Dynamic modeling and simulations of the wave glider

Wave glider is a new wave-powered autonomous marine vehicle, which is composed of a submerged glider connected to a surface floater via a tether. Such an advanced vessel is designed to harvest energy in ocean surface waves to generate forward thrust. Equipped with solar panel and battery as well as some dedicated sensors, the wave glider is able to achieve long duration missions via sea-side control. In this paper, a 4-DOF (degree-of-freedom) mathematical model of the wave glider is established using Newton–Euler approach. The second-order wave drift force on the horizontal plane and the first order wave force on the vertical direction are considered. The hydrodynamic parameters were calculated using the potential flow theory and empirical formula. Furthermore, motion simulation of the wave glider with respect to the sensitivity analysis to some key environmental factors and the heading control ability is conducted. The simulation results are presented and discussed in detail, which provides theoretical guidance and reference for wave glider design.     

Fractional order attitude stability control for sub-satellite of tethered satellite system during deployment

This paper investigates the sub-satellite attitude stabilization control of a tethered satellite system (TSS) during deployment stage. The dynamic model of sub-satellite motion is first established using Euler equations. During the tether deployment stage, the stability characteristics of attitude motion are analyzed with dissymmetric junction points between tether and sub-satellite. Then, a fractional-order attitude controller with memory ability is proposed to achieve stable control of the sub-satellite attitude, in which a dynamic model is linearized by using the feedback linearization method. Finally, validity of the fractional order controller and the advantages over an integer order controller are examined using numerical simulation. Comparing with the corresponding integer order controller, numerical simulation results indicate that the proposed sub-satellite attitude controller based on fractional order can not only stabilize the sub-satellite attitude, but can also respond faster with smaller overshoot.     

Model-based control strategies for systems with constraints of the program type

The paper presents a model-based tracking control strategy for constrained mechanical systems. Constraints we consider can be material and non-material ones referred to as program constraints. The program constraint equations represent tasks put upon system motions and they can be differential equations of orders higher than one or two, and be non-integrable. The tracking control strategy relies upon two dynamic models: a reference model, which is a dynamic model of a system with arbitrary order differential constraints and a dynamic control model. The reference model serves as a motion planner, which generates inputs to the dynamic control model. It is based upon a generalized program motion equations (GPME) method. The method enables to combine material and program constraints and merge them both into the motion equations. Lagrange’s equations with multipliers are the peculiar case of the GPME, since they can be applied to systems with constraints of first orders. Our tracking strategy referred to as a model reference program motion tracking control strategy enables tracking of any program motion predefined by the program constraints. It extends the “trajectory tracking” to the “program motion tracking”. We also demonstrate that our tracking strategy can be extended to a hybrid program motion/force tracking.     

How to make dull cellular automata complex by adding memory: Rule 126 case study

Using Rule 126 elementary cellular automaton (ECA), we demonstrate that a chaotic discrete system — when enriched with memory — hence exhibits complex dynamics where such space exploits on an ample universe of periodic patterns induced from original information of the ahistorical system. First, we analyze classic ECA Rule 126 to identify basic characteristics with mean field theory, basins, and de Bruijn diagrams. To derive this complex dynamics, we use a kind of memory on Rule 126; from here interactions between gliders are studied for detecting stationary patterns, glider guns, and simulating specific simple computable functions produced by glider collisions. © 2010 Wiley Periodicals, Inc. Complexity, 2010     

On the theory of fugoid motions

In 1891 Zhukovslii in his paper “On soaring of birds” [1] solved the problem of the motion of a body of high lift — drag ratio in an atmosphere of constant density. In [2] this problem was considered in greater detail, but the basic assumption of a constant density was made here as well. There have recently appeared numerous papers concerning the analytical solution of the problem of entry into the atmosphere with orbital and escape velocities [3 to 5]. But these studies were concerned primarily with the problems of ballistic entry and entry with low lift — drag ratio. In considering oscillatory states, the authors limited their treatment to small angles between the trajectory and local horizon. In the present paper we consider the problem without imposing any limitations on the slope of the trajectory or initial velocity. The case examined will be that of a hypothetical glider spacecraft of sufficiently high lift — drag ratio. It is interesting to note that the solution of this problem reduces to the solution of Zhukovskii's problem, but for an atmosphere of variable density. The associated trajectories are termed “fugoid”. All of our assumptions about the parameters of such a glider are of a particular hypothetical character.     

