Adaptive time-varying super-twisting global SMC for projective synchronisation of flexible manipulator

In this paper, a synchronisation strategy between a controlled master and three-slave two-link flexible manipulators is proposed. Two out of the three slaves are identical with the master, whereas the third one is non-identical. The master and the slave manipulators are modelled by assumed modes and lumped parameter methods, respectively. The 12 states of the master manipulator are synchronised to the 8 states of each slave manipulator. Such projective synchronisation is also not available in the literature. A global sliding mode controller is designed first for the master manipulator to track the desired trajectory. Next, the synchronisation between the master and the slaves is achieved by designing an adaptive time-varying super-twisting global sliding mode controller. The simulation results reveal that the performances of the proposed controller in terms of (i) steady-state error of synchronisation, (ii) synchronisation time and (iii) links deflection are much better than the existing controller proposed in 2016.     

Analysis of complex parametric vibrations of plates and shells using Bubnov-Galerkin approach

Summary The Bubnov-Galerkin method is applied to reduce partial differential equations governing the dynamics of flexible plates and shells to a discrete system with finite degrees of freedom. Chaotic behaviour of systems with various degrees of freedom is analysed. It is shown that the attractor dimension of a system has no relationship with the attractor dimension of any of its subsystems.This work has been partially supported by Department of Mathematics of the Central European University in Budapest.     

A DYNAMIC MODEL FOR ROCKET LAUNCHER WITH COUPLED RIGID AND FLEXIBLW MOTION

The dynamics of a coupled rigid-flexible rocket launcher is reported. The coupled rigid-flexible rocket launcher is divided into two subsystems, one is a system of rigid bodies,the other a flexible launch tube which can undergo large overall motions spatially. First, the mathematical models for these two subsystems were established respectively. Then the dynamic model for the whole system was obtained by considering the coupling effect between these two subsystems. The approach, which divides a complex system into several simple subsystems first and then obtains the dynamic model for the whole system via combining the existing dynamic models for simple subsystems, can make the modeling procedure efficient and convenient.     

Dynamic Synthesis of Substructures∗

ABSTRACT

A new approach is presented to synthesize dynamic properties of a system that is composed of multiple degree of freedom subsystems attached to a multiple degree of freedom primary system at several points. Natural frequencies and mode shapes of the combined system are obtained in terms of modal properties of the primary system, subsystems, and their interaction parameters. The present solution is compared to the exact solution as well as approximate solutions obtained by earlier investigators. Derived properties can be used in conjunction with any response spectrum or random vibration formulation, to obtain the deterministic or probabilistic dynamic response of subsystems to any arbitrary excitation.     

Diffusive coupling, dissipation, and synchronization

We consider the synchronization of diffusive coupled systems in situations where the synchronization is a consequence of the dissipation in the coupling as well as ones where there is an interaction between the inherent damping in the subsystems and the coupling. It is not required that the subsystems be identical, and they are allowed to have chaotic dynamics. Both discrete and continuous versions are discussed. We also consider coupled oscillators where the dynamics of each oscillator is determined by circuitry across a lossless transmission line.     

Nonlinear Dynamics of Two-Degrees-of-Freedom Fluid Conveying Elasto-Visco-Plastic Model System

The local and global nonlinear dynamics of a two-degrees-of-freedom model system conveying fluid is studied. The undeflected model consistsof an inverted T formed by three rigid rods, with the tips of the twohorizontal rods resting on the viscous foundation. The foundationexhibits a visco-elasto-plastic response, including the Bauschingereffect. The vertical rigid rod of an annular cross-section is subjectedto a conservative (dead) force. Also, it conveys fluid having bothstatic and pulsation components. First, the method of multiple scales isused for the analysis of the local dynamics of the system withvisco-elastic response. Attention is focused on modal interactionphenomena in weak excitation at primary resonance and on hardsub-harmonic excitation. Two different asymptotic expansions areutilised to get a structural response for typical ranges of excitationparameters. Numerical integration of the governing equations is thenperformed to validate the results of asymptotic analysis in each case. Afull global nonlinear dynamics analysis of the visco-elasto-plasticsystem is performed. The role of plastic deformations in thedestabilisation of the system is discussed. Large-amplitude nonlinearoscillations of the visco-elasto-plastic system are studied, includingthe influence of material hardening and of static and periodiccomponents of pulsating fluid. Chaotic regimes of motion with andwithout plastic effects are considered. The results of the analysis maybe used in devices composed of a rather short tube connected to a notcompletely fixed foundation resting on the soil exhibitingelasto-plastic behaviour.     

Asteroid debris: Temporary capture and escape orbits

We investigate the dynamical behaviour of debris ejected from the surface of an asteroid, due to a generic – natural or artificial – surface process. We make an extensive statistical study of the dynamics of particles flowing from the asteroid. We observe different behaviours: particles which fall again on the asteroid surface, or rather escape from its gravitational field or are temporary trapped in orbit around the asteroid. The tests are made by varying different parameters, like the size of the asteroid, its eccentricity, the angular velocity of the asteroid, the area-to-mass ratio of the debris.We also extend the study to the case of a sample of binary asteroids with a mass ratio equal to 10⁻³; we vary the distance of the moonlet from the asteroid, to see its effect on the debris dynamics.Our simulations aim to identify regions where the debris can temporarily orbit around the asteroid or rather escape from it or fall back on the surface. These results give an important information on where a spacecraft could be safely stay after the end of the process which has produced the debris.     

激光选区熔化增材制造中的粉体热动力学行为

激光选区熔化(SLM)可以直接成形近全致密、性能接近锻件的复杂结构金属零件, 是金属增材制造(3D打印)领域的热点技术之一. SLM成形过程中粉末颗粒的热/动力学行为复杂, 与零件成形缺陷及力学性能紧密相关. 本文介绍了离散单元法(DEM)与计算流体力学(CFD)联合建模在SLM中的创新应用, 结合粉末床原位测试及成形在线监测, 探索SLM粉末铺设和粉末床熔融两个工艺环节的复杂粉体热/动力学行为机制. 研究发现, 粉末铺设过程中: 粉体的黏结效应、壁面效应和渗流效应3种机制相互竞争、共同支配粉末动力学行为并最终决定粉末床铺设质量. 粉末床熔融过程中: 熔池喷发的高温金属蒸汽带动环境保护气体形成内旋涡流, 由此驱动散体粉末形成复杂流固耦合运动, 导致粉末床飞溅与剥蚀现象; 热浮力效应对粉末运动不起主导作用. 文中提出了DEM-CFD双向动态耦合模型, 可以充分考虑离散粉末与熔池蒸发气体之间的热力耦合作用, 为SLM粉体熔融热/动力学行为的仿真模拟提供了一种新途径.      

Generalized Darboux transformation and parameter-dependent rogue wave solutions to a nonlinear Schrödinger system

Objectives of the paper are (1) to design two new real and complex no equilibrium point hyperchaotic systems, (2) to design synchronisation technique for the new systems using the contraction theory and (3) to validate the results by using circuit realisation. First a new no equilibrium point hyperchaotic system is developed using a 3-D generalised Lorenz system; then using the new system a new complex no equilibrium point hyperchaotic system is reported. Both the new systems have hidden chaotic attractors. Various dynamical behaviours are observed in the new systems like chaotic, periodic, quasi-periodic and hyperchaotic. Both the systems have inverse crisis route to chaos with the variation of parameter a and crisis route to chaos with the variation of parameters \(b,\ c\) and d. These phenomena along with hidden attractors in a complex hyperchaotic system are not seen in the literature. Synchronisation between the identical new hyperchaotic systems is achieved using the contraction theory. Further the synchronisation between the identical new complex hyperchaotic systems is achieved using adaptive contraction theory. The proposed synchronisation strategies are validated using the MATLAB simulation and circuit implementation results. Further, an application of the proposed system is shown by transmitting and receiving an audio signal.     

