Nonlinear Dynamic Model Research Articles

Modeling and anti-sway control method for vertical lift-up/lay-down process of slender-beam payload

The existing crane control methods mainly aim at suppressing the oscillation of the payloads during the transportation process. However, during the vertical lift-up/lay-down process of the slender-beam payload (SBP), such as the installation of the wind turbine towers, rocket assembly, and pipeline laying, one end of the SBP is lifted up and the other end is in contact with the ground. In this situation, the external disturbance may cause the SBP to sway around the contact point. In this paper, a nonlinear three-dimensional dynamic model for the vertical lift-up/lay-down process of the SBP is established. On this basis, a control method for suppressing oscillation during the lift-up/lay-down process of the SBP is proposed by adopting the non-singular terminal sliding mode control (NTSMC). The stability of the NTSMC is proved based on the Lyapunov method. Simulations and experiments are carried out to verify the effectiveness of the proposed method.

Modeling and simulation of magnetostrictive actuators based on ΔE effect Preisach model

Based on the classical Preisach model, combined with the magneto-mechanical coupling effect of Giant magnetostrictive materials (GMM), this paper introduces the Everett function to optimize the classical Preisach hysteresis model and improve its accuracy. By importing dynamic parameters, the dynamic Preisach hysteresis model is established. Combined with the constitutive model of GMM, a dynamic Preisach hysteretic nonlinear magnetostrictive actuator model based on the ΔE effect is established. Then, the finite element simulation is carried out by Comsol software and compared with the theoretical model simulation. The results show that the error between the magnetostrictive strain of the established hysteresis model and the finite element simulation results is less than 100 ppm, which verifies the accuracy of the proposed model. Finally, the curves of magnetic field intensity, magnetic induction intensity, magnetization, magnetostrictive strain and ΔE effect of GMA are obtained by using this model.

Nonlinear spreading behavior across multi-platform social media universe.

Understanding how harmful content (mis/disinformation, hate, etc.) manages to spread among online communities within and across social media platforms represents an urgent societal challenge. We develop a non-linear dynamical model for such viral spreading, which accounts for the fact that online communities dynamically interconnect across multiple social media platforms. Our mean-field theory (Effective Medium Theory) compares well to detailed numerical simulations and provides a specific analytic condition for the onset of outbreaks (i.e., system-wide spreading). Even if the infection rate is significantly lower than the recovery rate, it predicts system-wide spreading if online communities create links between them at high rates and the loss of such links (e.g., due to moderator pressure) is low. Policymakers should, therefore, account for these multi-community dynamics when shaping policies against system-wide spreading.

Distributed Adaptive Tracking Control of Hidden Leader-Follower Multi-Agent Systems with Unknown Parameters

The distributed leader-follower control of multi-agent systems is discussed. Each agent is expressed in a discrete-time and non-linear dynamic model with an unknown parameter and can be affected by its neighbors’ history information. For each agent, to identify the parameter, one switching set of the parameter estimates is constructed and the optimal parameter estimate is chosen based on the index switching function. Using the given desired reference signal, the leader agent’s control law is designed, and relying on the neighbors’ history information, each follower agent’s local control law is designed. With the designed distributed tracking adaptive control laws, the whole system tracks the given desired reference signal, and in the face of strong couplings the closed-loop system ultimately reaches an agreement. Finally, by comparing simulations of the control strategy with a normal projection algorithm, the results indicate that the adaptive control method with a switching set of the parameter estimates is effective in improving the control performance.

