图 7-1 开环采样系统结构图
图 7-2 闭环采样系统结构图
\[
G(z) = G_1(z)G_2(z) = \mathscr{Z}\left[\frac{2}{s+2}\right] \cdot \mathscr{Z}\left[\frac{5}{s+5}\right] = \frac{2z}{z-\mathrm{e}^{-2T}} \cdot \frac{5z}{z-\mathrm{e}^{-5T}}
\]
\[
= \frac{10z^2}{(z-\mathrm{e}^{-2T})(z-\mathrm{e}^{-5T})}
\]
(2) 图 7-2 闭环采样系统:由于
\[
C(z) = G(z)E(z)
\]
\[
E(z) = \mathscr{Z}[R(s) - H(s)C(s)] = R(z) - H(z)C(z)
\]
故有
\[
C(z) = G(z)[R(z) - H(z)C(z)]
\]
\[
C(z) = \frac{G(z)R(z)}{1+G(z)H(z)}
\]
7-9 试用 \(C(s)\) 和/或 \(C(z)\) 表示图 7-3 中各采样系统的输出。根据系统之构成,图中 \(G,H\) 可以指 \(G(s)\) 或 \(G(z)\),\(H(s)\) 或 \(H(z)\)。
图 7-3 采样系统结构图
解 图 7-3(a)采样系统 \(C(z) = RG(z)\)
图 7-3(b)采样系统 \(C(z) = R(z)G(z)\)
图 7-3(c)采样系统 \(C(s) = G(s)E^*(s)\)
而
\[
E(s) = R(s) - H(s)C(s) = R(s) - H(s)E^*(s)G(s)
\]
\[
E^*(s) = \frac{R^*(s)}{1+HG^*(s)}
\]
则有
\[
C^*(s) = G^*(s)E^*(s) = \frac{G^*(s)R^*(s)}{1+HG^*(s)}
\]
\[
C(z) = \frac{G(z)R(z)}{1+HG(z)}
\]
・380・