Bifurcation,chaos, and their control in a wheelset model

In this paper, we present an improved wheelset motion model with two degrees of freedom and study the dynamic behaviors of the system including the symmetry, the existence and uniqueness of the solution, continuous dependence on initial conditions, and Hopf bifurcation. The dynamic characteristics of the wheelset motion system under a nonholonomic constraint are investigated. These results generalize and improve some known results about the wheelset motion system. Meanwhile, based on multiple equilibrium analysis, calculation of Lyapunov exponents and Poincaré section, the chaotic behaviors of the wheelset system are discussed, which indicates that there are more complex dynamic behaviors in the railway wheelset system with higher order terms of Taylor series of trigonometric functions. This paper has also realized the chaos control and bifurcation control for the wheelset motion system by adaptive feedback control method and linear feedback control. The results show that the chaotic wheelset system and bifurcation wheelset system are all well controlled, whether by controlling the yaw angle and the lateral displacement or only by controlling the yaw angle. Numerical simulations are carried out to further verify theoretical analyses.     

Systematic Modelling Using Lagrangian DAEs

A treatment for formulating equations of motion for discrete engineering systems using a differential-algebraic form of Lagrange's equation is presented. The distinguishing characteristics of this approach are the retention of constraints in the mathematical model and the consequent use of dependent coordinates. A derivation of Lagrange's equation based on the first law of thermodynamics is featured. Nontraditional constraint classifications for Lagrangian differential-algebraic equations (DAEs) are defined. Model formulation is systematic and lays a foundation for developing DAE-based tools and algorithms for applications in dynamic systems and control.     

The motion in a perfect fluid of a body containing a moving point mass

The motion of a system (a rigid body, symmetrical about three mutually perpendicular planes, plus a point mass situated inside the body) in an unbounded volume of a perfect fluid, which executes vortex-free motion and is at rest at infinity, is considered. The motion of the body occurs due to displacement of the point mass with respect to the body. Two cases are investigated: (a) there are no external forces, and (b) the system moves in a uniform gravity field. An analytical investigation of the dynamic equations under conditions when the point performs a specified plane periodic motion inside the body showed that in case (a) the system can be displaced as far as desired from the initial position. In case (b) it is proved that, due to the permanent addition of energy of the corresponding relative motion of the point, the body may float upwards. On the other hand, if the velocity of relative motion of the point is limited, the body will sink. The results of numerical calculations, when the point mass performs random walks along the sides of a plane square grid rigidly connected with the body, are presented.     

Comparison of a Filter- and a Model Predictive Control Based Motion Cueing Algorithm

Motion Cueing Algorithms (MCA) include control strategies to take into account the motion-based driving simulator's restrictions concerning workspace limits and dynamic boundaries. A typical 6-DoF simulator consists of a motion system which exhibits three translational and rotational degrees of freedom. Its actuators are capable of realizing accelerations, velocities and positions in a limited range. Based on these facts MCAs aim to generating realistic simulations of the driving motion (such as a driving manoeuvre) in order to immerse persons in virtual environments provided by the simulator. Filter-based, classical MCAs belong to the most applied algorithms and mainly consist of linear transfer functions. Whereas, Model Predictive Control (MPC) algorithms rest upon a reduced model of the technical system's dynamics and, optionally, a model of the human motion perception system. An optimization problem subject to the restrictions of the motion system predicts the control variables over a time horizon. This paper addresses the strengths and weaknesses of the two stated approaches with focus on Motion Cueing errors. These errors describe discrepancies between the motion that is to be simulated (e.g. a driving manoeuvre) and the motion that is eventually provided by the combination of the MCA and the motion simulator. On basis of the results, it gives an outlook why optimization based algorithms have a higher potential to improve driving simulation. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Free vibration characteristics of a functionally graded beam by finite element method

This paper presents the dynamic characteristics of functionally graded beam with material graduation in axially or transversally through the thickness based on the power law. The present model is more effective for replacing the non-uniform geometrical beam with axially or transversally uniform geometrical graded beam. The system of equations of motion is derived by using the principle of virtual work under the assumptions of the Euler–Bernoulli beam theory. The finite element method is employed to discretize the model and obtain a numerical approximation of the motion equation. The model has been verified with the previously published works and found a good agreement with them. Numerical results are presented in both tabular and graphical forms to figure out the effects of different material distribution, slenderness ratios, and boundary conditions on the dynamic characteristics of the beam. The above mention effects play very important role on the dynamic behavior of the beam.     

Analysis of flow characteristics of granular material unloaded on nonlinear vibration inclined platform

In this study, the repeated discontinuous friction between granular material and contact platform and structural nonlinearity of inclined vibration platform giving rise to the vibration flow-aiding unloading is a complicated process, which has significant effects on the dynamic behaviors and flow characteristics of granular material. A simplified mathematical model of the inclined vibration platform and granular material is deduced by mechanical properties. Based on the equations of motion and a good degree of accuracy and applicability of the process with calculated data reported in the literature, the approximate analytical solution and flow properties are investigated by using the modified incremental harmonic balance method and numerical integration method. Moreover, the influences of friction coefficient, excitation amplitude, nonlinear stiffness and inclined angle on the complicated dynamic behaviors are explored and discussed. It is shown that the different motion paths of granular material on inclined vibration platform are observed depending on the different parameters. The increasing friction coefficient has complicated effects on the nonlinear dynamic behaviors of the granular material. The excitation amplitude and nonlinear stiffness can effectively control the flow characteristics of granular material at low excitation frequency but the inclined angle presents opposite property. The research may contribute to improve unloading efficiency, predict the motion state of granule and provide a theoretic foundation for further design the unloading system.     

