Balancing on tightropes and slacklines

Balancing on a tightrope or a slackline is an example of a neuromechanical task where the whole body both drives and responds to the dynamics of the external environment, often on multiple timescales. Motivated by a range of neurophysiological observations, here we formulate a minimal model for this system and use optimal control theory to design a strategy for maintaining an upright position. Our analysis of the open and closed-loop dynamics shows the existence of an optimal rope sag where balancing requires minimal effort, consistent with qualitative observations and suggestive of strategies for optimizing balancing performance while standing and walking. Our consideration of the effects of nonlinearities, potential parameter coupling and delays on the overall performance shows that although these factors change the results quantitatively, the existence of an optimal strategy persists.     

Performance assessment of run-to-run control in semiconductor manufacturing based on IMC framework

The objective of this paper is to propose a universal methodology for performance assessment of run-to-run control in semiconductor manufacturing. The slope of the linear semiconductor process model is assumed to be known or subjected to mild plant/model mismatch. Based on an internal model control framework, analytical expressions of minimum variance performance (MVP) and best achievable performance (BAP) for a series of run-to-run control schemes are derived. In the methodology, closed-loop identification is utilised as the first step to estimate the noise dynamics via routine operating data, and numerical optimisation is employed as a second step to calculate the best achievable performance bounds of the run-to-run control loops. The validity of the methodology is justified by examples of performance assessment for EWMA control, double EWMA control and RLS-LT control, even under circumstances where the processes encounter model mismatch, metrology delay and more sophisticated noises. Several essential characteristics of run-to-run control are discovered by performance assessment, and valuable advice is offered to process engineers for improving the run-to-run control performance. Furthermore, a useful application example for online performance monitoring and optimal tuning of run-to-run controller demonstrates the advantage of the methodology.     

Slowing down and stretching DNA with an electrically tunable nanopore in a p-n semiconductor membrane

We have studied single-stranded DNA translocation through a semiconductor membrane consisting of doped p and n layers of Si forming a p-n-junction. Using Brownian dynamics simulations of the biomolecule in the self-consistent membrane-electrolyte potential obtained from the Poisson-Nernst-Planck model, we show that while polymer length is extended more than when its motion is constricted only by the physical confinement of the nanopore. The biomolecule elongation is particularly dramatic on the n-side of the membrane where the lateral membrane electric field restricts (focuses) the biomolecule motion more than on the p-side. The latter effect makes our membrane a solid-state analog of the α-hemolysin biochannel. The results indicate that the tunable local electric field inside the membrane can effectively control dynamics of a DNA in the channel to either momentarily trap, slow down or allow the biomolecule to translocate at will.     

Optimal control of diffuser shapes for non-uniform flow

A simplified model is used to identify the diffuser shape that maximises pressure recovery for several classes of non-uniform inflow. We find that optimal diffuser shapes strike a balance between not widening too soon, as this accentuates the non-uniform flow, and not staying narrow for too long, which is detrimental for wall drag. Three classes of non-uniform inflow are considered, with the axial velocity varying across the width of the diffuser entrance. The first case has inner and outer streams of different speeds, with a velocity jump between them that evolves into a shear layer downstream. The second case is a limiting case when these streams are of similar speed. The third case is a pure shear profile with linear velocity variation between the centre and outer edge of the diffuser. We describe the evolution of the time-averaged flow profile using a reduced mathematical model that has been previously tested against experiments and computational fluid dynamics models. The model consists of integrated mass and momentum equations, where wall drag is treated with a friction factor parameterisation. The governing equations of this model form the dynamics of an optimal control problem where the control is the diffuser channel shape. A numerical optimisation approach is used to solve the optimal control problem and Pontryagin’s maximum principle is used to find analytical solutions in the second and third cases. We show that some of the optimal diffuser shapes can be well approximated by piecewise linear sections. This suggests a low-dimensional parameterisation of the shapes, providing a structure in which more detailed and computationally expensive turbulence models can be used to find optimal shapes for more realistic flow behaviour.     

