Question

Steady-state error of the following second-order system for a unit ramp input is \[ \frac{C(s)}{R(s)} = \frac{\omega_n^2}{s^2+2\zeta\omega_n s+\omega_n^2}. \] The steady-state error is:

• A. \(\frac{\zeta}{2\omega_n}\)
• B. \(\frac{2\zeta}{\omega_n}\)
• C. \(\frac{\omega_n}{2\zeta}\)
• D. \(\frac{2\omega_n}{\zeta}\)

Hint:

For a standard Type-1 system, the velocity error coefficient is \(K_v = \frac{\omega_n}{2\zeta}\). Since steady-state error for a unit ramp input is given by \(e_{ss} = \frac{1}{K_v}\), directly reciprocating \(K_v\) gives \(\frac{2\zeta}{\omega_n}\).

Answer 1

The Correct Option is B