For a critically damped system, the closed-loop poles are

Question

Question

This question was previously asked in

ESE Electrical 2016 Paper 1: Official Paper

Attempt Online

Answer 1

System	Damping ratio	Roots of the Characteristic equine.	Root in the ‘S’ plane
Undamped	ξ =0	s = ±jωn Imaginary
Underdamped (Practical system)	0 ≤ ξ ≤ 1	\(- \xi {\omega _n} \pm j{\omega _n}\sqrt {1 - {\xi ^2}} \) Complex Conjugate
Critically damped	ξ = 1	-ωn Real, equal and negative
Overdamped	ξ > 1	\(- \xi {\omega _n} \mp j{\omega _n}\sqrt {{\xi ^2} - 1} \) Real and unequal

Important Points:

If the poles are the real and left side of the s-plane, the step response approaches a steady-state value without any oscillations.
If the poles are the complex and left side of the s-plane, the step response approaches a steady-state value with the damped oscillations.
If poles are non-repeated on the jω axis, the step response will have fixed amplitude oscillations.
If the poles are the real and right side of the s-plane, the step response reaches infinity without any oscillations.
If the poles are the real and right side of the s-plane, the step response reaches infinity without any oscillations.
If the poles are the complex and right side of the s-plane, the step response reaches infinity with damped oscillations.