INFICON XTC/C Thin Film Deposition Controller - Manual (Page 146)

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XTC/C - XTC/2 Operating Manual
A controller model used extensively is the PID type, shown in Laplace form in
equation [10] .
[10]
Where
Š M(s) = manipulated variable or power
Š K
c
= controller gain (the proportional term)
Š T
i
= integral time
Š T
d
= derivative time
Š E(s) = process error
Figure 5-8 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 5-8 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:
[11]
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.
M s
( )
K
c
1
1
T
i
s
-------- T
d
s + +
⎝ ⎠
⎛ ⎞
Es =
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
=