Engineering How Can I Find the H-infinity Norm of a Transfer Function?

Click For Summary
To find the H-infinity norm of a transfer function, the user initially considers using the Bode plot but struggles with it. They express a preference for calculating the minimum value of the function |G(iω)| using calculus methods, specifically differentiation. The user calculates a value of approximately 24.21 for the denominator, questioning its accuracy in relation to expected values. Ultimately, they realize their earlier calculations contained errors, determining the maximum value is actually 1/14.30908802. The discussion highlights the challenges of finding the H-infinity norm through analytical methods.
billtodd
Messages
136
Reaction score
33
Homework Statement
below
Relevant Equations
below
I want to find ##\|G\|_\infty##, the solution in the pic uses the Bode plot. But to tell you the truth I am worse at drawing it.
So basically what I thought is I want to find: ##|G(i\omega)|=1/\sqrt{(25−\omega^2)^2+9\omega^2}##.
So basically I much prefer to find the minimum value of what is in the sqrt from highschool calculus methods (differentiating and equating to zero).
I found something of the sort of 24.21 in the denominator, which is close to 25 but far from 15.
Am I correct in my reasoning?
 

Attachments

  • 1725115814527.png
    1725115814527.png
    78.1 KB · Views: 41
Physics news on Phys.org
never mind I get the max is at 1/14.30908802. I had some really bad error.
 
  • Like
Likes FactChecker
I have a question that I couldn’t fully understand its logic. The professor asked us to calculate the shear resistance and moment about the X and Y axis, using the given cross-section and the values of compressive and tensile stresses. I understand how to get the moment, but I’m confused about how to find the shear resistance from these stresses. Could you explain or clarify the method?

Similar threads

  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
2
Views
1K
  • · Replies 1 ·
Replies
1
Views
4K
Replies
2
Views
2K
Replies
6
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K