基于分段线性系统的宽频振动能量收集器

研究了一种基于分段线性系统的宽频振动能量收集器,主要由抗磁稳定悬浮结构、弹性膜及感应线圈组成。 在静止状 态下,悬浮磁铁不需要任何外界能量稳定地悬浮在热解石墨板之间。 当振动能量采集器受到水平振动激励时,悬浮磁铁在两热 解石墨板之间摆动;当摆动幅度比较大时,悬浮磁铁将与弹性膜发生碰撞使系统刚度呈阶段性变化;随着悬浮磁铁运动,感应线 圈中的磁通量发生变化产生感应电动势,从而使外界振动能转化为电能。 当水平激励振幅为 5 mm 时,系统的工作带宽达到 3. 2 Hz,最大输出电压达到 78 mV,最大输出功率为 56. 3 μW;当水平振动激励的加速度为 3 m/ s 2 时,系统的工作带宽达到 2 Hz,最大输出电压为 44 mV,最大输出功率为 18 μW。     

Window functions and sigmoidal behaviour of memristive systems

A common approach to model memristive systems is to include empirical window functions to describe edge effects and nonlinearities in the change of the memristance. We demonstrate that under quite general conditions, each window function can be associated with a sigmoidal curve relating the normalised time‐dependent memristance to the time integral of the input. Conversely, this explicit relation allows us to derive window functions suitable for the mesoscopic modelling of memristive systems from a variety of well‐known sigmoidals. Such sigmoidal curves are defined in terms of measured variables and can thus be extracted from input and output signals of a device and then transformed to its corresponding window. We also introduce a new generalised window function that allows the flexible modelling of asymmetric edge effects in a simple manner. Copyright © 2016 John Wiley & Sons, Ltd.     

How to represent continuous piecewise linear functions in closed form

This paper presents a simple approach to representing continuous piecewise linear functions in closed form for arbitrary dimensions. The absolute value function is used to embed non‐linearity, its usage increasingly nested as the dimension is increased. Copyright © 2006 John Wiley & Sons, Ltd.     

Bifurcation analysis of a piecewise smooth system with non‐linear characteristics

In previous works, there are no results about the bifurcation analysis for a piecewise smooth system with non‐linear characteristics. The main purpose of this study is to calculate the bifurcation sets for a piecewise smooth system with non‐linear characteristics. We first propose a new method to track the bifurcation sets in the system. This method derives the composite discrete mapping, Poincaré mapping. As a result, it is possible to obtain the local bifurcation values in the parameter plane. As an illustrated example, we then apply this general methodology to the Rayleigh‐type oscillator containing a state‐ period‐dependent switch. In the circuit, we can find many subharmonic bifurcation sets including global bifurcations. We also show the bifurcation sets for the border‐collision bifurcations. Some theoretical results are verified by laboratory experiments. Copyright © 2005 John Wiley & Sons, Ltd.     

基于分段线性插值法的应变片式扭矩传感器的温度补偿

本文针对应变片式扭矩传感器的温度漂移现象,建立基于分段线性插值法的温度补偿模型,将扭矩和温度的二维标定数据嵌入到数据融合软件算法中,根据精度要求分为多个不同区间并将区间内的标定点代入线性表达式,输出预测扭矩值,从而实时矫正该传感器扭矩随温度的漂移,使其具有温度自补偿功能。研究结果表明,利用分段线性插值法补偿后该传感器的灵敏度温度系数由7.615×10^(-4)/℃提升至1.429×10^(-4)/℃,温度附加误差相对值由2.67%提升至0.5%,均提升了5倍以上。该方法简单有效,实现了扭矩传感器的实时温度补偿,提高了扭矩传感器的温度稳定性。     

A novel compact piecewise‐linear representation

A new compact MAX representation for 2‐D continuous piecewise‐linear (PWL) functions is developed in this paper. The representation is promising since it can be easily generalized into higher dimensions. We also establish the explicit functional form of basis function and demonstrate that the proposed basis function is the elementary ‘building block’ from which a fully general 2‐D PWL function can be constructed. In addition, we reveal the relationship of basis function with minimal degenerate intersection and Hinging Hyperplane, which shows that the MAX model can unify Chua's canonical expression, Li's representation, lattice PWL function and Bremann's Hinging Finding Algorithm into one common theoretical framework. Copyright © 2005 John Wiley & Sons, Ltd.     

An analogue model of the memristor

The paper presents a working electrical scheme modeling the memristor. The scheme allows experimenting with the model under various testing signals. The user can use it to verify the theoretical presumptions about the memristor properties. Examples of several typical measurements are shown. Copyright © 2010 John Wiley & Sons, Ltd.     

