A new algorithm for the extraction of the surface waves for the Green’s function in layered dielectrics

There exist the complicated waveguide modes as well as the surface waves in the electromagnetic field induced by a horizontal electric dipole in layered lossless dielectrics between two ground planes. In spectral domain, all these modes can be characterized by the rational parts with the real poles of the vector and scalar potentials. The accurate extraction of these modes plays an important role in the evaluation of the Green’s function in spatial domain. In this paper, a new algorithm based on rational approximation is presented, which can accurately extract all the real poles and the residues of each pole simultaneously. Thus, we can get all the surface wave modes and waveguide modes, which is of great help to the calculation of the spatial domain Green’s function. The numerical results demonstrated the accuracy and efficiency of the proposed method.     

An exponential stability result for the wave equation

We consider a system described by the one-dimensional linear wave equation in a bounded domain with appropriate boundary conditions. To stabilize this system, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the proposed controller is a proper rational function which consists of a strictly positive real function and some poles on the imaginary axis. We then show that under some conditions the closed-loop system is exponentially stable.     

Automation of the stabilization diagrams for subspace based system identification

For the continuous real-time monitoring of structures, the realization of a fully automatic real time system identification without any human intervention is the most crucial step. In this study, a new technique for the automation of the stability diagrams is developed that uses the modal phase collinearity (MPC) in order to quantify the spatial consistency of the identification results. In the new technique, the stabilization diagram is modeled as a histogram composed of overlapping bins. New strategies for the multiple occurrence of poles in the neighboring bins and double poles within a bin are developed. A new cluster validity index is proposed which can solve the problem caused by the scale of measurements and which can be directly calculated from non-normalized data. The threshold limits are defined for the proposed index. The results of the study show that the automation of the pole selection process from the stabilization diagrams is successfully realized. It is also shown that for local modes, the MPC value will be substantially smaller as compared to the global modes and can be used as a quick, efficient and powerful measure of global versus local response behavior.     

Stabilization and disturbance rejection for the wave equation

We consider a system described by the one-dimensional linear wave equation in a bounded domain with appropriate boundary conditions. To stabilize the system, we propose a dynamic boundary controller applied at the free end of the system. The transfer function of the proposed controller is a proper rational function of the complex variable and may contain a single pole at the origin and a pair of complex conjugate poles on the imaginary axis, provided that the residues corresponding to these poles are nonnegative; the rest of the transfer function is required to be a strictly positive real function. We then show that depending on the location of the pole on the imaginary axis, the closed-loop system is asymptotically stable. We also consider the case where the output of the controller is corrupted by a disturbance and show that it may be possible to attenuate the effect of the disturbance at the output if we choose the controller transfer function appropriately. We also present some numerical simulation results which support this argument     

A robust method for the computation of new closed‐form Green's functions for microstrip structures

A robust approach for the computation of new closed‐form Green's functions is considered to calculate the symmetrical microstrip Green's functions. In this method, the surface‐wave poles are first extracted using a recursive contour integration method. Then, the remainder is approximated by a series of complex exponentials using the Prony's method or the generalized pencil‐of‐function method (GPOF) along the extended rooftop shaped path in k_ρ‐plane. Subsequently, an analytical identity is employed to obtain the new spatial‐domain Green's functions. It is observed that this method can evaluate the spatial‐domain Green's functions accurately and efficiently for both near and far fields. In addition, there is no erroneous results in the near‐field region when z ≠ z′ and ρ → 0. © 2011 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2011.     

Direct tip regulation of a single-link flexible manipulator by adaptive variable structure control

Direct tip position regulation of flexible manipulators is one of the most challenging control tasks. There are mainly three problems to be addressed in order to achieve good performance. The first two control problems arise owing to the unstable zeros and complex poles in the system nominal part which is dominated by a transfer function. The third problem is the existence of unstructured uncertainties owing to the truncation of high-order resonance modes and system nonlinearities. Because of the above difficulties and in particular the non-minimum-phase nature, tip regulation task of flexible manipulators is usually solved indirectly: direct control of joint angle and suppression of the flexible link vibration. The aim of this study is to investigate the direct approach for tip regulation. Since the tip transfer function contains unstable zeros and the first few dominant flexible modes (complex poles), a reference model of the same order is selected which does not have any finite zero but all negative real poles. In order to force the system to follow the reference model in the presence of the unstructured uncertainties, a variable structure controller is adopted in which the switching surface is derived from the reference model. When in sliding mode, the system performs as the reference model. Hence there will be no vibration and the tip position regulation can be achieved when the system approaches steady state. To improve the system responses further, an adaptation law with dead-zone scheme is combined with the variable structure controller. Simulation results show that link vibrations have been eliminated and the control profile is fairly smooth.     

