INFICON Cygnus 2 Thin Film Deposition Controller User Manual
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Cygnus 2 Operating Manual
T
i
= integral time
T
d
= derivative time
E(s) = process error
represents the controller algorithm and a process with first order lag
plus a dead time. The process block implicitly includes the dynamics of the
measuring devices and the final control elements, in our case the evaporator power
supply. R(s) represents the rate setpoint. The feedback mechanism is the error
generated by the difference between the measured deposition rate, C(s), and the
rate set point, R(s).
Figure 14-8 PID controller block diagram
The key to using any control system is to choose the proper values of K
c
, T
d
and
T
i
. Optimum control is a somewhat subjective quantity as noted by the presence of
several mathematical definitions as shown below.
The Integral of the Squared Error (ISE) is a commonly proposed criterion of
performance for control systems.
It can be described as:
[10]
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.
K
c
1
1
T
i
s
------- T
d
s
+
+
K
p
L
– s
exp
T
1
s 1
+
-------------------------------
R s
E s
S
C s
setpoint
error
[controller]
[process]
+
deposition
rate
ISE
e
2
t
dt
=
IAE
e t
dt
=