Experiment and optimum of the asphalt paver’s parameters to ameliorate the working performance

In this paper, the experimental study of the asphalt paver is performed to assess the effect of the vibrational screed system’s operating parameters on the asphalt paver’s working performance. Then, the nonlinear dynamic models of the vibrational screed system and tamper system are built to assess in detail the effect of the working parameters of the vibrational screed system and optimise its working parameters to ameliorate the asphalt paver’s working performance. Both the vertical acceleration and angular acceleration of the vibrational screed system computed via their Root Mean Square ( RMS a) value have been selected as the evaluation indexes. Results showed that the acceleration at the measured points has been unevenly distributed on the vibrational screed system’s length, thus, the working performance of the asphalt paver is quite low. With the vibrational screed system’s working parameters optimised, the average value of RMS a with optimisation is increased by 7.67% whereas the average deviation of RMS a between the measurement points with optimisation is greatly reduced by 34.2% in comparison without optimisation. Consequently, the working performance of the asphalt paver has obviously ameliorated.

Research on the Simulation Method for Equivalent Stiffness of Bolted Connection Thin Plate Structures

Bolted connections are widely used in assembly structures, and their dynamic characteristics are often affected by stiffness, damping, excitation, and other factors. In order to solve the problems of low computational efficiency of fine modeling and large computational error of linearized equivalent modeling of bolted structures, this paper proposes a dynamic characteristic parameter identification method for bolted structures based on the multiscale method and considering the influence of nonlinear factors. In this method, the bolted connection characteristics are simulated in the form of a combination of shear stiffness, torsional stiffness, nonlinear stiffness, and viscous damping coefficient and identified according to the test measurement frequency and frequency response function. At the same time, by establishing the nonlinear dynamic model of bolted structure, the influence of different bolt preloads and excitation forces on the dynamic characteristics of bolted structure is studied.

An LMI-based robust state-feedback controller design for the position control of a knee rehabilitation exoskeleton robot: Comparative analysis

Rehabilitation exoskeleton robots play a crucial role in restoring functional lower limb movements for individuals with locomotor disorders. Numerous research studies have concentrated on adapting the control of these rehabilitation robotic systems. In this study, we investigate an affine state-feedback control law for robust position control of a knee exoskeleton robot, taking into account its nonlinear dynamic model that includes solid and viscous frictions. To ensure robust stabilization, we employ the Lyapunov approach and propose three methods to establish stability conditions using the Schur complement, the Young inequality, the matrix inversion lemma, and the S-procedure lemma. These conditions are formulated as Linear Matrix Inequalities (LMIs). Furthermore, we conduct a comprehensive comparison among these methods to determine the most efficient approach. At the end of this work, we present simulation results to validate the developed LMI conditions and demonstrate the effectiveness of the adopted control law in achieving robust position control of the knee exoskeleton robot.

Nonlinear dynamic modelling and analysis of a rotating composite thin-walled beam considering ice coating

For rotating structures operating in severe weather conditions, ice coating phenomenon is an established issue that impairs the reliability and effectiveness of the structures by changing the dynamic behaviors. To explore the influence mechanisms of ice coating on the dynamic behaviors of rotating structures, this work presents an analytical dynamic model for nonlinear forced vibration of a composite thin-walled beam under both rotating and ice coating conditions. The ice coating is considered as C-shaped configuration which can affect the system parameters of the beam, especially aerodynamic performance. With effect of out-of-plane warping taken into account, the nonlinear dynamic equation of the beam is established using Hamilton's principle. The Galerkin discrete method together with the incremental harmonic balance method (IHB) as well as pseudo arclength continuation technique are adopted to obtain the periodic response of the nonlinear system. Then, a detailed parametric study on natural frequency, frequency-response and bifurcation behaviors is numerically conducted. Special attention is paid to the effects of ice coating, rotating angular velocity, inflow velocity and design parameters on the linear and nonlinear dynamic behaviors of the beam. Results reveal a prominent change in natural frequency, vibration amplitude and cusp bifurcation of multivalued region under the combined effects of ice coating and rotating motion. Such ice-induced changes exhibit the requirement of vibration control and optimization design consideration for rotating structures operating in icing coating conditions.

