TELKOM
NIKA
, Vol.14, No
.1, March 2
0
1
6
, pp. 162~1
7
0
ISSN: 1693-6
930,
accredited
A
by DIKTI, De
cree No: 58/DIK
T
I/Kep/2013
DOI
:
10.12928/TELKOMNIKA.v14i1.2746
162
Re
cei
v
ed O
c
t
ober 2
1
, 201
5; Revi
se
d Ja
nuar
y 19, 20
1
6
; Acce
pted
February 6, 2
016
Active Disturbance Rejection Control of Thermal Power
Unit Coordinated System Based on Frequency Domain
Analysis
Ruiqing Zha
ng*
1
,Liang
y
u
Ma
2
, Yongguang Ma
2
, Yang Liang
1
, Li
w
e
i Geng
1
1
Colle
ge of Me
chan
ical a
nd El
ectrical En
gin
e
e
rin
g
, Agricultu
r
al Univ
ersit
y
o
f
Hebei,
Baod
ing
071
00
1, Hebe
i, Chin
a
2
School of Co
n
t
rol and C
o
mp
uter Engi
ne
erin
g,
North Chi
na
Electric Po
w
e
r Univers
i
t
y
,
Baod
ing
071
00
3, Hebe
i, Chin
a
*Corres
p
o
ndi
n
g
author, em
ail
:
zhrqingc
n@1
26.com
A
b
st
r
a
ct
F
o
r the
multi-i
n
put a
n
d
multi-
o
u
t
put, strong-c
oup
lin
g
non
lin
e
a
r
featur
es of coord
i
nate
d
sy
stem
f
o
r
thermal p
o
w
e
r unit,
it is difficult
for traditio
nal PID co
ordi
nated c
ontro
l
sche
m
e to
me
et the pow
er gr
i
d
de
ma
nd w
h
ich
often partici
p
a
tes in p
eak r
egu
latio
n
a
nd
freque
ncy mo
dul
ation. In thi
s
pap
er, inver
s
e
Nyquist
array
is e
m
p
l
oye
d
t
o
carry o
u
t frequ
ency
do
ma
in a
nalys
is of
the
pla
n
t mod
e
l. T
hen
Pseu
do-
dia
gon
ali
z
a
t
io
n
is
used
to
de
sign
the st
atic
dec
oup
li
ng
co
mp
ens
ation
matrix of th
e sy
stem. A
bove
on
these, the l
i
n
e
a
r active
distu
r
banc
e rej
e
ctio
n contro
ller
ofevery ch
ann
el
in co
ordi
nate
d
system c
an
b
e
desi
gne
d rep
e
ctively.
Dyn
a
m
ic co
up
lin
g
and syst
e
m
unknow
n
p
a
r
t
s are obse
r
ved by
exten
d
e
d
state
observer
o
f ADRC
and is com
p
ens
ated to thesystem
i
n
ti
m
e
.
The simul
a
tion tests show
that
the
disturb
ance
re
j
e
ction
resu
lts
of t
he
lo
ad
a
n
d
the
ma
in
ste
a
m pr
essure
f
o
r the
co
ord
i
na
ted co
ntrol
sys
tem
und
er LADR
C i
s
better than th
at of PID control.
Ke
y
w
ords
:
thermal
pow
e
r
unitco
o
rdi
nate
d
syste
m
, li
near
active
disturb
ance
r
e
jecti
on c
ontr
o
ller
,
freque
ncyd
omain a
nalys
is, extende
d stat
e observ
e
r, pseu
dod
iag
o
n
a
li
z
a
t
i
on
Copy
right
©
2016 Un
ive
r
sita
s Ah
mad
Dah
l
an
. All rig
h
t
s r
ese
rved
.
1. Introduc
tion
With the i
n
creasi
ng d
e
ma
ndof po
we
r a
nd in
cr
ea
sing
ly close atte
ntion to e
n
vironment
peopl
e p
a
y, large
the
r
mal
po
we
r u
n
its have
be
com
e
the
main
u
n
its of
po
we
r gri
d
in
Chin
a
becau
se
of th
eirs hi
gh
efficiency, lo
w e
m
issi
on,
l
oad
re
gulating
se
nsitiv
e a
nd
other adva
n
tag
e
s.
