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

The damping ratio ${\xi}$ of the unit-step response of a second-order discrete system is a function of only the location of the closed-loop poles and is not directly related to the location of the system zero. However, the peak overshoot of the response is the function of both the damping ratio ${\xi}$ and an angle ${\alpha}$, which is the phasor angle of the damped sinusoidal response and is determined by the relative location of the zero with respect to the closed-loop poles. Therefore, if the zero and the open-loop poles are relatively adjusted, through pole-zero cancellation, to maintain the desired (or designed) closed-loop poles, the damping ratio ${\xi}$ will also be maintained, while the angle ${\alpha}$ changes. Accordingly, when the closed-loop system poles are fixed, the peak overshoot is considered as a function of the angle ${\alpha}$ or the system zero location. In this paper the effects of the relative location of the zero on the system performance of a second-order discrete system is studied, and a design method of digital compensator which achieves a minimum peak overshoot while maintaining the desired system mode and the damping ratio of the unit step response is presented.

이차 이산 시스템의 Peak Overshoot을 최소화하기 위한 영점의 위치 설계