5-63 设系统结构图如图5-117(a)所示，系统闭环对数幅频渐近特性如图5-117(b)所示，\(\dfrac{U(s)}{R(s)}\)的对数幅频渐近特性如图5-117(c)所示。已知\(\dfrac{C(s)}{R(s)}\)和\(\dfrac{U(s)}{R(s)}\)都是最小相位传递函数，试确定系统中的传递函数\(G_1(s)\)和\(G_2(s)\)。
(a) 结构图
(b) 系统闭环对数幅频渐近特性
(c) \(\dfrac{U(s)}{R(s)}\)对数幅频渐近特性
图5-117 系统结构图和对数幅频渐近特性曲线
解 由图5-117(b)可得，系统的闭环传递函数为
\[\Phi(s)=\dfrac{0.1s\left(\dfrac{s}{20}+1\right)\left(\dfrac{s}{50}+1\right)}{\left(\dfrac{s}{10}+1\right)\left(\dfrac{s}{15}+1\right)\left(\dfrac{s}{100}+1\right)}\]
由图5-117(c)可得，系统的传递函数为
\[G_{ur}(s)=\dfrac{\dfrac{s}{50}+1}{\left(\dfrac{s}{10}+1\right)\left(\dfrac{s}{15}+1\right)\left(\dfrac{s}{100}+1\right)}\]
再由系统的结构图5-117(a)可知
\[\Phi(s)=\dfrac{G_1(s)G_2(s)}{1+G_1(s)G_2(s)},\qquad G_{ur}(s)=\dfrac{G_1(s)}{1+G_1(s)G_2(s)}\]
则传递函数为
\[G_2(s)=\dfrac{\Phi(s)}{G_{ur}(s)}=0.1s\left(\dfrac{s}{20}+1\right)\]
再由系统的闭环传递函数\(\Phi(s)\)可得
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