-freedom NES (S-DOF NES) system and the 2-DOF NES system as a function of external excitation velocity. The results indicate that the vibration suppression performance of the first-level NES (NES1) oscillator is first stimulated. As the external excitation intensity gradually increases, the vibration suppression performance of the second-level NES (NES2) oscillator is also triggered. The 1:1:1, high-frequency, and low-frequency transient resonance captures are observed between the primary structure and NES1 and NES2 oscillators over a wide frequency range. The 2-DOF NES demonstrates superior efficiency in suppressing vibrations of the primary structure and exhibits enhanced robustness to varying external excitation intensities. This provides a new strategy for structural vibration suppression and online power supply for health monitoring devices. Full article

This research is based on the acoustic package design of new energy vehicles, investigating the application of the hybrid Finite Element–Statistical Energy Analysis (FE-SEA) model in predicting the high-frequency dynamic response of automotive structures, with a focus on the modeling and correction methods for hybrid point connections. New energy vehicles face unique acoustic challenges due to the special nature of their power systems and operating conditions, such as high-frequency noise from electric motors and electronic devices, wind noise, and road noise at low speeds, which directly affect the vehicle’s ride comfort. Therefore, optimizing the acoustic package design of new energy vehicles to reduce in-cabin noise and improve acoustic quality is an important issue in automotive engineering. In this context, this study proposes an improved point connection correction factor by optimizing the division range of the decision circle. The factor corrects the dynamic stiffness of point connections based on wave characteristics, aiming to improve the analysis accuracy of the hybrid FE-SEA model and enhance its ability to model boundary effects. Simulation results show that the proposed method can effectively improve the model’s analysis accuracy, reduce the degrees of freedom in analysis, and increase efficiency, providing important theoretical support and reference for the acoustic package design and NVH performance optimization of new energy vehicles. Full article

Aiming at the problems of traditional calibrated visual servo systems relying on precise model calibration and the high training cost and low efficiency of online reinforcement learning, this paper proposes a Multi-Network Mean Delayed Deep Deterministic Policy Gradient Algorithm with Behavior Cloning (MN-MD3+BC) for uncalibrated visual adaptive control of robotic arms. The algorithm improves upon the Twin Delayed Deep Deterministic Policy Gradient (TD3) network framework by adopting an architecture with one actor network and three critic networks, along with corresponding target networks. By constructing a multi-critic network integration mechanism, the mean output of the networks is used as the final Q-value estimate, effectively reducing the estimation bias of a single critic network. Meanwhile, a behavior cloning regularization term is introduced to address the common distribution shift problem in offline reinforcement learning. Furthermore, to obtain a high-quality dataset, an innovative data recombination-driven dataset creation method is proposed, which reduces training costs and avoids the risks of real-world exploration. The trained policy network is embedded into the actual system as an adaptive controller, driving the robotic arm to gradually approach the target position through closed-loop control. The algorithm is applied to uncalibrated multi-degree-of-freedom robotic arm visual servo tasks, providing an adaptive and low-dependency solution for dynamic and complex scenarios. MATLAB simulations and experiments on the WPR1 platform demonstrate that, compared to traditional Jacobian matrix-based model-free methods, the proposed approach exhibits advantages in tracking accuracy, error convergence speed, and system stability. Full article

The accurate estimation of parameters in dynamical systems stands for an open key research issue in modeling, control, and fault diagnosis. The presence of noise in input and output signals poses a serious challenge for accurate real-time dynamical system parameter estimation. This paper proposes a new robust algebraic parameter estimation methodology for integer-order dynamical systems that explicitly incorporates the signal filtering dynamics within the estimator structure and enhances noise attenuation through fractional differentiation in frequency domain. The introduced estimation methodology is valid for Liouville-type fractional derivatives and can be applied to estimate online the parameters of differentially flat, oscillating or vibrating systems of multiple degrees of freedom. The parametric estimation can be thus implemented for a wide class of oscillating or vibrating, nth-order dynamical systems under noise influence in measurement and control signals. Positive values are considered for the inertia, stiffness, and viscous damping parameters of vibrating systems. Parameter identification can be also used for development of actuators and control technology. In this sense, validation of the algebraic parameter estimation is performed to identify parameters of a differentially flat, permanent-magnet direct-current motor actuator. Parameter estimation for both open-loop and closed-loop control scenarios using experimental data is examined. Experimental results demonstrate that the new parameter estimation methodology combining signal filtering dynamics and fractional calculus outperforms other conventional methods under presence of significant noise in measurements. Full article

