I have read in many texts that the closed loop system damping factor can be approximated as:
\$\Phi_m= 100 * \zeta\$
With \$\Phi_m\$ as the phase margin and \$\zeta\$ as the damping ratio.
The actual relation between the two is more complicated and I think requires numerical method to solve.
How is the approximation made in a second order control system, and when is it valid to consider the approximation (what's the range of the phase margin)?