Theoretical modeling and dynamics analysis of a rotating piezoelectric laminated beam with different setting angles

Dynamics modeling and analysis of a rotating piezoelectric laminated beam (RPLB) considering the effect of the setting angle is presented in this paper. The rotating piezoelectric energy harvester can be simplified as a RPLB which is fixed at a rotating hub. It is easy to know that a steady transversal deformation would be produced due to the transversal component of centrifugal force when the beam is not along the radial direction (the setting angle is not equal to 0° or 180°). However, the variation of steady transversal deformation and its effect were rarely considered by existing theoretical models about the rotating harvesters. To this end, a novel nonlinear dynamics model of the RPLB is developed by the combination of floating frame reference (FFR) and absolute nodal coordinate formulation. In the model, the position coordinates and gradients on the FFR are used as the nodal coordinates to describe deformation field. The enthalpy, elastic and kinetic energies of the RPLB are derived with consideration of the piezoelectric constitutive equation and the rotation of the FFR. Thus, the dynamics equations of the RPLB can be developed by using the Lagrange's equations of second kind. The results obtained from the model show agreement with those obtained from the previous literatures, which verifies the correctness of the model. Several examples are presented to analyze the effects of rotating speed, setting angle and tip mass on steady transversal deformation, output voltage and modal characteristics.

A comprehensive misalignment-rub-impact nonlinear dynamic spindle model considering contact angle and fit clearance under EHL

A comprehensive misalignment-rub-impact nonlinear dynamic spindle model considering contact angle and fit clearance under EHL

Modelling, analysis and validation of a dynamic dense medium separation circuit model for detecting medium losses

Dense medium separation circuits use a dense medium to separate low density waste material from high density valuable minerals. Since the dense medium is an expensive consumable, it is recovered after separation of the valuable minerals from waste. A dynamic nonlinear model of a dense medium separation circuit of an iron ore plant in South Africa is developed to track the flow of medium in the circuit. An extended Kalman filter is designed for estimating observable but unmeasured states. The model is validated using online plant data. This paper serves as a precursor for further work to detect and mitigate expensive medium losses in the circuit.

Study on dynamic performance of high-speed railway vehicle using roller rig and numerical simulation

The development of high-speed trains has increased the demand for dynamic vehicle tests on roller rigs. This study presents a nonlinear multi-body dynamic model of a vehicle system running on a roller rig and an actual track. Dynamic tests for a high-speed vehicle were performed using a full-scale roller rig to validate the numerical model. The hunting stability characteristics of the vehicle were investigated by performing a comparative analysis of the roller rig tests and numerical simulations of the vehicle on roller rigs and tracks. The results indicate that the critical hunting speed of the vehicle on a roller rig is lower than that on a track, particularly under significantly high or low equivalent conicity and yaw damper failure conditions. The characteristics of the hunting stability, riding performance, and lateral acceleration of the bogie frame were comparable in both rig tests and line operations, exhibiting consistent trends under the normal operation of the suspension system with the wheel/rail matches existing within the ideal range of equivalent conicity. However, the lateral acceleration or lateral Sperling index of the carbody could better detect the carbody hunting under low equivalent conicities, particularly when the lateral acceleration of the bogie was not sufficiently effective.

Stationary dimpled drops under linear flow

The axially symmetric deformation of a drop in a viscous fluid, under the influence of an externally imposed flow having simultaneous rotating and compressional or extensional components, is addressed. In the previous studies, two families of stationary drop shapes were constructed by simulating the dynamics of drop deformation: stable singly connected shapes with respect to axisymmetric disturbances, and unstable toroidal shapes. These two branches coexist at the same flow conditions, but were not connected. In this study, we obtain a new family of branches of unstable highly deformed stationary drops connecting with the stable flattened shapes and the toroidal ones. We use a method based on classical control theory. The controller is designed for a two-state dynamic model of the system and is employed on a high-order nonlinear dynamic model of the drop deformation. Through this feedback-control-centred approach, an extended collection of unstable stationary solutions is constructed, which spans the range from the loss of stability to the dimpled shapes almost collapsed at the centre. In the latter region, which was never obtained in previous studies, a multiplicity of solutions is identified.

