Figure 2-3, Ise e, T( ) t d – INFICON Composer Gas Concentration Controller User Manual
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Composer Operating Manual
controllers.
R(s)
represents the concentration set point. The feedback
mechanism is the error generated by the difference between the measured
concentration,
C(s)
, and the target concentration,
R(s)
.
Figure 2-3 PID Controller Block Diagram
The key to using any control system is to choose the proper values of
Kc
,
Td
and
Ti
. 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:
[26]
Where error =
e
= target - measured concentration. 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 also been frequently
proposed as a criterion of performance:
[27]
This criterion is more sensitive to small errors, but less sensitive to large errors,
than ISE.
Alternately, Graham and Lathrop
1
introduced the integral of time multiplied by
the absolute error (ITAE) as a criterion of performance:
1.Graham, D., and Lathrop, R .C., “The Synthesis of Optimum Transient Response: Criteria and
Standard Forms, Transactions IEEE, vol. 72 pt. II, November 1953
set point error
R(s) + E(s)
Σ
K
c
(1+s/T
i
+ T
d
*s)
K
p
exp(-L/s)
T1s + 1
concentration
C(s)
[process]
[controller]
ISE
e
2
t
( ) t
d
0
∞
∫
=
IAE
e t
( ) t
d
0
∞
∫
=