Predators indirectly control vector-borne disease: linking predator–prey and host–pathogen models

Pathogens transmitted by arthropod vectors are common in human populations, agricultural systems and natural communities. Transmission of these vector-borne pathogens depends on the population dynamics of the vector species as well as its interactions with other species within the community. In particular, predation may be sufficient to control pathogen prevalence indirectly via the vector. To examine the indirect effect of predators on vectored-pathogen dynamics, we developed a theoretical model that integrates predator–prey and host–pathogen theory. We used this model to determine whether predation can prevent pathogen persistence or alter the stability of host–pathogen dynamics. We found that, in the absence of predation, pathogen prevalence in the host increases with vector fecundity, whereas predation on the vector causes pathogen prevalence to decline, or even become extinct, with increasing vector fecundity. We also found that predation on a vector may drastically slow the initial spread of a pathogen. The predator can increase host abundance indirectly by reducing or eliminating infection in the host population. These results highlight the importance of studying interactions that, within the greater community, may alter our predictions when studying disease dynamics. From an applied perspective, these results also suggest situations where an introduced predator or the natural enemies of a vector may slow the rate of spread of an emerging vector-borne pathogen.     

Stability,control and reliability of a ship crane payload motion

This paper investigates the stochastic dynamics, stability and control of a ship-based crane payload motion, as well as the first time passage type of failure. The simplified nonlinear model of the payload motion is considered, where the excitation of a suspension point is imposed due to the heaving motion of waves. The latter enters the system parametrically, leading to a Mathieu type nonlinear equation. The stability boundaries are numerically calculated, using the Lyapunov exponent approach. The control strategy, based on the feedback bang–bang control policy, is implemented to minimize the load's swinging motion. Finally, the first time passage problem is addressed employing Monte-Carlo sampling of the failure process.     

Optimal pricing policy for a deteriorating product by dynamic tracking control

We study the optimal selling price of a deteriorating product under a deterministic situation in a finite time horizon where the time horizon is either known or unknown. Inventory holding cost is expressed as a quadratic function of the current inventory level. Given a known time horizon, we develop a model by considering the deterioration dynamics of the product, and show its equivalence to a generalised optimal control problem of a linear quadratic form, i.e. an optimal dynamic tracking problem with constraints on the control variable. An optimal pricing policy is derived based on the maximum value principle. The control policy takes a state feedback form; it exhibits a closed-loop relationship between the optimal selling price (control variable) and the optimal inventory level (state variable). Given an unknown time horizon, an optimal pricing policy is derived through a similar approach when the initial inventory level meets certain conditions. Numerical situations are conducted to illustrate the effectiveness of the derived price control policies. Some interesting managerial insights are discussed.     

具有加强诊断措施的Filippov HIV/AIDS传染病模型（英）

本文建立 Filippov HIV/AIDS 传染病模型,用以刻画如下诊断措施：一旦已诊断 HIV 感染者数量超过某一水平,便启用加强的诊断措施;否则实施普通的诊断措施．应用等效控制法讨论了所建立模型的滑动模式区域和滑动动力学,在此基础上通过定性分析讨论了模型的全局动力学．数值结果表明,当阈值水平足够高或足够低时,HIV 感染者数量最终稳定在一个相对较高或较低的水平;若选取一个恰当的阈值,HIV 感染者数量最终会围绕该阈值波动．这说明阈值水平的选取对控制 HIV 至关重要,据此可确定是否有必要实施加强的诊断措施．     

热塑性模型沙颗粒表面修饰

颗粒形貌对模型沙的水下休止角、起动流速、堆积密度等性能有显著影响。通常的粉碎方法对塑料模型沙不规则颗粒形貌的控制和改善是十分困难的。而采用合成的树脂颗粒作为模型沙,成本较高,且过于圆滑,亦不能根据相似比尺的要求调整其密度,给泥沙动力学研究造成不便。本文中针对一种新型的热塑性模型沙粉碎颗粒,利用树脂加热微熔时一定程度的可塑性,通过搅拌摩擦获得形貌接近天然泥沙的较圆滑模型沙颗粒。     

