Finite-time control of DC–DC buck converters via integral terminal sliding modes

This article presents novel terminal sliding modes for finite-time output tracking control of DC–DC buck converters. Instead of using traditional singular terminal sliding mode, two integral terminal sliding modes are introduced for robust output voltage tracking of uncertain buck converters. Different from traditional sliding mode control (SMC), the proposed controller assures finite convergence time for the tracking error and integral tracking error. Furthermore, the singular problem in traditional terminal SMC is removed from this article. When considering worse modelling, adaptive integral terminal SMC is derived to guarantee finite-time convergence under more relaxed stability conditions. In addition, several experiments show better start-up performance and robustness.     

圆环孔径衍射高斯光束远场发散角研究

基于夫琅禾费衍射理论,通过对衍射积分的核函数进行近似,推导并得出了简洁的经圆环形孔径衍射的高斯光束远场发散角的近似解析式。在不同衍射孔径外径和不同遮拦比的条件下,将该解析式与严格的夫琅禾费衍射积分进行比较,发现二者求出的远场发散角接近一致,最大误差不超过2.7%。与传统数值积分求取光束发散角相比,该近似解析式在避免繁琐的积分运算同时保持了较高的精度。该解析式成立条件为高斯光束的束腰直径大于等于3.5倍中心遮拦直径,且小于等于孔径直径;在实际工程应用中,特别是具有大口径、小遮拦比特点的空间激光通信光学天线这一应用场景,该条件一般能够被满足。     

Splicing losses between dissimilar optical waveguides

A simple computational formalism has been derived for the analysis of splicing and return losses between different optical waveguides. It has been found that the splicing loss can be approximated by the overlap integral method as long as total reflectance is negligible. The reciprocity of splicing loss between two single-mode waveguide is theoretically confirmed while return loss is found nonreciprocal. The return loss can be tolerably approximated by simple Fresnel formula except near the resonance. When close to the resonance, the deviation from Fresnel approximation is found to be strongly dependent on the structure of the waveguide and the refractive index difference between the core and clad     

Failure criteria of flip chip joints during accelerated testing

The criteria used to determine electrical failure was explored during accelerated testing of underfilled flip chip joints as a function of both different thermal cycling conditions and different sampling methods. The criteria was based on resistance measurements of daisy-chained solder joints monitored in situ and by endpointing. The sensitivity of the resistance criteria was found to depend strongly on test conditions and often could not be categorized into simple pass/fail groupings. Also, extremely small resistance changes were measured for joints with through-cracks generated by fatigue. Experimental error associated with fixing the cycles to failure was minimized by monitoring the absolute changes in resistance as a function of cycling time while simultaneously measuring the temperature dependence of resistance as the joints degrade. Failure times derived from interval part monitoring closely approximated in situ monitoring, but the resistance measurements for mild cycling conditions required a high degree of accuracy. Finally, a tunneling model is proposed to explain the resistance behavior of cracked joints.     

Error performance of selection combining and switched combining systems in Rayleigh fading channels with imperfect channel estimation

In this paper, we present a general analysis of the performance of selection combining (SC), switch-and-stay combining (SSC), and switch-and-examine combining (SEC) systems in Rayleigh fading channels with imperfect channel estimation (ICE). The complex channel estimate and the actual fading are modeled as jointly Gaussian random variables. For SC systems with channel estimation error, closed-form expressions are obtained for the error rates of M/sub s/-ary pulse amplitude modulation (PAM) and rectangular-quadrature amplitude modulation (QAM), and simple single integral formulas with finite integration limits are derived for the symbol error probability of arbitrary two-dimensional (2-D) modulation formats. These error probability expressions are then applied to three types of channel estimation errors potentially encountered in practical systems to study their impact on the performance of selection diversity. Moreover, single integral formulas with finite integration limits are derived for the performance of SSC and SEC systems with minimum mean square error (MMSE) channel estimation. Optimum switching thresholds for 2-D modulation formats with MMSE based switched combining are acquired through numerical computation.     

Quadratic phase error loss in circular apertures

A very simple expression in closed form has been derived for the loss in gain of a circular aperture suffering quadratic phase error. It is applicable to amplitude distributions that can be approximated by a truncated Gaussian form that tapers to any arbitrary edge value.     