Hyperchaos and horseshoe in a 4D memristive system with a line of equilibria and its implementation

We study a four‐dimensional system modified from a three‐dimensional chaotic circuit by adding a memristor, which is a new fundamental electronic element with promising applications. Although the system has a line of infinitely many equilibria, our studies show that when the strength of the memristor increases, it can exhibit rich interesting dynamics, such as hyperchaos, long period‐1 orbits, transient hyperchaos, as well as non‐attractive behaviors frequently interrupting hyperchaos. To verify the existence of hyperchaos and reveal its mechanism, a horseshoe with two‐directional expansion is studied rigorously in detail by the virtue of the topological horseshoe theory and the computer‐assisted approach of a Poincaré map. At last, the system is implemented with an electronic circuit for experimental verification. Copyright © 2013 John Wiley & Sons, Ltd.     

An efficient piecewise‐linear DC analysis method for general non‐linear circuits

The convergence problems of conventional DC analysis can be partly avoided by using piecewise‐linear analysis. This paper proposes a piecewise‐linear DC analysis method that can efficiently handle arbitrary couplings between non‐linear circuit elements. Piecewise‐linear modelling of the non‐linear circuit elements is automatically performed during simulation, using simplicial subdivisions. The number of linear regions, and thereby iterations, is considerably reduced by combining the common parts of separate simplicial subdivisions. Due to these reasons and since the method is formulated with the commonly used modified nodal approach, it has been possible to implement the method in the general‐purpose circuit simulator APLAC. The correct operation of the method is demonstrated with three examples. Copyright © 1999 John Wiley & Sons, Ltd.     

分段多项式拟合法测量光纤几何参数

光纤几何参数是影响光纤性能的一个重要指标。灰度法为光纤几何参数测量的一种常用方法,测量时需要对光纤通光照明以区分纤芯和包层。由于光并不完全集中于纤芯传播（部分光在包层中传播）,导致纤芯与包层的界面难以区分。为了准确找出纤芯边缘,本文利用两段多项式分别拟合纤芯和包层区域的光强灰度分布,求得两段多项式的交点对应的灰度值作为纤芯和包层的分界点,从而得到纤芯的边缘数据。利用分段三次Hermite插值对测量数据进行矫正,降低误差点对拟合的影响。通过对两组成像质量不同的光纤端面图像进行测量,用标准仪器先后测得纤芯的直径和不圆度为10.068µm、0.616%和10.397µm、0.766%,本文方法的测量值为9.999µm、0.716%和10.020µm、0.857%。实验表明,本文方法对光纤几何参数的测量具有较好的准确性和稳定性,而且从理论上讲,本文方法较之常用的灰度法更具有物理意义和测量原理上的合理性。     

Unknown piecewise constant parameters identification with exponential rate of convergence

The scope of this research is the identification of unknown piecewise constant parameters of linear regression equation under the finite excitation condition. Compared to the known methods, to make the computational burden lower, only one model to identify all switching states of the regression is used in the developed procedure with the following two-fold contribution. First of all, we propose a new truly online estimation algorithm based on a well-known DREM approach to detect switching time and preserve time alertness with adjustable detection delay. Second, despite the fact that a switching signal function is unknown, the adaptive law is derived that provides global exponential convergence of the regression parameters estimates to their true values in case the regressor is finitely exciting somewhere inside the time interval between two consecutive parameters switches. The robustness of the proposed identification procedure to the influence of external disturbances is analytically proved. Its effectiveness is demonstrated via numerical experiments, in which both abstract regressions and a second-order plant model are used.     

一种基于直方图的自适应分段线性变换法

针对灰度图像分段线性变换转折点选取的问题,提出了在直方图基础上使用Otsu法和格拉布斯法,设计了一种得到分段线性变换函数双转折点的方案。该方案自动选取双转折点,确定了灰度变换曲线,对图像的背景区、过渡区和目标区进行了很好的区分。该方案将背景和目标之间的过渡区进行线性增强,从而为边沿检测提供了有效的预处理方案。实验表明该方案寻找分段线性变换的转折点简单高效,具有较好的应用前景。     

基于电压为线性函数的开断潮流计算及开断函数选择

为进行快速开断潮流计算,可将电力系统节点电压展开为关于开断支路导纳的泰勒级数,若采用简单的线性开断函数,由于节点电压与支路导纳之间有很强的非线性关系,电压泰勒级数收敛非常缓慢。通过严格的数学推理,提出一种使节点电压与开断支路导纳呈线性关系的开断函数,并证明该开断函数的存在性及唯一性。由线性电压函数可快速精确地计算开断系统的潮流。对IEEE 14节点系统的仿真结果验证了所提方法的正确性。     

