Internati
o
nal
Journal of Ele
c
trical
and Computer
Engineering
(IJE
CE)
Vol
.
5
,
No
. 3,
J
une
2
0
1
5
,
pp
. 43
6~
44
2
I
S
SN
: 208
8-8
7
0
8
4
36
Jo
urn
a
l
h
o
me
pa
ge
: h
ttp
://iaesjo
u
r
na
l.com/
o
n
lin
e/ind
e
x.ph
p
/
IJECE
PID Controller Design for Two
Tanks Liquid Level Control
System using Matlab
Mo
st
af
a A.
Fe
l
l
a
ni
*
,
A
b
o
uba
k
er
M
.
Ga
baj
**
* Control Engin
eering
Depar
t
ment, Faculty
of
Electron
i
c Technolog
y
,
Ben
i
-Walid
,
Lib
y
a
Em
ail:
alf
e
ll
ani
@gm
a
il.com
** Computer Department, Facu
lty
of Edu
c
a
tion, Tripoli
Univer
sity
, T
r
i
pol
i Li
by
a
Em
ail:
kgaba
ja
@gm
a
il.com
Article Info
A
B
STRAC
T
Article histo
r
y:
Received Oct 30, 2014
Rev
i
sed
Ap
r
22
, 20
15
Accepte
d
May 8, 2015
The industrial application
of C
oupled
Tank S
y
stem (CTS) is
widely
used
es
peci
all
y
in ch
e
m
ical proces
s
in
dus
trie
s. The co
ntrol of liquid level in tanks
and flow between tanks is a prob
lem in
the process technologies.
The process
techno
logies req
u
ire liqu
i
ds to be pum
ped, stored in tanks, and then pumped
to anoth
e
r tan
k
s
y
s
t
em
ati
c
a
l
l
y
.
Th
is pap
e
r
presents development of
Proportional-In
tegral-Der
ivative (PID) c
ontroller for con
t
rolling
the d
e
sired
liquid level of
the CTS. Var
i
o
u
s c
onvention
a
l techn
i
ques of
PID tuning
m
e
thod will be tested in order
to
obtain th
e PID controller
param
e
ters
.
Simulation is
conducted with
in MA
TLAB environment to
verif
y
th
e
perform
ances
of
the
s
y
s
t
em
in
t
e
rm
s
of
Rise
Time
(Ts),
Se
ttl
in
g Tim
e
(Ts),
Stead
y
State Err
o
r (SSE) and Overshoot
(OS). The trial and
erro
r method of
tunning will b
e
i
m
p
lem
e
nted and
all th
e perform
ance resul
t
s will
be anal
y
z
ed
us
ing M
A
TLAB. It h
a
s
been d
e
m
ons
trated tha
t
perform
ances
of
CTS
can b
e
improved with
appropriate techn
i
que of PID
tunin
g
methods.
Keyword:
Co
up
led tank
syste
m
PI
D con
t
ro
ller
PID tun
i
ng
m
e
th
od
Water lev
e
l con
t
ro
l
Copyright ©
201
5 Institut
e
o
f
Ad
vanced
Engin
eer
ing and S
c
i
e
nce.
All rights re
se
rve
d
.
Co
rresp
ond
i
ng
Autho
r
:
Ab
o
uba
ke
r M
.
Gaba
j
C
o
m
put
er De
p
a
rt
m
e
nt
, Facul
t
y
of
Ed
uca
tion
,
Tripo
li Un
iversity, Tripo
li Lib
y
a
Em
a
il:k
g
a
b
a
j
a
@g
m
a
il.co
m
1.
INTRODUCTION
Propo
rtion
a
l Integ
r
al Deriv
a
ti
v
e
(PID) con
t
ro
llers ar
e
wid
e
ly u
s
ed
in
i
n
dustrial p
r
actice sin
ce last six
decade
.
