Question

A compensator transfer function for a feedback system is given by,
$C\left(s\right)=\frac{4s+1}{0.4s+1}$
The inferences which can be drawn by analysis of transfer function are given below:
1. The transfer function shows nature of a lead compensator.
2. The value of $\alpha$ for the compensator is 0.1.
3. The compensator increases the bandwidth in a closed loop system leading to faster time response.
Which of the given inferences are correct?

• A. 1 and 2 only
• B. 2 and 3 only
• C. 1 and 3 only
• D. 1, 2 and 3

Answer 1

The correct option is D 1, 2 and 3

We can analyze from given transfer function that zero lies closer to origin than a pole so it is lead compensator.
Comparing with standard form,
Transfer function, $C\left(s\right)=\frac{4s+1}{0.4s+1}=\frac{1+Ts}{1+\alpha Ts}$
T = 4,
$\alpha$T = 0.4
$\alpha$×4=0.4
$\alpha =\frac{0.4}{4}=0.1$
Lead compensator in a closed loop system increases the bandwidth of the system and hence leads to faster time response.