This paper addresses the trajectory tracking control problem of Autonomous Underwater Vehicles (AUVs). A comprehensive mathematical model is first established based on Newtonian mechanics, incorporating both kinematic and dynamic equations. By reasonably neglecting the minor influence of roll motion, a five-degree-of-freedom (5-DOF) underactuated AUV model is derived. Considering the strong nonlinearities, high coupling, and time-varying hydrodynamic parameters typical of underwater environments, a fuzzy adaptive PID controller is proposed. This controller combines the adaptability of fuzzy logic with the structural simplicity and reliability of PID control, making it well-suited to the demanding requirements of AUV motion control. Extensive simulation experiments are conducted to evaluate the controller’s performance under various operating conditions. The results show that the fuzzy adaptive PID controller significantly outperforms conventional PID and standalone fuzzy logic controllers in terms of convergence speed and oscillation suppression. Furthermore, a theoretical stability analysis is provided to ensure that the proposed control system remains stable under time-varying fuzzy gain scheduling, confirming its effectiveness and potential for practical application in underwater vehicle control. Full article

This paper addresses the path tracking problem of underactuated unmanned surface vessels (USVs) in the presence of unknown external disturbances. A fixed-time adaptive integral sliding mode control (AISMC) method, incorporating a nonlinear disturbance observer (NDO), is proposed. Initially, a three-degree-of-freedom dynamic model of the USV is developed, accounting for external disturbances and model uncertainties. Based on the vessel’s longitudinal and transverse dynamic position errors, a virtual control law is designed to ensure fixed-time convergence, thereby enhancing the position error convergence speed. Next, a fixed-time NDO is introduced to estimate real-time external perturbations, such as wind, waves, and currents. The observed disturbances are fed back into the control system for compensation, thereby improving the system’s disturbance rejection capability. Furthermore, a sliding mode surface is designed using a symbolic function to address the issue of sliding mode surface parameter selection, leading to the development of the adaptive integral sliding mode control strategy. Finally, compared with traditional SMC and PID, the proposed AISMC-NDO offers higher accuracy, faster convergence, and improved robustness in complex marine environments. Full article

Brushless DC (BLDC) motors are commonly used in electric vehicles (EVs) because of their efficiency, small size and great torque-speed performance. These motors have a few benefits such as low maintenance, increased reliability and power density. Nevertheless, BLDC motors are highly nonlinear and their dynamics are very complicated, in particular, under changing load and supply conditions. The above features require the design of strong and adaptable control methods that can ensure performance over a broad spectrum of disturbances and uncertainties. In order to overcome these issues, this paper uses a Fractional-Order Proportional-Integral-Derivative (FOPID) controller that offers better control precision, better frequency response, and an extra degree of freedom in tuning by using non-integer order terms. Although it has the benefits, there are three primary drawbacks: (i) it is not real-time adaptable, (ii) it is hard to choose appropriate initial gain values, and (iii) it is sensitive to big disturbances and parameter changes. A new control framework is suggested to address these problems. First, a Reinforcement Learning (RL) approach based on Deep Deterministic Policy Gradient (DDPG) is presented to optimize the FOPID gains online so that the controller can adjust itself continuously to the variations in the system. Second, Snake Optimization (SO) algorithm is used in fine-tuning of the FOPID parameters at the initial stages to guarantee stable convergence. Lastly, cascade control structure is adopted, where FOPID controllers are used in the inner (current) and outer (speed) loops. This construction adds robustness to the system as a whole and minimizes the effect of disturbances on the performance. In addition, the cascade design also allows more coordinated and smooth control actions thus reducing stress on the power electronic switches, which reduces switching losses and the overall efficiency of the drive system. The suggested RL-enhanced cascade FOPID controller is verified by Hardware-in-the-Loop (HIL) testing, which shows better performance in the aspects of speed regulation, robustness, and adaptability to realistic conditions of operation in EV applications. Full article