Since the b
o
il
er in large th
ermal p
o
wer
unit o
ften em
ploys the on
ce-throug
h boil
e
r unit with
ou
t
a
drum, the tra
n
sition p
r
o
c
e
ss, whe
r
e wa
ter is evap
ora
t
ed to steam, is insta
n
t, and this ma
ke
s the
dynamic p
a
rameters of once
-
throug
h boiler u
n
i
t, such a
s
the unit load resp
onse quality, the
main ste
a
m
pre
s
sure, an
d other pa
ra
meters, pr
esent stronge
r
cou
p
ling
and stron
g
e
r
no
nl
inear
prop
ertie
s
[1-5], and these
make the u
n
itmore diffi
cult to be controlled. The
r
ef
ore, in ord
e
r
to
improve th
e
unit load
re
spon
se
spe
e
d
and
en
sure
the
main ste
a
m
pressu
re para
m
eter
m
o
re
stable; in
re
cent years it
is becoming
a
hot re
sea
r
ch
to maste
r
t
h
e
basi
c
cha
r
a
c
t
e
rist
ic
s of
la
r
g
e-
cap
a
cityt he
rmal po
we
r u
n
it, and to
re
sea
r
ch a
n
ad
vance
d
control strategy fo
r the
coo
r
di
n
a
ted
s
y
s
t
em of the unit [6-8].
The varia
b
le
param
eter
PID control
with
feed forward is
wide
spread
used
in boiler
turbine
coordinated control
system
of power plant, but in this strategy, more auxiliary link and
non-th
eo
retical skill
s com
p
onent
s are int
r
odu
ce
d into
the system, so that t
he controller st
ru
cture
is mo
re
comp
lex, tuning
pa
ramete
rs of
contro
lle
r
are
s
eriou
s
dep
en
dent o
n
exp
e
r
ien
c
e, a
nd t
he
strategy
is n
o
t ea
sy to
meet the
hig
h
pe
rf
orm
a
n
c
e
co
ntrol
re
quire
ment
s [
9
-10]. In
mo
dern
freque
ncy do
main theo
ry, the inverse
Nyquist
array (INA) me
thod for mult
ivariate anal
ysis
requi
re
s that
the sy
stem
ha
sonly the
diago
nal
d
o
minan
ce,
a
nd do
es not
need
a p
r
e
c
ise
mathemati
c
al
model for the controlled o
b
ject,
but also the pre
c
om
pen
sation a
r
ray optimized
by
the p
s
eud
o d
i
agon
alizatio
n
algo
rithm h
a
s
g
ood
de
co
upling
effect
to the sy
ste
m
, and th
us
has
been
re
sea
r
ched an
d ap
pl
iedto mult
ivariable sy
stem
of chemi
c
al,
aero
s
p
a
ce, p
o
we
r pla
n
t, and
other field
[1
1-12]. Th
e a
c
tive distu
r
ba
nce
reje
ction
cont
rol (A
DRC) a
s
simila
ting the soul
of
mode
rn cont
rol
theo
ry,
pionee
red by Professo
r Jin
gqing Ha
n,
is
a ne
w
mo
del-in
dep
end
ent
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Active
Distu
r
ban
ce Reje
ction Co
ntrol of Therm
a
l Power Unit Coo
r
d
i
nated… (Rui
qing Zha
n
g
)
163
controlle
r [1
3], which u
s
e the uni
qu
e ESO to
e
s
timate
the disturban
ce of
both
internal
uncertaintie
s
and
extern
a
l
distu
r
ba
nce
s
in
sy
stem, and
autom
a
t
ically compe
n
sate
s th
e t
o
tal
disturban
ce,
thus for no
nlin
ear, l
a
rg
e in
e
r
tia, un
ce
rtain
time-d
elay
complex
syste
m
s, thi
s
m
e
th
od
has b
e
tter control qu
ality [14-15]. But ADRC
woul
d be improv
ed and pe
rfe
c
ted for com
p
lex
indu
strial p
r
o
c
e
ss
appli
c
at
ions, a
nd e
s
peci
a
lly
the
nume
r
ou
s p
a
r
amete
r
s tuni
ng p
r
oble
m
s in
ADRC have
become a
fundame
n
tal
probl
em to
be solved in
pra
c
tical
ap
plicatio
n. Since
feedba
ck con
t
rol stru
cture of
Li
ne
ar ADRC p
r
op
osed
by Profe
s
so
r
Gao [1
6] em
p
l
oys lin
ea
r fo
rm,
and it not onl
y make
s the theoretical
an
alysis of
A
D
RC furthe
r dev
elopme
n
t [17
-
19], but al
so
its
para
m
eters t
uning i
s
grea
tly simplified, and ea
sy to be u
s
ed in
pra
c
tice. A large
numb
e
r of
applie
d
re
se
a
r
ch
es have shown
t
hat LA
DRC ha
s a
strong a
b
ility to cont
rol
co
mplex nonli
n
ea
r
uncertain o
b
j
e
cts.
