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\(\therefore\) 令 \(\left|G\left(jw_c\right)\right|=1\) 即 \(\left|\dfrac{1}{w_c\sqrt{w_c^2+1}}\right|=1\) ， 解得 \(w_c=0.786rad/s\)

\(\therefore \gamma=180°+\varphi_c\left(\omega_c\right)=180°-90°-\arctan0.786=51.832°>0\)

又 \(\because r(t)=t\)　　\(\therefore k_v=\lim\limits_{s\to0}s\cdot G(s)=\lim\limits_{s\to0}s\cdot\dfrac{1}{s(s+1)}=1\)

\(\therefore e_{ss}(\infty)=\dfrac{R_1}{k_v}=1\)

（2）\(\because G_1(s)=\dfrac{k(s+b)}{s+a}\)

\(\therefore\) 校正后系统的开环传递函数为：　\(G'(s)=G(s)\cdot G_1(s)=\dfrac{k(s+b)}{s(s+1)(s+a)}\)

又 \(r(t)=t\)　　\(\therefore K_1'=\lim\limits_{s\to0}s\cdot G'(s)=\lim\limits_{s\to0}s\dfrac{k(s+b)}{s(s+1)(s+a)}=\dfrac{k\cdot b}{a}\)

\(\therefore e_{ss}(\infty)=\dfrac{k_1}{k_v}=\dfrac{a}{kb}=0.1\)

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