TELKOM
NIKA
, Vol.13, No
.2, June 20
15
, pp. 547 ~ 5
5
5
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v13i2.1322
547
Re
cei
v
ed
De
cem
ber 1
2
, 2014; Re
vi
sed
March 30, 20
15; Accepted
April 18, 201
5
Experimental Validation of a Multi Model PI Controller
for a Non Linear Hybrid System in LabVIEW
M.Kaly
an Chakrav
arthi*
1
,
Nith
y
a
Venkates
an
2
Schoo
l of Elect
r
onics En
gin
e
e
r
ing,
VIT
Universit
y
,
Vand
alur-K
el
a
m
bakkam ro
ad
, Chenn
ai, T
a
mil Nad
u
, India
6001
27
*Corres
p
o
ndi
n
g
author, e-ma
i
l
: maddik
e
raka
l
y
a
n
@vit.ac.i
n
1
, nithy
a
.v@vit.ac.in
2
A
b
st
r
a
ct
In this pa
per a
real ti
me S
i
n
g
l
e
Sph
e
rica
l T
a
nk Li
qui
d Lev
el
System (SST
LLS) h
a
s be
en
chose
n
for investigation. This paper
descr
ibes
the design and
dev
elopm
e
nt of a M
u
lti Mo
del PI Controller (MMP
IC)
using classic
a
l controller tuning
techniques for a singl
e spheric
a
l nonlinear tank
system
. System
ide
n
tificatio
n
of
these differe
nt regio
n
s of no
nlin
ear
pr
oces
s are don
e usi
ng bl
ack box
mo
de
lin
g, w
h
ich is
ide
n
tified to
b
e
no
nli
near
an
d ap
proxi
m
ate
d
to be a F
i
rs
t Order Plus Dea
d
T
i
me (F
OPDT
) mod
e
l.
A
prop
ortion
al
a
nd i
n
tegr
al c
o
ntroll
er is
des
ig
n
ed usin
g L
abVIEW
an
d Che
n
-Hro
nes-
R
esw
i
ck
(CH
R
),
Z
huan
g-Athert
on (Z
A), and S
k
ogesta
d
’
s Inte
rnal Mo
del
Con
t
roller (SIMC) tuni
ng
meth
ods
are i
m
pl
e
m
e
n
te
d
in r
eal
ti
me. T
he
pa
per
prov
i
des th
e
deta
ils
ab
out
th
e
dat
a ac
quis
i
tio
n
u
n
it, show
s th
e
imple
m
entati
o
n
of
the control
l
er a
nd co
mp
arisi
o
n
of
the results of PI tuning me
t
hods use
d
for an MMPI Contr
o
ller.
Ke
y
w
ords
: Graph
ical Us
er Interface (GUI),
PI Contro
ll
er, Che
n
-Hro
nes-
R
esw
i
ck (CHR
), Z
huang-Athe
rton
(Z
A), and Skog
estad
’
s Intern
al
Model C
ontrol
l
e
r (SIMC), Lab
VIEW
1. Introduc
tion
In comm
on t
e
rm
s, mo
st o
f
the indu
stri
es h
a
ve typical problem
s
raise
d
be
ca
use of the
dynamic
non
linear b
ehavi
o
r of the sto
r
age tan
ks. It’
s only be
cau
s
e of the inh
e
rent no
n linea
rity,
most of the chemi
c
al p
r
ocess ind
u
stries
a
r
e in
need of cl
assical cont
rol techniq
u
e
s
.
Hydro
m
etallu
rgical in
du
stri
es, foo
d
p
r
o
c
e
s
s indu
stri
es,
con
c
rete
mixing ind
u
s
trie
s a
nd
waste
water treatm
ent indu
stri
es have b
een
a
c
tively usin
g
the sp
he
rical
tanks a
s
a
n
i
n
tegral
proce
ss
element. Du
e to its cha
nging
cro
s
s
se
ction an
d non line
a
rity, a sphe
ri
cal
tank provid
es a
chall
engin
g
p
r
oble
m
for the level contro
l.
