TELKOM
NIKA Indonesia
n
Journal of
Electrical En
gineering
Vol. 12, No. 12, Decembe
r
2014, pp. 81
6
1
~ 816
5
DOI: 10.115
9
1
/telkomni
ka.
v
12i12.63
49
8161
Re
cei
v
ed
Jun
e
21, 2014; Revi
sed Septe
m
ber
27, 201
4; Acce
pted
Octob
e
r 16, 2
014
Step Responses of Tuned Conventional Controller for
Three Tank System
Kunal Chakr
aborty
*
1
, Rahul Dev
Basak
2
, Dipak K
u
m
a
r Du
tta
3
1,2
Department of Electrical En
gin
eeri
ng,
IMPS Coll
ege of E
ngi
neer
in
g & T
e
chn
o
lo
g
y
,
Mald
a, W
e
st Beng
al, 73
210
3,
India,
Ph./F
ax:
0351
2-2
715
55
/0351
2-2
781
15
3
Departme
n
t of Computer Sci
ence & En
gin
e
e
rin
g
, IMPS Colleg
e
of Eng
i
ne
erin
g & T
e
chnolog
y,
Mald
a, W
e
st Beng
al, 73
210
3,
India,
Ph./F
ax:
0351
2-2
715
55
/0351
2-2
781
15
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: kunal
ind
i
a
n
0
03@
gmai
l.com
1
, rahul19
88.e
e
.
imps@gma
il.c
o
m
2
,
ddd
ipak
76
@g
mail.com
3
Abstract
In this pa
per
mode
lin
g of a te
mp
eratur
e mea
s
ur
in
g tank sys
tem h
a
s be
en
don
e an
d the
n
a tune
d
PID Co
ntroll
er
hav
e b
e
e
n
us
ed for
contr
o
lli
ng th
e st
e
p
re
spons
es of
the
system. T
he
prop
osed
syst
e
m
extends to
a th
ree tank syste
m
& e
a
ch ta
nk
has sa
me a
m
o
unt of li
qui
d. The res
u
lt
s of c
o
mputer s
i
mul
a
ti
o
n
for the system
w
i
th Proportion
al, Integral
and
Derivati
v
e
(PID) Control
l
ers
are show
n h
e
r
e
usin
g MATLAB
(R20
07b) softw
are.
Ke
y
w
ords
:
tem
p
eratur
e, tanksystem
, contr
o
l,
nonlinear control,
PID controller
Co
p
y
rig
h
t
©
2014 In
stitu
t
e o
f
Ad
van
ced
En
g
i
n
eerin
g and
Scien
ce. All
rig
h
t
s reser
ve
d
.
1. Introduc
tion
The tem
p
e
r
at
ure
mea
s
u
r
e
m
ent of li
qui
d in
a ta
nk can b
e
cont
rol
l
ed by
cla
s
si
cal
and
advan
ce
cont
rol alg
o
rithm
PID. Here we are
co
nsi
d
ering
a three
tank n
on-i
n
tera
cting
syst
em.
We o
b
serve
d
that tank1 a
ffects
the
dynamic be
havior of tan
k
2,
simila
rly for t
ank2 affect
s
the
dynamic be
h
a
vior [2]
of ta
nk3
an
d vice
versa,
be
ca
u
s
e th
e flo
w
ra
te dep
end
s
o
n
the
differe
n
c
e
betwe
en liqui
d levels
h
1
an
d h
2
.Thu
s a
chang
e in the
inlet flow rate
affects the li
quid level in t
he
tank, which in
tern affect
s th
e tempe
r
ature of the li
quid
.
Basically it i
s
a the
r
mal p
r
ocess. Vari
o
u
s
type of temperatu
r
e sensor RT
D,
T/C, thermi
stor [1], [9-10]. In th
at particul
a
r
proje
c
t we u
s
ed a
mercury the
r
mometer a
s
sensor. Mathe
m
atical mo
de
l of three tank method giv
e
a third orde
r [6
]equation. Ea
ch ta
nk give
s a
tra
n
sfe
r
f
unctio
n
of fi
rst o
r
de
r
syst
em. A lot of
work ha
s
be
en
carrie
d out o
n
the tempe
r
ature
control
in term
s
of its stabili
zatio
n
. Many attempts have b
een
made to
con
t
rol the
re
sp
onse of tem
peratu
r
e
me
asu
r
ing
sy
ste
m
. This met
hod i
s
utili
ze
d to
investigate [3
] global pro
p
e
r
ties of the de
sign
ed contro
ller.
