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method for determining the parameters of the PID control system. Particle Swarm Op-
timization PSO is an optimization method that has some advantages, namely a simple
algorithm, its implementation easier, faster convergence and effective in computing[6],
[7], [8].
In this paper, the optimization PID con- trol system using PSO applied to the temper-
ature control system. To increase the effec- tiveness of PSO used a strategy LDIWLinear
Decreasing Inertia Weight which is the best method currently in the process of optimiza-
tion PSO[9] which was presented in the ap- plication program Matlab Simulink for con-
trolling the prototype of temperature control system that consists of aheater and sensor as
an actual device of the control system. Op- timization of the PID parameter by PSO is
repeated until convergence is reached so that the parameters obtained is the optimal pa-
rameters of the control system. The results of optimization are used as a parameter in PID
control system for optimal control system simulation process on the temperature con-
trol system.
2. Proportional, Integral and Derivative PID Controller
Proportional control serves to amplify the signal of activator errors error signal which
will accelerate the output of the system reaches a point of reference. Integral control in principle
aims to eliminate errors during state conditions offset which is usually generated by propor-
tional control. Derivative control can be called as controlling the pace, because the output of con-
trol proportional to the rate of change of the error signal. The combination of the three controllers
becomes Proportional Integral Differential PID controller[4], [10]. Block diagram of the PID con-
trolis shown in Figure1
.
Figure1 .
Diagram block of the PID control
The equation for PID control Propor- tional Integral Differential [4]:
. :5;
21 H1
H1 2
1 2 . 2
.
2 1 2 1I.
1
21. 2
+ .
J :; :; . .
. =
2 2
2 2
2 2
, 2
2
:A; - 2
+ +
M .
+ D
. 5 .
:;
N :;
where: ut
= PID controller output signal Kp
= Proportional coeficient Ti
= Integral time Td
= Derivative time Ki
= Integral coeficient Kp⁄Ti Kd
= Derivatif coeficient Kp.Td et
= signal Error
3. Particle Swarm Optimization PSO
PSO is one of optimization techniques based on evolutionary computing tech-
niques. This method has a good robust to solve problems that have nonlinear charac-
teristic sand non differentiability, multiple optimal and large dimension through adap-
tation derived from social-psychology of the theory[11], [12]. This method inspired by the
dynamic motion of a lock of birds or ish in search of food. They move together in a group
and not individuals. They use the concept of partnership, where each of information dis-
seminated within the group. Suppose there
are lock of ish that randomly search for foo- din a region and there is only one meal there.
All birds do not know where the location of these foods, but they know how far they are
from the food in each iteration. So the most
effective strategyis to follow the ish closest to the food. PSO initialized with a population
of random solutions and ind the most opti- mal solution store new the members of the
population. Each particle is called a random solution. Each particle moves in space prob-
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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
