1
\$\begingroup\$

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.

Lengthy phase margin calculation

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)?

\$\endgroup\$
2
  • \$\begingroup\$ Do you have a link to the assertion? \$\endgroup\$
    – Andy aka
    Commented Jun 22, 2016 at 11:06
  • \$\begingroup\$ It's a design ROT for systems that are, ostensibly, 2nd order, and should be treated as such. \$\endgroup\$
    – Chu
    Commented Jun 22, 2016 at 13:59

2 Answers 2

7
\$\begingroup\$

You can see when the approximation is good simply by plotting the two curves.

enter image description here

\$\endgroup\$
3
\$\begingroup\$

The mentioned approximation for the phase margin (100*damping factor) applies to a second order system only when the damping factor is smaller than 1/SQRT(2)=0.7071 or when the phase margin is smaller than app. 65 deg. (Ref.: R.C. Dorf, Modern Control Systems, 6th edition, Addison-Wesley).

\$\endgroup\$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.