T
h
e invention
of
PID control
is in 1910 (largely
owi
ng t
o
Elme
r Sperry’s s
h
ip aut
opil
o
t) and the
st
rai
ght
fo
rwa
r
d
Zi
e
g
l
e
r-
Ni
c
h
ol
s (Z-
N
) t
u
ni
ng r
u
l
e
i
n
19
4
2
[1]
.
T
oday
,
PID i
s
use
d
i
n
m
o
re t
h
an 90
% of
pract
i
cal
co
nt
r
o
l
sy
st
em
s, ran
g
i
n
g f
r
om
cons
um
er el
ect
roni
cs suc
h
as cameras to industri
al processes s
u
ch as
ch
em
ical p
r
o
cesses. Th
e PID con
t
ro
ller
help
s to
g
e
t
ou
r o
u
t
p
u
t
(v
el
o
c
ity, te
m
p
eratu
r
e, po
sitio
n)
wh
ere
we
want it, in a short tim
e
, with m
i
nim
a
l overs
hoot, and wit
h
little error
[2].
It also the m
o
s
t
adopte
d
controllers
i
n
t
h
e i
n
d
u
st
ry
due t
o
t
h
e
g
o
od c
o
st
a
nd
gi
ven
be
nefi
t
s
t
o
t
h
e i
n
d
u
st
ry
[
3
]
.
M
a
ny
n
o
n
l
i
n
ear
pr
ocesse
s
can be
co
n
t
r
o
lled usin
g th
e w
e
ll
k
now
n and in
du
str
i
ally pr
ove
n
PI
D c
o
nt
r
o
l
l
e
r [
4
]
.
A c
o
n
s
i
d
e
r
abl
e
di
rec
t
perform
a
nce increase
(fina
n
ci
al
gai
n
)
i
s
d
e
m
a
nded
w
h
e
n
r
e
pl
aci
n
g
a
con
v
e
n
t
i
onal
c
ont
rol
sy
st
em
wi
t
h
a
n
adva
nce
d
o
n
e
[
4
]
.
The m
a
i
n
t
e
nance c
o
st
s
of
an i
n
a
d
eq
uat
e
con
v
e
n
t
i
onal
c
ont
rol
s
o
l
u
t
i
o
n
m
a
y
be l
e
ss ob
vi
o
u
s.
Th
e trick
y
p
a
rt o
f
con
t
ro
ller desig
n
is to
figure ou
t j
u
st how
m
u
ch
o
f
a correctiv
e effort th
e con
t
ro
ller sh
ou
ld
appl
y
t
o
t
h
e
pr
ocess i
n
eac
h c
a
se. Som
e
si
t
u
at
i
on re
qui
res t
i
ght
er c
ont
rol
of t
h
e
pr
ocess
vari
a
b
l
e
t
h
an
On
-O
ff
cont
rol
ca
n
pr
o
v
i
d
e.
Proportional c
ont
rol
provide
s
bette
r c
o
ntrol because its output op
e
r
ate linearly any
w
here betwee
n
fu
lly ON an
d
fu
lly OFF [5
]. As its n
a
m
e
i
m
p
l
ies, its
out
put
c
h
an
ges
pr
op
o
r
t
i
onal
l
y
t
o
t
h
e i
n
p
u
t
err
o
r si
gn
al
.
Propo
rtion
a
l co
n
t
ro
ller
sim
p
l
y
m
u
ltip
lies th
e error
b
y
a con
s
tan
t
t
o
co
m
p
u
t
e its n
e
x
t
o
u
t
p
u
t
.
In
1
9
30s
t
h
e
co
nt
r
o
l
en
gi
neers
di
sc
overed that t
h
e e
r
ror could
be
elim
inated altogethe
r
by
au
to
m
a
tical
ly resettin
g
th
e set
po
in
t to an arti
ficially h
i
g
h
v
a
lu
e [3
]-[6
].