With the rapid development of deep-sea resource exploration and marine scientific research, wheeled remotely operated vehicles (ROVs) have become crucial for seabed operations. However, under complex seabed conditions, traditional ROV control systems suffer from insufficient trajectory tracking accuracy, poor disturbance rejection capability, and low dynamic torque distribution efficiency. These issues lead to poor motion stability and high energy consumption on sloped terrains and soft substrates, which limits the effectiveness of deep-sea engineering. To address this, we proposed a comprehensive motion control solution for deep-sea wheeled ROVs. To improve modeling accuracy, a coupled kinematic and dynamic model was developed, together with a body-to-terrain coordinate frame transformation. Based on rigid-body kinematics, three-degree-of-freedom kinematic equations incorporating the slip ratio and sideslip angle were derived. By integrating hydrodynamic effects, seabed reaction forces, the Janosi soil model, and the impact of subsidence depth, a dynamic model that reflects nonlinear wheel–seabed interactions was established. For optimizing disturbance rejection and trajectory tracking, a hierarchical control method was designed. At the kinematic level, an improved model predictive control framework with terminal constraints and quadratic programming was adopted. At the dynamic level, non-singular fast terminal sliding mode control combined with a fixed-time nonlinear observer enabled rapid disturbance estimation. Additionally, a dynamic torque distribution algorithm enhanced traction performance and trajectory tracking accuracy. Full article

This paper presents the design, implementation, and experimental results of a six-degree-of-freedom Delta-type parallel manipulator, in which all actuators were realized using proprietary pneumatic muscles. The objective of the study was to evaluate the suitability of this type of actuator for applications in parallel robotics, with particular attention to their dynamic properties, nonlinearities, and potential limitations. In the first part of the article, the details of the manipulator’s construction and the kinematic model, covering both the forward and inverse kinematics, are presented. The control system was based on antagonistic pairs of pneumatic muscles forming servo drives responsible for the motion of individual arms. The experimental investigations were focused on analyzing trajectory-tracking accuracy and positioning repeatability, both in unloaded conditions and under additional payload applied to the end-effector. The results indicate that positioning errors for simple trajectories were generally below 1 mm, whereas for complex trajectories and under load, they increased, particularly during changes in motion direction, which can be attributed to friction and hysteresis phenomena in the muscles. Repeatability tests confirmed the ability of the manipulator to repeatedly reach the desired positions with small deviations. The analysis carried out confirms that pneumatic muscles can be effectively applied to drive parallel manipulators, offering advantageous features such as high power density and low mass. At the same time, the need for further research on nonlinearity compensation and durability enhancement was demonstrated. Full article

This study presents a comprehensive dynamic analysis of mechanical systems incorporating elastic joints and introduces an adaptive vibration actuator with an integrated transmission variator. The system’s behavior is modeled through kinematic and dynamic formulations, utilizing both analytical and numerical methods. The analysis reveals that the inclusion of elastic elements enables a force adaptation effect, allowing the output element to adjust dynamically to variations in external loading. Under conditions of constant input power, the output speed varies inversely with the load, ensuring reliable adaptive performance. Furthermore, the elastic joints facilitate internal force redistribution, enhancing energy efficiency and reducing mechanical losses. These findings hold relevance for applications in industrial automation and robotics, where consistent functionality under variable load conditions is essential. Full article

The increasing incorporation of renewable energy sources, such as photovoltaic and wind power, results in considerable variability and uncertainty within modern power systems, thereby complicating load frequency control. Conventional controllers, including PI and PID, often fail to provide sufficient performance in dynamic conditions. This study introduces a Two-Degree-of-Freedom PID (2DOF-PID) controller optimized through the Bee Algorithm (BA) for Load Frequency Control (LFC) in a two-area interconnected power system that includes renewable energy sources. The BA is employed to enhance controller parameters according to two objective functions: the Integral of Time-weighted Absolute Error (ITAE) and the Integral of Time-weighted Squared Error (ITSE). Simulation studies utilizing MATLAB/Simulink are conducted to evaluate the comparative effectiveness of PI, PID, and 2DOF-PID controllers. The results demonstrate that the 2DOF-PID controller consistently outperforms conventional PI and PID controllers in terms of frequency stability. The ITAE optimization of the 2DOF-PID results in a reduction in the ITAE index by more than 95% compared to PI and PID controllers, a decrease in settling time by approximately 40–60%, and a near elimination of overshoot and undershoot. Through ITSE optimization, the 2DOF-PID achieves an error reduction exceeding 90% and ensures smooth convergence with minimal oscillations. The PID controller has slightly improved effectiveness in minimizing tie-line power deviation, whereas the 2DOF-PID demonstrates greater resilience and damping capability in frequency regulation across both regions. The findings confirm that the Bee Algorithm-tuned 2DOF-PID controller serves as a robust and effective approach for frequency management in systems primarily reliant on renewable energy sources. Future research should incorporate multi-objective optimization algorithms that concurrently address frequency and tie-line power variations, thereby providing a more equitable control framework for practical Automatic Generation Control (AGC) operations. Full article