Liquid level
control syste
m
s have al
ways pull
ed th
e attention of industry for its very
importa
nt ma
nipulate
d
pa
rameter
of level, whi
c
h find
s many a
ppli
c
ation
s
in va
riou
s field
s
. An
accurate kno
w
led
ge of an
adequ
ate m
odel is
often
not
ea
sily available. An in
sufficie
n
cy in
this
asp
e
ct
of mo
del d
e
si
gn
ca
n al
ways lea
d
to a
failu
re
in some
no
n
linear regio
n
with hi
ghe
r
n
o
n
linearity. The
eviden
ce th
at many re
se
arche
r
s
are
workin
g in th
e nonli
nea
r
model
s an
d thei
r
controlling st
rategies [1],[2], whi
c
h in turn explai
n about the
pr
ocess dynami
cs around
a larger
operating re
gion than th
e co
rre
sp
ond
ing linea
r m
odel
s have
been g
a
inin
g
great po
pul
arity
[3].The no
n li
near mo
del
s
are
obtain
ed f
r
om fi
rst
prin
ciple a
nd fu
rth
e
r from th
e p
a
ram
e
ters
wh
ich
appe
ar
within su
ch mo
d
e
ls that are
obtaine
d
fro
m
the data
of the pro
c
e
ss. However the
conve
n
tional
method
s for
developin
g
such m
odel
s
a
r
e still in
sea
r
ch. On
ce the
model h
a
s b
e
en
develop
ed, the need for th
e controlle
r d
e
sig
n
com
e
s
in to picture t
o
maintain th
e pro
c
e
ss u
n
der
steady state.
Propo
rtional I
n
tegral
De
rivative (PID) co
ntrolle
r is the
name that is
widely he
ard
as
a pa
rt of the
pro
c
e
s
s control indu
stry. Despit
e
mu
ch
advan
ceme
nt in control
th
eory
whi
c
h h
a
s
been
re
centl
y
seen, PID cont
rolle
rs
are
still ex
tensively u
s
e
d
in the p
r
oce
s
s ind
u
st
ry.
Conve
n
tional
PID controll
ers a
r
e
simpl
e
, inexpen
sive in co
st [4], easy to design and robu
st
provide
d
the
system i
s
line
a
r.
The PID
controlle
r op
erates with
th
re
e paramete
r
s, which
can
b
e
easily tun
ed
by trial an
d
error, o
r
by
usin
g di
ffere
nt tuning
strategie
s
an
d
rule
s availa
bl
e in
literature
su
ch a
s
Zi
egla
r
Nichol
s [5], Z
huan
g a
nd At
herton
[6].Th
e
se
rule
s h
a
ve thei
r b
a
ses
laid
on ope
n-lo
op
stable first or second o
r
d
e
r
plu
s
dead ti
me pro
c
e
s
s model
s. The
r
e are ma
ny other
method
s a
n
d
app
roa
c
he
s
whi
c
h h
a
ve p
e
riodi
cally
ev
olved to imp
r
ovise the
pe
rforma
nce of P
I
D
tuning, T
he
software
a
nd t
e
ch
nolo
g
y ha
ve bee
n a
s
si
sting th
e m
a
n
k
ind
to
de
sig
n
an
d im
plem
ent
more
sop
h
ist
i
cated
cont
ro
l algorithm
s.
Despite all the effort, industri
e
s e
m
p
hasi
z
e mo
re
on
robu
st and transparent proc
e
s
s co
ntrol
stru
cture tha
t
uses
simpl
e
controllers which m
a
ke
s
PID
controlle
r the most wid
e
ly impleme
n
ted
controlle
r.
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 547 – 55
5
548
SSTLLS
ha
s been
a mod
e
l
for quite a many
ex
pe
ri
ments pe
rformed in
the
n
ear pa
st.
Nithya et al
[7] have d
e
si
gned
a mo
d
e
l ba
sed
con
t
roller fo
r
a spheri
c
al
tan
k
, whi
c
h
gave
a
comp
ari
s
o
n
betwe
en IM
C and
PI co
ntrolle
r u
s
ing
MATLAB. Na
resh
Nan
dol
a et al
[8] h
a
ve
studie
d
an
d
mathemati
c
al
ly desig
ned
a
pre
d
ictive
co
ntrolle
r for
no
n linea
r hyb
r
i
d
syste
m
. A g
a
in
sched
uled PI controll
er was de
sign
ed
usin
g a simul
a
tion on MATLAB for a seco
nd order
no
n
linear sy
stem
by Di
ne
sh K
u
mar et al
[9]
whi
c
h
gave i
n
formation
ab
o
u
t se
rvo t
r
acking fo
r differe
nt
set point
s. A fraction
al ord
e
r PID contro
ller was
d
e
si
gned fo
r liqui
d level in sp
h
e
rical tan
k
using
MATLAB, which compa
r
e
d
the perfo
rma
n
ce of fra
c
ti
o
nal ord
e
r PID with cla
ssi
cal
PI controller
by
Sunda
ravadiv
u
et al [10].
