Page 68 - 2024-Vol20-Issue2

64 | Al-Najari, Hen, Paw, & Marhoon

PSO algorithm where the PID controller performance parame-
ters are rise time=0.881s, settling time=1.7s, overshoot=0.103,
peek time=1s, negative part=0, and delay time=0. The ob-
tained results show that the best tuning method for PID con-
troller is using the PSO algorithm.

TABLE IV.
PID TUNING PARAMETERS

Fig. 14. Multi step response G fitted Function Tuning Method Kp Ki Kd
Original Ziegler Nichols 8.2868968 0.3526 48.6948
Original MATLAB Tuner 4.009956 0.3172 -41.4847
Approximated MATLAB Tuner 0.4136 -16.4537
Fitted MATLAB Tuner 6.3718 9.0686 1196.3479
Fitted PSO Algorithm 268.534479 100.2575 14345.3379

20000

Parameter TABLE III. Value TABLE V.
m PSO TUNING PARAMETERS 3 PID PERFORMANCE PARAMETERS
n 100
Description 0.9 Function Tuning Method Rise Settling Overshoot Peek Negative Delay
wmax number of variables 0.4 Time(s) Time(s) (percentage) Time(s) Part Time(s)
wmin 2 Original Ziegler Nichols 10.7 206 24.3 1.24 0 18.2
c1 and c2 population size 1 Original MATLAB Tuner 25.3 130 6.2 1.06 0 18.2
r1 and r2 max inertia weight Approximated MATLAB Tuner 16.6 87.4 2.99 1.03 -1.623 6.838
min inertia weight -500 Fitted MATLAB Tuner 25.6 160 0.42 1 0 0
LB acceleration factors c1 and c2 20000 Fitted PSO Algorithm 0.881 1.7 0.103 1 0 0
UB uniformly distributed random factors r1 and r2 1000
maxiter lower bounds of variables VII. CONCLUSION
maxrun upper bounds of variables 1
maximum number of iteration This paper proposed the design and implementation of a PID
maximum number of runs controller for the PH loop of the cooling tower. Three methods
were used to tune the PID controller. The transfer function of
time absolute error (ITAE) is selected as the objective function the PH loop is first order plus delay time FOPDT. The transfer
of the system [13]. function of the PH loop FOPDT was passed in three stages of
conversion. The original transfer function (Goriginal) of the PH
8 (10) loop was calculated using the data-driven method. Yokogawa
recorder was installed locally to record the input-output data.
ITAE = t|e(t)|.dt The (Goriginal) was tuned by two methods Ziegler Nichols and
MATLAB Tuner. The problem with the (Goriginal) response is
0 the delay time. The delay time causes problems with the con-
trol. This problem was solved using the pade approximation
The flowchart of the PSO algorithm is shown in Fig. 15 method. The approximated transfer function (Gapproximated)
[19]. The PID controller tuning activity was done using PSO has a negative part. The negative part of (Gapproximated) ef-
algorithm to find the best PID controller parameters Kp, Ki, fects during a control on the process. This problem was
and Kd. Table III shows the tuning parameters of the PSO solved using curve fitting and system identification toolbox of
algorithm. MATLAB. The fitted transfer function (G fitted) was tuned in
MATLAB Tuner and PSO algorithm tuning methods. The re-
Fig. 16 shows the block diagram of the PID-based PSO sults showed that the PID controller performance parameters
tuning. Fig. 17 shows the PSO convergence characteristic. were optimized using the PSO algorithm tuning method.

Fig. 18 and Fig. 19 show the fitted function G fitted re- CONFLICT OF INTEREST
sponse based on PSO tuning.
The authors have no conflict of relevant interest to this article.
VI. RESULTS AND DISCUSSION

Table IV shows the PID controller tuning parameters (Kp,
Ki, and Kd) based on three tuning methods. The best pa-
rameters that give the best response to the fitted function
were found using the PSO algorithm tuning method. The
PID controller parameters are Kp=20000, Ki=100.2575, and
Kd=14345.3379. Table V shows the PID controller perfor-
mance parameters. The best response was found using the