- #1
Hessami
- 9
- 0
Homework Statement
I have a transfer function in the laplace domain, and I have been asked to:
"Develop Relationships in terms of the constant parameters and adjust K such that the constants are: A = 2, B = 1, C = 3, a = 3, b = 1"
After finding this relationship, I am asked to convert it back to time domain, find damped natural frequency, and adjust K for critical Damping.
I drew up this graph in MSpaint, sorry about the terrible quality, but it should hopefully be enough to get the general drift. As far as i can tell it's a graph of the response (laplacian?) against the undamped natural frequency multiplied by time, and it looks like a decaying cosine function. (at least the original does!).
Homework Equations
Transfer function (Laplace Domain) = K/[(s+a)(s+b-A.B)+K.C.B]
The Attempt at a Solution
I derived the Transfer Equation from a block diagram that I was given, and I am confident that I got that part correct.
I'm not sure what this question means by "develop relationships in terms of the constant parameters and adjust K such that the constants are... etc" , because as far as I can tell, the constants are not actually related to each other, and the Value of K has no bearing on what the other constants will be, right?
Following this, the rest should be fairly straightforward:
1) Convert back to time domain using the Laplace transform table,
2) Find my damped natural frequency from measuring periods on the graph.
3)Arranging the equation into
(D^2)/(omega^2) + D(2.E/omega) + 1
where D = differential operator, omega = undamped natural freq, E = damping ratio.Substituting natural frequency found in 3, and then making E = 1 for critical damping, to find the adjusted K value.TL;DR -
What is being asked in the phrase "Develop Relationships in terms of the constant parameters and adjust K such that the constants are: A = 2, B = 1, C = 3, a = 3, b = 1"?
Should I substitute the constants into the equation, and find the equations for s?
Please help me! I've been stumped on this all week and can only feel myself getting stupider!
Last edited: