误差分析
\(\lambda\) 型系统
\(\lambda\) 型系统的传递函数一般可以写为
\[
G(s)=\frac{K \prod_k\left(c_i s+1\right) \prod_l\left(d_l^2 s^2+2 \zeta_l d_l s+1\right)}{s^\lambda \prod\left(a_i s+1\right) \prod\left(b_j^2 s^2+2 \zeta_j b_j s+1\right)}
\]
| system | Unit Step | Unit Ramp | Unit Acceleration |
|---|---|---|---|
| 0-type | \(\frac{1}{1+K_p}\) | \(\infty\) | \(\infty\) |
| I-type | 0 | \(\frac{1}{K_v}\) | \(\infty\) |
| II-type | 0 | 0 | \(\frac{1}{K_a}\) |
With
\[
K_{\mathrm{p}}=G(0) \quad K_{\mathrm{v}}=\lim _{s \rightarrow 0} s \cdot G(s) \quad K_{\mathrm{a}}=\lim _{s \rightarrow 0} s^2 \cdot G(s)
\]