分数阶控制系统的空间根轨迹分析法  

Space Root Locus: Classical Analysis Method for Fractional-order Control Systems

作　　者：王萌[1] 汪纪锋[1] 李元凯[1] 

机构地区：[1]重庆邮电大学,重庆400065

出　　处：《重庆工学院学报》2007年第15期105-111,共7页Journal of Chongqing Institute of Technology

基　　金：重庆市教委自然科学基金资助项目(KJ060506);重庆邮电大学研究项目资助(A2005-47)

摘　　要：提出并论证了分数阶控制系统的空间根轨迹分析方法.通过任意阶次引起黎曼面的伸缩得出非整数次方程解的分布与阶次的关系,并由受分数阶影响的主黎曼面构造出分数阶控制系统特征根的运动空间,根据分数阶控制系统根轨迹的相角、幅值条件与阶次条件得到此空间下的系统根轨迹.论述了几何描述与解析2种方法,并给出空间根轨迹与平面根轨迹在主黎曼面意义下的等价关系.This paper puts forward and demonstrates space root locus method of fractional-order control systems. Through the flex of Riemann surfaces caused by arbitrary orders, this paper obtains the relationship between the orders and roots distribution of fractional-order equations, constructs a space in which the characteristic roots of fractional-order control systems move by the main Riemann surfaces with different fractional orders, obtains the root locus in the space due to phase, magnitude and order conditions of fractional-order control systems. In addition, it discusses the two methods of geometric description and analytic expression and presents the equivalence relationship between space and plane root locus in team of Riemann Surface.

关 键 词：分数阶 控制系统 主黎曼面空间 空间根轨迹 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]