How to solve a transfer function equation in Matlab

How to use Matlab to solve for ω for transfer function equation below:

Magnitude of | (0.001325 s + 110.4) / ( 1.872e-33 s^5 + 3.052e-24 s^4 + 7.143e-16 s^3 + 1.059e-09 s^2) | = 1

s = jω

Manual calculation shows that ω = 164.294e3*2pi

and verify ω = 164.294e3*2pi in Matlab gets abs = 1 and angle = 50.455 degress, which is correct.

However, it is very time consuming to do manual calculation.

Is there a quick way to convert transfer function in s to complex function in jω, then get the magnitude of that complex function = 1 (or other value)?

The abs function only able to get magnitude of complex function if we know ω, but not abs(complex(jω)) = 1.

[Joe Suat Chai]

sorry, amendment on angle, should be -129.5458 deg (50.4542 deg is indeed phase margin)

>> abs(-0.6367 - 0.7711i)

ans = 1.0000

>> angle(-0.6367 - 0.7711i)

ans = -2.2610 rad

>> -2.2610*180/pi

ans = -129.5458 deg

>> -129.5458+180

ans = 50.4542 deg (phase margin)

*Substitute ω = 164.294e3*2pi into (ω*0.001325i + 110.4)/(1.872e-33i*ω^5 + 3.052e-24*ω^4 - 7.143e-16i*ω^3 - 1.059e-09*ω^2) will get -0.6367 - 0.7711i

Answer 1

[Paul]

The function allmargin in the Control System Toolbox solves for abs(H(jw)) = 1 (among other things)

>> G

G =
 
                       0.001325 s + 110.4
  -------------------------------------------------------------
  1.872e-33 s^5 + 3.052e-24 s^4 + 7.143e-16 s^3 + 1.059e-09 s^2
 
Continuous-time transfer function.

>> s = allmargin(G);
>> s.PMFrequency/2/pi

ans =

   1.6429e+05