On the dynamic pull-in of electrostatic actuators with multiple degrees of freedom and multiple voltage sources

This study considers the dynamic response of electrostatic actuators with multiple degrees of freedom that are driven by multiple voltage sources. The critical values of the applied voltages beyond which the dynamic response becomes unstable are investigated. A methodology for extracting a lower bound for this dynamic pull-in voltage is proposed. This lower bound is based on the stable and unstable static response of the system, and can be rapidly extracted because it does not require time integration of momentum equations. As example problems, the dynamic pull-in of two prevalent electrostatic actuators is analyzed.     

Shape optimizations and static/dynamic characterizations of deformable microplate structures with multiple electrostatic actuators

Micromirrors used in many optoelectronic devices can be considered as microplates. The functions and accuracy of the micromirrors depend on the static and dynamic deflection shapes of microplates. The objective of this study is to develop an efficient method for predicting the shapes of the microplates subjected to unsymmetrical electrostatic forces produced by electrostatic actuators such that micromirrors can be effectively optimized and controlled in their real time operation. The non-classical boundary conditions which result from the microfabrication process were modeled with artificial springs at the edges. A classical energy method using boundary characteristic orthogonal polynomials was applied to formulate the equations of motion of the microsystem. Based on this method, influence functions were built and least squares method was used to optimize the desired deflection under electrostatic forces from the electrostatic actuators. Softening effect of the electrostatic stiffness was also evaluated and considered in the simulation. Static deflections and dynamic responses were compared with those from finite element analysis (FEA) using Reduced Order Modeling (ROM) method. This study found that the static and dynamic responses of microplates predicted from the proposed method were highly consistent with those calculated from FEA. However, the proposed method is simpler and more efficient than FEA and can be conveniently used for any non-classical boundary condition situations. These features make the proposed method useful to effectively control and optimize the shape of a microplate with multiple electrostatic actuators.     

Computation of static shapes and voltages for micromachineddeformable mirrors with nonlinear electrostatic actuators

In modeling micromachined deformable mirrors with electrostatic actuators whose gap spacings are of the same order of magnitude as those of the surface deformations, it is necessary to use nonlinear models for the actuators. In this paper, we consider micromachined deformable mirrors modeled by a membrane or plate equation with nonlinear electrostatic actuator characteristics. Numerical methods for computing the mirror deformation due to given actuator voltages and the actuator voltages required for producing the desired deformations at the actuator locations are presented. The application of the proposed methods to circular deformable mirrors whose surfaces are modeled by elastic membranes is discussed in detail. Numerical results are obtained for a typical circular micromachined mirror with electrostatic actuators     

面向大型工程多安全指标的解析可追溯安全控制方法

安全控制是开展一系列大型工程的重要前提之一,但大型工程往往受多种因素影响且同时需要考虑多个安全指标,对此,提出一种基于置信规则库(belief rule base, BRB)的具有解析和可追溯特征的多目标安全控制方法.首先,面向多个安全指标建立多个BRB;其次,计算各影响因素对各安全指标的贡献度,根据贡献度值得到面向单个安全指标的关键因素序列;再次,综合获得面向多个安全指标的关键因素序列;最后,仅针对面向多安全指标的关键因素开展多目标优化.以隧道施工过程中地面沉降值和建筑斜率作为目标开展安全控制.实例结果表明,所提出方法能够精准识别关键因素,通过优化关键因素可以有效降低地面沉降值和建筑斜率.此外,还进一步研究了关键因素数量对安全控制过程和结果的影响.     

Fast and robust numerical method for inverse kinematics with prioritized multiple targets for redundant robots

In this paper, a new numerical method for inverse kinematics with prioritized multiple targets is proposed. The proposed method is constructed based on the virtual spring model and joint-based damping control. The targets are prioritized by adjusting the effect of the virtual springs. The proposed method has the following three features. First, it does not require complex calculations such as a Jacobian matrix projection into the null space. Second, it can solve prioritized inverse kinematics problems in the position level without integrating the joint velocity. Third, it is robust to parameter variations and singular configurations. The second feature is motivated by the background that most industrial robots in factories are used as position-controlled robots. Simulation experiments using a 9-DOF redundant robot show that the proposed method is faster and more robust than the conventional method. The proposed method is expected to be useful for helping to avoid collisions between links and obstacles using the redundancy.     

