Fuzzy Logic Based PI Control of a pH Neutralization Process*PMI Noida - 2011*

PMI Noida - 2011

1. Introduction Control of the pH neutralization process plays an important role in many industrial applications such as wastewater treatment, biotechnology, pharmaceuticals, and chemical processing. Control of the pH neutralization process is viewed as a representative benchmark for modeling and control of highly nonlinear processes. Conventional PI controllers are generally insufficient to control extremely nonlinear pH neutralization processes. Fuzzy logic based PI controllers are customizable, as it is easier to understand and modify their rules, which not only use a human operators strategy but also are expressed in natural linguistic terms.

*PMI Noida - 2011*

PMI Noida - 2011

The problem of control of pH neutralization process in this paper has been divided into two parts. The first part being the development of the dynamic model of the pH neutralization process. The second part being the design of fuzzy logic based PI controller. The proportional gain (Kc) for P controller is derived using the Mamdani type Fuzzy Inference System (FIS) and the Sugeno FIS is used to derive the integral time (Ti) for I controller. Using SIMULINK the combined Fuzzy logic based PI controller was then tested on dynamic model of pH neutralization process for servo operations.*PMI Noida - 2011*

PMI Noida - 2011

2. Dynamic Modeling of pH Neutralization ProcessV = the volume of the CSTR;Ca, Fa = the concentration and flow rate of process stream; Cb, Fb = the concentration and flow rate of titration stream; Fa + Fb = the flow rate of effluent stream; xa = the concentration of acid component (chloride ion) in the effluent stream; xb = the concentration of base component (sodium ion) in the effluent stream.*PMI Noida - 2011*

PMI Noida - 2011

Dynamic pH neutralization process model for strong acid-strong base*PMI Noida - 2011*

PMI Noida - 2011

pH titration curve for strong acid-strong base*PMI Noida - 2011*

PMI Noida - 2011

3. Design of Fuzzy Logic based PI Controller*PMI Noida - 2011*Fuzzy controller consists of an input stage (also known as input fuzzifier), a processing stage (also known as FIS), and an output stage (also known as output defuzzifier). The input stage maps sensors or other inputs to the appropriate membership functions and degree of membership. The processing stage invokes appropriate rules and generates a result for each, then combines the results of the rules. There are two popular types of FIS, namely Mamdani type and the Sugeno type. Finally the output stage converts the combined results back into a control output value.

PMI Noida - 2011

*PMI Noida - 2011*

PMI Noida - 2011

To calculate Kc based on Mamdani FIS, the error (e) is chosen as input and Kc is chosen as output. The settings for the trapezoidal shaped input (e) membership functions are as follows: Negative Very Large (NVL) = [-7 -7 -5.5 -5]Negative Large (NL) = [-5.5 -5 -4.5 -4]Negative Medium (NM) = [-4.5 -4 -3 -2.5]Negative Small (NS) = [-3 -2.5 -1 -0.5]Zero (Z) = [-1 -0.5 0.5 1]Positive Small (PS) = [0.5 1 2.5 3]Positive Medium (PM) = [2.5 3 4 4.5]Positive Large (PL) = [4 4.5 5 5.5]Positive Very Large (PVL) = [5 5.5 7 7]3.1 Mamdani FIS to calculate Kc*PMI Noida - 2011*

PMI Noida - 2011

The fuzzy rules for Mamdani FIS are as follows: If (e is NVL) then (Kc is VL)If (e is NL) then (Kc is L)If (e is NM) then (Kc is A)If (e is NS) then (Kc is S)If (e is Z) then (Kc is VS)If (e is PS) then (Kc is S)If (e is PM) then (Kc is A)If (e is PL) then (Kc is L)If (e is PVL) then (Kc is VL)

The settings for the trapezoidal shaped output (Kc) membership functions are as follows: Very Small (VS) = [-10 0 20 30]Small (S) = [20 30 50 60]Average (A) = [50 60 70 80]Large (L) = [70 80 100 110]Very Large (VL) = [100 110 130 140]*PMI Noida - 2011*

PMI Noida - 2011

To calculate Ti based on Sugeno FIS, the set point (SP) is taken as input variable and Ti is taken as output variable. The settings for the trapezoidal shaped input (SP) membership functions are as follows: Super Acidic (SA) = [-1 0 1.5 2]Very Acidic (VA) = [1.5 2 2.5 3]Acidic (A) = [2.5 3 4 4.5]Mildly Acidic (MA) = [4 4.5 6 6.5]Neutral (N) = [6 6.5 7.5 8]Mildly Basic (MB) = [7.5 8 9.5 10]Basic (B) = [9.5 10 11 11.5]Very Basic (VB) = [11 11.5 12 12.5]Super Basic (SB) = [12 12.5 14 15]3.2 Sugeno FIS to calculate Ti*PMI Noida - 2011*

PMI Noida - 2011

The fuzzy rules for Sugeno FIS are as follows: If (SP is SA) then (Ti is T1)If (SP is VA) then (Ti is T2)If (SP is A) then (Ti is T3)If (SP is MA) then (Ti is T4)If (SP is N) then (Ti is T5)If (SP is MB) then (Ti is T6)If (SP is B) then (Ti is T7)If (SP is VB) then (Ti is T8)If (SP is SB) then (Ti is T9)

The settings for the constant output (Ti) membership functions are as follows: T1 = 1350T2 = 1362T3 = 1375T4 = 1388T5 = 1400T6 = 1412T7 = 1425T8 = 1438T9 = 1450*PMI Noida - 2011*

PMI Noida - 2011

Fuzzy logic based PI control*PMI Noida - 2011*

PMI Noida - 2011

For SP = 7 the error is less than 0.1.For SP = 6 the error is less than 0.02.For SP = 8 the error is less than 0.03.pH variation*PMI Noida - 2011*

PMI Noida - 2011

4. Simulation Results And DiscussionsServo control*PMI Noida - 2011*

PMI Noida - 2011

The proposed fuzzy logic based PI controller gives satisfactory performance for servo operations.

To improve the intelligent controller performance advance optimization techniques based on neural network, genetic algorithm, etc. must be used. 5. Conclusion*PMI Noida - 2011*

PMI Noida - 2011

[1] Jhonson M.A. and Moradi M.H., 2005, PID Control: New Identification and Design Methods, Chapter 9, Springer, Nottingham (London), P.340.[2] Reznik L., Fuzzy Controllers, Chapter 1, Newnes, 1997, P.5.[3] McAvoy T.J., Hsu E. and Lowenthals S., Dynamics of pH in controlled stirred tank reactor. Ind. Eng. Chem. Process Des. Develop., (11), 1972, pp. 68.[4] Liptak B.G., 2006, Instrument Engineers Handbook: Process Control and Optimization, 4th Edition, Chapter 8, CRC Press, Florida (USA), P.2045.[5] Bhanot S., 2008, Process Control: Principles and Applications, Chapter 18, Oxford University Press, New Delhi (India), P.425.[6] Mamdani E.H., Application of fuzzy logic to approximate reasoning using linguistic synthesis. IEEE Transactions on Computers, (26), 1977, pp. 1182.[7] Takagi T. and Sugeno M., Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, (1), 1985, pp.116.6. References*PMI Noida - 2011*

PMI Noida - 2011

Thank you*PMI Noida - 2011*

PMI Noida - 2011