109年 - 109 國立中山大學_碩士班招生考試_電機系(乙組)：控制系統#106059

2. Design a feedback controller to regulate the output of the plant

to any prescribed constant level without any steady-state error, and make the resulting closed-loop poles
at s =-70,-100.

(a) A Nyquist path is shown in Fig. 1.

Sketch the Nyquist plot of this system for K ＞0 in accordance with fig. 1, and indicate clearly I. the
intersection(s) of the Nyquist plot with real and imaginary axes if any II. each mapping of point
a:(0+jω,ω→∞⁺),6:(0+jω,ω→0⁺),c:(,φ→0⁺)and d:(0-jω,ω→∞⁺) in your

plot.

(b) Suppose that the Nyquist plot ( K ＞0) you obtained in part (a) is depicted in Fig. 2, where the
solid line is part of the Nyquist plot when ω is from ∞ ⁺ to 0⁺, and it has an intersection with axis
-Re(L(s)) at -K.

Using Nyquist criterion, determine the range of K ＞ 0 such that the closed-loop system can be stabilized.
If the system is unstable due to the range of K, find the number of closed-loop pole(s) in the right-half of
s-plane.