Design of the Zero Location for Minimizing the Peak Overshoot of Second Order Discrete Systems

이차 이산시스템의 Peak Overshoot을 최소화하기 위한 영점의 위치 설계

  • Lee, Jas-Seok (Dept. of Control and Instrumentation Eng., Chung-Ang Univ.) ;
  • Chung, Tae-Sang (School of Electrical and Electronics Eng., Chung-Ang Univ.)
  • 이재석 (중앙대학교 제어계측학과) ;
  • 정태상 (중앙대학교 전자전기공학부)
  • Published : 1999.11.20

Abstract

The damping ratio $\zeta$ of a continuous 2nd order response which passes all the points of the discrete response of a 2nd order discrete system(envelope curve) is a function of only the location of the closed-loop pole and ie not at all related to the location of the zero. And the peak overshoot of the envelope curve is uniquely specified by the damping ratio $\zeta$, which is a function of solely the closed-loop pole location, and the angle $\alpha$ which is determined by the relative location of the zero with respect to the closed-loop complex pole. Therefore, if the zero slides on the real axis with the closed-loop complex poles being fixed, then the angle $\alpha$ changes however the damping ratio $\zeta$ does not. Accordingly, when the closed-loop system poles are fixed, the peak overshoot is function of $\alpha$ or the system zero. In this thesis the effects of the relative location of the zero on the system performance of a second order discrete system is studied.

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