Question

Consider the following statements regarding the effect of adding a pole in the open-loop transfer function on the closed-loop step response:

1. It increases the maximum overshoot.

2. It increases the rise time.

3. It reduces the bandwidth.

Which of the above statements are correct?
1. 1, 2 and 3
2. 1 and 2 only
3. 2 and 3 only
4. 1 and 3 only

Answer 1

Correct Answer - Option 1 : 1, 2 and 3

Effects of adding a pole to the forward path transfer function:

The addition of a pole at s = -1/T to the forward transfer function of the prototype transfer function gives

\(G\left( s \right) = \frac{{\omega _n^2}}{{s\left( {s + 2\zeta {\omega _n}} \right)\left( {1 + Ts} \right)}}\)

In general, the effect of adding a pole to the forward path transfer function is to make the closed-loop stable, while decreasing the bandwidth.

For large values of T, the unit-step response reveals the following:

• The rise time increases with the decrease in bandwidth
• The larger values of the resonant peak also correspond to a larger maximum overshoot in the unit-step response.