Consider the given Bode plot of a system and find the transfer function.

Concept:

One pole provides a slope of -20 dB/decade.

One zero provides a slope of +20 dB/decade.

The frequencies where the bode plot changes slope are known as the cross-over frequencies.

Explanation:

The cross-over frequencies are: $\frac{1}{{\tau }_1},\frac{1}{{\tau }_2},\frac{1}{{\tau }_a},\frac{1}{{\tau }_b},\frac{1}{{\tau }_3}$ and $\frac{1}{{\tau }_4}$

The initial slope is -20 dB/decade, hence a pole at the origin is present.

Hence, the transfer function is:

$T(s)=\frac{K(s{\tau }_a+1)(s{\tau }_b+1)}{s(s{\tau }_1+1)(s{\tau }_2+1)(s{\tau }_3+1)(s{\tau }_4+1)}$