PWARX Model Identification Based on Clustering Approach - Complex System Modelling and Control Through Intelligent Soft Computations - page 178

composed of a salt and water. The general formula for acid base neutralization

-

reactions can be written as:

acid þ base ! salt þ water ð 28 Þ

The process of pH neutralization (see Fig. 5 ) is constituted essentially of a
treatment tank of cross sectional area A, a mixer, acid and base injection pipes, a pH
probe, a level sensor to measure the level h in the tank and a discharge valve
(Henson and Seborg 1994 ; Salehi et al. 2009 ). It consists of an acid stream q 1 ,
buffer stream q 2 and base stream q 3 that are mixed in the tank. The ef

uent stream
q 4 exits the tank via the discharge valve with an adjusted pH m . The streams q fg

fl

4
i ¼ 1

are characterized by the following parameters:

4
i

4
i

W a fg

1 are the charge related quantities for qif fg 1 .

￿

¼ ¼

4
i¼1 are the mass balance quantities for qif fg

4
i¼1 .

W b fg

￿

The pH probe introduces a delay time s in the measured pH m value such as

pH m ¼ .

The objective of the pH neutralization process is to control the pH value of the

pH ð t sÞ

ef fl uent through manipulating the base fl ow rate q 3 while considering the acid fl ow

rate q 1 and the buffer ow rate q 2 as disturbances.

The dynamic model of the neutralization process is developed as follows:

fl

The pH value of the obtained solution is derived from the conservation equa-
tions and equilibrium reactions as follows:

￿

K a1
H þ

2K a1 K a2
H þ

þ

K w
H þ

½

2

½

H þ

W a4 þ

þ

W b4

2

½ ¼ 0 : ð 29 Þ

K a1
H þ

K a1 K a2
H þ

½

1 þ

þ ½

½

Fig. 5 A pH neutralization
process