Nonlinear Dynamical Modeling and Free Vibration of Functionally Graded Cylindrical Shell in Air-gap Magnetic and Thermal Fields

Nonlinear dynamical modeling and free vibration of ferromagnetic functionally graded (FG) cylindrical shell in air-gap magnetic and thermal fields are investigated in this work. The shell is surrounded by an armature, and the air-gap layer generated by physical isolation exists between the two structures. The air-gap magnetic field in this space is generated by the armature, which induces the nonlinear magnetization of ferromagnetic materials. The nonlinear heat conduction characteristics along the shell thickness are considered. Under the theory framework for dual-nonlinear magneto-thermal effect, the magneto-thermoelastic dynamical model is established using Hamilton principle. The discrete governing equations and the natural frequency expression separately are derived by Galerkin and Krylov-Bogoliubov-Mitropolski (KBM) methods. Subsequently, the natural frequency characteristics under different parameter conditions are systematically analyzed. The results indicate that magnetic potential, initial air-gap thickness, and volume fraction index have a significant impact on natural frequencies. Temperature has a complex effect on natural frequencies corresponding to different circumferential wave numbers.

Roll stability of all-terrain forklift trucks considering different road types

All-terrain forklift trucks often work on complex terrain such as soft and muddy terrain in the wild, making them prone to rolling and rollover. In this work, a seven-degree-of-freedom nonlinear dynamic model and a wheel-ground interaction model between resilient wheels and soft/hard road surfaces based on the structural characteristics of the articulated steering + swinging bridge of an all-terrain forklift truck are established. The mechanism of all-terrain forklift trucks’ roll instability and a simulation comparison of four types of road models (rigid, sandy, loam, and clay) are analyzed. All-terrain forklift trucks are least prone to rolling when being driven on rigid roads. On soft roads, sand brings the greatest risk of rollover, followed by loam and clay. The roll stability indexes HR-LTR and SR-LTR considering different road surfaces are proposed. The safety limit of roll stability based on the indexes is divided, and an anti-rollover control strategy based on road surface recognition is proposed. On the basis of the road surface recognition results, corresponding stability index calculation methods and actuator control algorithms are selected. Simulation and experimental results show that with the use of no control and TTR-based hierarchical control, the forklift truck yaw velocity is reduced by up to 73.31% and 63.52%, respectively, and the roll angle is reduced by up to 72.7% and 48.27%, respectively. The proposed roll stability index and anti-rollover control strategy for different road surfaces can effectively improve the roll stability of all-terrain forklift trucks when being driven on different complex road surfaces, reduce the risk of rollover, and improve the rollover stability of all-terrain forklift trucks on different complex roads, thereby improving the safety of all-terrain forklift trucks.

Dynamic Realized Minimum Variance Portfolio Models

This article introduces a dynamic minimum variance portfolio (MVP) model using nonlinear volatility dynamic models, based on high-frequency financial data. Specifically, we impose an autoregressive dynamic structure on MVP processes, which helps capture the MVP dynamics directly. To evaluate the dynamic MVP model, we estimate the inverse volatility matrix using the constrained l 1 -minimization for inverse matrix estimation (CLIME) and calculate daily realized non-normalized MVP weights. Based on the realized non-normalized MVP weight estimator, we propose the dynamic MVP model, which we call the dynamic realized minimum variance portfolio (DR-MVP) model. To estimate a large number of parameters, we employ the least absolute shrinkage and selection operator (LASSO) and predict the future MVP and establish its asymptotic properties. Using high-frequency trading data, we apply the proposed method to MVP prediction.

Using Kolmogorov Entropy to Verify the Description Completeness of Traffic Dynamics of Highly Autonomous Driving

In this paper, we outline the analysis of a fully provable traffic system based on the Kolmogorov entropy. The completeness of the traffic node dynamics is realized in the form of a nonlinear dynamical model of the participating transport objects. The goal of this study is to determine the completeness of transport nodes based on the Kolmogorov entropy of the traffic trajectories of a node with an unspecified number of actors, like cars and pedestrians. The completeness of a highly autonomous driving detection system describing a traffic node could be realized if the entropy-based error-doubling time of the trajectories of the Euler–Lagrange equation interpreted at the transport junction is less than 1.3.