Analysis of DPSK error rate due to multipath delay spread

The intersymbol interference (ISI) produced by multipath channel delay spread can be approximated as Gaussian noise. The equivalent average signal-to-noise power ratio (SNR) is defined. Very simple expressions for average bit error rate (BER) due to delay spread are derived for linear quaternary DPSK (QDPSK) transmission with differential detection over mobile radio Rayleigh fading channels.<>     

Performance of an array receiver with a Kalman channel predictorfor fast Rayleigh flat fading environments

We develop an approach for using an antenna array for tracking fast Rayleigh flat fading channels and suppressing cochannel interference. The fast flat fading process is assumed to be a general autoregressive (AR) process in order to characterize temporal variation of channels and evaluate its effect on the receiver structure and performance. The optimal array receiver structure that minimizes the probability of error for BPSK signals is derived, which includes a Kalman filter to predict the fading channels. A simple integral expression for the probability of error is also derived for the optimal receiver. In particular, we analyze the case with identical shaping filters. An irreducible probability of error is shown to exist due to the prediction error of multiple channels. Another interesting observation from the study is that the diversity gain with m antenna elements in the presence of k interferences is usually greater than (m-k), even in the presence of channel prediction error. Simulations are carried out to verify the theoretical analysis     

A Simple Polynomial Approximation to the Gaussian Q-function and Its Application

A simple polynomial approximation to the Gaussian Q-function is proposed, based on the observation that a Gaussian random variable can be well approximated by a sum of uniform random variables. The approximation can be used to obtain accurate explicit approximations to problems that otherwise do not have explicit solutions or approximate explicit solutions. As an example, an explicit expression for the average symbol error rate of M-ary pulse amplitude modulation in lognormal channels is derived using the new approximation, and the approximate symbol error rate is shown to be very close to the exact value.     

An approximation of the radiation integral for distorted reflectorantennas using surface-error decomposition

The physical optics/aperture integration (PO/AI) formulation is often used to analyze the radiation patterns of reflector antennas. In this study, the PO/AI radiation integrals for distorted reflector antennas are addressed. The surface error of the antennas is approximated by a series of surface expansion functions. The radiation integral is decomposed into a series of radiation-type integrals, each of which corresponds to one of the surface expansion functions. Each of these radiation-type integrals is then weighted by amplitude coefficients. The advantage of performing the decomposition is that each of the radiation-type integrals can be computed and the pattern data stored. The computation of the pattern for a distorted reflector antenna with a changing error profile is performed by recalling the pattern data for each perturbation term and weighting it with the amplitude coefficient. This facilitates rapid evaluation of the radiation integral in cases where the error profile is changing (for example, time-varying errors). The superposition of integrals presented in this paper was shown to be valid for surface-error profiles up to 0.1 λ rms amplitude     

Indirect Sliding Mode Control of Power Converters Via Double Integral Sliding Surface

The steady-state regulation error in power converters that use the conventional hysteresis-modulation-based sliding mode controller can be suppressed through the incorporation of an additional integral term of the state variables into the controller. However, it is found that with the indirect type of sliding mode controller (derived based on the equivalent control approach), the same approach of integral sliding mode control is ineffective in alleviating the converter's steady-state error. Moreover, the error increases as the converter's switching frequency decreases. This paper presents an in-depth study of the phenomenon and offers a solution to the problem. Specifically, it is proposed that an additional double-integral term of the controlled variables to be adopted for constructing the sliding surface of indirect sliding mode controllers. Simulation and experimental results are provided for verification.     

Design of Near-Allpass Strictly Stable Minimal-Phase Real-Valued Rational IIR Filters

In this brief, a near-allpass strictly stable minimal-phase real-valued rational infinite-impulse response filter is designed so that the maximum absolute phase error is minimized subject to a specification on the maximum absolute allpass error. This problem is actually a minimax nonsmooth optimization problem subject to both linear and quadratic functional inequality constraints. To solve this problem, the nonsmooth cost function is first approximated by a smooth function, and then our previous proposed method is employed for solving the problem. Computer numerical simulation result shows that the designed filter satisfies all functional inequality constraints and achieves a small maximum absolute phase error.      

一种基于 PI 控制的数字低压差稳压器高速可调节模型

数字低压差线性稳压器由于可以在低电源电压下工作而被广泛使用。在数字低压差线性稳压器中,其利用模数转换器和积分器进行稳压操作。但是当负载出现瞬态电压变化,其稳定时间将会很长。在PI控制系统中,积分系数大的电路建立时间很短,会产生过冲,然后输出才会稳定。积分系数小的模型输出可以直接稳定,但是建立时间太长。提出了一种高速可调节电路模型,目的是利用电压传感器和时间数字转换器(TDC),并在电路中加入2种不同积分系数的积分器。首先利用电压传感器和时间数字转换技术(TDCT)实现模数转换以得到数字信号。随后判断数字信号与基准电压,在误差很大时,控制电路选择大积分系数,输出到PI控制;误差小时,控制电路选择小的积分系数,这样可以使电路结合不同积分系数电路的优点,从而达到同时缩短电路建立时间和稳定时间的目的。     

TD‐CFIE Formulation for Transient Electromagnetic Scattering from 3‐D Dielectric Objects

