Technique for handling Dead Time in Laplace Transforms - PowerPoint PPT Presentation

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Technique for handling Dead Time in Laplace Transforms

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Definition of the dead time problem ... This velocity profile is characteristic of turbulent flow and can be modeled as plug flow. ... – PowerPoint PPT presentation

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Title: Technique for handling Dead Time in Laplace Transforms


1
Technique for handling Dead Time in Laplace
Transforms
  • Plug flow in pipes

2
Definition of the dead time problem
Consider flow (q) in a pipe where the flow occurs
with nearly uniform velocity across the
crossection
This velocity profile is characteristic of
turbulent flow and can be modeled as plug flow.
In cases where a concentration or a dilution
problem is being considered, the primary change
that occurs as the fluid moves down the pipe may
be the delay in time from one end to the other.
3
http//www.tpub.com/content/doe/h1012v3/css/h1012v
3_40.htm
4
Real translation
We can take the Laplace transform of this
relationship using the Real Translation theorem
The transfer function relating C2 to C1 is
t0 can be determined from the characteristics of
the pipe, L,D, and the flowrate, q
also
or
5
Dead time for plug flow in a pipe
Substituting for V and solving for t0
6
Transfer functions in series
7
Block diagram algebra
8
Matlab example
  • Consider using Matlab to plot system response for
    t 3, t02

gtgt num1 gtgt den3,1 gtgt systf(num,den,'inputde
lay',2) Transfer function
1 exp(-2s) ------- 3 s
1 gtgtstep(sys)
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