In a control system, the response is critically damped if:

Question

Question

This question was previously asked in

BHEL Engineer Trainee Electrical 2019 Paper

Answer 1

The general expression of transfer function of the standard second-order system is:

\(TF = \frac{{C\left( s \right)}}{{R\left( s \right)}} = \frac{{\omega _n^2}}{{{s^2} + 2\zeta {\omega _n}s + \omega _n^2}}\)

Where,

ζ is the damping ratio

ωn is the undamped natural frequency

Characteristic equation: \({s^2} + 2\zeta {\omega _n} + \omega _n^2 = 0\)

Roots of the characteristic equation are: \(- \zeta {\omega _n} + j{\omega _n}\sqrt {1 - {\zeta ^2}} = - \alpha \pm j{\omega _d}\)

α is the damping factor

The nature of the system is described by its ‘ζ’ value