# Deriving transfer function of ramp response out of a plot

1. Dec 14, 2015

### JasonHathaway

1. The problem statement, all variables and given/known data
The first order ramp unit response is shown in the graph below. Determine:
1. The transfer function.
2. Plot the error function e(t) then determine its maximum magnitude and the time
http://s24.postimg.org/cdbhqm80j/Capture.png

2. Relevant equations
G(s)=(1/T)/(S+1/T) ......... G(s): Standard first order T.F, , T (or tau) is the time constant.
T is the time to reach 63,2% of the final output value.

3. The attempt at a solution
I know how to solve this if the input was the step unit as shown in the graph:

But that is not my case in ramp unit. How can I get the time constant while the curve is going upward forever?
The only thing I knew that if I plot the error function, then its steady state value will be T (tau or time constatnt). Any help?

Last edited: Dec 14, 2015
2. Dec 14, 2015

### BvU

Well, if you are sure (I'm not: the dimension of that difference is the dimension of c, not of time) then you draw a straight line from 0 that ends up parallel ?

3. Dec 15, 2015

### rude man

You know that you need some kind of differentiator since a ramp input gives an eventual constant output, but a simple Ts/(Ts+1) won't give you an oscillatory response, will it.
So, what 2nd order transfer function would?
EDIT: there is an error in the posting of the problem. If the oscillatory response shown is due to a ramp input, the response to a step input of the same network cannot be the straight line (=1) shown.

Last edited: Dec 15, 2015
4. Dec 15, 2015

### BvU

Good thing you shed some light on this one. I was under the impression the system in the exercise is a first order system! (The attached response picture (not the step response picture in the post itself) sure strengthened that impression).

5. Dec 15, 2015

### rude man

The OP assumned a 1/(Ts+1) filter which of course is totally inappropriate. And see my comment on the contradiction in the way the problem is posed.
The oscillatory response precludes any 1st order system. In regard to synthesizing the filter I don't think one can design a passive filter of any order with an oscillatory response. I think an active filter would be needed but I guess that is not the OP's concern.

6. Dec 15, 2015

### BvU

The oscillatory response was only in an illustration the OP brought in as something familiar. The actual problem is about a ramp response. A yellow line with rather little to go by....http://postimg.org/image/tqls5h3bl/full/

7. Dec 15, 2015

### rude man

Don't think so. The roblem referred to a responbse with
Oh, OK. So the prolem is undefined. With Ts/(Ts+1) he/she would at least get an error function and an eventual constant output.