Problem 예제.

Multiple Choice • Views 733 • Comments 1 • Last Updated at 1 month ago

다음 상태 변수 신호 흐름 선도가 나타내는 방정식은?

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$\dfrac{d^2}{dt^2}c(t)+5\dfrac{d}{dt}c(t)+4c(t)=r(t)$

$\dfrac{d^2}{dt^2}c(t)-4\dfrac{d}{dt}c(t)-5c(t)=r(t)$

$\dfrac{d^2}{dt^2}c(t)-5\dfrac{d}{dt}c(t)-4c(t)=r(t)$

$\dfrac{d^2}{dt^2}c(t)+4\dfrac{d}{dt}c(t)+5c(t)=r(t)$

Solution

$C = x_1$

$x_1 = \dfrac{1}{s}x_2 \Rightarrow x_2 = sC$

$x_2 = \dfrac{R-4x_2 -5x_1}{s} \Rightarrow (\dfrac{4}{s} +1 )x_2 = \dfrac{R-5C}{s}$

$(\dfrac{4}{s} +1)sC = \dfrac{R-5C}{s}$

$s^2C + 4sC = R-5C$

$s^2C + 4sC + 5C = R$

$\dfrac{d^2c(t)}{dt^2}+4\dfrac{dc(t)}{dt}+5c(t)=r(t)$

Correct answer: 4