Spring Damper System Research Articles

A Dual Triggering Scheme to Adaptive Fuzzy Resilient Control of Switched Nonlinear Systems Against Mixed Attacks.

A dual event-triggered adaptive fuzzy resilient control scheme for a class of switched nonlinear systems with vanishing control gains under mixed attacks is proposed in this article. The scheme proposed achieves dual triggering in the channels of sensor-to-controller and controller-to-actuator by designing two new switching dynamic event-triggering mechanisms (ETMs). An adjustable positive lower bound of interevent times for each ETM is found to preclude Zeno behavior. Meanwhile, mixed attacks, that is, deception attacks on sampled state and controller data and dual random denial-of-service attacks on sampled switching signal data, are handled by constructing event-triggered adaptive fuzzy resilient controllers of subsystems. Compared with the existing works for switched systems with only single triggering, more complex asynchronous switching caused by dual triggering and mixed attacks and subsystem switching is addressed. Further, the obstacle caused by vanishing control gains at some points is eliminated by proposing an event-triggered state-dependent switching law and introducing vanishing control gains into a switching dynamic ETM. Finally, a mass-spring-damper system and a switched RLC circuit system are applied to verify the obtained result.

Modeling and comfort analysis of arrayed air cushion mattress for pressure ulcer prevention and assisted repositioning

Assisting immobile individuals with regular repositioning to adjust pressure distribution on key prominences such as the back and buttocks is the most effective measure for preventing pressure ulcers. However, compared to active self-repositioning, passive assisted repositioning results in distinct variations in force distribution on different body parts. This incongruity can affect the comfort of repositioning and potentially lead to a risk of secondary injury, for certain trauma or critically ill patients. Therefore, it is of considerable practical importance to study the passive turning comfort and the optimal turning strategy. Initially, in this study, the load-bearing characteristics of various joints during passive repositioning were examined, and a wedge-shaped airbag configuration was proposed. The airbags coupled layout on the mattress was equivalently represented as a spring-damping system, with essential model parameters determined using experimental techniques. Subsequently, different assisted repositioning strategies were devised by adjusting force application positions and sequences. A human-mattress force-coupled simulation model was developed based on rigid human body structure and equivalent flexible springs. This model provided the force distribution across the primary pressure points on the human body. Finally, assisted repositioning experiments were conducted with 15 participants. The passive repositioning effectiveness and pressure redistribution was validated based on the simulation results, experimental data, and questionnaire responses. Furthermore, the mechanical factors influencing comfort during passive assisted repositioning were elucidated, providing a theoretical foundation for subsequent mattress design and optimization of repositioning strategies.

Design and Control of Upper Limb Rehabilitation Training Robot Based on a Magnetorheological Joint Damper.

In recent years, rehabilitation robots have been developed and used in rehabilitation training for patients with hemiplegia. In this paper, a rehabilitation training robot with variable damping is designed to train patients with hemiplegia to recover upper limb function. Firstly, a magnetorheological joint damper (MR joint damper) is designed for the rehabilitation training robot, and its structural design and dynamic model are tested theoretically and experimentally. Secondly, the rehabilitation robot is simplified into a spring-damping system, and the rehabilitation training controller for human movement is designed. The rehabilitation robot dynamically adjusts the excitation current according to the feedback speed and human-machine interaction torque, so that the rehabilitation robot always outputs a stable torque. The magnetorheological joint damper acts as a clutch to transmit torque safely and stably to the robot joint. Finally, the upper limb rehabilitation device is tested. The expected torque is set to 20 N, and the average value of the output expected torque during operation is 20.02 N, and the standard deviation is 0.635 N. The output torque has good stability. A fast (0.5 s) response can be achieved in response to a sudden motor speed change, and the average expected output torque is 20.38 N and the standard deviation is 0.645 N, which can still maintain the stability of the output torque.

