A review on some classes of algebraic systems

ABSTRACT

In this paper, we review some algebraic control system. Precisely, linear and bilinear systems on Euclidean spaces and invariant and linear systems on Lie groups. The fourth classes of systems have a common issue: to any class, there exists an associated subgroup. From this object, we survey the controllability property. Especially, from those coming from our contribution to the theory.     

微制造平台微振动的最优控制

采用混合隔振技术建立了微制造平台隔振系统。该系统以空气弹簧和橡胶层作为被动隔振元件、超磁致伸缩致动器作为主动隔振元件，并采用最优控制理论设计其主动控制器。研究了在不同的性能指标加权阵的情况下，该主动振动控制系统对基础干扰和由微制造设备产生的直接干扰所引起的微制造平台振动的控制效果。研究表明性能指标加权阵对振动控制效果影响非常大。通过大量的仿真实验确定了一组性能指标加权阵，使所设计的主动控制系统能在较宽的频率范围对基础干扰和直接干扰所引起的微制造平台振动进行有效的控制。     

Mass Transfer in a Flat Gas/Liquid Interface using non‐Newtonian Media

Gas/liquid mass transfer has been investigated using a stirred vessel gas/liquid contactor using non‐Newtonian media and carbon dioxide as absorbent and gas phase, respectively. The volumetric mass transfer coefficients at different operational variables have been determined. Non‐Newtonian media (liquid phase) were prepared as aqueous solutions of sodium carboxymethyl cellulose salt. The influence of the rheological properties, polymer concentration, stirring rate, and gas flow rate on mass transfer was studied for these liquid phases. Kinematic viscosity and density experimental data were used to calculate the average molecular weight corresponding to the polymer employed. The Ostwald model has been used to fit the rheological behavior of aqueous solutions of the polymer employed as absorbent phase. Reasonably good agreement was found between the predictions of the proposed models and the experimental data of mass transfer coefficients.     

An original approximate method for estimating the invariant probability distribution of a large class of multi-dimensional nonlinear stochastic oscillators

This paper proposes an original method for obtaining analytical approximations of the invariant probability density function of multi-dimensional Hamiltonian dissipative dynamic systems under Gaussian white noise excitations, with linear non-conservative parts and nonlinear conservative parts. The method is based on an exact result and a heuristic argument. Its pertinence is attested by numerical tests.     

A stochastic model for localized disturbances and its applications

A stochastic model for local disturbances, particularly for a temporal harmonic with random modulations in amplitude and/or phase, is proposed in this paper. Results for the second moment responses of a linear single-degree-of-freedom system to this type of stochastic loading demonstrate a significant change in response characteristics due to a small uncertainty. A local phenomenon may last much longer and resonance may be smeared to a broad range. Integrated with wavelet transform, the proposed approach may be used to model a random process with non-stationary frequency content. Especially, it can be effectively used for Monte Carlo simulation to generate large size of samples that have similar characteristics in time and frequency domains as a pre-selected mother sample has. The technique has a great potential for the case where uncertainty study is warranted but the available samples are limited.     

弹性-粘弹性复合结构随机响应的各阶谱矩的计算方法

提出了一种新的计算弹性-粘弹性复合结构随机响应的各阶谱矩的计算方法，它是一种时域复模态分析方法。利用此方法获得了弹性-粘弹性复合结构在白噪声、滤过白噪声等典型平稳随机激励下随机响应的各阶谱矩的解析表达式，分析了粘弹性对各阶谱矩的影响。此计算方法简便、易用，无论单自由度或多自由度系统均适用，为进一步研究弹性-粘弹性复合结构在随机激励下的可靠性打下良好基础。     

On a large-gain theorem

The aim of this paper is to give a general quantitative requirement which the loop gain must satisfy in order to stabilize a given unstable (possibly nonlinear and time-varying) plant, namely that the gain must exceed one.     

H∞-control with measurement-feedback for Pritchard-Salamon systems

In this paper we extend the finite-dimensional results for the H_∞-control problem with measurement-feedback to a large class of infinite-dimensional systems, allowing for a certain type of unboundedness in the input and output operators (the Pritchard-Salamon class). The main result of the paper relates the solvability to the suboptimal H_∞-control problem to the existence of stabilizing solutions to certain operator Riccati equations. Furthermore, a characterization of all suboptimal controllers is given.     

An explicit finite difference method for finite-time observers

In this paper we present a numerical method for estimating the current state of a nonlinear control system. We use finite differences to discretize a modified version of the finite-time observer equations in James. The discretized equations are simple and easily programmed. The convergence and accuracy of the scheme is proved, and the scheme enjoys a number of important properties: availability of rate of convergence estimates, good robustness characteristics, and the ability to handle certain types of discontinuities in the observations. The major disadvantage is that the number of grid points required increases exponentially with the number of state dimensions.