杨平《自动控制原理》附加例题
解：可列出系统的微分方程如下1 d i( t ) = ( u i u 0 ) + C1 ( u i u 0 ) R1 dt u = iR + 1 idt 1 将微分方程作拉氏变换 0 C2 ∫
1 I(s) = R [U i (s) U 0 (s)] + C1s[U i (s) U 0 (s)] 1 U (s) = R I(s) + 1 I(s) 2 0 C 2s 消去I(s)可得 U 0 (s) (τ 1s + 1)(τ 2 s + 1) G (s) = = U i (s) τ 1τ 2 s 2 + (τ 1 + τ 2 + τ 3 )s + 1 式中：τ 1 = R 1C1 ,τ 2 = R 2 C 2 ,τ 3 = R 1C 2