Nonlinear vibrations of a linkage mechanism: theory and experiment

Linkage mechanisms have a wide range of applications in truck-mounted cranes, folding mechanical arms of transport vehicles and so on due to their simple and effective design. Vibration problems in the linkage mechanisms seriously affect the stability and reliability of crane machines or transport vehicles. Therefore, in this study, an effective nonlinear dynamic model of a linkage mechanism with spring-damping systems is developed and experimentally validated to explore the nonlinear vibration properties. The geometric nonlinearity of the linkage mechanism is considered and the Lagrange equation is employed to establish the nonlinear dynamic equations. Based on the harmonic balance method (HBM), the nonlinear vibration properties of the structural system are analyzed. The nonlinear primary resonance response of the linkage mechanism calculated from the HBM is compared with those of the Runge–Kutta method and the experimental result, which validates the effectiveness and accuracy of the proposed nonlinear dynamic model. The influences of some parameters, such as the spring stiffness, the lengths of connecting rods, and the installation positions of the spring-damping system, on the nonlinear vibration characteristic of the linkage mechanism are analyzed. Based on the numerical results, the folding mechanical arms or truck-mounted cranes can be conveniently designed to avoid irreparable damage to the structure caused by nonlinear primary resonance and instability phenomena, which provides new insight into the stability analysis and design of various linkage mechanisms required in engineering applications.

Modeling and Control of Two Degree of Freedom Bionic Foot

Many people are affected by conditions like stroke, spinal cord diseases, cerebral palsy, and nerve injuries, leading to impaired leg function. Bionic foot assist in maintaining stability and posture, offering vital aid to those with mobility issues for improved quality of life and rehabilitation. Consequently, the use of bionic foot has increased. Bionic foot comprising electrical and mechanical components, provide comfort and support for individuals with mobility problems. An encouraging solution is to introduce bionic foot robots to help patients having mobility problems during their recovery journey. Designed to mimic the human skeletal system, these robots offer valuable assistance in restoring the natural gait cycle of patients having mobility problems. The proposed approach introduces a bionic foot designed to support movement of human ankle joint, marking a significant advancement in rehabilitation technology. Although human ankle joint actually exhibits 3 DOF motion, we consider 2 DOF motion of human ankle joint i.e., plantarflexion and dorsiflexion and, inversion and eversion as they are dominant during normal motion of human body. We designed two systems to control the motion of human ankle joint. Firstly, we have used two actuators, one for each degree of freedom to control the motion of ankle joint. Secondly, we have used an actuator to control the plantarflexion and dorsiflexion motion and Spring-Damper system to control the inversion and eversion motion of the human ankle joint. For both systems, we derive the mathematical model and then we design the PD controller using MATLAB/Simulink. For plantarflexion and dorsiflexion motion, we give standard pattern of human ankle gait as input and for inversion and eversion motion, we provide pulsating signal as our input for both the systems. After implementation, the response of the human ankle motion was precise, accurate and smooth. The torque applied by the actuators was also in the acceptable range.

Study on the bearing characteristics of overrun hydraulic support under impact loading

In order to study the effects of stress change and adaptability of the overrun hydraulic stent under impact load, the rigid–flexible coupling numerical model of the stent is established using multi-body dynamics simulation software ADAMS. In the model, the stent is flexibilized using the HyperMesh module, and the column and jack are equivalently replaced with a spring damping system. By applying impact loads to different positions above the front roof beam of the stent, the dynamic response characteristics of the column and the articulation point are obtained at different positions with different strengths. The results show that when the impact load is applied to different positions of the front roof beam, the steady-state response force of the column shows an overall “M" distribution, and along the length direction of the roof beam, the steady-state response force of the column shows an upward trend, and the maximum steady-state response force of the column is 547 kN at point (1, 6); when the impact load is applied to both sides of the front roof beam, the response at the articulation point is greater, resulting in a higher maximum simple harmonic response at that articulation point. When the impact load acts on both sides of the front roof beam, the response of the articulation point is greater, with a maximum simple harmonic response coefficient of 0.75 and a maximum excitation response coefficient of 0.28; when the impact loads of different strengths act on the whole front roof beam, the force acting on the column and pin shaft at the articulation point will produce a large impact, reducing its adaptability. To address this, we can consider changing the top plate stress conditions using methods like high-pressure injection of water and control the gradual and slow release of the top plate stresses. The results of the study provide a reference for the structural strength design and reliability analysis of the hydraulic support, which is of practical significance and value for improving the safe mining of the coal mining face.

