Asymptotic behavior of the root-loci of Linear, time-invariant, multivariable, and negative unity feedback system is studied in relation to the system stability and its performance.
As the feedback gain goes to infinity, some of the loci terminate to certain finite points, which are called Finite Zeros, while the others terminate to certain imaginary points at infinity along the asympotes, which are called Infinite Zeros. Kouvaritakis and Edmunds presented algorithms to find the finite and infinite zeros, and then to design controllers to improve the stability of a given system.
In this work, since the design algorithm formulated by them is proven to be not valid in general, a new design algorithm is suggested. The computer programs and numerical schemes are developed to compute the finite and infinite zeros, and then to be used in designing a controller for better stability.
Linear time-invariant multivariable system에 negative unity feedback을 걸어줄 때 closed-loop system의 characteristic equ의 root locus는 gain이 무한히 커질 때, 일부점 (F. Z., finite zero) 는 유한점을 향해, 나머지 점 (I. Z. ; Infinite zero) 는 가상의 무한점을 향해 움직인다.
이 논문에서는 주어진 system의 F. Z. 와 I. Z. 를 수치적으로 구하고, 이를 이용하여 이 system의 안정을 위해 controller를 design하는 방법 및 program을 개발하였다.
