分数阶控制系统稳定性分析与控制器设计:扩展频率域法

Stability Analysis and Controller Design for Fractional-order Control Systems:The Extended Frequency Domain Method

鉴于整数阶控制系统主要进行正频域分析,本文论述了分数阶控制系统的扩展频域方法。它通过对分数阶系统传递函数的基本分解获得系统频率特性曲线,此过程是唯一和可逆的。本文根据扩展频域分析法扩展了Nyquist稳定性判据,得到能够直观判断任意阶控制系统稳定性的通用判据。另外,扩展频域分析法为分数阶控制器提供了便于设计的直观形式,文章提供了具有新结构的超前滞后补偿器和分数阶P(ID)μ控制器的设计步骤。最后举例用扩展频域法对分数阶系统进行稳定性分析和超前滞后补偿器的综合。

Considering the integer-order syslems analysis is happened only in positive frequency domain, this paper is concemod about the extended frequency analysis method for fractional-order control systems. This method gets frequency response diagrams through decomposing fractional-order system transfer functions. The procedure is unique and reversible. An Extended Nyquist stability criteria for systems with arbitrary orders are established. The P（ID）^μ controller and a new kind of lead-lag compensators are also provided.