A Cubature Kalman Filter for parameter identification and output-feedback attitude control of liquid-propellant satellites considering fuel sloshing effects

The problem of parameter identification and output-feedback attitude stabilization is addressed for liquid-propellant satellites in the presence of fuel sloshing. The sloshing is described by a 2-degree-of-freedom pendulum. A torsional spring-damper system is utilized to model the flexibility of the diaphragm passive strategy and the fuel viscosity. By employing the control Lyapunov function methodology, a nonlinear backstepping-type state-feedback control law is constructed to stabilize the satellite and cancel the fuel sloshing. Then, to make the controller more feasible in practice, the required states of the controller, stiffnesses, and dampers are considered to be unavailable. Thus, a Cubature Kalman Filter is developed to estimate the system states and identify the fuel parameters. The state-feedback control law in conjunction with the Cubature Kalman Filter approach provides an output-feedback control law. This work owns the following two major novelties. One is identifying the stiffness and damping coefficients of the fuel and another is developing a Cubature Kalman Filter for estimating the resultant nonlinear system states. Lastly, comparative simulations verify and highlight the main results of the proposed methodology in relation to the existing methods. The findings suggest that the Cubature Kalman Filter offers potential advantages over the methods outlined in previous works, particularly in terms of reducing RMS error and improving state estimation convergence. The average reduction in RMS error for state convergence is 24 %, while the estimation process is found to be 63 % faster when compared to existing methods.

Analytical estimates for deformation behavior of fluid-filled elastomers with random microstructures

Macroscopic response of fluid filled elastomers with random microstructures, is obtained for aligned, cylindrical pores with circular cross-section. Results are derived for mono-disperse as well as poly-disperse pores, for Newtonian fluids. The obtained estimates are validated for plain strain compression loadings using numerical simulations performed in commercial multiphysics software COMSOL. Good agreement is observed between the analytical estimates and numerical solutions for different initial porosities and loading rates. Standard deviation in numerical results is seen to be high for polydisperse pores. Nonetheless, the mean response in numerical solutions matches well with analytical estimates. The obtained results can form the basis for design and fabrication of a new class of materials which have the potential to replace conventional spring–damper systems, particularly where space is limited.

An improved van der Pol wake oscillator model for a 1DOF circular cylinder undergoing vortex induced vibrations

An optimization procedure is presented for prescribing the empirical coupling parameters of a modified coupled van der Pol (VDP) wake oscillator and mass–spring–damper system for a one degree of freedom (1DOF) circular cylinder system undergoing vortex induced vibrations (VIV). This approach allows for the generalization of the traditional VDP model to cover a large VIV parameter range. The procedure is developed using experimental data covering the parameter space: 3<U∗<11, 8<m∗<20, 0.003<ζ<0.063, ReD=4000. The VDP model contains empirical coupling coefficients that describe the regime specific dynamic damping, ϵ, and wake coupling, β. Two calibration procedures are considered and the improvements over the traditional VDP model in predicting the VIV response are discussed. Subsequently, a regression fit is used to prescribe the two empirical coupling coefficients as functions of m∗, ζ and U∗. The generalized model results in a better prediction of the VIV response in terms of identification of lock-in regimes, lock-in frequency and amplitude response over several regimes when compared to the classical models. The use of a functional representation replaces the need for using tables and reduces user input for determining regime-specific coupling coefficients.

Event-based performance guaranteed tracking control for constrained nonlinear system via adaptive dynamic programming method

An optimal tracking control problem for a class of nonlinear systems with guaranteed performance and asymmetric input constraints is discussed in this paper. The control policy is implemented by adaptive dynamic programming (ADP) algorithm under two event-based triggering mechanisms. It is often challenging to design an optimal control law due to the system deviation caused by asymmetric input constraints. First, a prescribed performance control technique is employed to guarantee the tracking errors within predetermined boundaries. Subsequently, considering the asymmetric input constraints, a discounted non-quadratic cost function is introduced. Moreover, in order to reduce controller updates, an event-triggered control law is developed for ADP algorithm. After that, to further simplify the complexity of controller design, this work is extended to a self-triggered case for relaxing the need for continuous signal monitoring by hardware devices. By employing the Lyapunov method, the uniform ultimate boundedness of all signals is proved to be guaranteed. Finally, a simulation example on a mass–spring–damper system subject to asymmetric input constraints is provided to validate the effectiveness of the proposed control scheme.

