Discrepancies in Step Response

Translate This Thread From English to

Threaded View

Subject
Author
Posted on

Discrepancies in Step Response
ssylee
01-30-2010

ssylee posted on
January 30, 2010, 3:06 pm

rate this thread

EXCELLENT
VERY GOOD
GOOD
FINE
BAD

Report it

I'm going through a solution of a problem from a problem set. However,
I don't know how to get the step response of this transfer function
properly: G(s) = 10/(s+1)/(s+10). Using the Laplace transform tables,
I got a transfer function of g(t) = 10/9*(exp(-t) - exp(-10*t))*u(t),
with the graph shown here (http://imagebin.ca/img/EBd-Li.jpg ). I have
entered this system's transfer function and plotted its step response
in Matlab (http://imagebin.ca/img/SRLhIXU.jpg ). However, even the
Matlab plot disagrees with the textbook solutions (http://imagebin.ca/
img/Y6BqRb.png). I have no idea how the textbook solutions plot is
computed. It would be great to hear your opinions.

Jerry Avins posted on
January 30, 2010, 3:36 pm
Permalink

Re: Discrepancies in Step Response

ssylee wrote:

I see room for confusion. With three division signs in a row, what
divides what? Matlab and the textbook seem to agree except for an offset
of one in the time axix. Since Matlab forces the origins of its arrays
to 1, that doesn't surprise me.

Matlab's and the textbook's plots show the asymptotic response (t->00)
to be unity. The other shows it to be zero. Understanding the order of
operations in your expression, you should be able to check that.

Jerry
--
Engineering is the art of making what you want from things you can get.
��

Tim Wescott posted on
January 30, 2010, 5:36 pm
Permalink

Re: Discrepancies in Step Response

On Sat, 30 Jan 2010 12:06:19 -0800, ssylee wrote:

"Using the Laplace transform tables, I got a transfer function of g(t) ="

Transfer functions (in the context of linear systems theory) do not exist
in the time domain. Think about that. Then think about what someone
means when they say "step response". What exactly is a "step response"
of a system -- don't give it in terms of some regurgitated Laplace-domain
stuff, tell me what is the system input in the time domain, and what do
you expect out of it?

Perhaps then you'll see your error.

--
www.wescottdesign.com

Tim Wescott posted on
January 30, 2010, 5:38 pm
Permalink

Re: Discrepancies in Step Response

On Sat, 30 Jan 2010 12:06:19 -0800, ssylee wrote:

And the graph in the book is shifted over by one -- it's probably a
typo. Matlab's plot is correct.

--
www.wescottdesign.com

pnachtwey posted on
January 30, 2010, 8:25 pm
Permalink

Re: Discrepancies in Step Response

Did you forget the step forcing function 1/s?
Assuming G(s) is supposed to be 10/((s+1)(s+10)) the response should
look like a
first order response except there will be a slight inflection due to
the second pole.
Your plot looks like you forgot the step forcing function 1/s.
Now your transfer function is (1/s)*(10/((s+1)(s+10)).
The simple thing to do is to use wxMaxima or some other CAS to do the
inverse Laplace transform.
I get
f(t)=-10*%e^-t/9+%e^-(10*t)/9+1

Peter Nachtwey