An efficient decomposition and dual-stage multi-objective optimization method for water distribution systems with multiple supply sources

This paper proposes an efficient decomposition and dual-stage multi-objective optimization (DDMO) method for designing water distribution systems with multiple supply sources (WDS-MSSs). Three phases are involved in the proposed DDMO approach. In Phase 1, an optimal source partitioning cut-set is identified for a WDS-MSS, allowing the entire WDS-MSS to be decomposed into sub-networks. Then in Phase 2 a non-dominated sorting genetic algorithm (NSGA-II) is employed to optimize the sub-networks separately, thereby producing an optimal front for each sub-network. Finally in Phase 3, another NSGA-II implementation is used to drive the combined sub-network front (an approximate optimal front) towards the Pareto front for the original complete WDS-MSS. Four WDS-MSSs are used to demonstrate the effectiveness of the proposed approach. Results obtained show that the proposed DDMO significantly outperforms the NSGA-II that optimizes the entire network as a whole in terms of efficiently finding good quality optimal fronts.     

一类多执行机构系的滑模控制设计及其应用

针对一类具有多执行机构的非线性系统,利用滑模控制和backstepping技术,研究了输出跟踪问题.针对执行机构的不同特点,利用离散执行机构实现滑模控制中的不连续控制量,利用连续执行机构实现滑模控制中的连续控制量.然后利用backstepping技术实现连续执行机构的输出对滑模控制中的连续控制量的有限时间收敛.将提出的设计方法应用于导弹直接侧向力与气动力复合控制系统设计,并进行了仿真验证.     

Robust H/sub /spl infin// and mixed H/sub 2//H/sub /spl infin// filters for equalization designs of nonlinear communication systems: fuzzy interpolation approach

Generally, it is difficult to design equalizers for signal reconstruction of nonlinear communication channels with uncertain noises. In this paper, we propose the H/sub /spl infin// and mixed H/sub 2//H/sub /spl infin// filters for equalization/detection of nonlinear channels using fuzzy interpolation and linear matrix inequality (LMI) techniques. First, the signal transmission system is described as a state-space model and the input signal is embedded in the state vector such that the signal reconstruction (estimation) design becomes a nonlinear state estimation problem. Then, the Takagi-Sugeno fuzzy linear model is applied to interpolate the nonlinear channel at different operation points through membership functions. Since the statistics of noises are unknown, the fuzzy H/sub /spl infin// equalizer is proposed to treat the state estimation problem from the worst case (robust) point of view. When the statistics of noises are uncertain but with some nominal (or average) information available, the mixed H/sub 2//H/sub /spl infin// equalizer is employed to take the advantage of both H/sub 2/ optimal performance with nominal statistics of noises and the H/sub /spl infin// robustness performance against the statistical uncertainty of noises. Using the LMI approach, the fuzzy H/sub 2//H/sub /spl infin// equalizer/detector design problem is characterized as an eigenvalue problem (EVP). The EVP can be solved efficiently with convex optimization techniques.     

An enriched finite element method for efficient solutions of transient heat diffusion problems with multiple heat sources

Engineering with Computers - We propose an efficient formulation using the framework of Generalized Finite Element Method (GFEM) for the solutions of transient heat diffusion problems having...     

Analytical and experimental validations of a numerical band-limited Green’s function approach for modelling acoustic emission waves

Dynamic Green’s functions are essential for modelling acoustic emission (AE) wave propagation and for the quantitative characterisation of AE sources. In this work, a method for evaluating the Green’s function of a body using the finite element method is presented. The advantage of the proposed method is that it can be used to model realistic geometries, material properties and sources that cannot be treated analytically. The numerical results presented in this paper are compared with known analytical solutions of the Green’s function for an infinite isotropic plate and also with experimental measurements of AE waves generated by known artificial AE sources (ball impact and pencil lead break).     