Study on the influence of pin shaft clearance on the bearing performance of the hydraulic support

The pin clearance is a significant factor affecting the bearing capacity of the hydraulic support, but the effect of the pin clearance is often neglected in the current studies. Therefore, on the basis of considering the Equal stiffness spring damping system of the column, the dynamic simulation model of the hydraulic support without clearance was constructed to study the static bearing capacity of the hydraulic support. Moreover, as per the contact model of the connecting pin clearance, the dynamic simulation model of the single-pin clearance hydraulic support was established. The effect of single pin clearance on the load of the front and rear columns of the hydraulic support and the transmission force at key bearing points was analyzed. Meanwhile, the influence of single pin clearance at different positions on the bearing capacity of the hydraulic support was compared. Through the design of orthogonal test, the change of the transmission force of the bearing points under the coupling of multi-pin clearance was studied.

Design of proportional integral observer‐based resilient control for periodic piecewise time‐varying systems: The finite‐time case

AbstractThe prime intent of this study is to scrutinize the state estimation and finite‐time (FT) stabilization problems for a class of periodic piecewise time‐varying systems (PPTVSs) in the presence of external disturbances, immeasurable states and gain fluctuations by dint of resilient control. Moreover, the proportional integral observer system is built in line with the output of the PPTVSs to reconstruct the states of the PPTVSs, since the state dynamics of the system are often not measurable. Meanwhile, the output signals are quantized with the use of a logarithmic quantizer prior to being fed into the constructed observer systems. Further, the fluctuations in the controller and observer gain matrices are considered to occur in a random manner and they pursue the pattern of a Bernoulli distributed white sequence. Subsequently, by means of Lyapunov stability theory and the matrix polynomial lemma, the adequate requirements for ascertaining the FT boundedness and IO‐FT stabilization of the addressed system are procured in the context of linear matrix inequalities. Thereupon, on the premise of the established criteria, the gain matrices of the controller and observer are obtained. Ultimately, the simulation results have been showcased including the mass spring damper system to exemplify the efficacy and usefulness of the theoretical conclusions drawn.

Deep learning-based soil compaction monitoring: A proof-of-concept study

The dynamic behavior of the vibratory drum of a soil compactor for earthworks is known to be affected by soil stiffness. Real-time monitoring techniques measuring the acceleration of vibratory drums have been widely used for soil compaction quality control; however, their accuracy can be affected by soil type and conditions. To resolve this problem, a novel deep learning-based technique is developed. The method allows the regression estimation of soil stiffness from vibration drum acceleration responses. By expanding the range of applicability and improving accuracy, the proposed method provides a more reliable and robust approach to evaluate soil compaction quality. To train the estimation model, numerous datasets of noise-free waveform data are numerically generated by solving the equations of motion of the mass–spring–damper system of a vibratory roller. To validate the effectiveness of the proposed technique, a field experiment is conducted. A good correlation between the estimated and measured values is demonstrated by the experimental results. The correlation coefficient is 0.790, indicating the high potential of the proposed method as a new real-time monitoring technique for soil compaction quality.

Composite fault reconstruction and fault-tolerant control design for cyber-physical systems: An interval type-2 fuzzy approach

This article scrutinizes the stabilization and fault reconstruction issues for interval type-2 fuzzy-based cyber–physical systems with actuator faults, deception attacks and external disturbances. The primary objective of this research is to formulate the learning observer system with the interval type-2 fuzzy technique that reconstructs the actuator faults as well as the immeasurable states of the addressed fuzzy based model. Further, the information of reconstructed actuator faults is incorporated in the developed controller with the imperfect premise variables for ensuring the stabilization of the system under consideration. At the same time, the H∞ technique is employed to reduce the impact of external disturbances in the considered model. In addition to that, the deception attacks are represented as a stochastic variable that satisfies the Bernoulli distributions. On the ground of this, a set of sufficient criteria is deduced in the context of linear matrix inequalities to affirm the stability of the addressed systems. Furthermore, the requisite gain matrices are computed by resolving the obtained linear matrix inequality based stability criteria. At last, two simulation examples, including the mass–spring–damper system are exhibited to demonstrate the usefulness of analytical findings of the developed strategy.

