Neural Computing and Applications

, Volume 23, Supplement 1, pp 19–28 | Cite as

Adaptive fuzzy tuning of PID controllers

  • Morteza Esfandyari
  • Mohammad Ali Fanaei
  • Hadi Zohreie
Original Article
First Online:
Received:
Accepted:

Abstract

In this paper, the performances of fuzzy proportional-integral-derivative (PID) and classic PID controllers are compared through simulation studies. For this purpose, the level control of a two interacting tanks system, temperature control of unstable continuous stirred tank reactor (CSTR), and pH control of pH neutralization process were selected. In the level control process, results indicated that both of classic and fuzzy PID controllers have approximately the same performance. However, adjusting the classic PID controller is simpler than fuzzy PID controller. Therefore, in simple processes like level control in two interacting tanks, classic PID controllers are preferred. In an unstable CSTR, classic PID controller is not suitable due to the instability of the system. Fuzzy PID controller is more useful than classic PID controller in this type of systems. In pH neutralization process, using classic PID controller is inappropriate because of nonlinearity of the system and the fuzzy PID controller is more efficient.

Keywords

Classic PID controller Fuzzy PID controller Level control Temperature control of an unstable CSTR pH control Adaptive fuzzy control 

List of symbols

Kp

Proportional gain

Ki

Integral gain

Kd

Derivative gain

e(t)

Error at time t

de(t)

Derivative of error at time t

Vp

Signal inlet to control valve (m)

Fi(t)

The tank i inflowing liquid (cm3/s)

hi

The liquid level in tank i (cm)

Ai

Cross-sectional area of tank i (cm2)

Ri

Resistances of tank i (cm/(cm3/s))

NH

Negative high

NL

Negative low

ZO

Zero

PL

Positive low

PH

Positive high

L

Low

H

High

VS

Very small

S

Small

M

Medium

B

Big

qc

Cooling-jacket flow rate

t

Time

x1f

Dimensionless reactor feed concentration

x2f

Dimensionless reactor feed temperature

x3f

Dimensionless cooling-jacket temperature

xi

Dimensionless concentrations

[AC−]

Concentration of acetate ion (mol/l)

C1

Acid concentration (mol/l)

C2

Base concentration (mol/l)

F1

Acid flow rate (l/min)

F2

Base flow rate (l/min)

[HAC]

Concentration of acetic acid (mol/l)

Ka

Acid equilibrium constant

Kw

Water equilibrium constant

[Na+]

Concentration of sodium ion (mol/l)

ν

Volume of CSTR

Greek letter

β

Dimensionless heat of reaction

γ

Dimensionless activation energy

δ

Dimensionless heat-transfer coefficient

δ0

Nominal dimensionless heat-transfer coefficient

δ1

Reactor-to-cooling-jacket volume ratio

δ2

Reactor-to-cooling-jacket density heat capacity ratio

k(x2)

Dimensionless Arrhenius reaction rate nonlinearity

\( \phi \)

Nominal Damkohler number based on the reactor feed

ε

Concentrations of the acid

ξ

Concentrations of the base

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Copyright information

© Springer-Verlag London 2012

Authors and Affiliations

  • Morteza Esfandyari
    • 1
  • Mohammad Ali Fanaei
    • 1
  • Hadi Zohreie
    • 1
  1. 1.Department of Chemical EngineeringFerdowsi University of MashhadMashhadIran

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