2nd Order Standard Form

Topics: Feedback Control Systems

A second order system has a polynomial of degree 2 in the denominator of its transfer function. In standard form, the transfer function is

$$T(s) = \frac{\omega_n^2}{s^2 + 2 \zeta \omega_n + \omega_n^2}$$

where

• $\zeta \geq 0$ is the damping factor
• $\omega_n \geq 0$ is the undamped natural frequency

There 4 distinguished cases based on the damping factor:

• $\zeta = 0$: undamped system
• $0 \leq \zeta < 1$: underdamped system
• $\zeta = 1$: critically damped system
• $\zeta > 1$: overdamped system