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 3,
J
u
ne 2
0
1
5
:
43
6 – 4
4
2
43
7
Th
e PID
con
t
ro
llers fun
c
tio
n is to
m
a
in
tain
th
e ou
tpu
t
at a lev
e
l th
at there is no
d
i
fferen
ce
(error)
b
e
tween
th
e pro
cess
v
a
riab
le
an
d th
e
set po
i
n
t in
as fast resp
on
se as
p
o
ssib
l
e.
Th
e
ob
j
e
ctiv
e
o
f
t
h
e co
n
t
ro
ller in
t
h
e lev
e
l co
n
t
ro
l is t
o
m
a
int
a
i
n
a l
e
vel
se
t
poi
nt
at
a gi
v
e
n
val
u
e a
n
d b
e
abl
e
to accept
ne
w s
e
t poi
nt val
u
es
dynam
i
cally.
Thi
s
pap
e
r c
o
nsi
d
e
r
s t
h
e
d
e
si
gni
ng
o
f
P
I
D
C
o
nt
r
o
l
l
e
r
t
o
c
o
nt
rol
c
o
u
p
l
e
d
t
a
n
k
s
y
st
em
usi
ng
M
A
TLAB s
o
ft
ware
. This so
ftware is use
d
to
create th
e sim
u
l
i
nk m
odel
fo
r PI
D C
ont
rol
l
er an
d per
f
o
rm
ance
fo
r eac
h
pa
ram
e
t
e
r f
o
r
P
I
D
C
ont
rol
l
e
r
has
b
een si
m
u
l
a
t
e
d.
The
pe
rf
orm
a
nces o
f
PI
D C
o
nt
r
o
l
l
e
r ar
e e
v
a
l
uat
e
d
in term
s
of ove
r
shoot, rise ti
me and steady st
ate error.
Then, the gain for each pa
ram
e
ter
will also be tuned i
n
th
is software an
d th
e
v
a
lid
ity
for each
p
a
ram
e
ter will b
e
com
p
ared
u
s
i
n
g th
e
referen
c
e v
a
lu
e (set
po
in
t).
2.
MODELING
OF THE
COUPLED T
ANK SYSTEM
C
onsi
d
er t
h
e p
r
oces
s co
nsi
s
t
i
ng
o
f
t
w
o i
n
t
e
r
act
i
ng
liqu
i
d tan
k
s
i
n
th
e
Figure 1. Th
e
vo
lumetric flo
w
in
to
tank1
is
q
in
(cm
3
/
m
in
), the vo
lu
m
e
tric flo
w
rate fro
m
t
a
n
k
1
t
o
tank2
is q
1
(cm
3
/min
), and
th
e
vo
lumetric
flo
w
rate fr
om
tank
2 is q
o
(c
m
3
/min
). Th
e
h
e
igh
t
o
f
t
h
e liq
u
i
d
lev
e
l is h
1
(cm
)
i
n
t
a
nk1
and
h
2
in
tank2
(cm
)
.
Bo
th
tan
k
s
h
a
v
e
th
e sam
e
cro
ss section
a
l
area deno
tes the area
o
f
tank1
is
A
1
(cm
2
) and area
of ta
nk2 is
A
2
(cm
2
).
Fi
gu
re
1.
The
bl
oc
k
di
ag
ram
of
t
w
o i
n
t
e
ract
i
n
g
l
i
qui
d
t
a
nks
For tank 1
(1
)
Ass
u
m
i
m
g
lin
ear re
sistance t
o
flow we
have
:
(2
)
An
d
(3
)
(4
)
Taki
n
g
La
pl
ac
e t
r
ans
f
orm
on
bot
h si
des
of
e
quat
i
o
n
(
4
) t
h
e
n
:
(5
)
Or
1
(6
)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
PID Controller
Desi
gn for
Tw
o Tanks Li
qu
id Level Control
System usi
n
g
Matlab
(Abo
uba
ker M.
