New exact solutions of the Tzitzéica-type equations in non-linear optics using the expa function method

One specific class of non-linear evolution equations, known as the Tzitzéica-type equations, has received great attention from a group of researchers involved in non-linear science. In this article, new exact solutions of the Tzitzéica-type equations arising in non-linear optics, including the Tzitzéica, Dodd–Bullough–Mikhailov and Tzitzéica–Dodd–Bullough equations, are obtained using the exp_a function method. The integration technique actually suggests a useful and reliable method to extract new exact solutions of a wide range of non-linear evolution equations.     

Active disturbance rejection based trajectory linearization control for hypersonic reentry vehicle with bounded uncertainties

This paper investigates a novel compound control scheme combined with the advantages of trajectory linearization control (TLC) and alternative active disturbance rejection control (ADRC) for hypersonic reentry vehicle (HRV) attitude tracking system with bounded uncertainties. Firstly, in order to overcome actuator saturation problem, nonlinear tracking differentiator (TD) is applied in the attitude loop to achieve fewer control consumption. Then, linear extended state observers (LESO) are constructed to estimate the uncertainties acting on the LTV system in the attitude and angular rate loop. In addition, feedback linearization (FL) based controllers are designed using estimates of uncertainties generated by LESO in each loop, which enable the tracking error for closed-loop system in the presence of large uncertainties to converge to the residual set of the origin asymptotically. Finally, the compound controllers are derived by integrating with the nominal controller for open-loop nonlinear system and FL based controller. Also, comparisons and simulation results are presented to illustrate the effectiveness of the control strategy.     

在广西全面开展悬移质泥沙简测的可行性和重要性

通过对百色等水文站泥沙资料分析 ,并结合广西河流及泥沙特性和社会对泥沙资料的精度要求 ,得出了在广西实行悬移质泥沙简测的可行性。为满足广西国民经济可持续发展需要 ,提出了在广西改革悬移质泥沙测验方式的必要性和紧迫性     

QFT control design for an approximately linearized pneumatic positioning system

A block‐oriented approximate feedback linearization for control of a pneumatic cylinder positioning system is introduced and a rather detailed discussion is presented on the uncertain linearization residual characterization. It is shown that making use of the characterized gain–phase information of the linearized system leads to a more reasonable trade‐off between performance and stability in the QFT control design and thus results in high control performance. Simulation and experimental results are shown. Copyright © 2003 John Wiley & Sons, Ltd.     

A family of lower- and higher-order transversal linearization techniques in non-linear stochastic engineering dynamics

Sample pathwise numerical integration of noise-driven engineering dynamical systems cannot generally be performed beyond a limited level of accuracy, especially when the noise processes are modelled using (filtered) white noises. Recently, a locally transversal linearization (LTL) strategy has been proposed by the author (Proc Roy Soc London A 2001; 457 :539–566) for direct integration of deterministic and stochastic non-linear dynamical systems. The present effort is focussed on a host of extensions along with detailed theoretical error analyses of the linearization approach, especially as applied to problems in non-linear stochastic engineering dynamics. Thus, to begin with, estimates of local and global error orders in the basic LTL scheme are obtained separately for the displacement and velocity vectors when the system is driven either by a set of additive noises or by an arbitrary combination of (independently evolving) additive and multiplicative noises. Following this, a new family of higher-order LTL schemes is proposed in order to improve upon the basic LTL method and the associated error orders are established. A stepwise implementation of the lower- and higher-order versions of the LTL method, along with certain computational aspects, is also outlined. The proposed schemes are numerically illustrated, to a limited extent, for a single degree-of-freedom (SDOF) and a two degree-of-freedom (TDOF) non-linear engineering systems under additive and/or multiplicative white noise excitations. Copyright © 2004 John Wiley & Sons, Ltd.     