Some considerations for estimator-based compensator design

In this paper some criteria are presented for dividing the closed-loop system poles of a feedback system between the estimator and the controller when using an estimator-based compensator. The criteria are based on frequency response considerations, but are related to some well-known facts in the time domain. It is well known, for example, that the closed-loop system poles are the poles of the estimator in union with the controller poles. It is also well known that the time response of the closed-loop plant states due to a command depends only on the closed-loop control poles, and the response of the estimate error depends only on the closed-loop estimator poles. In the frequency domain, the following can be said: the open-loop compensator transfer function from the sensor measurement to the control and the closed-loop transfer function from the sensor measurement to the system output are both independent of how the closed-loop poles are distributed between the controller and the estimator, but the closed-loop transfer function from the command to the control or system output is not. Placing the slower closed-loop poles in the controller causes the control gains to be smaller, which in turn causes the effect of the command signal to be attenuated, both at the control and at the closed-loop system output. Making use of these facts allows the closed-loop poles to be divided between the controller and the estimator on a more intelligent basis than ‘the estimator poles should be three times faster than the controller poles’. In an example, these concepts are applied to the design of a platform despin control system for a dual-spin satellite.     

On the design of single-loop single-input-output feedback control systems in the complex-frequency domain

This paper is concerned with single-loop, single-input-output, feedback control systems consisting of a plant, controller, and feedback sensor each modeled by a rational transfer function. The plant can be unstable, nonminimum phase, and even improper. The objective is the determination of the controller transfer function for which the system is asymptotically stable and design objectives are met. This has always been the goal in feedback system design. What is novel about the approach presented here is that the family of all stabilizing controller transfer functions is parameterized in terms of a rational functionK (s). The design method allows for complete freedom in the selection of all closed-loop system poles (except those associated with hidden modes). This is accomplished through the choice of the denominator polynomial forK (s). The remaining design freedom lies in the selection of the numerator ofK (s). This freedom is utilized to shape the system sensitivity function and to achieve specified steady-state error coefficients. A numerical example in which the plant is unstable and nonminimum phase is presented to illustrate the above points. The final design is compared with alternative designs and the tradeoffs are clearly displayed.     

SIMO和MISO系统绝对稳定性问题的一个猜想和几个推论

首先分析了具有多个非线性特性的 SIMO 和 MISO 系统的绝对稳定性问题, 指出应用已知的频域判据来解决上述问题很难奏效. 然后, 基于所有孤立部分传递函数都正实的充分必要条件给出了上述系统为稳定的一个猜想, 当传递函数的零极点都位于虚轴上时, 由这一猜想得到了一个已知的结论; 当传递函数的零极点都位于实轴上时, 由这一猜想得到了一个新的结论, 本文证明该结论是正确的; 最后, 根据这一猜想, 给出了传递函数极点位于复平面的一个例子, 它涉及到一类系数矩阵为时变正定矩阵的振动方程的稳定性问题, 值得去深入研究.     

Explicit form for impedance of cauer networks

In this paper a new procedure is established to obtain in closed form the poles and zeros of the impedance function of a first Cauer Network. The technique involves the continued fraction representation of the corresponding Laplace transform as a rational function whose numerators and denominators can be represented by tridiagonal determinants.     

Analytic phase margin design

Doyle et al. (1992) presented an algorithm for analytic phase margin control design. Without special care, however, the compensator computed with this algorithm may not be a real rational function, The problem is evident when the plant has real unstable poles. In this case the algorithm requires a mapping of real points into complex values, and it is not clear that the resulting compensator has real coefficients. The purpose of this paper is to show how a complex mapping required in this algorithm can always be selected so that the compensator does have real coefficients     

Systematic and efficient root finder for computing the modal spectrum of planar layered waveguides

An efficient and systematic strategy to find the propagation constants of real, complex, and leaky modes of covered and uncovered planar multilayered isotropic/uniaxial waveguides is presented. This strategy first builds up a pole-free characteristic function and then makes use of a root-searching scheme based on an integral nature method to search for its zeros. For uncovered waveguides, the branch points of the characteristic function can be removed by introducing the upper half-space vertical wavenumber as the working variable. Examples of the efficiency, reliability, and robustness of the presented technique are given for both covered and uncovered waveguides, which sets up this technique as a very convenient CAD tool. The method is also applied to study a new and interesting problem: the evolution of the modes of a grounded dielectric waveguide when increasing the permittivity of the upper semi-infinite medium. © 2003 Wiley Periodicals, Inc. Int J RF and Microwave CAE 14, 73–83, 2004     

具有承袭性的切触有理插值算法

有理插值是函数逼近的一个重要内容,而降低切触有理插值的次数和解决切触有理插值函数的存在性是有理插值的一个重要问题。切触有理插值函数的算法大都是基于连分式进行的,其算法可行性是有条件的,且计算量较大。利用牛顿多项式插值承袭性的思想和分段组合的方法,构造出了一种无极点的切触有理插值函数,并推广到向量值切触有理插值情形;既解决了此类切触有理插值函数存在性问题,又降低了切触有理插值函数的次数。给出误差估计,并通过数值实例说明该算法具有承袭性、计算量低、便于实际应用等特点。     

