梅森公式求解：

回路：\(L_1 = \dfrac{-T_2}{s(s+T_1)}\)，\(\Delta = 1 - L_1 = \dfrac{s(s+T_1)+T_2}{s(s+T_1)}\)

\(\dfrac{C(s)}{R(s)}\)前向通路：\(P_1 = \dfrac{K_2}{s+T_1}\)，\(\Delta_1 = 1\)；\(P_2 = \dfrac{K_1}{s(s+T_1)}\)，\(\Delta_2 = 1\)

故\(\dfrac{C(s)}{R(s)} = \dfrac{\dfrac{K_2}{s+T_1}+\dfrac{K_1}{s(s+T_1)}}{\dfrac{s(s+T_1)+T_2}{s(s+T_1)}} = \dfrac{K_2s+K_1}{s(s+T_1)+T_2}\)

\(\dfrac{C(s)}{N(s)} = \dfrac{1}{1+\dfrac{T_2}{s(s+T_1)}} = \dfrac{s(s+T_1)}{s(s+T_1)+T_2}\)

四、

1.

极点：\(0, -1, -2\)

渐近线：实部\(-1\)，开角\(\pm 60°\)、\(-180°\)

会分点：\(\dfrac{1}{d}+\dfrac{1}{d+1}+\dfrac{1}{d+2}=0 \Rightarrow d=-0.423\)

虚轴交点：

\(D(s) = s(s+1)(s+2)+K^* = s^3+3s^2+2s+K^*\)

列劳斯表：

77