INFICON Cygnus Thin Film Deposition Controller User Manual
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Cygnus Operating Manual
where error = e = setpoint minus the measured rate. The ISE measure is relatively
insensitive to small errors, but large errors contribute heavily to the value of the
integral. Consequently, using ISE as a criterion of performance will result in
responses with small overshoots but long settling times, since small errors
occurring late in time contribute little to the integral.
The integral of the absolute value of the error (IAE) has been frequently proposed
as a criterion of performance:
[11]
This criterion is more sensitive to small errors, but less sensitive to large errors,
than ISE.
Graham and Lathrop
12
introduced the integral of time multiplied by the absolute
error (ITAE) as an alternate criterion of performance:
[12]
ITAE is insensitive to the initial and somewhat unavoidable errors, but it will weight
heavily any errors occurring late in time. Optimum responses defined by ITAE will
consequently show short total response times and larger overshoots than with
either of the other criteria. It has been found that this criteria is generally most
useful for deposition process control.
The most satisfactory performance criterion for deposition controllers is the ITAE.
There will be overshoot, but the response time is quick, and the settling time is
short. For all of the above integral performance criteria, controller tuning relations
have been developed to minimize the associated errors. Using manually entered
or experimentally determined process response coefficients, ideal PID controller
coefficients can be readily calculated for the ITAE criteria as shown below.
[13]
[14]
[15]
For slow systems, in order to help avoid controller windup (windup is the rapid
increase in control signal before the system has the chance to respond to the
changed signal), the time period between manipulated variable (control voltage)
changes is lengthened. This allows the system to respond to the previous controller
setting change, and aggressive controller settings can be used. A secondary
advantage is that immunity to process noise is increased since the data used for
12.Graham, D., and Lanthrop, R.C., “The Synthesis of Optimum Transient Response: Criteria and
Standard Forms, Transactions IEEE, vol. 72 pt. II, November 1953.
IAE
e t
dt
=
ITAE
t e t
dt
=
K
c
1.36 K
p
L T
1
0.947
–
=
T
i
1.19T
1
L T
1
0.738
=
T
d
0.381T
1
L T
1
0.995
=