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showed that the performance of fuzzy PID control is better.
We used a relatively accurate model obtained by test for
level process control. In this model, nonlinear behavior of
process and manual valves is considered.
Level control systems are common within the process
industries. Obviously, maintaining a vessel’s level at a
desired value (or within desired limits) is critical for the
successful operation of process plant.
3.2 Experimental setup
Figure 3 shows a photograph of experimental setup of two
interacting tanks system. The schematic diagram of this
system is also shown in Fig. 4.
In this experimental setup, the cross-sectional area of
tank 1 and 2 is 187.29 and 100 cm2
, respectively. Signalinlet to control valve (m) is variable from 4 to 20 mA. The
models of inlet flow rate to first tank (F1(t)) and the
resistance of manual valves 1 and 2 that obtained through
the tests are shown in Table 1.
3.3 Mathematical modeling of experimental setup
The basic model equation of interacting two-tank system is
given bywhere F1(t) is the tank 1 inflowing liquid (cm3
/s), F2(t)is
the tank 1 outflowing liquid or the tank 2 inflowing liquid
(cm3
/s), F3 (t) is the tank 2 outflowing liquid (cm3
/s), A1 is
the tank 1 cross-sectional area (cm2
), A2 is the tank 2 cross-
sectional area (cm2
), h1 is the liquid level in tank 1 (cm), h2
is the liquid level in tank 2 (cm), R1 and R2 are manual
valve resistances of tank 1 and tank 2 (cm/(cm3
/s)).
In this paper, the nonlinear model of two-tank system is
simulated in Matlab/simulink software. Then, the control
algorithms are applied on the simulated process.
3.4 Simulation results
In this paper, Zeigler-Nichols (Z-N) tuning method [35]is
used to find the initial guess of classic PID parameters.
Then, these parameters are optimizing by optimization
function in the MATLAB software. The resulted parame-
ters are shown in the Table 2.
In design of fuzzy PID controller, for the input variables
(e(t) and de(t)), five membership functions NH, NL, ZO,
PL, and PH are used. They are NH, negative high; NL,
negative low; ZO, zero; PL, positive low; and PH, positive
high. For each output variables (Kp, Ki, and Kd), four tri-
angle membership functions are used as shown in Fig. 5.
Here, ‘‘ZO,’’ ‘‘L,’’ ‘‘H,’’ and ‘‘PH’’ are ‘‘Zero,’’ ‘‘Low,’’
‘‘High,’’ and ‘‘Positive High,’’ respectively.
Generally, fuzzy rules are dependent on the control
purpose and the type of a controller. The rule sets that are
used are shown in Table 3.
According to proportional gain calculated by Z-N
method which is 3.75, membership function is considered
[0, 5] and for integral and derivative gains are considered
[0, 0.05] and [0, 6], respectively.
The performances of two controllers (classic PID and
fuzzy PID) are compared through simulation results when aset point change is applied. The closed loop responses of
second tank level for two controllers are shown in Fig. 6.
The values of integral absolute error (IAE) are also shown
in Table 4.
As can be seen from the results, the classic and fuzzy
PID controllers have roughly the same performances.
However, tuning the classic PID is simpler than the fuzzy
PID. Therefore, for controlling the simple processes such
as two interacting tanks, classic PID is preferred.controllers, adaptive controllers, model predictive control
(MPC), and controllers in the basis of neural network have
been imposed to unstable CSTR by researchers [40–45].