INFICON XTC/3 Thin Film Deposition Controller Operating Manual - Manual (Page 207)

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XTC/3 Operating Manual
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 8-8 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:
[7]
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:
[8]
This criterion is more sensitive to small errors, but less sensitive to large errors,
than ISE.
Graham and Lathrop 7 introduced the integral of time multiplied by the absolute
error (ITAE) as an alternate criterion of performance:
[9]
7.Graham, D., and Lanthrop, R.C., “The Synthesis of Optimum Transient Response: Criteria and
Standard Forms, Transactions IEEE, vol. 72 pt. II, November 1953.
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 =
ITAE t e t   
dt =