Bipartite Polar Classification for Surface Reconstruction

In this paper, we propose bipartite polar classification to augment an input unorganized point set ? with two disjoint groups of points distributed around the ambient space of ? to assist the task of surface reconstruction. The goal of bipartite polar classification is to obtain a space partitioning of ? by assigning pairs of Voronoi poles into two mutually invisible sets lying in the opposite sides of ? through direct point set visibility examination. Based on the observation that a pair of Voronoi poles are mutually invisible, spatial classification is accomplished by carving away visible exterior poles with their counterparts simultaneously determined as interior ones. By examining the conflicts of mutual invisibility, holes or boundaries can also be effectively detected, resulting in a hole‐aware space carving technique. With the classified poles, the task of surface reconstruction can be facilitated by more robust surface normal estimation with global consistent orientation and off‐surface point specification for variational implicit surface reconstruction. We demonstrate the ability of the bipartite polar classification to achieve robust and efficient space carving on unorganized point clouds with holes and complex topology and show its application to surface reconstruction.     

Full wave solution of dielectric loaded waveguides and shielded microstrips utilizing finite difference and the conjugate gradient method

Dynamic analysis of waveguide structures containing dielectric and metal strips is presented. The analysis utilizes a finite difference frequency domain procedure to reduce the problem to a symmetric matrix eigenvalue problem. Since the matrix is also sparse, the eigenvalue problem can be solved quickly and efficiently using the conjugate gradient method resulting in considerable savings in computer storage and time. Comparison is made with the analytical solution for the loaded dielectric waveguide case. For the microstrip case, we get both waveguide modes and quasi-TEM modes. The quasi-TEM modes in the limit of zero frequency are checked with the static analysis which also uses finite difference. Some of the quasi-TEM modes are spurious. This article describes their origin and discusses how to eliminate them. Numerical results are presented to illustrate the principles.     

Representation Theorems for Analytic Machines and Computability of Analytic Functions

We present results concerning analytic machines, a model of real computation introduced by Hotz which extends the well-known Blum, Shub and Smale machines (BSS machines) by infinite converging computations. The well-known representation theorem for BSS machines elucidates the structure of the functions computable in the BSS model: the domain of such a function partitions into countably many semi-algebraic sets, and on each of those sets the function is a polynomial resp. rational function. In this paper, we study whether the representation theorem can, in the univariate case, be extended to analytic machines, i.e. whether functions computable by analytic machines can be represented by power series in some part of their domain. We show that this question can be answered in the negative over the real numbers but positive under certain restrictions for functions over the complex numbers. We then use the machine model to define computability of univariate complex analytic (i.e. holomorphic) functions and examine in particular the class of analytic functions which have analytically computable power series expansions. We show that this class is closed under the basic analytic operations composition, local inversion and analytic continuation.     

Identification of rational approximate models inH∞ using generalized orthonormal basis

Robust identification with FIR models fails to be successful when the number of coefficients to be estimated becomes large, caused by lightly damped modes of the plant or poles very close to the unit circle. The paper presents a two-stage algorithm to obtain a low-order approximate model in frequency domain in a generalized orthonormal basis with guaranteed H^∞ error bound for deterministic linear time-invariant stable systems, the first stage being an L^∞ rational approximation and the second nonlinear step being an H ^∞ rational approximation     

Numerical study for two-point boundary value problems using Green''s functions

In this paper, we study the Green's function to find numerical solutions of second-order ordinary differential equations for two-point boundary value problems. We derive some properties of Green's function which can be applied to a Green's function integral formula. And we discuss and analyze numerical solutions which are obtained by the Green's function method and a shooting method.     

Pole‐zero analysis and wavelength scaling of carbon nanotube antennas

Carbon nanotube (CN) antennas have applications in the THz electromagnetic spectrum. Nanotubes have a highly dispersive and frequency dependent conductivity model. In this article, we compare the poles and zeros in the input impedance of CN antennas at different lengths. We used model‐based parameter estimation to approximate the input impedance of the antenna with a rational function in the complex frequency domain. Despite dispersive conductivity of CN, the imaginary part of the poles and zeros are respectively the integer multiples and odd multiples of the imaginary part of the first pole and zero. However, the real part of poles is almost constant, while the pattern was not observed for the real part of zeros. We also show that CN dipoles operating between 43 and 53 GHz are well matched if the source impedance is much higher than 50 ohms, and even higher than 12.9 kΩ. The fundamental resonances (f₀) of CN dipoles plotted versus their inverse‐half‐length (1/L) are linearly related, but the intercept of the fitted straight line is non‐zero unlike that for perfect electric conductor (PEC) dipoles. This leads to non‐linear variation in wavelength scaling of CN dipoles. The resonant CN antennas are relatively much shorter than PEC dipoles.