DOMINANT POLE

The poles of a system (those closest to the imaginary axis in the s-plane) give rise to the longest lasting terms in the transient response of the system.Then those poles are called dominant poles

The poles which are far from imaginary axis are called insignificant poles because their their exponential terms decay very fast.

If we find inverse Laplace transform to a transfer function, in the response we get exponential terms with powers in terms of poles, not with zeros. So we have only dominant poles and we won’t have dominant zeros.

y(t) = (2 − 2.222e^-t + 0.2469e^−10t − 0.0022e^−100t)u(t)

Note that

The first term (2) is the forced response. It remains as long as the input remains equal to 1.

The second term (-2.22e-t) has an initial condition 9x larger than any other term and it decays slower than the other terms.

The steady state response is when t = -∞

Substitute the some value t in y ( t ).you can clearly notice which term is affecting the steady state value. The terms which are affecting more is called dominant. Hence, the pole at s=-1 dominates the response (and is termed the dominant pole).

Dominant pole approximation  

Solution

Select the pole which is near to jω axis

So, dominant pole is -1.This controls the system response

Know divide other poles with the dominant pole. Generally If the value when divided by other poles with the dominant pole is greater than 5, then that pole is subjected to dominant pole approximation.

So from the given transfer function poles at -6, -7 are subjected to dominant pole approximation

How to apply subjected to dominant pole approximation

Take the values that are subjected to dominant pole approximation as common from those expressions in which the values that are subjected to dominant pole approximation are present. Then substitute S = 0 in the expressions in which the values that are subjected to dominant pole approximation are present.

  

Solution

The dominant conjugate poles are -(1+j2),-(1−j2)