变参数FOPDT型系统的强鲁棒自适应PI控制器设计

针对基于非线性模型控制器设计困难的问题,将非线性系统用变参数形式的一阶惯性加延迟(FOPDT)模型描述,并进行控制器设计,从而简化控制器的设计过程并提高控制性能.采用一种新型的自适应比例积分(PI)控制器结构,通过增益参数切换和积分复位实现高精度的设定点跟踪和扰动抑制性能.仿真及实验结果表明:文中方法使系统控制精度提高10倍,达到0.01°;超调量有所减少;模型变化时,阶跃响应和干扰抑制效果仍佳;与传统的PI方法比较,文中方法具有良好的动态、稳态响应性能和鲁棒性.     

哈密尔顿系统的分裂步多辛数值积分

对哈密尔顿系统而言,辛或多辛积分较传统的数值方法具有优越性。然而,此类数值格式大部分都是隐式的,从而在每一个时间步需要求解一个非线性的代数方程组,这将直接导致计算效率不高。在多辛积分中引进分裂步技巧,称之为分裂步多辛积分,可以弥补这一不足之处,这一数值方法的框架将在该文中简要地讨论,其中,数值例子给出了该方法在物理问题中的应用。     

基于积分束流变压器的加速器束团电荷量测量系统

 为满足清华大学加速器实验室光阴极微波电子枪实验平台的发展需求,设计了束团电荷量测量系统,可以实现实时测量加速器束团电荷量的目标。这套测量系统基于积分束流变压器,包括前置放大器、门控积分器、模数转换和数据传输模块。利用信号发生器模拟束流,对整套系统进行了离线测量实验。当前置放大器放大倍数取200和20时,AD转换值和束流电荷的比值分别为2.181 PC-1和0.195 PC-1,与理论值2.070 PC-1和0.207 PC-1基本吻合;其对应的电荷量测量误差分别小于2 PC和15 PC。测量结果和模拟束流电荷量值的拟合曲线线性度好,相关系数的平方均大于0.999 0。该结果验证了系统的可行性。     

一种基于SET/CMOS电路的二阶低通滤波器

在研究单电子晶体管(single electron transistor，SET)I-V特性的基础上，依据分区处理法，设计了一个SET、积分器电路，并采用级联方法实现了一个SET／CMOS二阶低通滤波器。仿真结果表明，该滤波器的幅频特性增益比采用其它方法描述SET I-V特性所构成的滤波器的幅频特性增益高出1倍多。     

VARIATIONAL INTEGRATORS FOR HIGHER ORDER DIFFERENTIAL EQUATIONS

We analyze three one parameter families of approximations and show that they are sympectic in Largrangian sence and can be related to symplectic schemes in Hamiltonian sense by different symplectic mapping.We also give a direct generalization of Veselov variational principlc for construction of scheme of higher order differential equations.At last,we present numerical experiments.     

用Velocity Verlet积分器改进HMC抽样方法

Hamilton Monte Carlo (HMC) 方法是一种常用的快速抽样方法. 在对哈密尔顿方程进行抽样时,HMC方法使用Leapfrog积分器,这可能造成方程的位置和动量的迭代值在时间上不同步,产生的误差会降低抽样效率及抽样结果的稳定性. 为此,本文提出了IHMC（Improved HMC）方法,该方法用Velocity Verlet积分器代替Leapfrog积分器,在每次迭代时都计算两变量在同一时刻的值. 为验证方法的效果,本文进行了两个数值实验,一个是将方法应用于非对称随机波动率模型（RASV模型）的参数估计,另一个是将方法应用于方差伽马分布的抽样. 结果显示,IHMC方法比HMC方法的效率更高,结果更稳定.     

On error estimates of an exponential wave integrator sine pseudospectral method for the Klein–Gordon–Zakharov system

In this article, we propose an exponential wave integrator sine pseudospectral (EWI‐SP) method for solving the Klein–Gordon–Zakharov (KGZ) system. The numerical method is based on a Deuflhard‐type exponential wave integrator for temporal integrations and the sine pseudospectral method for spatial discretizations. The scheme is fully explicit, time reversible and very efficient due to the fast algorithm. Rigorous finite time error estimates are established for the EWI‐SP method in energy space with no CFL‐type conditions which show that the method has second order accuracy in time and spectral accuracy in space. Extensive numerical experiments and comparisons are done to confirm the theoretical studies. Numerical results suggest the EWI‐SP allows large time steps and mesh size in practical computing. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 266–291, 2016     

Multi-symplectic variational integrators for the Gross–Pitaevskii equations in BEC

In this paper, a variational integrator is constructed for Gross–Pitaevskii equations in Bose–Einstein condensate. The discrete multi-symplectic geometric structure is derived. The discrete mass and energy conservation laws are proved. The numerical tests show the effectiveness of the variational integrator, and the performance of the proved discrete conservation law.     

Global fixed-time stabilization for a class of switched nonlinear systems with general powers and its application

This paper investigates the problem of global fixed-time stabilization for a class of uncertain switched nonlinear systems with the general powers, namely, the powers of the considered systems can be different odd rational numbers, even rational numbers or both odd and even rational numbers. By skillfully using the common Lyapunov function method and the adding a power integrator technique, a common state feedback control strategy is developed. It is proved that the proposed controller can guarantee that the state of the resulting closed-loop system converges to zero for any given fixed time under arbitrary switchings. Simulation results of the liquid-level system are provided to show the effectiveness of the proposed method.