Analytical and numerical modelling of AlGaN/GaN/AlN heterostructure based cantilevers for mechanical sensing in harsh environments

Some industrial areas as oil, automotive and aerospace industries, require electromechanical systems working in harsh environments. An elegant solution is to use III-V materials alloys having semiconductor, piezoelectric and pyroelectric properties. These materials, particularly nitrides such as GaN or AlN, enable design of advanced devices suitable for harsh environment. A cantilever structure based on AlGaN/GaN/AlN heterostructures coupled with a High Electron Mobility Transistor (HEMT) can act as an electromechanical device suited for sensing applications. In this article, we present the mechanical modelling of such a structure. An analytical and a numerical model have been developed to obtain the electrical charge distribution in the structure in response to mechanical stress. A theoretical electromechanical sensitivity of 3.5 μC m⁻² was achieved for the cantilever free end displacement of several hundreds of nanometres. Both models show good agreement, presenting less than 5% deviation in almost the whole structure. The differences between the two models that are pronounced near the clamped area can be explained by particular boundary conditions of the numerical model. The topological characterization and numerical modelling allowed the estimation of the equivalent intrinsic residual stress in the structure and the stress distribution within each layer. Finally, the dynamic mechanical characterization of fabricated cantilevers using laser interferometry is presented and compared to numerical modal analysis with less than 10% deviation between theoretical and experimental resonant frequencies. The obtained results enable the use of the analytical model for further study of the electromechanical coupling with the HEMT structure.     

An optimal approach to multiple tool selection and their numerical control path generation for aggressive rough machining of pockets with free-form boundaries

To machine pockets, especially ones with closed free-form boundary curves, roughing is crucial to part productivity, for this operation alone could take more than 60% of the total machining time. At present, there is a high demand from industry for a new machining technique that can efficiently cut pockets. Aggressive rough machining, in which the largest possible cutters are always employed and are fully immersed in workpieces, can be a solution. Although aggressive roughing is by far the most efficient machining strategy, compared to prior pocketing methods, no computer numerical control (CNC) programming technique has been developed to support it, resulting in few applications in machine shops. To address this urgent industrial need, based on the medial axis transform of a pocket, this work proposes an optimal approach to multiple tool selection and their numerical control (NC) path generation for aggressive roughing of the pocket. First, the NC paths of a specific tool are quickly generated using the pocket’s medial axis transform. Thanks to the unique characteristic of the medial axis transform, the paths can ensure the tool the largest accessible space for pocketing. At the same time, they can guarantee the tool to be free of gouging and interference. Then, an optimization model of selecting multiple cutters and generating their NC paths is built in order to achieve the highest efficiency of the aggressive rough machining. To demonstrate the advantages of this innovative approach, two examples are rendered, and their results are compared to those obtained by the existing methods. This approach can be directly implemented into current CAD/CAM software to promote aggressive rough machining of pockets in industry.     

Hypotrochoid spiral optimization approach for sizing and layout optimization of truss structures with multiple frequency constraints

Engineering with Computers - The primary aim of this article is to present a new improved version of the spiral optimization algorithm (SPO) for shape and size optimization of truss structures...     

An algorithm for sampling subsets of H/sub /spl infin// with applications to risk-adjusted performance analysis and model (in)validation

In spite of their potential to reduce computational complexity, the use of probabilistic methods in robust control has been mostly limited to parametric uncertainty, since the problem of sampling causal bounded operators is largely open. In this note, we take steps toward removing this limitation by proposing a computationally efficient algorithm aimed at uniformly sampling suitably chosen subsets of H/sub /spl infin//. As we show in the note, samples taken from these sets can be used to carry out model (in)validation and robust performance analysis in the presence of structured dynamic linear time-invariant uncertainty, problems known to be NP-hard in the number of uncertainty blocks.     

