Recursive and Residual Algorithms for the Efficient Numerical Integration of Multi-Body Systems

In this paper a family of methods for multi-body dynamic simulation is introduced. Equations of motion are obtained using a set of Cartesian coordinates and projected onto a set of independent relative coordinates using the concept of velocity transformation. Open-chain systems are solved directly following either a fully recursive or a semi-recursive procedure. Closed-chain systems are solved in two steps; kinematic loops are opened by removing either some kinematic joints or a rigid body, and the resulting open-chain system is solved; closure-of-the-loop conditions are imposed by means of a second velocity transformation. The dynamic formalisms have been developed so as to handle both non-stiff and stiff systems. Non-stiff systems are solved by means of an Adams–Bashforth–Moulton numerical integration scheme, which requires the computation of the function derivatives. Stiff problems are integrated by using either BDF or NDF methods, which require the computation of the residual of the equations of motion and, optionally, the evaluation of the Jacobian matrix. The proposed algorithms have been implemented using an Object-Oriented Programming approach that makes it possible to re-use the source code, keeping programs smaller, cleaner and easier to maintain. Practical examples that illustrate the performance of these implementations are included. These examples have also been solved using a commercial multi-body simulation package and comparative results are included. In most cases, the algorithms here presented outperform those implemented in the commercial package, leading to important savings in terms of total computation times.     

Linear Algebra Considerations for the Multi-Threaded Simulation of Mechanical Systems

A solution method suitable for the multi-threaded simulation ofmechanical systems represented in Cartesian coordinates isproposed and analyzed. In a state-space framework for thesolution of the Differential Algebraic Equations (DAE) ofMultibody Dynamics, the position/velocity stabilization and theacceleration computation are based on iterative solvers applied toequivalent reduced problems. The most in-depth computationalaspect analyzed is the preconditioning, i.e., the direct solutionof the reduced systems. Provided a topology index reduction is first applied to the model, the effort for the direct solution of the reduced systems is shown to be of order O(N _J ), where N _J is the number of joints in the model. The recurring theme of thepaper is the central role that the topology of the mechanicalsystem plays in the overall performance of the numericalsimulation. Based on the topology of the model, parallelcomputational threads can be established to start in the equationformulation and continue through the iterative numericalalgorithms employed for the numerical solution. Task schedulingthese parallel threads is expected to redeem real-time performancefor certain classes of complex applications.     

Numerical Analysis of Flexible Multibody Systems

Flexible multibody systems featurea coupled mathematical model with ODEs or DAEs governing the gross motion and PDEs describing the elastic deformation of particular bodies.Frequently, semidiscretization of elastic members leads to a stiff mechanical system with widely different time scales. Thispaper investigates the behavior of numerical time integration methodsat flexible multibody systems and gives some recommendations.Simulation results for a slider crank mechanism and a truck modelillustrate what can go wrong and how implicit methods like RADAU5 can beeffectively applied.     

Control System Design Automation for Mechanical Systems

In this paper, a user-friendly and comprehensive control system design package called Control System Design Automation (CSDA) is described. The system consists of five main blocks: a requirement interpretation block, a modeling block, an analysis/design block, a database management and knowledge base block, and a verification block. The requirement interpretation block transforms the specifications in terms of the application to those in terms of control. The analysis/design block selects an optimal control structure and determines the controller parameters. In addition to the conventional design methods, CSDA also contains the more recent design methods such as the LMI design approach and the Kessler/Manabe method. The LMI approach can obtain a controller which satisfies multiple specification items at the same time. The configuration of the system as well as the analysis/design block are described in detail in this paper.     

一种针对不确定机械系统的新型Lyapunov鲁棒控制方法

设计了一种针对不确定机械系统的鲁棒控制器.首先分析了质量矩阵的奇异性及上边界性质,展示了质量矩阵可能会因为模型的过度简化而变为半正定.而且,进一步研究了质量矩阵上边界的一致性.在质量矩阵正定及上边界的假设条件下,提出了一种新型鲁棒控制器以抑制机械系统中的不确定性效果.从理论上证明了设计的鲁棒控制器的一致有界性及最终一致有界性.最终趋近边界球的尺寸大小可由设计者决定.最后展示了仿真结果并作了讨论.     