Kalyan Cha
k
ravarthi
et al
have imple
m
ented a cl
a
ssi
cal a
nd g
a
in
sched
uled PI
controllers f
o
r a si
ngle
and du
al sp
heri
c
al tan
k
system
s in real time usi
ng
LabVIEW [11],[12]. An adaptive fuzzy
PID controll
er has been im
pl
emented for
controlling l
e
vel
pro
c
e
s
s [13].
A Fuzzy Imm
une PI
D
Cont
rol
wa
s
also
i
m
pleme
n
ted
on a
hyd
r
auli
c
system
,whi
ch
wa
s optimize
d
by PSO algorithm [14].
2. Experimental Proce
s
s
Descrip
tion
The lab
o
ratory set up fo
r th
is sy
stem ba
sically
con
s
ist
s
of two sphe
ri
cal inte
ra
ctin
g tanks
whi
c
h a
r
e
co
nne
cted
with
a man
ually
operable va
lv
e between
th
em. Both the
tanks h
a
ve
an
inflow a
nd o
u
tflow of water whi
c
h i
s
b
e
in
g pum
ped
by
the motor,
wh
ich
contin
uou
sly feed
s in t
h
e
water fro
m
t
he
water reservoir.
The
flow i
s
re
gulat
ed in
to the
tanks th
roug
h the
pne
um
atic
control valves, whose po
sition ca
n be co
ntrolled by ap
plying air to them.
Figure 1. Rea
l
time experi
m
ental set up
of the
p
r
oc
es
s
Figure 2. Interface
d
NI-DA
Q
mx 6211 Data
Acqui
sition M
odule
Card
A comp
re
sso
r
so a
s
to a
pply pre
s
sure to clo
s
e a
nd ope
n the
pneum
atic va
lves wa
s
use
d
. The
r
e i
s
al
so
provisi
on given
to
manually m
e
asu
r
e th
e flo
w
rate in
bot
h the tan
k
s u
s
ing
rotamete
r. Th
e level i
n
the
tanks a
r
e
bei
ng m
eas
ured
by a diffe
renti
a
l p
r
essu
re
transmitte
r
whi
c
h
has
a typical
output curren
t range
of 4-20mA.This
di
fferential p
r
e
s
sure tra
n
smitt
e
r is i
n
terfa
c
ed
to the com
p
uter conn
ect
ed thro
ugh t
he NI-DAQm
x
6211 d
a
ta
acq
u
isitio
n
card which
can
sup
port 16 a
nalog inp
u
ts
and 2 anal
og
output cha
n
nels
with a voltage ra
ngin
g
betwe
en ±10
Volts. The
sa
mpling
rate
o
f
the a
c
qui
siti
on
card m
o
d
u
le i
s
2
50Ks/
S with
16
bit
resolution.
T
h
e
grap
hical p
r
o
g
ram
written
in L
abVIEW is th
en
linked to th
e
se
t up th
rou
g
h
the a
c
q
u
isiti
o
n
module. Fig
u
r
e 1 sho
w
s
the real time
experim
e
n
ta
l setup of th
e pro
c
e
s
s.Th
e pro
c
e
s
s of
operation sta
r
ts
when pne
umatic cont
ro
l valve is clo
s
ed by applyin
g
the air to
a
d
just the flo
w
of
water
pump
e
d
to the tank. This p
ape
r talks o
n
ly
about
a single
sph
e
rical tank liq
uid level syst
em
(SSTLLS), so
we shall u
s
e
only the sphe
rical ta
n
k
on
e
for our usag
e throug
hout
the experime
n
t.
The level of
the wate
r i
n
tank i
s
m
easure
d
by the differe
ntia
l pre
s
sure transmitte
r an
d is
transmitted in the form o
f
current ran
ge of
4-20
m
A
to the inte
rfacin
g NI-DAQmx 6211
data
acq
u
isitio
n module
card to the Personal
Comp
uter
(P
C). After com
puting the co
ntrol algo
rith
m in
the PC,
cont
rol
sign
al is
transmitted t
o
the I/P
co
nverter whi
c
h pa
sses the
pre
s
su
re to
the
pneum
atic va
lve propo
rtio
nal to the current provi
ded
to it. The pneumatic valv
e is actuate
d
b
y
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Experim
ental Validation of a Multi Model
PI
Controller
for a Non Li
near .... (M. Kalyan
C.)
549
the sign
al provided by I/P conve
r
ter which in tu
rn
regulate
s
the
flow of wate
r in to the tank.
