The asymptotic Bode plot of a transfer function is shown in the figure. The transfer function $G(s)$ corresponding to the Bode plot is

$\frac{1}{(s+1)(s+20)}$
$\frac{1}{s(s+1)(s+20)}$
$\frac{100}{s(s+1)(s+20)}$
$\frac{100}{s(s+1)(1+0.05s)}$

Correct answer: $\frac{100}{s(s+1)(s+20)}$

Solution

From the asymptotic Bode plot, the initial slope indicates an integrator, and the break frequencies correspond to poles at $1$ and $20$ rad/s. The gain factor is determined from the magnitude level, leading to $G(s)=\frac{100}{s(s+1)(s+20)}$.

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