Fuzzy Logic based pH Control of a Neutralization Process

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• pH control is an indispensible part of water treatment system of many

industrial plants like wastewater treatment, biotechnology, pharmaceuticals,

and chemical processing.

• pH control of a neutralization process is recognized as a benchmark for

modeling and control of highly nonlinear chemical processes.

• Development of the first-principle based dynamic modeling of pH

neutralization process involves material balance on selective ions, equilibrium

constants and electroneutrality equations.

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I. INTRODUCTION

• Many different and practical approaches for pH control based on

Feedforward and Gain Scheduling techniques have been proposed in the

literature.

• Fuzzy logic based “intelligent” control can be described as a control

approach that is used to synthesize linguistic control rules of a skilled

operator.

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A. Neutralization system

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Schematic of neutralization system

II. DYNAMIC MODELING OF NEUTRALIZATION SYSTEM

Armfield multifunctional process control

teaching system (PCT40) and its accessories

(PCT41 and PCT41)

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Flow characteristics of pump A and pump B

Schematic of neutralization system

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B. Dynamic modeling of pH Neutralization Process

V = the volume of the CSTR

Ca, Fa = the concentration and flow rate of feed A

Cb, Fb = the concentration and flow rate of feed B

Fa + Fb = the flow rate of effluent stream

xa = the concentration of acid component (Cl-) in

the effluent stream

xb = the concentration of base component (Na+) in

the effluent stream

Dynamic pH neutralization process

model for strong acid-strong base

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1

pH

log10

log (1/[H+])[H+]sqrt

[(X^2)/4+Kw]^0.5

1s

Xb

1s

Xa

u2

X^2

X=(Xa-Xb)

1e-14

Kw

0.25

Gain1

0.5

Gain

Fb*Cb/V

Fa+Fb

Fa*Ca/V

1

u1/[H+]

(X^2)/4+Kw

(Fb*Cb/V)-(Fa+Fb)*Xb/V

(Fa+Fb)*Xb/V

(Fa+Fb)*Xa/V

(Fa*Ca/V)-(Fa+Fb)*Xa/V

5

Fb

4

Cb

3

V

2

Fa

1

Ca

pH titration curve

V = 1.95 L, Ca = 0.0487 mol/L, Fa = 0 to

6.229 mL/s (step change at 241 seconds),

Cb = 0.0285 mol/L, and Fb = 6.229 to 0

mL/s (step change at 151 seconds).

III. DESIGN OF THE CONVENTIONAL PID CONTROLLER

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Direct-action PID control of pH neutralization process

Flow rate variations of feed A for ultimate-gain method

At the point of sustained oscillations: pH set

point = 7; KCU = 166.67; TIU = TDU = 0; Fa = 0

to 6.229 mL/s; Fb = 1.682 mL/s.

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Optimized parameter values for PID control:

KC = (y/3) =10; TI = (t) = 30 sec; TD = (t/6) = 5 sec.

where ‘y’ is the peak to peak pH variation between the highest value of the overshoot and the

lowest value of the undershoot and ‘t’ is the time between these two values.

pH variations for ultimate-gain method

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IV. DESIGN OF THE FUZZY LOGIC BASED CONTROLLER

- Error, e(t) = (pHSP–pH)

- The universe of discourse

(UOD) for e(t) : [-4, 4] pH

units

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• The input variables used for the fuzzy logic based controllers are

- Change in error, ce(t) =

[e(t) - e(t-1)]

- The UOD for ce(t) : [-0.5,

0.5] pH units

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• The output variable represents the change of flow rate of feed A.

– The change in output, cu(t) = [u(t) - u(t-1)]

– The UOD for cu(t) : [-0.28, 0.28]*10-5 L/s

Fuzzy logic based pH control

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V. RESULTS AND DISCUSSIONS

A. Performance comparison of controllers for servo control

Response of PID controller for step changes in set point

Response of fuzzy controller for step changes in set point

For PID and fuzzy logic based controllers, the mean integral square error (ISE) are 0.0267

and 0.0018 pH unit respectively.

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B. Fuzzy logic based controller response for regulatory and servo operations

Response of fuzzy controller for regulatory operation

The mean IES for the

regulatory operations is

0.1822 pH unit.

The flow rate of feed B is subjected to a periodic disturbance of amplitude 1% of the

nominal value.

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Response of fuzzy controller for servo operations

The mean IES for

the servo operations

is 0.0094 pH unit.

• Based on mean ISE, it is concluded that the proposed fuzzy logic based controller

performs satisfactorily for both servo and regulatory operations.

• Performance of FLC is found to be better than the PID controller for the servo

operations.

• To improve the performance of the proposed fuzzy logic based controller, neural

network or genetic algorithm based optimization techniques can be used.

VI. CONCLUSION

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REFERENCES

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[3] R.A. Wright and C. Kravaris, “Nonlinear control of pH processes using strong acid equivalent,” Ind. Eng. Chem.

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[4] J.-P. Corriou, Process Control: Theory and Applications. New Delhi: Springer (India), 2008, pp. 153–157.

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[6] E.H. Mamdani, “Application of fuzzy logic to approximate reasoning using linguistic synthesis,” IEEE Trans.

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[7] T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control ,” IEEE

Trans. Systems, Man, and Cybernetics, vol. SMC-15, pp. 116-132, Jan.-Feb. 1985.

[8] PCT40 datasheet, Armfield Ltd., Hampshire, England, 2008.

[9] Instruments Engineers’ Handbook: Process Control and Optimization, 4th ed., CRC press, B.G. Liptak, Florida,

USA, 2006, pp. 2045-2047.

[10] E.H. Mamdani and S. Assilian, “An experiment in linguistic synthesis with a fuzzy logic controller,” Int. J. Man-

Machine Studies, vol. 7, pp. 1-13, Jan. 1975.

[12] S. Bhanot, Process Control: Principles and Applications. New Delhi: Oxford (India), 2008, pp. 424-427.

Thank you

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