A DEM-DLM/FD method for direct numerical simulation of particulate flows: Sedimentation of polygonal isometric particles in a Newtonian fluid with collisions

An efficient direct numerical simulation method to tackle the problem of particulate flows at moderate to high concentration and finite Reynolds number is presented. Our method is built on the framework established by Glowinski and his co-workers [Glowinski R, Pan TW, Hesla TI, Joseph DD. A distributed lagrange multiplier/fictitious domain method for particulate flow. Int J Multiphase Flow 1999;25:755-94] in the sense that we use their Distributed Lagrange Multiplier/Fictitious Domain (DLM/FD) formulation and their operator-splitting idea but differs in the treatment of particle collisions. Compared to our previous works [Yu Z, Wachs A, Peysson Y. Numerical simulation of particle sedimentation in shear-thinning fluids with a fictitious domain method. J Non Newtonian Fluid Mech 2006;136:126-139; Yu Z, Shao X, Wachs A. A fictitious domain method for particulate flow with heat transfer. J Comput Phys 2006;217:424-52; Yu Z, Wachs A. A fictitious domain method for dynamic simulation of particle sedimentation in Bingham fluids. J Non Newtonian Fluid Mech 2007;145:78-91], the novelty of our present contribution relies on replacing the simple artificial repulsive force based collision model usually employed in the literature by an efficient Discrete Element Method (DEM) granular solver. The use of our DEM solver enables us to consider particles of arbitrary shape (at least convex) and to account for actual contacts, in the sense that particles actually touch each other, in contrast with the repulsive force based collision model. We validate GRIFF,¹ our numerical code, against benchmark problems and compare our predictions with those available in the literature. Results, which, to the best of our knowledge, have never been reported elsewhere, on the 2D sedimentation of isometric polygonal particles with collisions are presented.     

Sufficient conditions for the preservation of the boundedness in a numerical method for a physical model with transport memory and nonlinear damping

Departing from a finite-difference scheme to approximate solutions of a nonlinear, hyperbolic partial differential equation which generalizes the Burgers–Huxley equation from fluid dynamics, we investigate conditions on the model coefficients and the computational parameters under which positive and bounded initial data evolve into positive and bounded new approximations. The model under investigation includes nonlinear coefficients of damping and advection, and the reaction term extends the reaction law of the classical Fisher–Kolmogorov–Petrovsky–Piscounov equation. The method can be expressed in vector form in terms of a multiplicative matrix which, under certain parametric conditions, becomes an M-matrix. Using the fact that every M-matrix is non-singular and that the entries of its inverse are positive, real numbers, we establish sufficient conditions under which the method provides new, positive and bounded approximations from previous, positive and bounded data and boundary conditions. The numerical results confirm the fact that the conditions derived here are sufficient for the positivity and the boundedness of the approximations; moreover, computational experiments evidence the fact that the method still preserves these properties for values of the model and the numerical parameters outside of the analytic regions of positivity and boundedness. We point out that our simulations show a good agreement between the numerical approximations computed through our method and the corresponding, analytical solutions.     

Discretized LKF method for stability of coupled differential‐difference equations with multiple discrete and distributed delays

Time‐delay systems described by coupled differential‐functional equations include as special cases many types of time‐delay systems and coupled differential‐difference systems with time delays. This article discusses the discretized Lyapunov–Krasovskii functional (LKF) method for the stability problem of coupled differential‐difference equations with multiple discrete and distributed delays. Through independently dividing every delay region that the plane regions consists in two delays to discretize LKF, the exponential stability conditions for coupled systems with multiple discrete and distributed delays are established based on a linear matrix inequality (LMI). The numerical examples show that the analysis limit of delay bound in which the systems are stable may be approached by our result. Copyright © 2011 John Wiley & Sons, Ltd.     

A symmetric eight-step predictor-corrector method for the numerical solution of the radial Schrödinger equation and related IVPs with oscillating solutions

In this paper we present a new optimized symmetric eight-step predictor-corrector method with phase-lag of order infinity (phase-fitted). The method is based on the symmetric multistep method of Quinlan–Tremaine, with eight steps and eighth algebraic order and is constructed to solve numerically the radial time-independent Schrödinger equation during the resonance problem with the use of the Woods–Saxon potential. It can also be used to integrate related IVPs with oscillating solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. We measure the efficiency of the methods and conclude that the new method with infinite order of phase-lag is the most efficient of all the compared methods and for all the problems solved.