Advanced Metaheuristics-Based Approach for Fuzzy Control Systems Tuning - Complex System Modelling and Control Through Intelligent Soft Computations - page 633

k l , given in Eq. 2 , will be linearly
increased at each iteration step so constraints are gradually enforced. In a generic
and typical optimization problem, the quality of the solution will directly depend on
the value of this algorithm control parameter. In this chapter and in order to make
the proposed approach simple, great and constant scaling penalty parameters, equal
to 10 4 , are used for numerical simulations. Indeed, simulation results show that with
great values of

On the other hand, the scaling parameters

k l , the control system performances are weakly degraded and the
effects on the tuning parameters are less meaningful. The proposed constrained and
improved algorithms convergence is faster than the case with linearly variable
scaling parameters.
The time-domain performances of the proposed metaheuristics-tuned PID-type
FLC structure are illustrated in Figs. 9 and 10 . Only simulations from the DSA and
PSO techniques implementation are presented. All results, for various obtained
decision variables, are acceptable and show the effectiveness of the proposed fuzzy
controllers tuning method. The robustness, in terms of external disturbances
rejection, and tracking performances are guaranteed with degradations for some
considered methods. The considered time-domain constraints for the PID-type FC
tuning problems, such as the maximum values of overshoot

max

d ¼ 20 % , steady

state E max
ss

¼ 0 : 0001 and settling time t max
s

¼ 0 : 9 s, are usually respected.

1.2

1

0.8

0.6

K e =1.2734;K d =7.9922; ʱ =3.2795; ʲ =33.2944

0.4

K e =1.6852;K d =5.0000; ʱ =5.6764; ʲ =28.2553
K e =1.4355;K d =5.0679; ʱ =2.0000; ʲ =43.3021

0.2

K e =1.2069;K d =9.2740; ʱ =3.4090; ʲ =50.0000

0

0 0.5 1 1.5 2 2.5

Time (sec)

Fig. 9 Step responses of the DSA-tuned PID-type fuzzy controlled system: ISE criterion case