On a determination of the optimal constant feedback gains for pole assignment in a sector region

Abstract

A problem of determination of feedback gains in order to achieve required performances is considered in this paper. We suggest a method that assigns any poles in a sector region which specifies the stability and damping factor by making use of coordinate transformations that is; the imaginary axis's parallel movement and the complex plane's rotation. At first we transform the system to the augmented system by using the above transformation. Next we can show any poles can be located in the specified region very easily by designing the feedback gains which minimize the cost function in the augmented system. Finally it is shown in two numerical examples that our proposed method is effective.