Question

What cause the main transient response of the system.

• A. Dominant roots

• B. Locus

• C. Asymptote centroid

• D. Auxiliary polynomial

Answer 1

Answer: A

Explaination:

• The dominant poles or roots of the denominator are main cause of transient response.
• The system response is dominated by the pair of complex conjugate poles or real poles which are closest to the imaginary axis.
• Since they decay slower, as they have relatively small real parts.
• Hence, these poles are called the dominant system poles.
• for example, let a second order system is as follows,
  • 
  • Here s = -1, -1000 are two poles.
  • s=-1000 is far away from the imaginary axis, but s= -1 is closer to imaginary axis.
  • Lets do partial fraction.
  • 
  • Lets take the inverse Laplace transform of this H(s).
  • 
  • With in no time, tends to 0 means sharply fall to 0.
  • But decays slowly. Hence this is bottleneck to transient response.
  • Hence, s=-1 is the dominant pole.
• Hence, the dominant poles decide the overall transient response.