In this paper, the vibration of a wheel running on a light rail equipped with rail dampers that use a mixed damping system (rubber–oil) is investigated under the excitation of random roughness on the rolling surfaces, to demonstrate the influence of such rail dampers on the dynamic behaviour at the wheel–rail interface. For this purpose, a model is adopted in which a rigid wheel moves at constant speed over a rail modelled as an infinite Timoshenko beam, supported by elastic foundations with an internal degree of freedom that represents the behaviour of the rail pads, sleepers, and ballast. The rail dampers are represented as two-mass oscillators, while the internal friction in the elastic components of the wheel–rail system is modelled using hysteretic damping. To obtain the time series of the rail and wheel displacements, as well as the wheel–rail contact force, the convolution theorem is applied in a heuristic manner, making use of the relationship between Green’s functions in the time and frequency domains through direct and inverse Fourier transforms. The results show that (a) rail dampers primarily affect rail dynamics and the wheel–rail contact force over a relatively wide frequency range, while having little influence on wheel motion; (b) rail dampers are highly effective in reducing rail vibration and the wheel–rail contact force when the rail pads are stiff, but considerably less effective when soft rail pads are used; and (c) they may slightly amplify the contact force at the lower edge of their effective frequency range. Full article

Robust control techniques are crucial for deploying robotic solutions in real applications and handling model uncertainties in robotic manipulators. The inertial parameters are fundamental to implementing control algorithms. While theoretical approaches to compute the system dynamics and the regressor matrix are well-established, they are computationally expensive and a practical implementation framework is still lacking. To address this challenge, we developed a new and efficient method to compute the Coriolis matrix based on Christoffel’s symbols. The result forms the basis of Thunder Dynamics, an open-source software package able to create standalone libraries that compute the system kinematics and dynamics for real-time adaptive control implementation. Thunder Dynamics enables users to create and compile user-defined functions on a robot, which can then be used in C++ or Python 3. To test the proposed framework, we implemented a Cartesian adaptive backstepping controller with axis-angle orientation using our tool. We tested the controller on a seven-degrees-of-freedom manipulator in both simulation and real-world scenarios, varying the levels of uncertainties in the inertial parameters. The results demonstrated that Thunder Dynamics is capable of meeting computational constraints given by the control loop frequency of real systems, permitting, for example, the implementation of advanced controls on commercial manipulators. Full article

The rapid expansion of urban rail transit networks has raised concerns about metro-induced vibrations in over-track structures. Floor vibration isolation systems provide an adaptable and efficient mitigation strategy, offering flexibility in architectural design while enhancing vibration comfort. This study investigates the dynamic characteristics and parameter optimization of such systems under multi-point excitations. A four-degree-of-freedom (4-DOF) model is developed to analyze the dynamic behavior of the isolation floor system, revealing that the height difference between the horizontal bearing installation plane and the centroid of the isolation plate critically induces “translation–rotation” coupling. Theoretical stability analysis and finite element simulations are employed to evaluate the effects of key parameters, including the isolation plate length, number of bearings, bearing arrangement, isolation frequency, and damping ratio. The results demonstrate that increasing the number of bearings reduces floor acceleration and displacement while improving response uniformity. The optimal isolation frequency range is identified as 3–5 Hz, balancing both isolation efficacy and uniformity. Additionally, increasing the bearing damping ratio to 0.05–0.1 can comprehensively mitigate vibration responses and improve vibration uniformity. Sensitivity analysis confirms that these optimal parameters exhibit strong robustness against ±20% practical deviations, ensuring reliable performance in engineering applications. These findings provide theoretical and practical guidance for optimizing floor isolation systems in over-track buildings, contributing to the sustainable development of urban rail transit networks. Full article