G
aba
j)
43
8
For tank 2
(7
)
Ass
u
m
i
ng linear re
sistance t
o
flow
we
ha
ve:
(8
)
(9
)
(1
0)
Taki
n
g
La
pl
ac
e t
r
ans
f
orm
on
bot
h si
des
of
e
quat
i
o
n
(
1
0
)
w
e
ha
ve:
(1
1)
.
1
(1
2)
To
ob
tain
,
w
e
ha
ve to ca
nce
l
h
1
(
s
)
in equ
a
tio
n
s
(5
) & (1
0)
.
1
1
1
0
1
1
1
1
(1
3)
Using
th
e
v
a
lues o
f
t
h
e
Parameters
sh
ow
n i
n
t
a
bl
e
1 we
d
r
i
v
e
d
t
h
e
fi
nal
t
r
ans
f
er
fu
nct
i
on
o
f
t
h
e sy
st
em
as
fo
llows:
0.0
1
6.25
7
.
5
1
(1
4)
Tabl
e 1.
Param
e
ters val
u
es
fo
r
two
tan
k
Para
m
e
ters
Value
Unit
A
1
250
cm
2
A
2
250
cm
2
R
1
0.
01
C
m
2
/
s
ec
R
2
0.
01
C
m
2
/
s
ec
H
1
30
cm
H
2
15
cm
3.
SIMULATION RESULT
By n
a
tu
re, liq
uid
lev
e
l co
n
t
rol syste
m
d
e
sig
n
is v
e
ry
m
a
th
e
m
atical
ly
o
r
ien
t
ated
and
with
ou
t th
e u
s
e
of com
put
er as
si
st
ance
m
o
st
desi
g
n
p
r
o
b
l
e
m
s
are very
t
e
di
o
u
s an
d bec
o
m
e
qui
t
e
l
e
ngt
hy
. C
o
m
put
er pr
o
g
ram
,
suc
h
as M
a
t
l
a
b
ha
ve
becom
e
an i
n
val
u
a
b
l
e
t
ool
i
n
a
n
e
ngi
n
eeri
n
g e
nvi
r
o
n
m
ent
.
To
sh
ow th
e co
nv
en
ien
ce
o
f
u
s
ing
MATLAB/SIMUL
INK software
package as a tool t
o
sim
u
late
and a
n
al
y
ze t
h
e beha
vi
o
r
o
f
t
w
o t
a
nks l
i
q
ui
d l
e
vel
co
nt
r
o
l
sy
st
em
, t
h
e sim
u
l
a
t
i
ons are c
o
n
d
u
ct
ed st
ep
by
st
ep.
Th
e system
is si
m
u
lated
and
t
h
e
resu
lts are sh
own
in th
e
fo
llo
wing
sub
s
ect
io
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 3,
J
u
ne 2
0
1
5
:
43
6 – 4
4
2
43
9
3.
1.
Si
mul
a
ti
o
n
Res
u
l
t
w
i
th
out
C
o
n
t
r
o
l
l
er
It
m
a
y b
e
o
b
s
erv
e
th
at fro
m
fig
u
re 2
,
t
h
e liq
u
i
d
will con
s
tan
tly o
v
e
rfl
o
w
. Th
is situ
atio
n
h
a
p
p
en
because of this
system
runni
ng wit
hout controller to c
o
ntrol the Pum
p
sp
e
e
d, s
o
the P
u
m
p
will continuously
p
u
m
p
th
e li
q
u
i
d
o
u
t
fro
m
th
e tan
k
un
til it o
v
erflow. PID con
t
ro
ller m
u
st be add
e
d to
con
t
ro
l t
h
e liqu
i
d
lev
e
l.
Fi
gu
re
2.
The
per
f
o
r
m
a
nce of
t
h
e c
o
u
p
l
e
d
t
a
nk
sy
st
em
wi
t
hout
c
o
nt
r
o
l
l
e
r
a.