Figure 2 sh
o
w
s the inte
rfa
c
ed
NI
-DA
Q
mx 6211 data
acqui
sition
card.
3. Sy
stem Id
entific
a
tion
and Con
t
roll
er Desig
n
3.1. Mathem
atical Modeli
ng of SSTLL
S
The SSTLLS is a system
whi
c
h is no
n linear in
n
a
tu
re by virtue of its varying diameter.
The dynami
c
s of this non li
nearity ca
n b
e
descr
i
bed b
y
the first ord
e
r differe
ntial equatio
n.
= q
1
- q
2
(1)
Whe
r
e, V is the volume of
the tank, q
1
is
the Inlet flow rate and, q
2
is
the Outlet flow rate. The
volume V of the sp
heri
c
al t
ank i
s
given b
y
,
V=
h
3
(2)
Whe
r
e h is th
e height of the tank in cm.
On ap
plicatio
n of the
stead
y state value
s
,
and
by solving the eq
ua
tions 1
and
2, the no
n
linear
sph
e
ri
cal tank can b
e
lineari
z
e
d
to the followin
g
model,
(3)
Whe
r
e,
τ
= 4
π
R
t
h
S
and
The
syste
m
i
dentificatio
n
of SSTLLS i
s
de
rived
usi
n
g the
bla
c
k b
o
x mod
e
ling.
Un
de
r
con
s
tant inflo
w
and
con
s
ta
nt outflow rat
e
s of wate
r, the tank i
s
all
o
we
d to fill from (0
-45
)
cm.
Each
sample
is acqui
red
by NI-DAQm
x
6211
from
t
he diffe
rential
pressu
re t
r
a
n
smitter thro
ugh
USB port in t
he ra
nge
of (4-20
)
mA an
d the data i
s
transfe
rred t
o
the PC.Thi
s data i
s
furt
her
scaled
in te
rms of l
e
vel in
cm.Employin
g
the
ope
n lo
op meth
od, f
o
r a
given
ch
ange
in th
e i
nput
variable; th
e
output respo
n
se
of the
sy
stem i
s
recorded. Zie
g
ler
and
Nichol
s [
5
] have o
b
tai
ned
the time co
nstant an
d time delay of
a FO
PDT
model by co
nstru
c
ting
a
tangent to the
experim
ental open loo
p
st
ep re
spo
n
se at its point
of inflection. Th
e intersectio
n
of the tangent
with the time axis provide
s
the estima
te of ti
me d
e
lay. The time con
s
tant
is estimated
by
cal
c
ulatin
g th
e tange
nt inte
rse
c
tion
with t
he st
e
ady
sta
t
e output valu
e divided
by the mo
del g
a
i
n
.
Che
ng a
nd
Hung [15]
have
also
pr
opo
se
d tange
nt an
d point
of inflection
metho
d
s fo
r e
s
timat
i
ng
FOPDT
mod
e
l pa
ramete
rs. The
majo
r disa
dvantag
e of all the
s
e metho
d
s i
s
the difficulty
in
locatin
g
the p
o
int of inflecti
on in p
r
a
c
tice
and may not
be accu
rate.
Prabhu
and
Chid
amba
ra
m
[16] have obt
ained th
e pa
ramete
rs of the first or
der plus time de
lay model fro
m
the rea
c
tio
n
curve
obtain
ed by solvin
g the nonlin
e
a
r differe
ntial
equation
s
m
odel of a di
stillation colu
mn.
Sunda
re
san
and K
r
ish
n
a
s
wamy [17]
ha
ve obtaine
d
t
he p
a
ram
e
ters of F
O
PDT
tran
sfer fun
c
tion
model
by
coll
ecting
the
op
en lo
op i
nput
-output
re
sp
o
n
s
e
of the
p
r
ocess a
n
d
that
of the m
odel
to
meet at two points
whi
c
h
descri
be the
two paramet
ers
τ
p
an
d
θ
. The propo
se
d times t
1
and t
2
,
are
estim
a
ted
from
a
step
respon
se
curve. The p
r
op
ose
d
time
s t
1
and
t
2
, are
e
s
timated f
r
om
a
step
re
sp
on
se curve.
Thi
s
time
co
rre
sp
ond
s to
the
3
5
.3% an
d 8
5
.3% re
sp
on
se
times.
The
time
con
s
tant an
d time delay are cal
c
ulate
d
as follo
ws.
