Page 65 - 2024-Vol20-Issue2

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

Fig. 4. Delay time calculation Fig. 6. Gain coefficient calculation

TABLE I.
FOPDT VARIABLES VALUES

Variable Description Value Unit
k Gain coefficient 0.0953 —-
? 18.2 min
t Delay time 6.40 min
Time constant

Where Goriginal(s) is the original function

Fig. 5. Time constant calculation IV. PID CONTROLLER

describe the whole system relying only on experimental data. PID is a linear controller, which is currently the most widely
The modeling process followed is the classical one used for used control strategy in actual engineering. The PID control
System Identification [11]. The pH regulation system has the method is simple and practical [13]. Generally, the PID con-
characteristics of non-linearity and time lag, which makes it troller is used as feedback controller in process industries.
difficult for the traditional controller to achieve accurate pH In spite of dynamic characteristics of process plant, the PID
control. The mathematical model of the PH regulation system controller provides excellent control performance. It has three
can be described using first-order system transfer function basic nodes i.e. Proportional, Integral and Derivative mode.
plus a delay time [12]. Equation (1) refers to the first-order To design a PID controller, three main parameters are to be
system transfer function plus a delay time (FOPDT). determined like Proportional gain (Kp), Integral gain (Ki)
and Derivative gain (Kd). The PID controller output can be
ke-? s obtained by using equation (3). Where u (t) represents the
G(s) = control signal and e (t) represents the error signal [14].

ts+1 (1)

Where k is the gain coefficient, ? is the delay time, and t t de(t)
is the time constant. u(t) = Kp.e(t) + Ki e(t).dt + kd. (3)
The input-output data was measured locally by installing a dt
Yokogawa recorder type DX1000. Fig. 4, 5, and 6 show the 0
calculation of FOPDT system variables that is shown in Table
1. The drawings of the PH response were opened using the V. PID CONTROLLER TUNING
Yokogawa data viewer program.
Three tuning methods were used to tune the PID controller,
From Table I, the transfer function of the PH loop is as which are Ziegler Nichols, MATLAB Tuner, and Particle
equation (2). swarm optimization PSO methods.

0.0953e-18.2s (2) A. Goriginal(s) tuning
Goriginal(s) = 6.4s + 1 As shown in equation (2), The Original transfer function
Goriginal(s) was tuned in two methods as below: