A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
laplace transformsprocess control
anonymous
 one year ago
laplace transformsprocess control

This Question is Closed

dan815
 one year ago
Best ResponseYou've already chosen the best response.5if you're ever in doubt just write out the laplace transform integral

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yep but f(t) is like two types of funtions... a ramp function which results in a new steady state value..

dan815
 one year ago
Best ResponseYou've already chosen the best response.5thats okay laplace transform is a linear operator so we can find laplace of each part and add it up

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so you propose finding the first function i.e the ramp function?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well a ramp function usually has a laplace of 1/s^2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i think we usually define it as A for the step change etc but yeah k is fine

dan815
 one year ago
Best ResponseYou've already chosen the best response.5okay wait we gotta do something else here, to make sure stuff after 30 mins is 0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0want to find the slope or leave it in variable notation?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thats what i'm confused about

dan815
 one year ago
Best ResponseYou've already chosen the best response.5okay you will find lapalce of these 3 functions

dan815
 one year ago
Best ResponseYou've already chosen the best response.5one is that first slope

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i don't get what you did on the bottom of the axis

dan815
 one year ago
Best ResponseYou've already chosen the best response.5the 2nd is a slope line starting from down there with that U_c(t) shift

dan815
 one year ago
Best ResponseYou've already chosen the best response.5the one on the bottom is

dan815
 one year ago
Best ResponseYou've already chosen the best response.5f(t)=ktb lets say and to that we applied a unit step function L{U_c(t)*f(tc)}=e^cs*L{f(t)}

dan815
 one year ago
Best ResponseYou've already chosen the best response.5you will add this so that the part after 30 mins gets negated

dan815
 one year ago
Best ResponseYou've already chosen the best response.5then you will simple add the constant function A

dan815
 one year ago
Best ResponseYou've already chosen the best response.5basically what i did was rewrite this as 3 other functions which sum to what we want

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that extended dotted line is your step function right?

dan815
 one year ago
Best ResponseYou've already chosen the best response.5but now all 3 functions have a way to be reprsented from t=0 time

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0let me grasp this on a piece of paper

dan815
 one year ago
Best ResponseYou've already chosen the best response.5okay wait maybe this is just silly lol

dan815
 one year ago
Best ResponseYou've already chosen the best response.5i wonder if we can just simply break out integral like this

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0nah i think you're on the right track

dan815
 one year ago
Best ResponseYou've already chosen the best response.5like can we just break the integrall ike this for a piecewise function

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what i don't get is why you sorta did the reciprocial on the bottom of the axis

dan815
 one year ago
Best ResponseYou've already chosen the best response.5yep u can do this just break it up and solve

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0but why did you draw the function with other parts, thats what i don't get...

dan815
 one year ago
Best ResponseYou've already chosen the best response.5forget that that is a long annoying way this is better

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so just worry about the orginal function?

dan815
 one year ago
Best ResponseYou've already chosen the best response.5yes just break it up piecewise like that

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so we know the laplace of the first integral is 1/s^2 and the laplace of the second is 1/s

dan815
 one year ago
Best ResponseYou've already chosen the best response.5yep just do these integrals like like normal style

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we would have to use by parts method on the first one tho?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{0}^{30}te ^{st}dt=\ \frac{ 1 }{ s }(30e ^{30s})\frac{ 1 }{ s^2 }(e ^{30s}1)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\int\limits_{30}^{\infty}e ^{st}=\frac{ 1 }{ s }e ^{30s}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0as lim t>infty of e^(st)=0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so would that be it?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0where A=55 and k=(7520)/(300)

dan815
 one year ago
Best ResponseYou've already chosen the best response.5lol maybe the other way was faster since we know the laplace transforms of the 3 functiosn right away hehe

dan815
 one year ago
Best ResponseYou've already chosen the best response.5but whatever good to know both ways

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0whats the other way?

