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Optimal Design of Stochastic Distributed Order Linear SISO Systems Using Hybrid Spectral Method

机译：混合谱法的随机分布阶线性SISO系统的优化设计。

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摘要

The distributed order concept, which is a parallel connection of fractional order integrals and derivatives taken to the infinitesimal limit in delta order, has been the main focus in many engineering areas recently. On the other hand, there are few numerical methods available for analyzing distributed order systems, particularly under stochastic forcing. This paper proposes a novel numerical scheme for analyzing the behavior of a distributed order linear single input single output control system under random forcing. The method is based on the operational matrix technique to handle stochastic distributed order systems. The existing Monte Carlo, polynomial chaos, and frequency methods were first adapted to the stochastic distributed order system for comparison. Numerical examples were used to illustrate the accuracy and computational efficiency of the proposed method for the analysis of stochastic distributed order systems. The stability of the systems under stochastic perturbations can also be inferred easily from the moment of random output obtained using the proposed method. Based on the hybrid spectral framework, the optimal design was elaborated on by minimizing the suitably defined constrained-optimization problem.
机译：分布式有序概念是分数阶积分和派生到δ阶无穷小极限的并行连接，最近已成为许多工程领域的主要关注点。另一方面，很少有数值方法可用于分析分布式订单系统，尤其是在随机强迫下。本文提出了一种新的数值方案，用于分析随机强迫下的分布阶线性单输入单输出控制系统的行为。该方法基于操作矩阵技术来处理随机分布式订单系统。现有的蒙特卡洛，多项式混沌和频率方法首先适用于随机分布阶数系统进行比较。数值算例说明了所提出的随机分布式订单系统分析方法的准确性和计算效率。随机扰动下的系统稳定性也可以很容易地从使用该方法获得的随机输出时刻推断出来。在混合频谱框架的基础上，通过最小化适当定义的约束优化问题，详细阐述了最佳设计。

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  • 来源
    《Mathematical Problems in Engineering》 |2015年第19期|989542.1-989542.14|共14页
  • 作者

    Pham Luu Trung Duong; Kwok Ezra; Lee Moonyong;

  • 作者单位

    Yeungnam Univ, Sch Chem Engn, Kyongsan 712749, South Korea;

    Univ British Columbia, Chem & Biol Engn, Vancouver, BC V5Z 1M9, Canada;

    Yeungnam Univ, Sch Chem Engn, Kyongsan 712749, South Korea;

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