τ
p
= 0.67(t
2
−
t
1
)
(4)
θ
= 1.3t
1
−
0.29t
2
(5)
At a con
s
tant
inlet and
outl
e
t flow rates,
the
sy
st
e
m
r
e
ach
e
s t
h
e
st
e
ady state. After that
a step in
cre
m
ent is given
by changi
ng
the flow
rate
and vario
u
s
values of the
same a
r
e ta
ken
and record
e
d
till the system be
co
m
e
s
stable a
gain. We ob
tain the mo
del of the p
l
ant
experim
entall
y
for a given
unit-ste
p
inpu
t. If the
plant
involves neith
er integ
r
ators nor domin
an
t
compl
e
x-conj
ugate p
o
le
s, then
su
ch
a u
n
it step
re
sp
o
n
se
curve m
a
y look S
-
shap
ed
curve.Su
ch
step respon
se cu
rve may
be gen
erate
d
experim
ent
ally or from
a dynami
c
si
mulation of t
he
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ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 547 – 55
5
550
plant. The S-sh
ape
d cu
rv
e may be ch
ara
c
teri
ze
d b
y
two con
s
ta
nts, delay time L and ti
me
con
s
tant
τ
. The experi
m
en
tal data are a
pproxim
ated to be an FOP
D
T mod
e
l.
3.2. Design
of PI Contr
o
ller
The derivation of transfer f
unction model w
ill
now pav
e the
way to
t
he controll
er design
whi
c
h sh
all be used to ma
intain the system to the optimal set poin
t. This can b
e
only obtain
e
d
by prope
rly selectin
g the tuning p
a
ra
me
ters K
p
and K
i
for a PI controller.
The co
nventi
onal FOP
D
T
model is give
n by,
G(s) =
(7)
Table 1
gives the tran
sfer f
unctio
n
s
de
si
gned
fo
r diffe
rent regio
n
s
of SSTLLS. It can
be
notice
d
that the delay exp
onent
ially increa
se
s as th
e degree of
non linea
rity increa
se
s. The
transfe
r fun
c
tion model
s a
r
e de
rived for five diffe
rent region
s across the varying diamete
r
of
SSTLLS.
By implement
ing the
rul
e
s
of PI tuning
b
y
the metho
d
s
ZA,
CHR a
nd SIMC
met
hod
s to
get the
follo
wing p
a
ramete
rs for the t
r
an
sfer fun
c
tion
spe
c
ified
in
T
able
1.The
p
a
ram
e
ters
of
K
p
and K
i
for different regio
n
s
of non linea
rity
are derive
d
and given in
Table 2.
Table 1. Tran
sfer fun
c
tion
model
s for dif
f
erent re
gion
s of SSTLLS
Region of Operat
ion
Transfer
Functio
n
0-9
9-18
18-27
27-36
36-45
4. Results a
nd Discu
ssi
ons
The
CHR, Z
A
and SIMC based MM
PI cont
roll
ers which were de
sign
ed
and a
r
e
impleme
n
ted
usi
ng th
e g
r
aphi
cal
p
r
og
rammin
g
cod
e
which i
s
written
on
L
abVIEW. Th
e
s
e
controlle
rs
were ap
plied to
SSTLLS and
the perfo
rm
a
n
ce of them
wa
s com
p
a
r
e
d
unde
r different
con
d
ition an
d
region
s of op
eration.
Table 2. CHR, ZA and SIMC tuned K
p
a
nd K
i
para
m
e
t
ers for diffe
rent regio
n
s of
non linea
rity
Tuning Method
Regions (cm)
Kp
Ki
CHR
0-9
0.12661
0.00095208
56
9-18
0.03359
0.00009610
00
18-27
0.04123
0.00007578
15
27-36
0.04055
0.00006251
04
36-45
0.03333
0.00004834
07
ZA
0-9
0.056
0.00061454
04
9-18
0.0135
0.00009504
00
18-27
0.0107
0.00008726
5016
27-36
0.00565
0.00007701
2199
36-45
0.00172
0.00006185
9370
SIMC
0-9
0.11390
0.00124993
9-18
0.01789
0.00012500
18-27
0.01210
0.00009868
2869
27-36
0.00599
0.00008164
6561
36-45
0.001757
0.00006319
0073
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TELKOM
NIKA
ISSN:
1693-6
930
Experim
ental Validation of a Multi Model
PI
Controller
for a Non Li
near .... (M. Kalyan
C.)