Shock Isolation of Light Vehicle Suspension by Modified Eye Leaf Spring

Background: Rickshaws are a popular and inexpensive mode of transportation in Bangladesh for short-distance travel. However, the eye leaf spring in a typical rickshaw suspension system does not provide adequate shock isolation. The coil spring-damper suspension system is more effective, but is costly and not affordable for most manufacturers. Thus, the goal is to modify the eye leaf spring to be inexpensive but a safe and comfortable suspension. Aim: The study aimed to modify the material and structure of the leaf spring to limit the stiffness and the shock energy within a certain range suitable for the rickshaw’s suspension. The focus of the study was on modifying the spring structure, which could be cost-effective. Methods: In this study, flexible bolted joints and EVA sheets have been used to change the spring structure. The study compared the performance of the modified spring with the typical eye leaf spring. Results: The modified eye leaf spring provided improved shock isolation and a more comfortable ride compared to the typical eye leaf spring. The changes made to the spring, such as the use of flexible bolted joints and EVA sheets, limited the stiffness and shock energy within a certain range suitable for the rickshaw’s suspension. The modified spring was also found to be cost-effective. Conclusion: The study has demonstrated the feasibility of using a modified eye leaf spring for light vehicle suspensions, specifically for rickshaws. The modifications made to the spring structure, such as using flexible bolted joints and EVA sheets, provided improved shock isolation, a more comfortable ride, and cost-effectiveness. The modified spring offers an inexpensive solution for manufacturers to produce rickshaws with a safer and more comfortable suspension system.

Scattering of Long Waves by Freely Oscillating Submerged Plates

Abstract We consider a horizontal, submerged plate in shallow water that is allowed to oscillate in the vertical direction due to the wave loads. The plate is attached to a linear spring and damper to control the oscillations. The focus of the study is on the transformation of the wave field by the submerged oscillating plate. To estimate energy scattering, wave reflection and transmission coefficients are determined from four wave gauges: two placed upwave and two placed downwave of the oscillating plate. The flow is governed by the nonlinear level I Green–Naghdi (GN) equations, coupled with the equations of the vertical oscillations of the plate. Time series of water surface elevation recorded at gauges upwave and downwave of the plate obtained by the GN model are compared with the available laboratory experiments and other data, and very good agreement is observed. Wave reflection and transmission coefficients are then determined for a range of involved parameters, including wave conditions (wavelength and wave height), initial submergence depth of the plate, plate length, and the spring-damper system attached to the plate. It is found that a submerged oscillating plate can have a remarkable effect on the wave field and that nonlinearity plays an important role in this wave–structure interaction problem. Discussion is provided on how the wave reflection and transmission coefficients vary with the wave conditions, plate characteristics, initial submergence depth, and spring-damper system properties.

Machine learning-assisted wearable triboelectric-electromagnetic vibration sensor for monitoring human rehabilitation training

