INFICON Cygnus Thin Film Deposition Controller - Manual (Page 210)

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Cygnus Operating Manual
Of these categories, the open loop methods are considered superior. They are
considered superior because of the ease with which the necessary experimental
data can be obtained and because of the elimination (to a large extent) of trial and
error when the technique is applied. The important response characteristics are
determined as shown in
Figure 9-7 .
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:
[8]
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 9-7 . 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.
Figure 9-7 Response of Process To An Open Loop Step Change
(At t=0 Control Signal is Increased)
Output
Input
------------------
K
p
L
– s
  exp
T
1
s 1 +
-------------------------------
=