Proportional, Integral and Derivative PID Controller
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85 I S M O S A T, Proceeding International Symposium For Modern School Development, ....
lems and has already achieved the best value, this value is called p best. Value of the “best”
others is the best value achieved by any par- ticle in the population, this value is called g
best. PSO has avelocity that would change the position of particles on each iteration. At
each iteration the value of the velocity and position of renewed[12].
Equation of PSO algorithm consists of velocity and position, the most fundamental
of which is as follows, velocity:
++
. :5;:;G
. :5;
21 H1
H1 2
1 2 . 2
.
2 1 2 1I.
1
21. 2
+ .
J :; :; . .
. =
+ B
B K LL
+ =
:; B +
2 2
2 2
2 2
, 2
2
:A; - 2
+ +
M .
+ D
. 5 .
:;
N :;
where: i
= particle index k
= iteration v
= velocity of particle x
= positionof particle p
= the best position of the particle pbest G
= the best position of the swarm gbest L
1,2
= learning rates R
1,2
= random numbers with interval [0 – 1]
W = inertia
In the method of standard PSO imple- mentation, it was found that the velocity of
particles in PSO updated too fast and the minimum value of the objective function is
often over looked. There fore, there is a re- vision or improvement of the standard PSO
algorithm. Improvements in the form of the addition of an inertia
θ to reduce speed. Usu- ally the value of
θ is made such that increas- ing iterations passed, the smaller the particle
velocity. This value varies linearly within the range of0.9to0.4. This inertia weights used to
dampen the paceduring the iterations, which allows birds to the target point more accu-
rately and eficiently than the original algo- rithm [9]. High inertia weight values increase
the portion of the global search global ex- ploration, whilea low value emphasizes lo-
cal search local search. For not very focused on one part and keep looking for new search
area in particular dimensional space, it is necessary tobe sought inertia weight value
θ which draw maintaining global and local search and to reach it and accelerate conver-
gence, aweight of inertia that decreases in value with increasing iterations used by the
formula [9]:
Figure2. Model of the optimal control system on temperature regulation