551
4.1. Chang
e
s in the Loa
d
The
CHR, Z
A
and SIM
C
tuned
co
ntrollers h
a
ve
been
used t
o
control
the
level of
SSTLLS whil
e applying a
load cha
n
g
e
of 7.5% fo
r
a set of set points. Initially to test
the
respon
se
of the tan
k
in its non line
a
r
re
gion, a
set p
o
int of 4.5 cm wa
s fed to
the pro
g
ra
m
and
the re
adin
g
s
were
re
corde
d
. Similar
me
thod
wa
s em
ployed fo
r th
e set poi
nts
o
f
2.25, an
d 9
cm
respe
c
tively. While a
pplyin
g
a set poi
nt of 2.25 from
4.5 cm, we
are inte
nding
to obse
r
ve the
negative set point trackin
g
performan
ce
.
Table 3. Co
m
pari
s
on of Ti
me Dom
a
in Analysi
s
for Se
rvo Re
spo
n
se for different
region
s
Parameter
Set
Point
(c
m)
Tuning Method
CHR
ZA
SIMC
Peak
Ti
me
(s
ec
)
4.5 62.203
53.453
26.64063
9 126.406
128.906
159.9844
22.5 76.796
84.89063
104.7031
27 168.484
162.437
204.1406
40.5 105.75
85.5
28.04688
45 156.156
146.25
123.289
Rise Time
(s
ec
)
4.5 55.9828
48.1078
23.97656
9 113.765
116.0156
143.9859
22.5 69.117
104.6109
94.2327
27 151.635
146.193
183.726
40.5 95.175
76.95
25.2421
45 140.540
131.625
110.7
Settling
Ti
me
(s
ec
)
4.5 28.953
21.0
17.10937
9 36.4531
37.0468
6.2969
22.5 35.546
15.90627
1.5938
27 20.95
39.1563
9.1563
40.5 51.0
1.34375
4.4531
45 17.098
8.8438
1.1406
The
simila
r p
r
ocess of o
b
serving th
e n
e
gative
set poi
nt tra
cki
ng i
s
also a
dopte
d
. At all
the level
s
, a
disturban
ce
i
s
a
dde
d to th
e sy
stem
to
observe it
s p
e
rform
a
n
c
e.
Similarly the
set
points are
ch
ange
d for the
re
gion
s of
18
-27
cm
an
d 3
6
-45
cm in
th
e SSTLLS. Fi
gure
s
3(a),
3(b),
3(c), 3(d), 3
(
e
)
, 3(
f), 3(g), 3(h), 3(i)
demo
n
strate th
e re
gulatory p
e
rf
orma
nce und
er the influ
e
n
c
e
of external di
sturb
a
n
c
e of
tuned MMPI
controlle
r
in t
he re
gion
s of
0-9
cm, 18
-2
7 cm
and
36-45
cm for
CHR,
ZA and SIMC tuned MMP
I
controlle
rs
re
spe
c
tively. Th
e perfo
rma
n
ce indi
ce
s of the
regul
atory re
spo
n
se can b
e
see
n
in Ta
ble 5.The de
sign
ed co
ntro
llers
were abl
e to compe
n
sate
the effec
t
of t
he load changes
.It c
a
n be notic
ed
from Table
5, that the ISE and IAE values
f
o
r
SIMC metho
d
are
relativel
y
lesse
r than
the
ZA and CHR m
e
thod i
n
the regi
on
s 0-9 cm and
36-
45
cm of
SSTLLS, where
the d
egree
of non
line
a
ri
ty
is
very
high.At the same time it
c
a
n be
see
n
that, in
all the
othe
r re
gion
s
of o
perat
io
n ZA
tuned
MMPI
controlle
r
sh
ows a
n
effici
ent
disturban
ce rejectio
n
and provide
s
relat
i
vely
le
sser I
SE and IAE value
s
a
c
ro
ss
the regi
on
s 9
-
18
cm, 18-27 cm
, 27-36
cm.
4.2. Variation of the Se
t Point
The CHR, Z
A
and SIMC
MMPI control
l
ers
we
re
run
for all differe
nt regio
n
s
of SSTLLS
whi
c
h
are
m
odele
d
in th
e Tabl
e 1.
