INFICON XTC/C Thin Film Deposition Controller - Manual (Page 145)

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XTC/C - XTC/2 Operating Manual
In general, it is not possible to characterize all processes exactly; some
approximation must be applied. The most common is to assume that the
dynamic characteristics of the process can be represented by a first-order lag
plus a dead time. The Laplace transform for this model (conversion to the s
domain) is approximated as:
[9]
Figure 5-7 Response of Process To An Open Loop Step Change
(At t=0 Control Signal is Increased)
Three parameters are determined from the process reaction curve. They are
the steady state gain, K
p
, the dead time, L, and the time constant, T
1
. Several
methods have been proposed to extract the required parameters from the
system response as graphed in
Figure 5-7 . These are: a one point fit at 63.2%
of the transition (one time constant); a two point exponential fit; and a weighted
least-square-exponential fit. From the above information a process is
sufficiently characterized so that a controller algorithm may be customized.
Output
Input
-------------------
K
p
L – s
( )
exp
T
1
s 1 +
-------------------------------- =