Control Systems Theory: Determing break frequency mathematically.

[btbam91]

Hey there.

I have an open loop transfer function TF = K/(t*s^2 + s) where K is known. Given a value for the break frequency (say, w_b = 10 rad/s), I have to determine the value of the time constant, t.

I understand how do this with a bode plot, but not entirely sure how to proceed mathematically.

Thank you!

btbam91

 

[rude man]

First, rewrite the function into K/s(Ts+1) = (K/T)/s(s + 1/T).
So now, looking at it that way, for what value of ω does the break occur?

I would like to see or have described your Bode plot with exact abscissa and ordinate values. If you did this right it's obvious what the gain and the time constant are. It's also very helpful to understand the relationship between your TF and the Bode plot.

BTW don't use t in your transfer function. t is always a variable. Use T or tau.