Inthis p
ape
r, aiming
60
0
M
W
su
percri
t
ical o
n
ce-th
r
ough
boile
r
unit, INA m
e
thod i
s
employed to
carry on the
system fre
q
u
ency dom
ain
analysi
s
, pse
udodi
agon
ali
z
ation met
h
o
d
is
use
d
to
con
d
u
ct the
pre-compen
satio
n
static
de
coup
ling de
sig
n
fo
r the
system,
and th
e mo
d
e
l
unkno
wn pa
rt
s of the sy
ste
m
and dyna
m
i
c distu
r
b
a
n
c
es a
r
e ob
se
rv
ed by ESO of ADRC, and
a
t
the sam
e
time the ob
serve
d
value is
co
mpen
sat
ed to
the system i
n
time. The si
mulation resu
lts
sho
w
the effe
ctivene
ss of the pro
p
o
s
ed
control strate
gy.
2. D
y
namic
Char
actertic
s
of Objec
t
Model
Coo
r
din
a
ted
system
of the on
ce-th
r
o
u
gh boil
e
r u
n
it is a
com
p
licated large
system. In
gene
ral, the
system
can b
e
see
n
a
s
a three
-
in
put
an
d three
-
outp
u
t
structu
r
e. Its input vari
ab
les
inclu
de the a
m
ount of fuel
B
, the main steam valve opening
μ
%
and feed water
W
, and
the
corre
s
p
ondin
g
outp
u
t vari
able
s
contai
n
main
ste
a
m
pressu
re
Pt
, the
real
unit
po
we
r
Ne
, an
d
interme
d
iate point’s enthal
py
H
. When t
he feed
wate
r of the
syste
m
in a
c
corda
n
ce
with
ce
rtain
coal
-water
ra
tio is adj
uste
d, the syste
m
can
be
si
mplified to a
two-in
put two-outp
u
t syst
em
sho
w
n in Fig
u
re 1. Since
there is a
strong cr
o
s
s-co
upling bet
we
en the variab
les, the syste
m
also po
se
s
nonlin
ear a
n
d
time-varyin
g
cha
r
a
c
teri
stics, and thu
s
the stabilit
y margin of the
system i
s
re
duced. It is difficult to achieve
goo
d control effe
ct throug
h u
s
in
g a singl
e lo
op
control.
Figure 1. The
simplified inp
u
ts and o
u
tpu
t
s of the power unit
In this pa
per,
the
plant
we di
scusse
d i
s
a
coo
r
din
a
ted cont
rol sy
stem of
the
600M
W
sup
e
rcriti
cal t
herm
a
l po
we
r unit
s
in
He
nan p
r
ovin
ce.
Its turbi
ne p
r
odu
ced
by Dongfan
g turbi
ne
factory with
signal shaft, three
cylinder four
exhaust, double back-press
ures, pure condensing
steam tu
rbin
e
,
use
s
a
com
p
lex ope
ratio
n
model
s
with variabl
e pressure; it has an intermedi
ate
rehe
at, and
i
s
in
supe
rcri
tical
con
d
itio
ns. T
he
boil
e
r m
ade
by
Don
g
fang
bo
iler fa
ctory i
s
a
supercriti
cal variable
parameters
facility. The rated
power
of uni
t
s
i
s
600M
W, and the obj
e
ct
pre
s
sure befo
r
e the turbi
n
e
is 24.1MPa.
The
experim
ental pl
atform is the Sta
r-9
0
system
develop
ed b
y
No
rth Chin
a
Ele
c
tric
Powe
r Unive
r
sity with the full scope si
m
u
lation abo
ut all kind
s of electri
c
po
we
r units. Base
d on
the Star-9
0
simulatio
n
sy
stem, the st
ep re
sp
on
se
data can b
e
acquired t
h
rou
gh m
a
tlab
comm
uni
cati
ng pro
g
ra
m with the sim
u
lator,
and the desi
gnin
g
model of 600MW supe
rcritical
unit at 10
0%
load i
s
e
s
tabl
ishe
d with
th
e improv
ed
g
enetic
algo
rit
h
m. The t
r
an
sfer fu
nctio
n
s of
the coo
r
din
a
ted syste
m
are followin
g
.
6.66
(
4
9
.
3
1
)
11
(
5
6.7
1
)(
24
7.1
1
)
1
23.5
1
ss
g
ss
s
(
1
)
Evaluation Warning : The document was created with Spire.PDF for Python.
ISSN: 16
93-6
930
TELKOM
NIKA
Vol. 14, No. 1, March 2
016 : 162 – 1
7
0
164
1.42
93
(
2
72
.5
1
)
12
(
1
7
5
.9
1
)
(
1
26
.3
1
)
10
1
s
g
ss
s
(
2
)
0.60
73
21
(
32.
7
1
)
1
41.
