A dominant pole is determined by

SOLUTION

Time constant: It gives the system behavior. If the time constant is large then the response will be slow, if the time constant is small then the response will be fast.

It is denoted by 'τ'

Practically any system takes 5 time-constant to reach a steady state.

 \( \tau= \frac{-1}{real~part~of~dominant~pole}\)

Dominant pole: The pole which is near to the imaginary axis is called the Dominant pole and it should be at least two octaves less than other poles

Insignificant pole: The pole which lies in the leftmost side.

The pole should. have the smallest time-constant, whereas the dominant pole has the largest time constant.

The insignificant poles are neglected because even if the insignificant poles are neglected, there is no much change in the system response.

Example:

Let the system response be

\(C(s) = \frac{1}{{(s+1)}{(s+10)}}\)

= \(\frac{\frac1{9}}{s+1}\)+ \(\frac{\frac{-1}{9}}{s+10}\)

\(c(t) = \frac{1}{9} e^{-t} - \frac{1}{9}e^{-10t}\)

\( \frac{1}{9} e^{-t}\): Dominant pole response

\(\frac{1}{9}e^{-10t}\): Insignificant pole response

Here τ =1 sec from dominant pole response.

 

So the dominant pole is the pole which is near to the imaginary axis, so it is at a lower frequency.