Design of H 2 Controllers for Sampled-Data Systems with Input Time Delays

This paper presents a general framework based on lifting technique for sampled-data systems with input time delays. By analyzing the properties of operator-valued matrices of lifted systems with input time delays, an extended lifting technique is obtained. It is then shown that, with the proposed lifting technique, the complex behavior of the system can be illustrated by two simple lifted systems, which construct the extended lifted system. The extended lifted system has the same induced norm as that of the original system with an input time delay, since the proposed lifting technique is an isometric isomorphism. Through applying the proposed lifting technique to sampled-data systems with input time delays, the time-invariant discrete-time system with infinite-dimensional input and output spaces is obtained. The equivalent discrete-time system, which is derived from the extended lifted system, can satisfy the problem of H ₂ sampled-data control systems with input time delays. Simulation results are given to show that the proposed method can guarantee a more stable system response than the conventional H ₂ sampled-data controller for the sampled-data systems with the various input time delays.     

Finite‐Time Sliding Mode Trajectory Tracking Control of Uncertain Mechanical Systems

The problem of finite‐time tracking control is studied for uncertain nonlinear mechanical systems. To achieve finite‐time convergence of tracking errors, a simple linear sliding surface based on polynomial reference trajectory is proposed to enable the trajectory tracking errors to converge to zero in a finite time, which is assigned arbitrarily in advance. The sliding mode control technique is employed in the development of the finite‐time controller to guarantee the excellent robustness of the closed‐loop system. The proposed sliding mode scheme eliminates the reaching phase problem, so that the closed‐loop system always holds the invariance property to parametric uncertainties and external disturbances. Lyapunov stability analysis is performed to show the global finite‐time convergence of the tracking errors. A numerical example of a rigid spacecraft attitude tracking problem demonstrates the effectiveness of the proposed controller.     

机械系统的拉格朗日法建模与仿真

针时拉格朗日法对复杂系统建模比较方便,但仿真比较困难的问题,通过具体实例,介绍了在拉格朗日法建模的基础上进行仿真的一种新方法,该方法通过将所建立的数学模型,先进行解耦后分别仿真,再应用叠加原理求得系统的仿真结果。     

Control Design for Artificial Swarm Mechanical Systems: Dynamics,Uncertainty, and Constraint

We consider an artificial swarm system consisting of multiple agents. The agents influence each other through the attraction/repulsion, which is related to the relative positions among them. Here the collective behavior of the agents mimics some biological swarm systems. The dynamic model for each agent is built by taking the uncertainty into account. Based on the dynamic model, we propose three types adaptive robust controls, including switching type, non‐switching type and fractional type, for each agent. The control design weaves together several intrinsic features of kinematics, dynamics, d'Alembert's principle, constraint, and uncertainty.     

柔性机械系统分布参数建模及其控制的研究与进展

近年来,柔性机械系统以其轻量化、低耗能、操作灵活等优势在航空航天、海底勘探、机器人、机械制造等领域得到了广泛关注,其建模和控制问题也成为了当今国内外学者研究的热点问题。在本文中,首先介绍了柔性机械系统的部分应用背景,紧接着汇总了柔性机械系统常见的分布参数建模方法、控制策略、控制方法以及实际工程问题。最后,对柔性机械系统分布参数建模与控制问题进行了总结,并对未来的研究方向进行了展望。     

具有异步时钟的长时延网络控制系统故障检测

考虑一类存在异步采样时钟的不确定长时延网络控制系统．假定其可能发生故障，设计了离散状态观测器，对其进行故障检测．当系统正常时，观测器系统的稳定性条件被近似为一个包含线性矩阵不等式条件的最小化问题；只要该最小化问题有解，则整个系统是渐近稳定的．当系统发生故障时，该观测器残差能够迅速发生跳变，从而检测出故障的发生．给出一个仿真示例验证了文中方法的有效性．     

Efficient Stochastic Simulation of Biological Systems with Multiple Variable Volumes

The application of concurrent calculi to the formalisation of biological systems constitutes a promising approach to the analysis in silico of biological phenomena. The Gillespie algorithm is one of the main models exploited for their stochastic simulation. While the original algorithm considers only one fixed-volume compartment, the simulation of biological systems often requires multi-compartment semantics. In this paper we present an enhanced formulation of an extended version of the algorithm which handles multiple compartments with varying volumes. The presented algorithm is used as basis for the implementation of an extension of the stochastic π-Calculus, called Sπ@, which allows an intuitive and concise formalisation of such systems. The algorithm is also efficient in presence of a high number of compartments and reactions, therefore Sπ@ represents the starting point for the development of an effective tool for the simulation of biological systems with dynamical structure even in presence of computationally expensive phenomena like diffusion.     

