双各向异性色散介质电磁波传播Z-时域有限差分分析

基于一种改进的Z变换-时域有限差分(Z-Finite-Difference Time-Domain,Z-FDTD)方法,即将双各向异性色散介质的频域本构方程先转化到Z域中,再利用Z变换的性质将其转换到时域,得到离散时域的FDTD迭代式,分析了双各向异性色散介质电磁波传播特性.由于Omega媒质是一种典型的双各向异性色散介质,以此为例编程计算了垂直入射在Omega介质板情形下产生的同极化和交叉极化电磁波的反射和透射情况,并通过算例和解析解对比验证了算法的正确性,最后对其电磁散射特性进行了分析.     

Flexible time domain averaging technique

Time domain averaging(TDA) is essentially a comb filter,it cannot extract the specified harmonics which may be caused by some faults,such as gear eccentric.Meanwhile,TDA always suffers from period cutting error(PCE) to different extent.Several improved TDA methods have been proposed,however they cannot completely eliminate the waveform reconstruction error caused by PCE.In order to overcome the shortcomings of conventional methods,a flexible time domain averaging(FTDA) technique is established,which adapts to the analyzed signal through adjusting each harmonic of the comb filter.In this technique,the explicit form of FTDA is first constructed by frequency domain sampling.Subsequently,chirp Z-transform(CZT) is employed in the algorithm of FTDA,which can improve the calculating efficiency significantly.Since the signal is reconstructed in the continuous time domain,there is no PCE in the FTDA.To validate the effectiveness of FTDA in the signal de-noising,interpolation and harmonic reconstruction,a simulated multi-components periodic signal that corrupted by noise is processed by FTDA.The simulation results show that the FTDA is capable of recovering the periodic components from the background noise effectively.Moreover,it can improve the signal-to-noise ratio by 7.9 dB compared with conventional ones.Experiments are also carried out on gearbox test rigs with chipped tooth and eccentricity gear,respectively.It is shown that the FTDA can identify the direction and severity of the eccentricity gear,and further enhances the amplitudes of impulses by 35%.The proposed technique not only solves the problem of PCE,but also provides a useful tool for the fault symptom extraction of rotating machinery.     

Quantitative feedback synthesis of sampled-data systems with time-delay by approximate Z-transform

In this paper, the equivalent disturbance rejection (EDR) in QFT design methodology is proposed for dealing with sampled-data systems with time-delay. This EDR is mainly to overcome the non-minimum phase zero generated by the first order Pade' approximation of the time-delay factor. Due to plant parameter uncertainty, the analogue controller is to be designed so that the system response lies within permissible bounds. By approximate Z-transform, the analogue controller can be transformed directly into a digital one and then the analogue plant is transformed into the digital plant, with sampling time as a free parameter. By adjusting the sampling time, the uncertain sampled-data system can be stabilized. In comparison with other approaches, our design framework is much more systematic by using only algebraic manipulations and transparent enough to guide the designer to realize the physical controller for the plant with prescribed bounds on its parameters.     

ROBUST SAMPLED-DATA CONTROL SYSTEMS ANALYSIS BY APPROXIMATE Z-TRANSFORM USING HIGHER-ORDER INTEGRATORS

In this paper, robust sampled-data control systems are analyzed in the frequency domain. Stability analysis of a sampled-data control system using higher-order integrators was proposed by Wang et al. in 1990 [1] and adopted in the approximate Z-transform by Wang et al. in 1997 [2]. We further apply the approximate Z-transform to analyze the stability boundary of a sampled-data control system in which the plant transfer function has bounds prescribed on its parameters.     

Another Look at Z-transform Technique for Deriving Unit Impulse Response Function

This paper presents a technique to derive the unit impulse response functions (UIRF) used for determination of unit hydrograph by employing the Z-transform technique to the response function derived from the Auto Regressive Moving Average (ARMA) process of order (p, q). The proposed approach was applied to reproduce direct surface runoff for single storm event data registered over four watersheds of area ranging from 0.42 to 295 km². It is observed that the UIRF based on ARMA (1, 2) and ARMA (2, 2) provides a better representation of the watershed response. Further, to test the superiority of the developed impulse response function form ARMA process, the direct runoff hydrographs were computed using the simple ARMA process and optimized Nash’s two parameter model and compared with the results obtained from UIRF’s of ARMA model. The performance of the models based on the graphical presentation as well as from the test statistics viz. RMSE and MAPE indicates that UIRF-ARMA (p, q) performs better than optimized Nash Model and mostly similar to simple ARMA (p,q) model. Further more, the ARMA process of order p ≤ 2 and q ≤ 2 is generally sufficient and less cumbersome than the Argand diagram based approach for UIRF derivation.     

Investigation of Buck-boost DC–DC Converter Operation in Discontinuous Conduction Mode (DCM) and the Effect of Converter Elements on Output Response Using a Mathematical Model Based on Laplace and Z-Transforms

In this paper, a new method based on Laplace and Z-transforms is proposed for mathematical modeling of a buck-boost DC–DC converter in discontinuous conduction mode (DCM). The Laplace transform is used to obtain the time response of the output voltage and inductor current. The Z-transform is used to analyze the transient and steady state responses. Using the determined initial values of output voltage and inductor current which are obtained by the final value theorem of Z-transform, the effect of converter elements on transient and steady state responses can be analyzed by using the proposed method. Finally, the results of theoretical analysis are compared to experimental and simulation results in PSCAD/EMTDC software.     

一类传染病扩散模型的研究

通过构造Z变换和Liapunov函数 ,对一类传染病扩散模型进行了研究 ,得到了全局渐近稳定解的充分条件 ,进而对有关传染病扩散的实际现象给出了合理的解释     

具有逐段常值变元的时滞微分方程的振动性

考虑多时滞情形下具有逐段常值变元的时滞微分方程的振动性.应用修改Z-变换,得到了时滞微分方程的特征方程,并且给出了时滞微分方程振动的充分必要条件,即时滞微分方程是振动当且仅当它的特征方程在(0,1)内没有根.本文结果推广了文献[1]中的结果.     

生产库存系统的稳定性和牛鞭效应分析

为了讨论供应链系统稳定性与牛鞭效应之间的关系,建立了生产库存控制系统的离散微分方程模型.基于Z-变换理论研究了生产库存系统的动态性.在库存充足和库存不充足2种运作机制下,研究了使生产库存系统稳定和不稳定的参数范围;在2种运作机制以及实际系统下,分别在稳定区域和不稳定区域中,基于不同的需求模式研究了生产交付速率波动性、系统稳定与不稳定性以及牛鞭效应,并给出了相应的数值仿真.结果显示,合理地选择库存和订单决策参数,不仅能够保证系统稳定,而且可以减小系统的牛鞭效应.基于稳定性分析的分段线性化是研究具有非线性特性生产库存订购系统的一种有效方法.该研究为改善供应链系统的库存和订单决策提供了有益的建议.     

On detecting predictability of one-sided sequences

We consider predicting and predictability for discrete time processes in a pathwise setting where only a sole one-sided semi-infinite sequence of past values is available, and where statistical properties of the ensemble of the paths are unknown. We obtain some sufficient conditions of predictability in the terms of degeneracy of frequency characteristics representing one-sided modifications of the Z-transform. These characteristics are defined for one-sided semi-infinite sequences representing of the past values. Some predictors are discussed.