Figure 4
(
a
)
,
Figure 4
(
b
)
and Fi
gu
re
4(c)
display
the
comp
ari
s
o
n
result
s of serv
o re
spo
n
ses
obtaine
d for
different regi
ons vi
z.;0-9
cm,18-2
7
cm
and
36-4
5
cm
re
spectively. Th
e set poi
nts
chosen for th
i
s
analysi
s
are
4.5, 9,
22.5, 27, 40.5 an
d 45
cm. The l
e
vel
varies fo
r bo
th the co
ntrol
l
ers
and th
eir cha
nge
s a
r
e
see
n
in Fig
u
r
e 4
(
a), Fi
gure
4(b) and Figure 4(c).It can be observed that the
level very swiftly oscillates for CHR and
ZA
method in
compa
r
isi
on to SIMC in most no
n
lin
ear regio
n
s
towards th
e curvatu
r
e of
the
spheri
cal tanks.It is seen
that
in the regions with
hi
ghest degree of non
linearity, SIMC tu
ned
MMPI control
l
er tra
c
k
s
the
set point in a v
e
ry
less ti
me whe
n
co
mpar
ed to that of CHR a
n
d
ZA
tuned control
l
ers. Ta
ble 3
gives the time domai
n
spe
c
ification
s
of the
present system. It is
evident from
Table 3 th
at the ri
se time
and
sett
ling time for differe
nt set point
s
for SIMC tun
ed
MMPI co
ntrol
l
er i
s
relativel
y
less in
the
non li
nea
r
re
gion
s
whe
n
compa
r
ed
with
CHR an
d Z
A
tuned controll
ers. Ta
ble 4
deal
s with th
e perfo
rman
ce indices li
ke
ISE and IAE for the different
set point
s in the entire
regi
on of operation. It
can be observed that
ISE and IAE values for th
e
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ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 547 – 55
5
552
SIMC metho
d
in no
n lin
ear
regio
n
of
4.5cm and
40
c
m
a
r
e
le
ss
w
hen
co
mp
ar
ed
to
th
a
t
C
H
R
an
d
ZA method. If keenly observed, SI
MC tuned control
l
er pe
rform
s
better than that of other two
method
s
with re
sp
ect to
ISE and IA
E cal
c
ulatio
n
s
. It ca
n be
inferred th
a
t
for faste
r
t
i
me
respon
se in
n
on linea
r re
gi
ons SIMC m
e
thod of t
uni
ng proves to
be the be
st method. But if the
empha
si
ze is more o
n
the error
redu
ction in
the
system, ZA
method give
s a be
st of its
perfo
rman
ce
in almo
st all t
he region
s
of ope
rati
on
s. It can
be ve
ry well
see
n
th
at extreme
n
on
linear re
gion
s 0-9
c
m
and
3
6
-45
c
m
have
a very le
ss
I
AE and ISE, thus p
r
ovin
g the efficie
n
cy
of
SIMC tuning
method ove
r
the ZA and CHR meth
od.
Figure 3(a
)
. Z
A
tuned MMPI Controlle
r’
s
Reg
u
latory Resp
on
se for region 0
-
9
c
m
Figure 3(b
)
. SIMC tuned M
M
PI Controlle
r’s
Reg
u
latory Resp
on
se for region 0
-
9
c
m
Figure 3(c).
C
HR tun
ed M
M
PI Controlle
r’s
Reg
u
latory Resp
on
se for region 0
-
9
c
m
Figure 3(d
)
. Z
A
tuned MMPI Controlle
r’
s
Reg
u
latory Resp
on
se for region 1
8
-2
7cm
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Experim
ental Validation of a Multi Model
PI
Controller
for a Non Li
near .... (M. Kalyan
C.)