dan815
 one year ago
Best ResponseYou've already chosen the best response.5you can do it the other way and compare the answer u are getting with this integration it should be equal

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i was confused what you did at first..how would u set the equations up in the first way

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so how would you go about doing the other way?

dan815
 one year ago
Best ResponseYou've already chosen the best response.5okay so first identify these 3 graphs

dan815
 one year ago
Best ResponseYou've already chosen the best response.5the first 2 are pretty straight forward can you figure out the 3rd one

dan815
 one year ago
Best ResponseYou've already chosen the best response.5laplace of the 3rd graph

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0isn't the third graph simply the first one just in diff order...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the first one has laplace k/s^2 the second identity has laplace A/s third.. well thats just a linear line then a slope like the question

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0anyone want to enlighten me?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry, the net just cut out

dan815
 one year ago
Best ResponseYou've already chosen the best response.5yep but now for the 3rd one we can use that step function trick

dan815
 one year ago
Best ResponseYou've already chosen the best response.5the 3rd graph is very similar to some step function line graph that is shifted down on the y axis now

dan815
 one year ago
Best ResponseYou've already chosen the best response.5so its just this one constant we tacked onto the function

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thats the heavside function right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so b would be the shift of 55 downards?

dan815
 one year ago
Best ResponseYou've already chosen the best response.575 i think because u gotta get rid of the stuff after that http://prntscr.com/8jtl4f

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we aren't starting from the origin tho?

dan815
 one year ago
Best ResponseYou've already chosen the best response.5yeah its the heaveside aplied to a line shifted right and down

dan815
 one year ago
Best ResponseYou've already chosen the best response.5right so its heave side to this function

dan815
 one year ago
Best ResponseYou've already chosen the best response.5just math it lol u get the theory now

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah now i see, so T(s) is just the sum of those 3 identities?

dan815
 one year ago
Best ResponseYou've already chosen the best response.5all u gotta think is what kind of functions can i add that i can take the laplace of easily

dan815
 one year ago
Best ResponseYou've already chosen the best response.5think of other ways to get starting functions

dan815
 one year ago
Best ResponseYou've already chosen the best response.5the sum of (1) + (2) + (3) = is the function you want

dan815
 one year ago
Best ResponseYou've already chosen the best response.5see what happens when you add graph 1 and 2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1443066102562:dw

dan815
 one year ago
Best ResponseYou've already chosen the best response.5all the values after 75 keep cancelling out

dan815
 one year ago
Best ResponseYou've already chosen the best response.5at every coordinate on x

dan815
 one year ago
Best ResponseYou've already chosen the best response.5thats what it means to add functions right

dan815
 one year ago
Best ResponseYou've already chosen the best response.5at every t value we add both of their y values

dan815
 one year ago
Best ResponseYou've already chosen the best response.5if they have the same slope and one is starting exactly negative of it, then u have to keep cancelling

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0makes much more sense!!!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so those two end up like that ok so we have

dan815
 one year ago
Best ResponseYou've already chosen the best response.5okay yes thats what ive been doing

dan815
 one year ago
Best ResponseYou've already chosen the best response.5now we add that constant function heavsided to get that constant line

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so graph 2 is just a ramp function shifted 30units of t to the right and shifted down 75 units dw:1443066491364:dw

dan815
 one year ago
Best ResponseYou've already chosen the best response.5finding the laplace transform of these functions is much simpler, now u can add them to get the desired effect

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so T(t) = t + u(t30) 75 + 55?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0cause the first has slope t, second has that shift of heavside function and the thirs is just a step function?

dan815
 one year ago
Best ResponseYou've already chosen the best response.5http://www.efunda.com/math/laplace_transform/rules.cfm list of some basic laplace properties

dan815
 one year ago
Best ResponseYou've already chosen the best response.5i gotta watch a lecture for my class right now, ill be back, work thru it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0np, i try get my head around it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@ganeshie8 could you help me with this?
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.