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into two types: the gain scheduling and the direct action
[8, 9].
Three PID parameters Kp, Ki, and Kd were, respectively,
calculated through fuzzy logic based on error and error rate
[13, 14].
During the last 35 years, fuzzy controllers have been
reported as appropriate controllers in the presence of
nonlinear behavior and even uncertainty in system [15].
Fuzzy logic is a powerful method for invoking feedback
control. This method works on the basis of some intelli-
gence rules. In many references [15–21], fuzzy control is
seen as a powerful tool for tuning of gain in comparison
with conventional methods.
In 1990, Tzafestas and Papanikolopoulos [14] presented
a classic tuning method for amounts of nominal gains of
PID controller. Then, they improved gains using exclusive
fuzzy gains. They compared their method with conven-
tional methods of Ziegler-Nichols and Kalman [22] and
observed transient and steady-state behavior of closed loop
system had been improved.
Passino [16] in 1995 presented an intelligence controller
for PID gains in the level of observer controller in fuzzy
rules that found lots of application in industry.
Li et al. [17, 18] in 1993 and 1997 presented a dual
fuzzy controller for a robot. In 1998, Bekit et al. [21]by
inspiration of fuzzy PID tuner improved efficiency of
conventional PID controller using a simple method for
tuning of Kp; Ki ; Kd. Efficiency of their method was tested
for a robot with 2 of freedom and it was shown that
performance of this controller was better than PID
controller.In 1998, a dual fuzzy P ? ID controller and analysis of
its steady-state conditions were presented by Li [20]. This
controller was made by an incremental fuzzy logic instead
of proportional term and conventional PID controller. This
controller had combined advantages of fuzzy controller and
conventional one. Fuzzy proportional term played an
important role in the improvement of over shoot and rise
time. In addition, conventional integral term reduced
steady-state error and conventional derivative term led to
smoother step response. In 2001, Li et al. [15] presented a
new method with dual structure consists of proportional
fuzzy control and conventional differential-integral control.
The need for increasing accuracy in industrial process
with progress of technology has led to applying the controlscience more important with respect to rich theory and
practical abilities in control of processes.
Study of fuzzy PID controller has been investigated in
many papers and its steady has been confirmed [23–29].
Efficiency of fuzzy PID controller has been shown in many
articles with computer simulations [30].
According to the papers and work done on fuzzy PID
controllers, performance of this type of controllers is better
than classic PID controllers for special processes (highly
nonlinear, non-minimum phase behavior and unsteady
behavior). But in relatively simple processes, performance
of fuzzy PID controllers is approximately the same as
classic PID controllers.
In this paper, three types of process concerning com-
plexity (relatively linear, highly nonlinear, and unstable)
have been used for the analysis of efficiency of fuzzy PID
controllers
Three mentioned processes are liquid level control in
two interacting tanks, pH control in neutralization process,
and temperature control in an unstable reactor.
The purpose of this paper is to study the adaptive tuning
of a fuzzy PID controller, which combines the traditional
PID controller and fuzzy control algorithm and using it for
controlling the level of two interacting tanks system,
temperature control of unstable CSTR and control of pH
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