553
Figure 3(e
)
. SIMC tuned M
M
PI Controlle
r’s
Reg
u
latory Resp
on
se for region 1
8
-2
7cm
Figure 3(f). CHR tun
ed M
M
PI controlle
r’s
Reg
u
latory Resp
on
se for region 1
8
-2
7cm
Figure 3(g
)
. Z
A
tuned MMPI Controlle
r’
s
Reg
u
latory Resp
on
se for region 3
6
-4
5cm
Figure 3(h
)
. SIMC tuned M
M
PI Controlle
r’s
Reg
u
latory Resp
on
se for region 3
6
-4
5cm
Table 4. Co
m
pari
s
on of pe
rforman
c
e in
di
ce
s of se
rvo resp
on
se for d
i
fferent regi
on
s
Set Point
(c
m)
Tuning
Method
ISE IAE
4.5
CHR
139.8357
226.4972
ZA 647.3612
512.4809
SIMC 136.6747
222.5321
9
CHR
268.7596
315.4242
ZA 26.27826
82.10396
SIMC 274.0812
320.6738
22.5
CHR
124.1946
211.2895
ZA 70.75993
149.6571
SIMC 140.9391
228.0648
27
CHR
129.8721
211.7776
ZA 99.09449
178.9191
SIMC 170.9055
245.9187
40.5
CHR
1228.188
668.8206
ZA 171.2032
243.3611
SIMC 1423.315
720.9027
45
CHR
57.54179
106.1665
ZA 51.49448
96.66933
SIMC 40.24258
85.69754
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 13, No. 2, June 20
15 : 547 – 55
5
554
Figure 3(i
)
. CHR tun
ed M
M
PI controlle
r’s
Reg
u
latory Resp
on
se for region 3
6
-4
5cm
Figure 4(a
)
.Servo Re
sp
on
se
s of CHR, ZA and
SIMC tuned
MMPI controll
ers fo
r re
gion
0-9cm
Figure 4(b
)
. Servo Re
sp
on
se
s of CHR,Z
A
and
SIMC tuned
MMPI controll
ers fo
r re
gion
18-
27cm
Figure 4(c).S
ervo Re
sp
on
se
s of CHR, ZA and
SIMC tuned
MMPI controll
ers fo
r re
gion
36-
45cm
Table 5. Co
m
pari
s
on of pe
rforman
c
e Indi
ce
s of regul
atory re
spo
n
se in different re
gion
s
Set Point
(c
m)
Tuning
Method
ISE IAE
4.5
CHR
5702.741
2598.228
ZA 5440.887
2574.304
SIMC 5134.143
2567.652
9
CHR
3029.299
1852.831
ZA 1979.908
1476.096
SIMC 2231.789
1553.274
22.5
CHR
2959.168
1942.761
ZA 885.3459
865.7407
SIMC 1414.623
1098.509
27
CHR
1156.216
1121.716
ZA 965.0554
998.3812
SIMC 1121.784
1055.477
40.5
CHR
1332.551
1013.717
ZA 3011.964
1270.751
SIMC 1056.572
1082.533
45
CHR
250.7785
456.9153
ZA 3289.437
1747.069
SIMC 107.6896
217.542
4. Conclusio
n
In this
study, a CHR, ZA
a
nd SIMC m
e
t
hod
s ba
se
d
MMPI Contro
ller
were de
si
gned fo
r
a SSTLLS proce
s
s. The m
odel i
dentifica
t
ion and MM
PI controlle
r desi
gn we
re
done u
s
ing a
n
NI-
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Experim
ental Validation of a Multi Model
PI
Controller
for a Non Li
near .... (M. Kalyan
C.)
555
DAQmx 621
1 data acqu
isition card
and La
bVIEW. Gra
phica
l prog
rammi
ng wa
s u
s
e
d
to
impleme
n
t the whol
e expe
riment. The
e
x
perime
n
tal
result
s eviden
tly prove that the influen
ce
of
set p
o
int
and
load
chan
ge
s a
r
e
smooth
for SIM
C
m
e
thod of
tunin
g
in
non
lin
e
a
r
regi
on
s. It
can
be also
see
n
that minimum oversh
oot, faster sett
lin
g time and rise time are o
b
tained. It has a
better capa
bil
i
ty of compe
n
satin
g
all the load
c
han
g
e
s. In the re
gion
s of lesser de
gre
e
of non
linearity ZA
m
e
thod
prove
s
to be
rel
a
tively effectiv
e for it provide
s
smaller value
s
of ISE,IAE and
all the time indices. The I
SE and IAE
values ju
stif
y that relatively a minimum erro
r is see
n
in
SIMC way of
tuning the
MMPI PI controller
tha
n
Z
A
and CHR
method
s for
both se
rvo a
n
d
regul
atory responses..It can be
concluded that SI
MC method based MMPI PI controller
can be
impleme
n
ted
in extreme n
on linea
r re
gi
ons o
n
re
al time SSTLLS usin
g NI-DA
Q
mx 6211 d
a
ta
acq
u
isitio
n module a
nd La
bVIEW in real
time.
Referen
ces
[1]
Bieg
ler LT
, Raw
l
in
gs JB. Optimizatio
n
appr
o
a
ches to no
nl
i
near mo
del pr
edictiv
e control
.
In chemic
al
process co
ntrol
,
CPCIV.
1991: 543-5
7
1
.
[2]
Kravaris C, Ar
kun Y. Geom
etri
c no
nli
n
e
a
r
control-A
n
Overvie
w
I
n
tern
ation
a
l j
our
nal
of che
m
ic
a
l
process co
ntrol
,
CPCIV.
1991: 477-5
1
5
.
[3]
Raich A, Wu
X, Cinar A.
A co
mp
arativ
e stud
y of neura
l
n
e
tw
orks and n
onl
ine
a
r time seri
es mod
e
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