Advanced Metaheuristics-Based Approach for Fuzzy Control Systems Tuning - Complex System Modelling and Control Through Intelligent Soft Computations - page 617

2.1 A Review of PID-Type Fuzzy Control Structure

The particular PID-type fuzzy controller structure, originally proposed by Qiao and
Mizumoto within the continuous-time formalism (Qiao and Mizumoto 1996 ), retains
the characteristics similar to the conventional PID controller. This result remains
valid while using a particular structure of FLC with triangular uniformly distributed
membership functions for the fuzzy inputs and a crisp output, the product-sum
inference and the center of gravity defuzzification methods (Bouall è gue et al. 2012a ,
b ; Eker and Torun 2006 ; Guzelkaya et al. 2003 ; Hagg

è ge et al. 2010 ; Toumi et al.

2014 ; Woo et al. 2000 ).
Under these conditions, the equivalent proportional, integral and derivative
control components of such a PID-type FLC are given by a K e P þ b K d D , b K e P

and a K d D , respectively, as shown in Qiao and Mizumoto ( 1996 ). In these

expressions, denote the

scaling factors associated to the inputs and output of the fuzzy controller. When
approximating the integral and derivative terms within the discrete-time framework
(Bouall

P and D represent relative coef cients, K e , K d , a and b

ge et al. 2010 ; Toumi et al. 2014 ), we can
consider the closed-loop control structure for a digital PID-type FLC, as shown in
Fig. 1 . The dynamic behaviour of

è gue et al. 2012a , b ; Hagg è

this PID-type FLC structure is strongly

depending on the scaling factors, dif cult and delicate to tune.

As shown in Fig. 1 , this particular structure of Mamdani fuzzy controller uses
two inputs: the error e k and the variation of error D e k , to provide the output u k that

describes the discrete fuzzy control law.

2.2 Optimization-Based Problem Formulation

The choice of the adequate values for the scaling factors of the described PID-type
FLC structure is often done by a trials-errors hard procedure. This tuning problem
becomes dif

cult and delicate without a systematic design method. To deal with

these dif culties, the optimization of these control parameters is proposed like a

e k

K

e

+
+

u k

K

+

d

_

+

Δ e k

+

Fuzzy Controller

1

1

z

z

Delay operator

Delay Operator

Fig. 1 Proposed discrete-time PID-type FLC structure