面向控制的分数阶微分模型的快速数值计算  

Control-oriented fast numerical approaches of fractional-order models

作　　者：曹红亮[1] 李曦[2] 邓忠华[1] 秦忆[1] 

机构地区：[1]华中科技大学控制科学与工程系自动化研究所,湖北武汉430074 [2]华中科技大学图像信息处理与智能控制教育部重点实验室,湖北武汉430074

出　　处：《控制理论与应用》2011年第5期715-721,共7页Control Theory & Applications

基　　金：国家"863"计划资助项目(2006AA05Z148);国家自然科学基金资助项目(60804031);华中科技大学自主创新研究基金资助项目(2010MS056)

摘　　要：求解分数阶控制系统的关键在于如何快速精确地计算分数阶微分.针对短记忆法和变步长记忆法的计算精度和计算复杂性顾此失彼的矛盾,本文提出了一种恒权重记忆法,它不舍弃历史数据,而是采用常值权重后全部记忆.在每个后继的采样周期,只需把新的数据简单叠加到历史数据上来考虑,从而极大地提高了计算精度和降低了计算复杂性,且有效地化解了两者之间的矛盾.数值结果表明恒权重记忆法在分数阶控制系统设计中的可行性和优越性.In the computation of fractional order derivatives,the crucial point is to balance the computation speed and the computation accuracy.The existing short memory principle or variable memory principle helps little in relaxing the contradiction.To deal with this problem,we proposed an equal-weight memory principle,in which an equal-weight is applied to all past data in history,and the result is reserved instead of being discarded.In each subsequent sampling period,only one new data is collected for consideration with the historical data.Therefore,the computation accuracy is improved and the computation complexity is reduced,thus,the contradiction is effectively relaxed.Results in numerical examples demonstrate the feasibility and superiority in applying the proposed principle to the design of fractional-order control systems.

关 键 词：分数阶微分 数字滤波器 短记忆法 变步长记忆法 恒权重记忆法 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]