直线压缩机用无内定子动磁式直线振荡电机的建模与分析

针对直线压缩机要求结构紧凑及力特性好的特点,提出一种新型动磁式直线振荡电机.该电机具有无需内定子、动子质量轻、加工难度小及力特性平稳等优点.在分析电机运行原理的基础上,建立了该电机的等效磁路模型,并推导了气隙磁链、电磁推力及电感的解析表达式.为验证等效磁路模型的正确性,建立了电机准二维有限元模型,并对电机气隙磁场分布及力特性进行了深入分析.实际加工了一台实验样机并进行了静态推力实验,样机测试结果、有限元分析结果和磁路分析结果较好吻合,证明了所建模型的正确性.     

An approximation for the input conductivity function of the non‐linear resistive grid

The 2‐term approximations for the input conductivity functions, i_in=f_in(v_in), of a grid of similar weakly non‐linear (parabolic) conductors, and the grid's symmetric cuts, measured between two close nodes, are derived, using a semi‐empirical method; the results of a relevant PSpice simulation are presented. The functions f_in(v_in) of the grid's symmetric cuts possess a common analytical feature. Simulation results show that the error in the calculation of the non‐linear terms in the input functions is less than 1 per cent. Copyright © 2001 John Wiley & Sons, Ltd.     

Synthesis of multiport resistors with piecewise‐linear characteristics: a mixed‐signal architecture

Non‐linear multiport resistors are the main ingredients in the synthesis of non‐linear circuits. Recently, a particular PWL representation has been proposed as a generic design platform (IEEE Trans. Circuits Syst.‐I 2002; 49 :1138–1149). In this paper, we present a mixed‐signal circuit architecture, based on standard modules, that allows the electronic integration of non‐linear multiport resistors using the mentioned PWL structure. The proposed architecture is fully programmable so that the unit can implement any user‐defined non‐linearity. Moreover, it is modular: an increment in the number of input variables can be accommodated through the addition of an equal number of input modules. Copyright © 2005 John Wiley & Sons, Ltd.     

Identification of task model using piecewise affine systems with variable switching points and its application

This paper considers a human‐operated task model based on identification techniques using switched systems expressed by mixed logical dynamical systems. In the system, each subsystem is expressed by a piecewise affine system. For a model to be identified, it is not easy to determine a number of subsystems in advance. In this paper, we propose a simultaneous identification technique which takes into account both a number of subsystems and parameters, so that a piecewise affine model of a human operation can be obtained. In addition, the obtained model is applied to automation. The effectiveness of the proposed method is illustrated by simulations and experiments. © 2011 Wiley Periodicals, Inc. Electr Eng Jpn, 176(1): 46–54, 2011; Published online in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/eej.21079     

Finding all solutions of piecewise‐linear resistive circuits using the dual simplex method

An efficient algorithm is proposed for finding all solutions of piecewise‐linear (PWL) resistive circuits using linear programming (LP). This algorithm is based on a simple test (termed the LP test) for non‐existence of a solution to a system of PWL equations in a given region. In the conventional LP test, the system of PWL equations is transformed into an LP problem, to which the simplex method is applied. However, this algorithm requires a very large number of pivotings because the simplex method is applied on many regions. In this paper, we introduce the dual simplex method to the LP test, which makes the average number of pivotings per region much smaller (less than one, for example) and makes the algorithm very efficient. By numerical examples, it is shown that the proposed algorithm could find all solutions of large‐scale problems, including those where the number of variables is 300 and the number of linear regions is 10³⁰⁰, in practical computation time. Copyright © 2002 John Wiley & Sons, Ltd.     

On simplex‐based piecewise‐linear approximations of non‐linear mappings

Simplex‐based piecewise‐linear (PWL) approximations of non‐linear mappings are needed when the robust PWL analysis is used to directly solve non‐linear equations. This paper proposes a straightforward technique for transforming the well‐known approximations into another form. This new form is computationally more efficient, since it preserves the sparse structure of the original Jacobian matrix. Furthermore, this new form of PWL approximation explicitly relates the simplex‐based PWL analysis to the conventional formulation of the Katzenelson algorithm. The proposed transform technique is also extended to treat groupwise‐separable mappings and, finally, non‐separable but sparse mappings that arise in real‐life simulation of large electronic circuits. In this paper, all these (transformed) simplex‐based PWL approximations are compared in terms of their generality and efficiency. The computational efficiency of the PWL approximation that utilizes sparsity is validated with realistic simulations. Copyright © 2005 John Wiley & Sons, Ltd.