INFICON Composer Gas Concentration Controller - Manual (Page 51)

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ITAE is insensitive to the initial and somewhat unavoidable errors, but it will
weight heavily 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.
Since the process response characteristics depend on the position of the
system (that is, concentration for this discussion), the process response is best
measured at the desired operating point of the system. This measured process
information (that is, process gain, K
p
, time constant, T
1
, and dead time, L) is
used to generate the best fitting PID control loop parameter values for the
specific system.
2.4 Fuzzy Logic
In recent years, fuzzy logic has drawn much attention from academic
researchers, and its application in the area of industrial control has gained rapid
popularity. Fuzzy logic control has seen successful implementation in myriads
of applications, from consumer products to large complex chemical plants. The
strength of fuzzy logic is that it does not require concrete mathematical
modeling of the process for effective control. Rather, it uses a number of rules
of thumb derived from the past experience of human operators or self-learning
fuzzy controller. Thus, highly nonlinear processes with many interacting
parameters, which are extremely difficult to model, have greatly benefited from
the application of fuzzy logic control. Even in the case of linear processes, fuzzy
control rarely requires elaborate and time consuming parameter tuning required
by conventional PID controllers. The ease of set up and tolerance for
imprecision makes this type of controller attractive. In the Composer, we have
implemented a fuzzy logic controller, in addition to a traditional PID controller.
The essence of a fuzzy logic controller, specific to our application is briefly
described below.
The departure of measured concentration from the set point constitutes error
and point to point variation of errors constitute change-in-error. The error and
the change-in-error are the working variables of the fuzzy engine. These
variables are categorized in linguistic terms, such as large negative, negative,
zero, positive, and large positive. A given magnitude of these variables can
have membership functions in all of the above mentioned categories in varying
degrees. The fuzzy engine itself comprises of a set of rules (wisdom of an
experienced operator). For example,
Š if the error is large negative (much above set point), then if the
change-in-error is large negative (fast moving away from set point).
ITAE t e t ( ) t d
0
∞
∫
=