2. Mechanic
al Cons
truc
tion
The sy
stem
comp
ri
se
s of
a mercu
r
y-i
n
-gla
ss the
r
mometer
pla
c
ed i
n
a liqu
i
d tank to
measure the
temperature
of t
he liqui
d
whi
c
h i
s
he
ated by st
ea
m throu
gh a
coil
system.
The
temperature
of the liquid (T
F
) varie
s
[5]
with time. T is the tempe
r
ature of the mercury in th
e well
of the therm
o
meter. T
he
followin
g
assumption
s a
r
e
made to d
e
termin
e the transfe
r fun
c
tion
relating the v
a
riation of the
thermomete
r (T) fo
r chan
g
e
in the temperatu
r
e of the
liquid (T
F
).
(1)
The exp
ansi
on o
r
contra
ction of
t
he gla
ss
walle
d well
contai
ning m
e
rcury
i
s
negligibl
e
(th
a
t means the
resi
stan
ce off
e
red by gla
ss wall for heat
transfe
r is n
e
g
ligible
)
(2) T
he liquid
film surroun
di
ng the bulb i
s
the only resi
stan
ce to the heat tran
sfer.
(3)
The m
e
rcury a
s
sum
e
s isothermal
con
d
it
ion through
out. The
system i
s
shown in
Figure 1.
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 12, Decem
ber 20
14 : 8161 – 81
65
8162
Figure 1. Three tank
s
y
s
t
em
3
.
Proposed
Mathema
t
ic
al Model
Applying
unsteady state heat balance
for th
e
bulb,
we
get
Input heat rate- Output heat ra
te=Rate of heat accumulation.
0
(
1
)
Where, A=su
rface area of the bulb for he
at transfer in
m
2
M=Mass of mercury in the
bulb, kg
C
P
=Heat cap
a
city of the mercury in kj/kg-k
U=Film heat transfer co
-efficient , kw/m
2
k
At steady state, the equation (1) can be rewritten as:
0
(
2
)
Subtracting Equation (2
) from Equation
(1).
Defining the deviation variables,
and
and sub
s
tituting in the
above equation, we get:
=MC
P
=
(
3
)
Defining time
constant
for the Thermom
e
ter,
Equation (3) can be rewritten as:
(
4
)
Taking Lapla
c
e transform, we get:
transfer function of Tank 1
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TELKOM
NIKA
ISSN:
2302-4
046
Step Respon
se
s of Tuned
Con
v
e
n
tional
Controlle
r Fo
r Three T
a
n
k
System
(Kun
al Cha
k
rabo
rt
y)
8163
Similarly, for
tank2 & tank3 we can get
a firs
t order system.
So we can able to
say that
the entire system is a third
order syste
m
. Here
we can constru
c
t the overall transfer function o
f
the three tank system as:
=
4
.
Transfe
r
Function M
o
deling
As per our problem, let us assume:
=time consta
nt for
tank1=0
.
5 miniute
=
time constant for
tank2=1
.
2 minute
=time consta
nt for
tank3=1
.
5 miniute
=
=0.25 min
=
=0.30 min
=
0.35 min
.
.
.
.
This transfer function is called plant trans
f
e
r
f
u
n
c
t
i
o
n
.
The entire experim
ental se
t up
is given in Fig
u
re 2.
Figure 2. Pro
posed expe
ri
mental set up
5
.
Closed L
oop Tuning
Process
As per o
u
r p
r
oblem, applyi
ng a clo
s
e
d
loop Tuni
ng te
chni
que
we can write:
1
0
Or,
1
.
.
.
.
0
Or,
0.9
3
.15
3
.
