由图可知:
\[-\frac{15}{8}k>-1 \Rightarrow 0<k<\frac{8}{15}系统稳定\]
\[k>\frac{8}{15}时，系统不稳定\]
五、
由图可知:
\[E(z)=R(z)-G_{ZOH}G_1G_2(z)E(z) \Rightarrow E(z)=\frac{R(z)}{1+G_{ZOH}G_1G_2(z)}\]
\[C(z)=E(z)G_{ZOH}G_1(z)\]
\[\Rightarrow \frac{C(z)}{R(z)}=\frac{G_{ZOH}G_1(z)}{1+G_{ZOH}G_1G_2(z)}\]
\[\Rightarrow D(z)=1+G_{ZOH}G_1G_2(z)\]
\[\Rightarrow D(z)=z^2+(0.184k-1.368)z+0.368+0.132k\]
朱莉判据:
\[D(1)>0,D(-1)>0,0.368+0.132k<1\]
\[\Rightarrow 0<k<4.79\]
六、
(1)
\[G(s)=\frac{k(\frac{s}{0.1}+1)}{s(\frac{s}{0.01}+1)(\frac{s}{2}+1)(\frac{s}{10}+1)}\]
设校正后 \(20\lg\frac{k}{0.01}-40\lg\frac{0.1}{0.01}-20\lg\frac{1}{0.1}=0 \Rightarrow k=10\)
\[\Rightarrow G(j\omega)=\frac{10(j10\omega+1)}{j\omega(j100\omega+1)(j0.5\omega+1)(j0.1\omega+1)}\]
(2)
\[G_c(s)=\frac{G(s)}{G_0(s)}=\frac{10s+1}{100s+1}滞后校正\]
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