Switching Converters Dynamics Considering Non-Ideality of the Error Amplifier within the Analogue Control System

The paper discusses a pulse voltage converter with a high switching frequency of a switch with an analog control system capable of providing the required conversion frequencies. The pulsed voltage converter under study has a control system with a proportional-integral regulator, implemented on the basis of a general-purpose operational amplifier. Operational amplifiers with such parameters are widely used as part of modern control microcircuits for pulse-width converters. In this work, the influence of the technological spread of the gain of the operational amplifier on the dynamics of the converter is studied. The studies were carried out both using the developed nonlinear dynamic model of the system, and using a small-signal open-loop dynamic model. A technique has been developed for selecting the parameters of the controller, taking into account the technological spread of the gain of the operational amplifier based on a nonlinear dynamic model. An analysis of the results obtained using a nonlinear dynamic model showed a significant influence of the specified spread on the dynamics of the system, even when the cutoff frequency of the open-loop control system is significantly removed from the frequency of the high-frequency pole of the operational amplifier. This must be taken into account when designing pulse voltage converters with analog control systems, namely, when choosing the parameters of regulators. It is shown that with the optimal values of the controller, selected according to the proposed method, the effect of technological gain spread on the frequency characteristics of an open circuit in the low-mid frequency regions is minimal, which indicates the effectiveness of the method.

Analysis of the vortex-induced vibration response characteristics of riser under the soft suspension evacuation condition

This paper establishes a nonlinear dynamic model for a suspended riser under the condition of considering realistic configurations, based on the principles of virtual work and Hamilton's variational principle. The nonlinearity of the model is manifested by considering vortex-induced vibration in the cross flow (CF) and in-line (IL) directions, as well as large deformations, taking into account the variable diameter of the riser in the compliant riser system. The model is discretized using the finite element method and solved using the Newmark-β method. Experimental validation is conducted to verify the effectiveness of the model. Utilizing the parameters of a riser in a well in the South China Sea, the paper explores the influence of different environmental and structural parameters on the VIV response characteristics of a compliant riser. Results show that the vibration frequency is controlled by both the bare tube and buoyant block when the buoyant block coverage rate is 25%, which can significantly inhibit VIV. With the increase of flow velocity, the VIV energy jumps from low order to high order, and the riser mode also transitions from low order to high order. The increase in suspension length transfers the vibration energy from high to low frequency, thus realizing energy transition and mode shape transformation. With the increase in LMRP weight, the vibration and natural frequencies of the riser increase synchronously, the vibration amplitude decreases, and the mode shape remains unchanged.

Adaptive Fuzzy Sliding Mode Control and Dynamic Modeling of Flap Wheel Polishing Force Control System

Polishing force is one of the key process parameters in the polishing process of blisk blades, and its control accuracy will affect the surface quality and processing accuracy of the workpiece. The contact mechanism between the polishing surface and flap wheel was analyzed, and the calculation model of the polishing force and nonlinear dynamic model of the polishing force control system was established. Considering the influence of friction characteristics, parameter perturbation, and nonlinear dead zone on the control accuracy of the polishing force system, an adaptive fuzzy sliding mode controller (AFSMC) was designed. AFSMC uses a fuzzy system to adaptively approximate the nonlinear function terms in the sliding mode control law, adopts an exponential approach law in the switching control part of the sliding mode control (SMC), and designs the adaptive law for adjustable parameters in the fuzzy system based on the Lyapunov Theorem. Simulation and experimental results show that the designed AFSMC has a fast dynamic response, strong anti-interference ability, and high control accuracy, and it can reduce SMC high-frequency chatter. Polishing experiments show that compared with traditional PID, AFSMC can improve the form and position accuracy of the blade by 42% and reduce the surface roughness by 50%.