2
0.0262
0
Now accordin
g to Routh Pr
ocess:
0.9
3.2
3.15
(1+0.02625
)
.
.
.
.
.
0
So by solving it,
=
3
88
.5
7=
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ISSN: 23
02-4
046
TELKOM
NI
KA
Vol. 12, No. 12, Decem
ber 20
14 : 8161 – 81
65
8164
No
w its Auxiliary equatio
n:
3.15
+(1
+
0.02
625
)=0
Or, 3.15
+(1
+
0.0262
5*38
8.57)=0
Or,
= -1
1.199
/3.15 = - 3.55
6
Or,
= -3.556
Or,
= 1.88
41
rad/sec
So,
&
=
.
.
= 3.33 min
/
cycle
6. Simulink
Design
Here
we
de
si
gn the
tune
d
controlle
r bl
o
c
k with
pla
n
t
transfe
r fu
ncti
on, sho
w
n i
n
Figure
3:
Figure 3. Simulink bl
ock
diagram
7
.
Differ
e
nt
Process Per
f
ormance Ind
i
ces
Table
1 indi
cate
different
perfo
rma
n
ce indi
ce
s th
at we
co
nsi
der fo
r thi
s
particula
r
experim
ent is defined a
s
:
Table 1. Diffe
rent pe
rform
a
nce in
dices
Performance In
d
e
xes
PID
ISE
1.24
ITSE
0.92
IAE
1.12
ITAE
2.05
8.
Tuning Parameter Ev
aluation
Table
2 i
s
d
e
f
ined the
different
pa
rame
ter value
for
desi
gning
the
syste
m
that
we
ca
n
get from clo
s
ed loop tuni
n
g
techni
que
-
Table2. Tun
ed paramete
r
value
Sl. no.
K
P
K
P
/T
I
K
P
T
D
1 233.142
110.025
136
2 233.142
75
124
9.
Simulatio
n
Resul
t
After simul
a
tion we get th
ree
step
re
sp
onses
fo
r diff
erent
parame
t
er & tuning
values.
These step
re
spo
n
ses a
r
e
sho
w
n in Fig
u
re 4
(
a), Fig
u
r
e 4(b) & Figu
re 4(c).
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
2302-4
046
Step Respon
se
s of Tuned
Con
v
e
n
tional
Controlle
r Fo
r Three T
a
n
k
System
(Kun
al Cha
k
rabo
rt
y)
8165
Figure 4(a
)
. Step respon
se
s of plant for
K
P
=233.1
42, K
P
/T
I
=110.02
5, K
P
T
D
=136
Figure 4(b
)
. Step respon
se
s of plant for
K
P
=233.1
42,
K
P
/T
I
=75,K
P
T
D
=124
Figure 4(c). S
t
ep respon
se
s of overall sy
stem
10. Conclus
i
on
Modelin
g of t
h
ree
tan
k
te
mperature
m
easurin
g
syst
em
sho
w
s th
at syste
m
i
s
unsta
ble
for a
certain
rang
e. Th
at’s why
we t
r
ied
to de
sign
a
convention
a
l contro
lle
r strat
egy
process so
that we
can
minimize the
steady
state
error &
maxi
mize th
e
settl
ing time. In
fu
ture
we
may
use
d
Geneti
c
Algorithm for desi
g
ning some ad
vance
control
ling strate
gy.
Referen
ces
[1]
DM Cons
idi
n
e
.
Process Ins
t
ruments an
d
Contro
l Ha
n
d
Book. 2
nd
editi
on, MCGr
a
w
Hi
ll Bo
ok
Comp
an
y. 19
7
4
[2]
Ang K
H
, GCY
Cho
ng, Y
Li. PI
D Co
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e
sig
n
a
nd T
e
c
hno
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T
r
ansactio
n
s
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ntrol Sys
t
ems T
e
ch
nol
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g
y.
2005; 1
3
(4)
:
559–5
76.
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ope
la
nd.
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he Desi
gn
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i
egl
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o
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uni
ng
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y
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e
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acifi
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ebsite, UR
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