Maths: Laplace Transforms screwing with my head!

hatchleader

Active Member
Got an assignment for control systems at uni and our lecturer is rubbish (so rubbish a number of us have complained)! she's given us the following and i'm meant to use laplace transform to solve this for V:

dv/dt+2v=9 with initial values v=0 when t=0

For some reason i can't seem to get my head around it. I've always struggled with the electronics side of my course purely because i struggle to visualise things the way i can for the mechanics side!

Any mathematicians out there able to break it down simply and easily?
 

Flimber

Distinguished Member
O....k...a...y...

...now let's just all step slowly away from the thread and nobody's going to come to any harm...(paces backwards slowly)...


....now RUNNNN!!!!!!!!!!!!!!!!!!!!

Is there a need for a Nerd's Forum around these parts ? :)
 

imightbewrong

Distinguished Member
I've not come across them but just did a quick google and it looks pretty straight forward.

Have you read this from the Wiki page on the topic? :)

 

imightbewrong

Distinguished Member
I mean, what's not to get ;)

The only hard be looks like 1) knowing how to transform a differential using laplace, and then 2) inverting it after a bit of a shufty for the solution.
 

hatchleader

Active Member
First half of wiki explanation is straightforward but from where it says: Next we take the laplace transform of both sides of the equation, I'm a bit stumped! As far as i can tell 'N' in my equation is 'v' but does that mean i need to view 'v' as 0 due to the statement that the initial values are v=0 when t=0?

I'm really confused!!
 

imightbewrong

Distinguished Member

Simba

Well-known Member
Got an assignment for control systems at uni and our lecturer is rubbish (so rubbish a number of us have complained)! she's given us the following and i'm meant to use laplace transform to solve this for V:

dv/dt+2v=9 with initial values v=0 when t=0

For some reason i can't seem to get my head around it. I've always struggled with the electronics side of my course purely because i struggle to visualise things the way i can for the mechanics side!

Any mathematicians out there able to break it down simply and easily?
wow this reminds me of the time when i did control systems...and the entire class's feedback was the same lol.

who is your lecturer...? I had a crazy Greek chap who sounded like Ren from Ren n Stimpy....class! :facepalm:

i never understood Laplace then so its been erased from my memory naturally.

I used Modern Control Systems (10th Edition i think) to get through the exam...conincidentally, the exam had questions straight from the book :laugh:.

This might be a holy grail for revision:

http://www.cpdee.ufmg.br/~palhares/solution_CSL_Dorf_Bishop.pdf
 
Last edited:

FruitBat

Well-known Member
I can't remember if I ever did any of this stuff, but from a quick read of wikipedia and some other places (like this), I think this is one way to do it:

1. Using a couple of facts (I assume that you don't need to prove everything from first principles):
Writing L(v) = F(s),
a) L(v') = sF(s) - v(0)
b) L(1) = 1/s
(if I've read correctly)

so, for v'+2v = 9:

L(v')+2(L) = L(9) (by linearity)

sF(s)+2F(s) = 9/s (we know that v(0) = 0)

F(s) = 9 / s(s+2)

Now you have to apply the inverse transform. I think that you're probably supposed to use tables here (not sure how to go about it otherwise).

This looks like it's going to be a trig function, but it needs to be put into the correct format, so (completing the square):

RHS = 9 / (s+1)^2 - 1

which (if I understand the tables correctly) is the transform of

9 * e^(-t) * sinh(t)

At this point, we can check back with the original equation:

Using various rules (product rule etc) and trig identities:


9 { -e^(-t) * sinh(t) + e^(-t) * cosh(t) } + {18 * e^(-t) * sinh(t)} = 9 (hopefully)

If you substitute the hyperbolics with their exponential formulae, I think this works (have to be careful with stray -1 factors).

Anyway, don't take my work for it. There could be mistakes in the above.
 

imightbewrong

Distinguished Member
Ah you just pipped me to it



;)
 

hatchleader

Active Member
beginning to work it out! Cheers for the help folks! gonna crack a few hours out on some practise questions then give this one a shot with FruitBats as a guide! if theres anything majorly different then i might be back!
 

imightbewrong

Distinguished Member

Oddbll

Standard Member
Are/were you at Northampton Uni by any chance, with Huijuan? I'm 2nd year there now and we have just had the same question, with no formal lectures we're told to do it and we're struggling a lot with it...how did you get on? Any answers would also be greatly appreciated....
 

johntheexpat

Distinguished Member
Google, doesn't give you the answer, but finds one of your fellow students trying to get help.:laugh::laugh:

How long 'til the lecturer herself turns up, works out who the OP is and then fails them for calling her useless?
 

Member 55145

Distinguished Member
btw the answers 42, trust me :zonked:
 

MrBlofeldt

Banned
Dear god, I remember having to do all this ***** when I did my electronic engineering degree (sorry, can't remember any of it, I know that's no help, just wanted to add my thoughts)... Let me just say one thing...

I never needed it...!
 

campy mccamper

Well-known Member
Dear god, I remember having to do all this ***** when I did my electronic engineering degree (sorry, can't remember any of it, I know that's no help, just wanted to add my thoughts)... Let me just say one thing...

I never needed it...!

Did they teach you the capacitor values in a rather unorthodox way?
 

pandemic

Well-known Member
Pandemic, goes to get his Engineering handbook out of dusty box. So he can turn to the table of Laplace Transforms page and reminisce about the good old days...
 

BB3Lions

Distinguished Member
I read the header as "Lapdance Transformers screwing with my head!"

I need to stop working for the weekend.
 

imightbewrong

Distinguished Member
I keeping seeing 'lapdance' as well.
 

Garry123

Well-known Member
I never got my head around laplace transforms when I was at Uni, i failed the module. Now I'm a Control and Instrumentation engineer and never use it :D. I had a crap lecturer as well, S planes and all that crap :boring:.
 

Trending threads

Top Bottom