The collective bursting dynamics in a modular neuronal network with synaptic plasticity

In this study, how the synaptic plasticity influences the collective bursting dynamics in a modular neuronal network is numerically investigated. The synaptic plasticity is described by a modified Oja’s learning rule. The modular network is composed of some sub-networks, each of them having small-world characteristic. The result indicates that bursting synchronization can be induced by large coupling strength between different neurons, which is robust to the local dynamical parameter of individual neurons. With the emergence of synaptic plasticity, the bursting dynamics in the modular neuronal network, particularly the excitability and synchronizability of bursting neurons, is detected to be changed significantly. In detail, upon increasing synaptic learning rate, the excitability of bursting neurons is greatly enhanced; on the contrary, bursting synchronization between interacted neurons is a little suppressed by the increase in synaptic learning rate. The presented findings could be helpful to understand the important role of synaptic plasticity on neural coding in realistic neuronal network.     

空间机器人执行器自适应分散容错控制算法设计

针对执行器发生部分失效故障的漂浮基空间机器人系统,提出了一种自适应H_∞分散容错控制算法。利用拉格朗日第二类方程建立了系统的动力学模型。根据分散原理将系统分解为以基座或臂杆为单元的多个子系统,并将表示执行器控制能力的有效因子融入到每个子系统,使得单个子系统的执行器故障不会影响相邻执行器的正常运行。通过对每个故障子系统设计形式一致的自适应容错算法实现对整个系统的容错控制。仿真结果表明,与现有某非奇异终端滑模容错算法相比,本文算法具有更快的跟踪速度和更高的跟踪精度。     

Error estimate for influence of model reduction of nonlinear dissipative autonomous dynamical system on long-term behaviours

Introduction Forsomenonlineardynamicalsystems,especiallyincomplexmechanicalvibrationand fluid structureinteractionsystems,thefiniteelementmethodisoftenusedtoapproachthe solutionofthegoverningequationduetothedifficultyofdescribingsysteminanalyticalform.Asa…     

Review of chaos in the dynamics and rheology of suspensions of orientable particles in simple shear flow subject to an external periodic force

We review results obtained over a period of about a decade on a class of technologically and fundamentally important problems in suspension rheology viz., the dynamics and rheology of dipolar suspensions of orientable particles in simple shear flow. The areas explored in this review include effects such as the fluid flow field, external forcing, Brownian diffusion, hydrodynamic interactions and their impact on the rheological properties of the suspension. The main feature of the presentation is the use of a uniform framework in which one or more of the above effects can be studied, based on Langevin type equations for particle orientations combined with a brute-force technique for computing orientational averages. These models are capable of capturing complex dynamical behaviour in the system such as the presence of subharmonics or chaos, both in the dynamics and rheology. The tools developed allow for investigating how chaos in the system is affected by Brownian diffusion and hydrodynamic interactions. The presence of chaos opens up a number of novel possibilities for dynamical and rheological behaviour of the system, which can be put to efficient use in many ways, e.g. in separating particles by aspect ratio and possibly developing computer controlled intelligent rheology. The results also have implications for certain areas of chaos theory, such as a new intermittency route to chaos and the possibility of non-trivial collective behaviour in spatially extended systems. These studies highlight certain deficiencies in current techniques in the literature for handling the rheology of dilute and semi-dilute suspensions. In the presence of Brownian motion the proposed method computes the averages by simulating a set of deterministic ordinary differential equations rather than stochastic differential equations. The systems considered may also serve as a paradigm for analysing how microscopic chaotic fluctuations in spatially extended systems affect macroscopic averages. We also attempt to put our results into context with respect to recent work on rheochaos in complex fluids such as liquid crystals and nematic polymers.     