Simula
ti
o
n
Result
with PID Contro
ller:
In
th
is secti
o
n th
e sim
u
lat
i
o
n
resu
lt with
t
h
e PID C
o
n
t
ro
llers h
a
s b
e
en
shown
and
th
e con
t
ro
ller
t
u
n
n
i
n
g m
e
t
hode. Fi
gu
re
3 sh
ows t
h
e pe
r
f
o
r
m
a
nce of t
h
e s
y
st
em
wi
t
h
pro
p
o
r
t
i
o
nal
co
nt
r
o
l
l
e
r. T
h
e set
p
o
i
n
t
i
s
set eq
u
a
l to
1
an
d
t
h
e propo
rtio
n
a
l
g
a
in
is set 2
0
.
Th
e
pl
ot
s
h
o
w
s t
h
at
pr
op
ort
i
o
nal
co
nt
r
o
l
l
e
r red
u
ced
b
o
t
h t
h
e
rise tim
e
and the steady state error.
Propo
rt
io
n
a
l con
t
ro
ller also
in
crea
se
d t
h
e o
v
ers
h
oo
t
and dec
r
ease
d
t
h
e
settlin
g
ti
m
e
b
y
sm
a
ll a
m
o
u
n
t.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
PID Controller
Desi
gn for
Tw
o Tanks Li
qu
id Level Control
System usi
n
g
Matlab
(Abo
uba
ker M.
G
aba
j)
44
0
Fi
gu
re
3.
The
per
f
o
r
m
a
nce of
t
h
e c
o
u
p
l
e
d
tan
k
system
with
propo
rtion
a
l co
n
t
ro
ller
Fig
u
r
e
4
sh
ows th
e p
e
rf
or
m
a
n
ce of
th
e syste
m
w
ith
p
r
opor
tio
n
a
l p
l
u
s
d
e
r
i
v
a
tiv
e con
t
roller
.
Th
e set po
in
t is
set eq
u
a
l to
1.
Th
e pro
p
o
r
tional g
a
in
is set eq
u
a
l to
2
0
and
d
e
ri
v
a
tiv
e g
a
i
n
is set eq
u
a
l to
1
0
. Th
is
p
l
o
t
sh
ows
th
at th
e d
e
riv
a
t
i
v
e
co
n
t
ro
ller red
u
c
ed
bo
th
the o
v
e
rshoo
t and
th
e settlin
g
time b
u
t
h
a
d
small effect o
n
the rise
tim
e
and the
steady state error.
Fi
gu
re
4.
The
per
f
o
r
m
a
nce of
t
h
e c
o
u
p
l
e
d
t
a
nk
sy
stem
with
propo
rtion
a
l Plu
s
in
teg
r
al con
t
ro
ller.
Fi
gu
re
5 sh
o
w
s t
h
e pe
rf
orm
a
nce o
f
pr
op
o
r
t
i
onal
-
i
n
t
e
g
r
al
cont
rol
l
e
r
.
Th
e set
poi
nt
i
s
set
equal
t
o
1.
Th
e
p
r
op
ortio
n
a
l
gain
is set eq
u
a
l to
2
0
an
d
in
teg
r
al g
a
i
n
is set eq
u
a
l to
1
2
. The p
l
o
t
sho
w
s that in
teg
r
al con
t
ro
ller
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
SN
:
2
088
-87
08
IJEC
E V
o
l
.
5, No
. 3,
J
u
ne 2
0
1
5
:
43
6 – 4
4
2
44
1
also reduce
d the rise tim
e
increase
d
the
overs
h
oot sam
e
as the proporti
onal controll
er does. T
h
e integral
cont
roller also eliminated
the
steady state error.
Fi
gu
re 5.
The
per
f
o
r
m
a
nce of
t
h
e c
o
u
p
l
e
d
t
a
nk
sy
st
em
wi
t
h
p
r
o
p
o
rt
i
o
nal
P
l
us
deri
vat
i
ve c
ont
rol
l
e
r
Fig
u
re
6
sh
ows th
e
p
e
rform
a
n
ce
o
f
t
h
e syste
m
with
PID
Co
n
t
ro
ller. The set po
in
t is
set eq
u
a
l t
o
1
.
