灵敏度函数恢复的非奇异H_∞方法

Abstract

在控制器设计的lTr方法中，说明在H∞范数意义下的灵敏度函数恢复与回路传递函数的恢复是不等价的，但灵敏度函数的恢复更适合鲁棒控制问题.通过把灵敏度函数恢复误差变换成控制器的线性分式变换式，得到一个非奇异结构的广义调节器问题，于是可利用标准的H∞输出反馈控制器设计方法求解.该控制器在保证灵敏度函数误差的H∞范数小于某一正数的同时可使闭环系统内稳定

In the design procedure for LTR based controller,there is difference between sensitivity recovery and loop transfer recovery in the sense of H ∞ norm.By formulating the recovery error of sensitivity function as a linear fraction transformation of controller,we can solve a generalized regulator problem with nonsingular structure which can be solved with Matlab toolbox.The controller we get from toolbox makes the H ∞ norm of recovery error of sensitivity function no more than a prescribed level and internally stabilize the system.The validity of the conclusions is verified in a design case of a two order system.