Vibration analysis of Euler–Bernoulli nanobeams by using finite element method

In the present study, an efficient finite element model for vibration analysis of a nonlocal Euler–Bernoulli beam has been reported. Nonlocal constitutive equation of Eringen is proposed. Equations of motion for a nonlocal Euler–Bernoulli are derived based on varitional statement. The finite element method is employed to discretize the model and obtain a numerical approximation of the motion equation. The model has been verified with the previously published works and found a good agreement with them. Vibration characteristics, such as fundamental frequencies, are illustrated in graphical and tabulated form. Numerical results are presented to figure out the effects of nonlocal parameter, slenderness ratios, rotator inertia, and boundary conditions on the dynamic characteristics of the beam. The above mention effects play very important role on the dynamic behavior of nanobeams.     

基于人机耦合的下肢外骨骼动力学分析及仿真

建立了一种包含人机交互力的人体-外骨骼模型，对人体和外骨骼分别采用7连杆的刚体模型进行建模，建立其D-H坐标系，得到人机模型在运动过程中的变化矢量.采用Newton-Euler方程建立动力学方程式，将人机之间的交互力简化为弹力，根据运动中人体和外骨骼质心之间的距离变化得到其相对位移，从而求得运动过程中交互力的大小.最终在ADAMS(automatic dynamic analysis of mechanical system)仿真软件中对动力学模型进行仿真，并将动力学方程得到的关节力矩代入到仿真中，验证了该人体-外骨骼模型的正确性.     

Nonholonomic dynamics and control of a spherical robot with an internal omniwheel platform: Theory and experiments

We present the results of theoretical and experimental investigations of the motion of a spherical robot on a plane. The motion is actuated by a platform with omniwheels placed inside the robot. The control of the spherical robot is based on a dynamic model in the nonholonomic statement expressed as equations of motion in quasivelocities with indeterminate coefficients. A number of experiments have been carried out that confirm the adequacy of the dynamic model proposed.     

A model of speculative behaviour with a strange attractor

An asset pricing model for a speculative financial market with fundamentalists and chartists is analysed. The model explains bursts of volatility in financial markets, which are not well explained by the traditional finance paradigms. Speculative bubbles arise as a complex non-linear dynamic phenomenon brought about naturally by the dynamic interaction of heterogeneous market participants. Depending on the time lag in the formation of chartists' expectations, the system evolves through several dynamic regimes, finishing in a strange attractor. Chaos provides a self-sustained motion around the rationally expected equilibrium that corresponds to a speculative bubble. In order to explain the role of Chartism, chaotic motion is a very interesting theoretical feature for a speculative financial market model. It provides a complex non-linear dynamic behaviour around the Walrasian equilibrium price produced by deterministic interactions between fundamentalists and chartists. This model could be a link between two opposite views over the behaviour of financial markets: the theorist's literature view that claims the random motion of asset prices, and the chartist's position extensively adopted by market professionals.     

Dynamic priority rule-based forward-backward heuristic algorithm for resource levelling problem in construction project

Resource levelling aims at minimizing the fluctuation of resource usage, which is accomplished by shifting non-critical activities within their float according to some heuristic rules. Most of these rules adopted a unidirectional scheduling based on a static priority rule. In this paper, we propose a dynamic priority rule-based forward-backward heuristic algorithm (FBHA). The FBHA optimizes resource allocation by shifting non-critical activities within their forward free float (FFF), forward total float (FTF) and backward free float (BFF), successively. A project is divided into several phases during each forward/backward scheduling module. In each phase, the shifting sequence and days of non-critical activities depend on a dynamic priority rule set. The FBHA is integrated into the Microsoft Project 2007 commercial software package to improve the performance of the software and facilitate the project planners. One example is analysed to illustrate the iteration process of the proposed FBHA. Another example with multiple precedence constraints is used to demonstrate the effectiveness of the proposed FBHA in complicated construction projects.     

On the Influence of High-Frequency Excitation on Systems with Dynamic Friction

By imposing high-frequency vibrations to a system, the characteristics of dry friction for low sliding velocities can be smoothed and, consequently, undesired friction induced phenomena such as stick-slip motion can be quenched. Many studies have been published so far, most of them focussing on the reduction of friction between metal surfaces and using classical Coulomb friction models. Within this contribution the effect of high-frequency excitation on dry friction taking into account dynamic friction models will be discussed. To this end, the friction law suggested by Dahl is used and the resulting friction characteristics are compared to those obtained for the classical Coulomb friction model. Using Dahl's friction model, a reduction of the smoothing effect is observed. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)