The
p
r
op
ortio
n
a
l
gain
is set equ
a
l to
12
, i
n
tegral g
a
in is se
t equ
a
l to
4 and
deriv
a
tiv
e
g
a
in
is set equ
a
l to 7
t
o
p
r
ov
id
e th
e
d
e
sired
respon
se. Th
e
p
l
o
t
shows th
at th
e ou
tpu
t
ach
ieves th
e set p
o
i
n
t
v
a
lue at ti
m
e
eq
u
a
l to
12
seco
nd
. T
h
e
ou
t
put
have
sl
i
g
h
t
l
y
overs
h
oot
b
e
fo
re st
a
b
i
l
i
ze at
t
i
m
e
equal
t
o
20
sec
o
n
d
.
Fi
gu
re
6.
The
per
f
o
r
m
a
nce of
t
h
e c
o
u
p
l
e
d
t
a
nk
sy
st
em
wi
t
h
p
r
o
p
o
rt
i
o
nal
P
l
us
deri
vat
i
ve
Pl
us i
n
t
e
gral
cont
rol
l
e
r
Evaluation Warning : The document was created with Spire.PDF for Python.
I
J
ECE
I
S
SN
:
208
8-8
7
0
8
PID Controller
Desi
gn for
Tw
o Tanks Li
qu
id Level Control
System usi
n
g
Matlab
(Abo
uba
ker M.
G
aba
j)
44
2
Fi
gu
re
7.
The
per
f
o
r
m
a
nce of
t
h
e c
o
u
p
l
e
d
t
a
nk
sy
st
em
wi
t
h
f
o
u
r
t
y
pes
o
f
c
ont
rol
l
e
rs
.
From
t
h
e sim
u
l
a
t
i
on
resul
t
s
sho
w
n i
n
fi
g
u
re
(2
, 3
,
4,
5
,
6 &
7) i
t
m
a
y
be co
ncl
u
d
e
d t
h
at
PI
D c
ont
rol
l
e
r
eli
m
in
ates th
e o
f
fset o
f
th
e
p
r
o
portio
n
a
l m
o
d
e
and
still p
r
ov
id
es fast respo
n
s
e. Th
is can
b
e
u
s
ed
fo
r v
i
rtu
a
lly
an
y pro
c
ess con
d
ition
in
cl
u
d
i
n
g
t
h
is liqu
i
d
l
e
v
e
l con
t
ro
l.
Th
e PID con
t
ro
ller is on
e of the m
o
st p
o
w
erfu
l bu
t
com
p
l
e
x co
nt
r
o
l
l
e
r m
ode o
p
e
r
at
i
ons c
o
m
b
i
n
es t
h
e p
r
op
ort
i
onal
,
i
n
t
e
g
r
al
,
and
de
ri
vat
i
v
e
m
odes. Thi
s
s
y
st
e
m
can be
use
d
f
o
r any
p
r
o
cess
con
d
i
t
i
on i
n
cl
udi
ng c
o
nt
r
o
l
l
i
ng
wat
e
r l
e
vel
i
n
a t
a
nk.
Th
e wat
e
r l
e
vel
can be
co
n
t
ro
lled
co
ntin
u
o
u
s
ly witho
u
t
m
a
n
u
a
l ad
ju
sting
of
the v
a
lv
e. Th
e PID al
g
o
rith
ms will au
to
m
a
tically
response t
o
the
syste
m
so that
the sy
stem
is stab
ilized
n
e
ar t
h
e set
po
in
t.
4.
CO
NCL
USI
O
N
Thi
s
pa
per
pr
esent
s
a sim
u
l
a
t
e
d l
e
vel
cont
r
o
l
of l
i
qui
d i
n
t
w
o t
a
n
k
sy
st
em
wi
th a di
ffe
re
nt
cont
rol
l
e
r'
s su
ch as Pro
p
o
rt
i
onal
-
I
n
t
e
g
r
al
-
D
eri
v
at
i
v
e (P
I
D
).