In this paper, we present a time domain combined field integral equation formulation (TD‐CFIE) to analyze the transient electromagnetic response from dielectric objects. The solution method is based on the method of moments which involves separate spatial and temporal testing procedures. A set of the RWG functions is used for spatial expansion of the equivalent electric and magnetic current densities, and a combination of RWG and its orthogonal component is used for spatial testing. The time domain unknowns are approximated by a set of orthonormal basis functions derived from the Laguerre polynomials. These basis functions are also used for temporal testing. Use of this temporal expansion function characterizing the time variable makes it possible to handle the time derivative terms in the integral equation and decouples the space‐time continuum in an analytic fashion. Numerical results computed by the proposed formulation are compared with the solutions of the frequency domain combined field integral equation.     

Failure time analysis for LMS algorithms

Few results are available in the literature on failure time (in contrast with long time average) analysis of the least mean square (LMS) adaptive algorithms (filters). Such analysis is extremely important when failure of the algorithm could cause failure of the entire system in which they are employed. A system may fail upon the first occurrence of a large error (any value far from 0), or upon staying far from 0 for a period of time (a clump of large errors). We use a Poisson approximation to study excursions (failure) of the LMS algorithm and its three signed variants. The distribution and the mean of the first excursion are approximated with the mean and distribution of an exponential distribution. The number of excursions in n units of time is approximated by a Poisson distribution. We also approximate the mean of an excursion length (clump size). The approximations are derived asymptotically as the excursion-defining set converges to the empty set, and as the algorithm step size converges to 0     

Least squared error FIR filter design with transition bands

The authors propose the use of transition bands and transition functions in the ideal amplitude frequency response to allow the analytical design of optimal least-squared-error FIR digital filters with an explicit control of the transition band edges. Design formulas are derived for approximations to ideal frequency responses which use pth-order spline transition functions. A mixed analytical and numerical method for zero-error weight in the transition bands and passband and stopband error weighting functions with an integral squared error approximation are derived. A variable-order spline transition function is developed, and a method for choosing the optimal order to minimize the integral squared approximation error is given     

Accurate Determination of Underground GPR Wavefront and B-Scan Shape From Above-Ground Point Sources

While the determination of the wavefront shape radiated by ground-penetrating radar (GPR) in contact with the ground is trivial, the refraction of rays at the ground surface from a point source in the air makes accurate determination of the transmitted wavefront challenging. Impulse GPRs usually have their emitters in air, transmitting waves through a quasi-planar interface into the soil. The waves radiated initially in air can be approximated as circular, but once they enter the soil half-space, they propagate with a wavefront shape that resembles a hyperbola. The exact shape is derived and shown to be well approximated by a hyperbola with specific parameters depending on the relative dielectric constant of the half-space epsiv' ( = n²), the height of the source h, and the propagation time from source to wavefront multiplied by the wave velocity in the half-space p. A correction formula is provided to reduce the error between the approximate hyperbola and the exact shape. In addition, an equation for the shape of the B-scan contour of a point scatterer is derived.     

道路清障车泵控马达调速系统优化研究

利用变量泵一定量马达容积调速系统传递函数，对道路清障车起升系统进行分析，以马达排量Dm为优化对象，基于误差绝对值积分（IAE）以及时间与绝对误差乘积积分（ITAE）个性能指标，对系统参数（马达排量）进行了优化，得到了上述两种性能指标下的最优解，为道路清障车起升系统参数设计、性能研究及应用提供了理论依据。     

Analysis of a sign algorithm with delayed data

An adaptive filter whose weights are adapted using a sign algorithm with a delayed error signal is analyzed. For stationary environments it is proved that the excess average absolute estimation error is bounded for all values of the error signal delay and the algorithm step size. For the nonstationary case when the optimal filter weights are time varying, the optimum step size which minimizes the excess average absolute error is derived. It is shown that the optimum step size does not depend on the additive noise power. The analytical results are supported by computer simulations     

Time Domain CalderÓn Identities and Their Application to the Integral Equation Analysis of Scattering by PEC Objects Part I: Preconditioning

Time domain electric field integral equations often are used to analyze transient scattering from perfect electrically conducting objects. When discretized using marching-on-in-time recipes they give rise to linear systems of equations that can be solved for the induced currents for all time steps. Unfortunately, when the scatterer is approximated by increasingly dense meshes, the condition number of these systems grows rapidly, slowing down the convergence of iterative solvers. Here, time domain CalderÓn identities are derived and subsequently used to construct a CalderÓn-preconditioned time domain electric field integral equation that can be discretized even with dense meshes using Buffa-Christiansen basis functions. Numerical results that demonstrate the effectiveness and accuracy of the proposed method are presented.