Wearable vibration sensors for human motion monitoring are beneficial for doctors to observe the process of patient rehabilitation diagnosis and treatment in real-time. However, realizing smart sensing and self-powering of wearable devices is still challenging. Herein we developed a portable and reproducible triboelectric-electromagnetic vibration sensor (TE-VS) composed of a rolling-type triboelectric nanogenerator (R-TENG) and a slider-type electromagnetic generator (S-EMG), which aims to achieve highly sensitive detection and rapid identification of human motion. The ingenious mechanical design of the TE-VS enables the R-TENG component to adopt tangential contact friction and the S-EMG component to mutually move between magnets and coils in a non-contact way, which greatly improves the capture efficiency of weak motion, reduces material wear and increases the service life of the device. Multi-channel self-powered sensing signals fusion in a miniaturized space aims to enhance the algorithms detection accuracy of TE-VS. Importantly, the spring damping system improves the device's response speed to external vibrations and reduces the impact of shocks, which contributes to improving operation stability. The output responses of different frequency responses and different accelerations were characterized, which validated the potential of TE-VS in gesture recognition and limb disorder detection. Additionally, TE-VS was also demonstrated as a powerful vibration energy harvester to fully charge a μF-level commercial capacitor in a short time. The proposed TE-VS realizes battery-free operation, solves the long-term power supply problem of wearable devices, and facilitates the real-time monitoring application of human rehabilitation exercises. This is definitely a promising application for human rehabilitation medical devices.

Development of Empirical Model for Electromagnetic Damping Coefficient Damper

The significance of the electromagnetic damper in vibration systems has attracted considerable interest from researchers, making it a prominent area of research. Various papers have been consulted to explore the vibration concept associated with electromagnetic dampers and their practical applications. A vibration test rig with a simple electromagnetic damper has been designed and tested to investigate the effect of electromagnetic force. An experimental study on the response of the electromagnetic damper was conducted. A logarithmic decrement method was deployed to find the damping coefficient, c, of a one-degree freedom system (mass spring damper system). A test rig and electromagnetic damper element were introduced as a damper in the system. Design factors included the type of geometry, type of material and the current supply to the system. The testing was conducted using the in-house developed vibration test rig. The data obtained from the experiment has been analysed to determine the electromagnetic damping performance. A factorial analysis was performed to identify the significant factors influencing the damping coefficient of the system. Two empirical models obtained through regression analysis of Excel and Minitab. It was found that the influential effects for the response are the type of material (aluminum), slotted geometry and a bigger amount of current (3 A). The application of a cylindrical conductor and magnet as a damper reduced the vibration response of spring mass damper.

Design and Optimization of a Permanent Magnet-Based Spring–Damper System

This paper reports the design and optimization of a permanent magnet-based spring. The aim of the optimization, performed using a particular form of the self-organizing map (SOM) algorithm, was to determine the dimensions of a ring PM-based spring with a force–displacement curve similar to a desired one. For each step in the optimization process, a spring composed of different ring-shaped magnets was analyzed using a semi-analytical model. Its characteristic was compared with the desired one to search for a minimum cost function obtained by subtracting the evaluated and the desired force–displacement curve. The resulting algorithm was efficient in the design of a spring with a desired characteristic. The geometry obtained was used to study an electrodynamic damper based on the exploitation of the interaction between the moving magnet of the spring and a conductive cylinder. A parametric analysis was performed: the damping effect grows when the cylinder thickness increases and decreases with the gap between the cylinder and the magnets. Also, the cylinder thickness needed to reduce to one the number of overshoots in the moving magnet’s position decreases with the gap increase. Computations were performed using the research code EN4EM (Electric Network 4 ElectroMagnetics) developed by the authors.

Passive Isolator Design and Vibration Damping of EO/IR Gimbal Used in UAVs

One of the most critical factors affecting the quality of the images captured by the surveillance systems used in the unmanned aerial vehicles is the vibrations transmitted from the aircraft to the gimbal. The gimbal used in unmanned aerial vehicles is essential equipment, holding the camera steadily and accurately and pointing it in the desired direction. Within the scope of this article, a passive vibration isolation system design has been made for the two-axis electro-optical gimbal used in the mini unmanned aerial vehicle. By choosing the spring-damper system among different methods, the design that isolates the harmonic vibration from the platform on a single axis has been made using the analytical method. The analytical method was used to create a design that isolates the harmonic vibration from the platform along a single axis. In addition, the part named 'Pan Yoke', which contains this damper system, was designed with a computer-aided design program, and natural frequency values were checked with Ansys modal analysis. The frequency of the vibration transmitted from the air vehicle to the gimbal and the natural frequency of the designed part have been determined to be close to each other, at around 200 Hz. The natural frequency values of this part were optimised with various design changes and topology optimisations to prevent the part from resonating.