单层多跨刚架在移动荷载作用下的影响量计算方法

讨论了桥梁、工业厂房和大型公共建筑中较多采用的单层多跨刚架在移动荷载作用下影响量的计算方法。以工程中计算连续梁的一次力矩分配法的概念和思路为基础,建立了结构中杆端真实抗转刚度和结点转角传递的概念及其相应计算公式,提出了一种单层多跨刚架超静定结构影响量的精确计算方法。算例表明,该方法较之传统的计算方法简捷,且既便于手算,也利于编制通用程序用于电算。     

Integrated Smart Sensor Calibration

In many applications electronic sensors are used toimprove performance and reliability of measurement systems. Suchsensors should provide a correct transfer from the physical signalto be measured to the electrical output signal. One importantstep to achieve this, is to calibrate each sensor by applyingdifferent reference input signals and adjusting the sensor transferaccordingly. Besides expensive reference equipment the calibrationprocess takes much time and attention per individual sensor,which means a considerable increase in sensor production costs.By including at the sensor or sensor interface chip a programmablecalibration facility the calibration of such smart sensors caneasily be automated and can be executed for a batch of sensorsat a time, thus minimizing the calibration time and costs. Thispaper presents a calibration method and options for integrationin the smart sensor concept, in hardware as well as in software.An advantage of the proposed method is that it does not needa large matrix of calibration data, which needs to be storedin a look-up table or converted into a correction formula, butinstead it uses a step-by-step approach to correct the sensortransfer at each calibration measurement until the error is sufficientlysmall.     

Least-squares integration of one-dimensional codistributions with application to approximate feedback linearization

We study the problem of approximating one-dimensional nonintegrable codistributions by integrable ones and apply the resulting approximations to approximate feedback linearization of single-input systems. The approach derived in this paper allows a linearizable nonlinear system to be found that is close to the given system in a least-squares (L ₂) sense. A linearly controllable single-input affine nonlinear system is feedback linearizable if and only if its characteristic distribution is involutive (hence integrable) or, equivalently, any characteristic one-form (a one-form that annihilates the characteristic distribution) is integrable. We study the problem of finding (least-squares approximate) integrating factors that make a fixed characteristic one-form close to being exact in anL ₂ sense. A given one-form can be decomposed into exact and inexact parts using the Hodge decomposition. We derive an upper bound on the size of the inexact part of a scaled characteristic one-form and show that a least-squares integrating factor provides the minimum value for this upper bound. We also consider higher-order approximate integrating factors that scale a nonintegrable one-form in a way that the scaled form is closer to being integrable inL ₂ together with some derivatives and derive similar bounds for the inexact part. This allows a linearizable nonlinear system that is close to the given system in a least-squares (L ₂) sense together with some derivatives to be found. The Sobolev embedding techniques allow us to obtain an upper bound on the uniform (L _∞) distance between the nonlinear system and its linearizable approximation. This research was supported in part by NSF under Grant PYI ECS-9396296, by AFOSR under Grant AFOSR F49620-94-1-0183, and by a grant from the Hughes Aircraft Company.     

带有集中质量的分布质量弹性转动横振精确解

求得了带有集中质量的分布质量弹性转轴系统横向自由振动的频率方程和振型函数的精确解析表达式，及其与不转动轴系统自由振动的频率方程和振型函数及转动角速度之间的精确解析关系     

Approximate feedback linearization of discrete-time non-linear systems using virtual input direct design

The design of feedback-linearization and poles-placement controllers for discrete-time non-linear plants, using Input/Output/State measurements only, is typically addressed via indirect design. In this paper we propose the use of a new technique, based on a Virtual Input Direct Design (VID²) approach. The main feature of such a technique is to reduce the control design problem into a standard non-linear mapping approximation problem, without calling for the preliminary construction of an appropriate model of the plant. As compared with the existing methods, the new one requires less computational effort, while taking full advantage of the non-linear approximation software tools already available. In this paper, the new method is described, a simple theoretical analysis is given, and some numerical examples are presented.