Vari
ous c
o
n
v
e
n
t
i
onal
t
echni
que
s of P
I
D t
uni
ng
m
e
t
hod
wer
e
t
e
st
ed i
n
or
de
r t
o
o
b
t
a
i
n
t
h
e PI
D c
ont
r
o
l
l
er pa
ram
e
t
e
rs. Si
m
u
l
a
ti
on
w
a
s co
nd
uct
e
d
wi
t
h
i
n
MATLAB environ
m
en
t to
verify th
e
p
e
rform
a
n
ces o
f
t
h
e syste
m
in
term
s o
f
Rise Ti
m
e
, Settlin
g
Ti
m
e
,
Steady State E
r
ror a
n
d Ove
r
s
h
oot. T
h
e liqui
d level syst
em
i
s
cont
rol
l
e
d
usi
n
g a si
m
p
l
e
P, P
I
, P
D
a
n
d
PI
D
cont
roller.
Hen
c
e it m
a
y b
e
con
c
lud
e
d
that th
e PID con
t
ro
ller is th
e m
o
st effectiv
e contro
ller t
h
at elimin
ates th
e
o
f
fset of th
e
p
r
o
portio
n
a
l m
o
d
e
and
still p
r
ov
id
es
fast
respo
n
s
e. Th
at is wh
y PID con
t
ro
ller h
a
s
b
e
en
ch
osen.
It m
a
y be further stated that
because
of the
a
c
tion
of Proportional
param
e
t
e
r, t
h
e
plot
result will respond to a
step
ch
an
g
e
v
e
ry q
u
i
ck
ly. Due to
th
e actio
n
o
f
In
tegral p
a
ra
m
e
ter, th
e syste
m
was ab
le t
o
return
ed
to
t
h
e set
poi
nt
val
u
e.
REFERE
NC
ES
[1]
J.
Swde
r,
G.
Wszoe
k
,
W.
Ca
rva
l
ho,
Progr
ammable controller design Electropn
eu
ma
tic S
y
s
t
ems, Journal of
Mater
i
al
Processing Tech
nolog
y
164-165
5 (2005) 14659-
1465
[2]
Aurelio Piazzi
and Antonio Visioli, A
Noncausal Approach
for
PID control, Jo
urnalof Process
Control, 4 Mar
c
h
2006.
[3]
Carl Knopse, Gu
est Ed
itor, PID
Control, IE
EE C
ontrol S
y
s
t
em M
a
gazine, Febru
a
r
y
2006.
[4]
S. Bennett, “Dev
elopment of
th
e
PID
controller,”
IEEE Contr
.
S
y
s
t
.
Mag
.
, vol. 13
,
Dec.
1993, pp. 5
8–65.
[5]
S. Song, L.
Xie and Wen-Ji
m Cai, “Auto-tun
i
ng
of Cascad
e Con
t
rol S
y
stems” IEEE Proceedings
of the 4th
world
Congress on Int
e
lligen
t Con
t
rol
and Autom
a
tion,
June
10-14, 200
2, Shanghai, P.R
.
Chin
a, pp 3339
-3343.
[6]
K. Passino, “To
w
ards bridging the perc
eiv
e
d gap between
con
v
ention
a
l and i
n
tell
igent
contro
l”, in Int
e
ll
igen
t
Control: Theor
y
and
Applicati
ons, IEEE Press, 19
96, ch
. 1
,
pp
. 1–
27. G
upta, M
.
M. and Sinh
a, N.K. editors.
[7]
K. Passino, “Bridging the gap
b
e
tween
conv
enti
onal
and in
tel
lig
ent
control
”
,
Speci
al Issue on
In
tell
igent
Con
t
ro
l,
IEEE Control S
y
stems Magazin
e
, vol. 13, June
1
993, pp
. 12–16
Evaluation Warning : The document was created with Spire.PDF for Python.