基于状态空间模型的机床加工精度分析

伺服进给系统的机电耦合特性直接影响数控机床的加工精度，单独针对伺服系统或机械系统建立的模型不足以准确分析系统参数对机床整机加工精度的影响。因此，综合考虑机床伺服系统与机械结构之间的耦合关系，建立伺服进给系统机电耦合动力学模型具有重要意义。首先，为保证伺服进给系统建模精度，利用状态空间法建立了机床机电耦合状态空间方程。其次，建立了伺服进给系统机电耦合Simulink模型，在此基础上采用复合控制提高系统的响应速度和加工精度。随后，利用多体动力学软件建立机床进给系统的刚柔耦合动力学模型，添加摩擦、阻尼等非线性因素，并导入Simulink与伺服系统建立耦合关系。最终，建立了卧式加工中心伺服进给系统的刚柔-机电耦合仿真加工平台，通过模拟机床加工轨迹以验证机电耦合状态空间模型的可靠性。结果表明：该状态空间模型能准确描述系统内部参数和系统输入输出的耦合关系；采用复合控制结构能有效提高系统的响应速度和加工精度。研究结果为数控机床的仿真建模和提高加工精度提供理论依据，为机床机电系统的设计提供有效指导。     

Learning differential equation models from stochastic agent-based model simulations

Agent-based models provide a flexible framework that is frequently used for modelling many biological systems, including cell migration, molecular dynamics, ecology and epidemiology. Analysis of the model dynamics can be challenging due to their inherent stochasticity and heavy computational requirements. Common approaches to the analysis of agent-based models include extensive Monte Carlo simulation of the model or the derivation of coarse-grained differential equation models to predict the expected or averaged output from the agent-based model. Both of these approaches have limitations, however, as extensive computation of complex agent-based models may be infeasible, and coarse-grained differential equation models can fail to accurately describe model dynamics in certain parameter regimes. We propose that methods from the equation learning field provide a promising, novel and unifying approach for agent-based model analysis. Equation learning is a recent field of research from data science that aims to infer differential equation models directly from data. We use this tutorial to review how methods from equation learning can be used to learn differential equation models from agent-based model simulations. We demonstrate that this framework is easy to use, requires few model simulations, and accurately predicts model dynamics in parameter regions where coarse-grained differential equation models fail to do so. We highlight these advantages through several case studies involving two agent-based models that are broadly applicable to biological phenomena: a birth–death–migration model commonly used to explore cell biology experiments and a susceptible–infected–recovered model of infectious disease spread.     

Modelling and performance of distributed algorithm for scheduling dissimilar machines with set-up

Distributed arrival time control is a highly decentralized scheduling approach where each part entity autonomously controls its arrival time to meet the due-date in real time. This paper presents differential equation-based models for distributed arrival time control of parallel dissimilar machines including sequence-dependent set-up and flowshop scheduling. The main objective was to show that the behaviour of general systems under distributed arrival time control was predictable. Convergence properties of the resulting nonlinear systems were established using the theory of discontinuous differential equations. Geometry was used to gain insight into the behaviour of these nonlinear systems. An approximation model was proposed for mean arrival times when the dynamics resulted in a non-unique steady-state. The model was tested using numerical simulation and agreed well. Geometric insights were also used to investigate scheduling performance of distributed arrival time control. Simulation results indicated that distributed arrival time control could provide significant improvement, typically more than 20%, over commonly used dispatching rules for due-date-based measures. Improved predictability and favourable performance made distributed arrival time control an attractive approach for decentralized control of Just-In-Time production.     

A method of seamlessly combining a crack tip molecular dynamics enclave with a linear elastic outer domain in simulating elastic–plastic crack advance

Molecular dynamics is applicable only to an extremely small region of simulation. In order to simulate a large region, it is necessary to combine molecular dynamics with continuum mechanics. Therefore, we propose a new model where molecular dynamics is combined with micromechanics. In this model, we apply molecular dynamics to the crack tip region and apply micromechanics to the surrounding region. Serious problems exist at the boundary between the two regions. In this study, we manage to solve these problems, and make possible the simulation of the process of crack propagation at the atomic level. In order to examine the validity of this model, we use α-iron for simulation. If the present model is valid, stress and displacement should vary continuously across the boundary between the molecular dynamics region and the micromechanics region. Our model exhibits just such behavior. This revised version was published online in August 2006 with corrections to the Cover Date.     

