Draw Bode plot for the function G(s). Find gain margin, phase margin and comment on stability. \[ G(s)= \frac{2(s+0.25)}{s^2(s+1)(s+0.5)} \]

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written 4.5 years ago by

teamques10 ★ 70k

Assuming H(s) = 1

$\therefore{}G\left(s\right)H\left(s\right)=\dfrac{2(s+0.25)}{s^2\ (s+1)(s+0.5)}=\dfrac{2\times{}0.25}{0.5}\ \ \dfrac{1+45}{s^2\left(1+s\right)\left(1+2s\right)}$

$k=\dfrac{2\times{}0.25}{0.5}=1 $

$s^n=s^{-2} $

$\therefore{}G\left(s\right)H\left(s\right)=\dfrac{1+45}{s^2\left(1+s\right)\left(1+2s\right)}\ $

$n=-2 $

Various factor of G(s) are

$ 2 \ poles\ at\ origin, straight\ line\ of\ slope - 40dB/dec\\ \ \ \ \ \ \ passing\ through\ intersection\ of \omega{}=1 \ \&\ 0dB. $
$Simple\ zero\ …

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