一种改进的同伦算法与H_∞鲁棒控制器设计

A Modified Homotopy Method and H ∞ Robust Controller Design

提出了一种具有阶次限制的鲁棒控制器设计方法,该算法将控制系统的性能指标转化为灵敏度函数问题,并利用Nevanlinna-Pick插值算法进行求解.提出了一种改进的同伦算法,将其用于求解由灵敏度函数产生的非线性方程.基于改进同伦算法设计的鲁棒控制器不仅避免了传统H∞控制中加权函数的选择问题,而且克服了鲁棒控制器阶次较高的缺陷.最后,文章以4阶系统为例,设计了具有阶次限制的H∞鲁棒控制器,通过与传统鲁棒控制器的比较可以看出,基于本文方法设计的控制器不仅具有较低的阶次,而且其控制性能也具有明显的优越性.

A novel method of robust controller design with de- gree constraint is proposed for feedback control systems, where the performance indices are firstly transferred to the sensitivity function problem that will be solved by Nevanlinna-Pick inter- polation. A modified homotopy method is presented to solve nonlinear equations induced by the sensitivity function prob- lem. A new controller based on modified homotopy method is designed without using weighting functions, which can also overcome the defect of high order. At last, the 4th order plant is considered and the corresponding H~ robust controller with de- gree constraint is designed. It is be shown from simulations that the robust controller has not only lower degree than traditional robust controller, but also superior quality obviously.