非线性机械系统PID控制渐近稳定性分析

应用Lyapunov直接稳定性理论和LaSalle不变性原理, 证明了不确定非线性机械系统常用线性PID控制的半全局渐近稳定性. 同时证明了为提高系统的响应速度而发展的一种非线性PI加D (NPI-D)控制系统的全局渐近稳定性. 两自由度机器人系统的数值仿真结果验证了NPI-D控制的良好性能.     

油料灌装自动控制系统误差分析

全面系统地分析影响油料灌装自动控制系统精度的各种因素,对于提高灌装精度具有重要的指导意义。本文针对油料定量灌装控制系统,详细分析了体积流量计和科里奥利质量流量计产生附加误差的来源,讨论了影响过冲量大小及造成过冲量误差的主要因素,给出了灌装控制系统总误差的计算公式。通过误差分析,总结出了提高灌装控制系统精度的基本途径。分析还表明,在设置小流量提前关阀的情况下,灌装控制系统的灌装精度主要取决于流量计及温度、压力等仪表的精度,过冲量误差对系统灌装精度的影响并不大。     

欠驱动机械系统的三类级联规范型

基于欠驱动机械系统的动力学,分析了其驱动模式;为了便于欠驱动机械系统的控制设计,针对具有动能对称性的欠驱动机械系统,提出了一种闭环全局坐标变换方案.该方案将欠驱动机械系统的动力学转换成具有结构特征的级联规范型（即严格反馈、严格前馈和非三角级联非线性系统）,并分别给出了Pendubot、倒立摆系统和TORA （Translational Oscillator with Rotational Actuator） 系统的级联规范型.     

一类欠驱动机械系统的非线性控制

针对一类欠驱动机械系统．分析了其数学模型,提出了一种基于部分反馈线性化的非线性控制方案．该方案利用精确线性化的方法将欠驱动系统直接激励部分线性化,将被动部分作为系统的内部动态考虑;并选择直接激励的自由度作为系统输出．进行系统的轨迹跟踪控制;通过分析系统的内部动态,证明了零动态的稳定性能保证控制系统的稳定性．最后通过对吊车的负载防摆控制的研究．验证了该方案的可行性．     

光盘轴向机械动态特性的计算机自动测试系统

光盘系统的开发者和光盘介质的提供者需要一种能自动、方便测量光盘轴向机械动态特性的测试系统 .本文系统介绍了一种新型、基于激光三角法的、适用于自动化生产线的光盘机械动态特性计算机自动测试系统 .系统构成框图、主要测试步骤以及测量结果和对测量结果的分析均在文中给出     

An A Posteriori Error Estimate for the Local Discontinuous Galerkin Method

In this work an a posteriori global error estimate for the Local Discontinuous Galerkin (LDG) applied to a linear second order elliptic problem is analyzed. Using a mixed formulation, an upper bound of the error in the primal variable is derived from explicit computations. Finally, a local adaptive scheme based on explicit error estimators is studied numerically using one dimensional problems.This revised version was published online in July 2005 with corrected volume and issue numbers.     

Just in Time Control of Constrained (<Emphasis Type="Italic">max</Emphasis>,+)-Linear Systems

This paper deals with just in time control of (max,+)-linear systems. The output tracking problem, considered in previous studies, is generalized by considering additional constraints in the control objective. The problem is formulated as an extremal fixed point computation. This control is applied to timetables computation for urban bus networks.

时延网络控制系统的H∞ 鲁棒预测控制

针对具有输入约束和外部扰动的不确定长时延网络控制系统(NCSs),研究了H_∞鲁棒预测状态反馈控制律的设计问题.基于预测控制的滚动优化原理,导出了闭环NCS渐近稳定且具有鲁棒性能指标上界的充分条件,给出了状态反馈控制律的设计方法.最后,通过仿真研究验证了所提出方法的有效性.