Question

The open-loop transfer function of the system is

• A. $\frac{30(\frac{s}{5}+1)}{s(\frac{s}{10}+1)(\frac{s}{2}+1)}$
• B. $\frac{30(\frac{s}{2}+1)}{s^2(\frac{s}{5}+1)(\frac{s}{10}+1)}$
• C. $\frac{1.65(0.2s+1)}{s(0.5s+1)(0.1s+1)}$
• D. $\frac{31.62(0.5s+1)}{s(0.2s+1)(0.1s+1)}$

Answer 1

The correct option is D $\frac{31.62(0.5s+1)}{s(0.2s+1)(0.1s+1)}$

$T.F=\frac{K(\frac{s}{2}+1)}{s(\frac{s}{5}+1)(\frac{s}{10}+1)}$
To obtain the value of K,

30 dB = 20 log K - 20 r log(1) $[\because r=1]$
1.5 = log K

$K={10}^{1.5}=31.62$

$T.F.=\frac{31.62(0.5s+1)}{s(0.2s+1)(0.1s+1)}$