拉盖尔-高斯光束通过有硬边光阑光学系统的传输

采用将硬边光阑展为有限个复高斯函数之和的方法,得到了拉盖尔-高斯光束通过有硬边光阑近轴ABCD光学系统中传输的近似解析公式,作了数值计算以说明传输公式的应用,并对使用该式的误差作了讨论。     

Adaptive predictive control algorithm based on Laguerre Functional Model

Laguerre Functional Model has many advantages such as good approximation capability for the variances of system time‐delay, order and other structural parameters, low computational complexity, and the facility of online parameter identification, etc., so this model is suitable for complex industrial process control. A series of successful applications have been gained in linear and non‐linear predictive control fields by the control algorithm based on Laguerre Functional Model, however, former researchers have not systemically brought forward the theoretical analyses of the stability, robustness, and steady‐state performance of this algorithm, which are the keys to guarantee the feasibility of the control algorithm fundamentally. Aimed at this problem, we introduce the principles of the Incremental Mode Linear Laguerre Predictive Control (IMLLPC) algorithm, and then systemically propose the theoretical analyses and proofs of the stability and robustness of the algorithm, in addition, we also put forward the steady‐state performance analysis. At last, the control performances of this algorithm on two different physical industrial plants are presented in detail, and a number of experimental results validate the feasibility and superiority of IMLLPC algorithm. Copyright © 2005 John Wiley & Sons, Ltd.     

有滞后环节的系统的闭环鲁棒辨识方法

提出一种新的针对带滞后环节的任意阶系统的闭环辨识方法。通过“三步法”，实现在闭环条件下的被控制对象的传递函数参数的辨识，所提出方法具有很强的鲁棒性。仿真例子表明该方法的有效性。     

MODELING AND PREDICTIVE CONTROL OF MIMO NONLINEAR SYSTEMS USING WIENER-LAGUERRE MODELS

In this work, a Weiner-type nonlinear black box model was developed for capturing dynamics of open loop stable MIMO nonlinear systems with deterministic inputs. The linear dynamic component of the model was parameterized using orthogonal Laguerre filters while the nonlinear state output map was constructed either using quadratic polynomial functions or artificial neural networks. The properties of the resulting model, such as open loop stability and steady-state behavior, are discussed in detail. The identified Weiner-Laguerre model was further used to formulate a nonlinear model predictive control (NMPC) scheme. The efficacy of the proposed modeling and control scheme was demonstrated using two benchmark control problems: (a) a simulation study involving control of a continuously operated fermenter at its optimum (singular) operating point and (b) experimental verification involving control of pH at the critical point of a neutralization process. It was observed that the proposed Weiner-Laguerre model is able to capture both the dynamic and steady-state characteristics of the continuous fermenter as well as the neutralization process reasonably accurately over wide operating ranges. The proposed NMPC scheme achieved a smooth transition from a suboptimal operating point to the optimum (singular) operating point of the fermenter without causing large variation in manipulated inputs. The proposed NMPC scheme was also found to be robust in the face of moderate perturbation in the unmeasured disturbances. In the case of experimental verification using the neutralization process, the proposed control scheme was found to achieve much faster transition to a set point close to the critical point when compared to a conventional gain-scheduled PID controller.     

A General Robust MPC Design for the State‐Space Model: Application to Paper Machine Process

Applying model predictive control (MPC) in some cases such as complicated process dynamics and/or rapid sampling leads us to poorly numerically conditioned solutions and heavy computational load. Furthermore, there is always mismatch in a model that describes a real process. Therefore, in this paper in order to prevail over the mentioned difficulties, we design a robust MPC using the Laguerre orthonormal basis in order to speed up the convergence at the same time with lower computation adding an extra parameter “a” in MPC. In addition, the Kalman state estimator is included in the prediction model and accordingly the MPC design is related to the Kalman estimator parameters as well as the error of estimations which helps the controller react faster against unmeasured disturbances. Tuning the parameters of the Kalman estimator as well as MPC is another achievement of this paper which guarantees the robustness of the system against the model mismatch and measurement noise. The sensitivity function at low frequency is minimized to tune the MPC parameters since the lower the magnitude of the sensitivity function at low frequency the better command tracking and disturbance rejection results. The integral absolute error (IAE) and peak of the sensitivity are used as constraints in optimization procedure to ensure the stability and robustness of the controlled process. The performance of the controller is examined via the controlling level of a Tank and paper machine processes.     

微孔结构对PMI泡沫准静态压缩性能的影响

基于BBC点集建立了聚甲基丙烯酰亚胺(PMI)闭孔泡沫的Kelvin十四面体模型和Laguerre模型,并采用有限元方法研究了其在准静态载荷作用下的压缩性能。分析了孔径大小、泡孔体积离散系数对压缩弹性模量、初始峰值应力和能量吸收能力的影响。结果表明:Kelvin十四面体模型可以较好地预测PMI泡沫的压缩弹性模量和峰值应力;在相同相对密度条件下,小孔径泡沫的初始峰值应力和能量吸收能力均高于大孔径泡沫,而压缩弹性模量则低于大孔径泡沫;随着泡孔体积离散系数的增大,闭孔PMI泡沫压缩弹性模量、初始峰值应力和能量吸收能力均减小。     

Model order reduction methods for coupled systems in the time domain using Laguerre polynomials

In this paper, based on Laguerre polynomials, we present new methods for model reduction of coupled systems in the time domain. By appropriately selected projection matrices, a reduced order system is produced to retain the topology structure of the original system. Meanwhile, it preserves a desired number of Laguerre coefficients of the system’s output, thereby providing good approximation accuracy. We also study the two-sided projection method in the time domain, as well as the stability of reduced order systems. Two numerical examples are used to illustrate the efficiency of the proposed methods.     

Subspace-based continuous-time identification of fractional order systems from non-uniformly sampled data

This work focuses on the identification of fractional commensurate order systems from non-uniformly sampled data. A novel scheme is proposed to solve such problem. In this scheme, the non-uniformly sampled data are first complemented by using fractional Laguerre generating functions. Then, the multivariable output error state space method is employed to identify the relevant system parameters. Moreover, an in-depth property analysis of the proposed scheme is provided. A numerical example is investigated to illustrate the effectiveness of the proposed method.     

Laguerre超群上的Hardy-Littlewood-Sobolev不等式

利用Laguerre超群K上的广义次拉普拉斯算子L定义K上的Riesz位势,并证明它是Lp(1p+∞)有界和弱(1,1)有界的,即证明K上的Hardy-Littlewood-Sobolev不等式.它为进一步分析K上的偏微分方程问题提供了一个有利的工具.     

Numerical inversion of multidimensional Laplace transforms by the Laguerre method

Numerical transform inversion can be useful to solve stochastic models arising in the performance evaluation of telecommunications and computer systems. We contribute to this technique in this paper by extending our recently developed variant of the Laguerre method for numerically inverting Laplace transforms to multidimensional Laplace transforms. An important application of multidimensional inversion is to calculate time-dependent performance measures of stochastic systems. Key features of our new algorithm are: (1) an efficient FFT-based extension of our previously developed variant of the Fourierseries method to calculate the coefficients of the multidimensional Laguerre generating function, and (2) systematic methods for scaling to accelerate convergence of infinite series, using Wynn's ε-algorithm and exploiting geometric decay rates of Laguerre coefficients. These features greatly speed up the algorithm while controlling errors. We illustrate the effectiveness of our algorithm through numerical examples. For many problems, hundreds of function evaluations can be computed in just a few seconds.