INFICON XTC/C Thin Film Deposition Controller User Manual
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XTC/C - XTC/2 Operating Manual
The integral of the absolute value of the error (IAE) has been frequently
proposed as an alternate criterion of performance:
[12]
This criterion is more sensitive to small errors, but less sensitive to large errors,
than ISE.
Graham and Lathrop
8
introduced the integral of time multiplied by the absolute
error (ITAE) as a criterion of performance:
[13]
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.
Since the process response characteristics depend on the position of the
system (i.e. deposition rate for this discussion), the process response is best
measured at the desired operating point of the system. This measured process
information (i.e. process gain, K
p
, time constant, T
1
, and dead time, L) is used
to generate the best fitting PID control loop parameters for the specific system.
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.
[14]
[15]
[16]
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
8.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
1.19T1
(
) L T
1
⁄
(
)
0.738
=
T
d
0.381T1
(
) L T
1
⁄
(
)
0.995
=