(左上角,撕角/透影处,字迹残缺,见 uncertain)
\[\approx \dfrac{X(s)}{N(s)}\]
(左侧竖排,疑似相邻页透影,非本页正文,未转写)
| 拉氏变换 | 时间函数 | Z变换 |
|---|---|---|
| \(\dfrac{1}{s+a}\) | \(e^{-at}\) | \(\dfrac{z}{z-e^{-aT}}\) |
| \(\dfrac{a}{s(s+a)}\) | \(1-e^{-at}\) | \(\dfrac{(1-e^{-aT})z}{(z-1)(z-e^{-aT})}\) |
| \(\dfrac{a}{s^{2}(s+a)}\) | \(t-\dfrac{1}{a}(1-e^{-aT})\) | \(\dfrac{Tz}{(z-1)^{2}}-\dfrac{(1-e^{-aT})z}{a(z-1)(z-e^{-aT})}\) |
(表格左侧手写批注,曲线指向表格)
\[\lim_{s\to 0} sE(s)\]
① 令 \(N(s)=0.\)
\[C(s)=\dfrac{\dfrac{1}{s(s+1)}}{1+\dfrac{1}{s(s+1)}}\times (s+1)\cdot R(s) = \dfrac{s+1}{s^{2}+s+1}\cdot R(s)\]
\[\underline{E(s)}=R(s)-C(s)\]
\[=R(s)\left[\dfrac{s^{2}+s+1-s-1}{s^{2}+s+1}\right]=\dfrac{s^{2}}{s^{2}+s+1}R(s)\]
\[\dfrac{E(s)}{R(s)} \qquad\qquad e_{ssr}=\lim_{s\to 0} sE(s)\]
② 令 \(R(s)=0\)
\[\dfrac{C(s)}{N(s)}=\dfrac{1}{1+\dfrac{1}{s(s+1)}}\cdot(\ \ )\quad\checkmark\]
\[\underline{E(s)}=R(s)-C(s)=-C(s)\ \cdots\]
\[e_{ssn}=\lim_{s\to 0}sE(s)\]
(右下角,零散笔画 "lin / lu / kw" 等,字迹不成文,未转写)
\[e_{ss}=e_{ssr}+e_{ssn}\]