考虑失谐的弱耦合周期天线结构的振动主动控制研究

建立了弱耦合周期天线结构的动力学计算模型,基于该模型研究了结构失谐前后的振动特性;并应用最优控制方法,对该结构失谐前后振动的主动控制进行了研究;数值仿真结果表明：弱耦合周期天线结构参数的小量失谐会导致结构振动模态产生明显的局部化,失谐前后的振幅之比约为30%;在进行此种结构的振动主动控制时必须考虑失谐的影响,否则会导致振动控制系统的失效。     

Effective connectivity determines the critical dynamics of biochemical networks

Living systems comprise interacting biochemical components in very large networks. Given their high connectivity, biochemical dynamics are surprisingly not chaotic but quite robust to perturbations—a feature C.H. Waddington named canalization. Because organisms are also flexible enough to evolve, they arguably operate in a critical dynamical regime between order and chaos. The established theory of criticality is based on networks of interacting automata where Boolean truth values model presence/absence of biochemical molecules. The dynamical regime is predicted using network connectivity and node bias (to be on/off) as tuning parameters. Revising this to account for canalization leads to a significant improvement in dynamical regime prediction. The revision is based on effective connectivity, a measure of dynamical redundancy that buffers automata response to some inputs. In both random and experimentally validated systems biology networks, reducing effective connectivity makes living systems operate in stable or critical regimes even though the structure of their biochemical interaction networks predicts them to be chaotic. This suggests that dynamical redundancy may be naturally selected to maintain living systems near critical dynamics, providing both robustness and evolvability. By identifying how dynamics propagates preferably via effective pathways, our approach helps to identify precise ways to design and control network models of biochemical regulation and signalling.     

Effect of porosity on the interface behavior of an Al2O3-aluminum composite: A molecular dynamics study

Molecular dynamics simulations are carried out to study the effect of porosity and temperature on a ductile-brittle interface under tensile and shear loadings. Traditionally the interface is characterized by a cohesive zone model (CZM) with the traction-separation law assumed or parameterized through experiments, where the experimental determination of the shape of the CZM has proven to be difficult. In this study a traction-separation law is thus obtained for an alumina-aluminum composite system by conducting molecular dynamics simulations. A statistical approach is suggested to characterize the cohesive strength in the parameterized traction-separation law via the Weibull distribution, which consequently governs the interface behavior of the composite.     

Real-time control of the 3-DOF sled dynamics of a -flux Maglev system with a passive sled

The real-time control of the three degrees of freedom (DOF) dynamics of an electrodynamic (EDS) Maglev vehicle is presented. The design is based on a 5-DOF state-space model of the sled dynamics that uses a simple algebraic model to describe the interaction between the -flux coils on the track and the permanent magnets on the sled. A first-order sliding mode controller with integral error term is used to control heave, pitch, and roll in real time from position-attitude information measured with sensors located on the sled. Experimental results show that control of the 3-DOF dynamics of the levitated vehicle in real time can be successfully achieved by the proposed method.     

两栖仿海龟机器人动力学建模与运动控制研究

为了提高两栖仿海龟机器人行走的稳定性,对其进行动力学建模,并基于PID (proportional integral derivative,比例积分微分)反馈控制策略提出了一种力/位控制模型。首先,根据机器人的运动学模型,得到了支腿的变换矩阵和雅可比矩阵,并利用虚功原理建立了足端与液压缸之间的力传递模型。然后,利用拉格朗日法对机器人进行动力学建模,推导了支腿的动力学方程,同时进行了动力学仿真,并将实时的足端受力导入动力学方程进行计算,验证了动力学模型的正确性。最后,搭建了液压仿真模型,并在ADAMS-AMESim-MATLAB联合仿真环境中开展了机器人运动仿真。仿真结果显示：与纯位置控制模式相比,力/位控制模式下机器人膝关节的转动更加平稳,液压缸的动力输出更稳定且功耗更小。研究结果对提高机器人运动的稳定性、增强运动控制系统的鲁棒性和提高液压系统的总效率具有借鉴意义。