受周期和白噪声激励的分段线性系统的吸引域与离出问题研究

离出行为是随机非线性系统的重要现象之一,而离出问题是除随机动力系统理论以外考察随机非线性系统随机稳定性的另一种重要的方法.分段线性系统是一个经典的非线性动力学模型,受随机激励后成为随机系统,但并不是严格的随机动力系统,因而此时随机动力系统理论也不适用.为了研究同时受周期和白噪声激励的分段线性系统,首先使用Poincaré截面模拟其在无噪声时确定性的动力学行为,然后使用Monte Carlo模拟对其在白噪声激励下的离出行为进行了数值仿真分析.其次,为了考察离出问题中的重要参数,系统的平均首次通过时间（mean first-passage time,MFPT）,使用van der Pol变换,随机平均法,奇异摄动法和射线方法进行了量化计算.通过对理论结果与模拟结果的对比分析,得到结论:当系统吸引子对应的吸引域边界出现碎片化时,理论结果与模拟结果的误差极大;而当吸引域边界足够光滑的以后,理论结果与模拟结果才会相当吻合.      

Finite-Range Repulsive Systems of Finitely Many Particles

We consider the dynamics of finite systems of spherical particles where a fraction of the kinetic energy may be lost during collisions. We show that the set of initial configurations leading to infinitely many collisions in finite time can have positive measure, contrary to the hard-collision (energy conservation) case, in which this particular set is claimed to be empty. We also show that after sufficient time a system will decouple into maximal subsystems. This generalizes proofs that in the hard-sphere case there can be at most finitely many collisions for almost all initial configurations.     

Simulating orthokinetic heterocoagulation and cluster growth in destabilizing suspensions

Using direct numerical simulation, we investigate the coagulation behavior of non-Brownian colloidal particles as exemplified by Al₂O₃ particles. This yields the so-called capture efficiency, for which we give an analytical expression, as well as other time-dependent variables such as the cluster growth rate. Instead of neglecting or strongly approximating the hydrodynamic interactions between particles, we include hydrodynamic and non-hydrodynamic interactions in a Stokesian dynamics approach and a comprehensive modeling of the interparticle forces. The resulting parallelized simulation framework enables us to investigate the dynamics of polydisperse particle systems composed of several hundred particles at the same high level of modeling we used for a close investigation of the coagulation behavior of two unequal particles in shear flow. Appropriate cluster detection yields all the information about large destabilizing systems, which is needed for models used in flow-sheet simulations. After non-dimensionalization, the results can be generalized and applied to other systems tending to secondary coagulation.     

Persistence,Permanence and Global Stability for an n-Dimensional Nicholson System

For a Nicholson’s blowflies system with patch structure and multiple discrete delays, we analyze several features of the global asymptotic behavior of its solutions. It is shown that if the spectral bound of the community matrix is non-positive, then the population becomes extinct on each patch, whereas the total population uniformly persists if the spectral bound is positive. Explicit uniform lower and upper bounds for the asymptotic behavior of solutions are also given. When the population uniformly persists, the existence of a unique positive equilibrium is established, as well as a sharp criterion for its absolute global asymptotic stability, improving results in the recent literature. While our system is not cooperative, several sharp threshold-type results about its dynamics are proven, even when the community matrix is reducible, a case usually not treated in the literature.     

RESEARCH FOR ATTRACTING REGION AND EXIT PROBLEM OF A PIECEWISE LINEAR SYSTEM UNDER PERIODIC AND WHITE NOISE EXCITATIONS

离出行为是随机非线性系统的重要现象之一,而离出问题是除随机动力系统理论以外考察随机非线性系统随机稳定性的另一种重要的方法.分段线性系统是一个经典的非线性动力学模型,受随机激励后成为随机系统,但并不是严格的随机动力系统,因而此时随机动力系统理论也不适用.为了研究同时受周期和白噪声激励的分段线性系统,首先使用Poincaré截面模拟其在无噪声时确定性的动力学行为,然后使用Monte Carlo模拟对其在白噪声激励下的离出行为进行了数值仿真分析.其次,为了考察离出问题中的重要参数,系统的平均首次通过时间（mean first-passage time,MFPT）,使用van der Pol变换,随机平均法,奇异摄动法和射线方法进行了量化计算.通过对理论结果与模拟结果的对比分析,得到结论：当系统吸引子对应的吸引域边界出现碎片化时,理论结果与模拟结果的误差极大;而当吸引域边界足够光滑的以后,理论结果与模拟结果才会相当吻合.