# Deriving transfer function of ramp response out of a plot

• JasonHathaway
In summary, the author attempted to solve for the time constant for a first order system with a ramp input, but was unsuccessful.
JasonHathaway

## Homework Statement

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

## Homework 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.

## 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:
JasonHathaway said:
The only thing I knew that if I plot the error function, then its steady state value will be T (tau or time constatnt).
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 ?

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:
rude man said:
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?
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).

BvU said:
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).
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.

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/

BvU said:
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/
Don't think so. The roblem referred to a responbse with
BvU said:
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/
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.

## What is a transfer function?

A transfer function is a mathematical representation of the relationship between the input and output of a system. It describes how the system responds to different input signals.

## Why is it important to derive the transfer function from a ramp response plot?

Deriving the transfer function from a ramp response plot allows us to understand the behavior and characteristics of a system. It helps us to analyze and predict the response of the system to different input signals, which is crucial in designing and controlling systems.

## What steps are involved in deriving a transfer function from a ramp response plot?

The steps involved in deriving a transfer function from a ramp response plot include identifying the input and output signals, calculating the slope of the response curve, finding the gain and time constant of the system, and using these values to write the transfer function in the appropriate form.

## What assumptions are made when deriving a transfer function from a ramp response plot?

When deriving a transfer function from a ramp response plot, it is assumed that the system is linear, time-invariant, and has constant coefficients. It is also assumed that the input and output signals are continuous and that there are no external disturbances affecting the system.

## How can the derived transfer function be used in practical applications?

The derived transfer function can be used to design controllers, predict system behavior, and analyze the stability and performance of a system. It is also used in simulation and modeling of systems to evaluate different scenarios and optimize system performance.

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