5
1
g
ss
(
3
)
0.72
82(
8
4
.9
1
)
22
(
201
.3
1
)
(
9
4.66
1
)
283
.6
1
s
g
ss
s
(
4
)
3. Frequen
c
y
Domain Analy
s
is of Coordinated Sy
stem
As
we all
kno
w
, a
pre
c
i
s
e
mathemati
c
al
model
is req
u
ired
to the
controlle
d o
b
je
ct in th
e
state
spa
c
e
t
heory, th
e d
e
s
ign
ed
co
ntro
ller
stru
ctu
r
e
for multiva
r
ia
ble
system
is quite
co
mple
x,
so that it is di
fficult to appl
y. In engineering,
frequ
en
cy domain an
a
l
ysis is
a com
m
only metho
d
s
of de
sign
an
d integ
r
ation
for
cont
rol
system. But coordi
nated
system is a
multiple-i
nput
san
d
multiple-outputs coupling system,the
Nyquist
m
e
th
o
d
often
ap
plied to
an
alysi
s
a
n
d
optimi
z
ed
desi
gn a
si
ng
le varia
b
le, h
a
s
no lo
nge
r any me
anin
g
[11]. In this se
ction,
we
use
the inve
rse
Nyqui
st array (INA) to co
n
duct thefrequ
ency
dom
ain
analysi
s
, and
adopt p
s
eu
do
diagon
alizati
on
to develop a
decouplin
g d
e
sig
n
for the above sy
ste
m
.
3.1. Multiv
ariable Con
t
rol Sy
stem Arch
itecture and
Freque
nc
y
Domain Analy
s
is
Stability is one of the most
important indexes
for cont
rol
sy
stem desi
gn. For
si
ngle-input
singl
e-o
u
tput
(SISO) sy
stem, the
ch
aracteri
stic root
s
su
rro
und
ed
by
(-1, j
0
) in a
clo
s
e
d
l
oop
system
can
determine the
distributi
on
of its
stability. But this
method isnot
suitabl
e for multi-i
n
put
and m
u
lti-out
put (MIMO
)
system, the
stability ident
ification
of m
u
ltivariable
system is jud
ged
throug
h the
prop
ertie
s
of
return difference det
e
r
mi
nant of the
system.
Multi
v
ariable syst
em
diagram is
sh
own in Fig
u
re
2.
Figure 2. Dia
g
ram of multi
v
ariable
cont
rol system
Whe
r
e,
G
(
s
) presents t
he co
ntrolle
d system
s, Kcp(
s
)
can
be se
en as a pre-
comp
en
sat
o
r,
Kc
(s
) is
dynamic corr
ector
,
H
(
s
) i
s
calle
d the f
eedb
ack g
a
i
n
matrix,
Q
(
s
)
rep
r
e
s
ent
s the system forward ch
ann
el
matrix, t
hen
the transfe
r functio
n
matri
x
of
the closed-
loop sy
stem can be written as:
1
()
(
)
()
c
GI
Q
s
H
s
Q
s
(5)
In which,
|
D
(
s
) |=|
I
+
Q
(
s
)
H
(
s
)
|
(
6
)
The above e
q
uation (6
) is
called the retu
rn
differen
c
e d
e
termin
ant of the system.
Based o
n
the
inverse
Nyq
u
ist array
(INA)of return difference matrix
D(s
)
, engin
eerin
gs
often use Ge
rsh
g
o
r
in theo
rem to get the circumfe
re
nce n
u
mbe
r
, whi
c
h is surround
ed with
the
points
(0, j0
)
by Gersh
gori
n
ci
rcl
e
s, a
n
d
then o
b
serv
e wh
ethe
r
D
(
s
) i
s
di
ago
nal
domin
an
ce,
and
finally they can judge the
stability of the system.
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Active
Distu
r
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ce Reje
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ntrol of Therm
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r
d
i
nated… (Rui
qing Zha
n
g
)
165
The inve
rse
Nyqui
st array
method
doe
s not
re
q
u
ire
the syste
m
completely d
e
c
ou
pled,
as long a
s
th
e comp
en
sat
ed system h
a
s diag
onal
domina
n
ce, whi
c
h ma
ke
s controll
er de
sign
become ea
sy
.
Whe
n
the nu
mber of in
put
variable
s
is
t
he sam
e
as the numbe
r
of output in system,
assume
d the numbe
r of input variable a
s
the q-th, at j
ω
0 point, thus INA for the system tra
n
sf
er
function mat
r
i
x
is expresse
d as a compl
e
x numbe
r.
0
()
,
,
1
,
,
ik
i
k
ik
g
jj
i
k
q
(7)
For the value
s
of m (m = 1,
..., q), we ca
n obtain a ma
trix Am.
In which,
,
∑
,
,
,
1
,
⋯
,
(
8
)
Eigenvalue
s
and eig
enve
c
tors of the m
a
trix Am
are comp
uted. T
he eige
nvect
o
rs
of the
minimum eig
envalue
s con
s
titute a colu
mn vector of
km, and the
n
throug
h all o
f
the m values;
finally we obt
ain the small
e
st
feature vectors, whi
c
h
constitu
te the
c
o
mpens
a
tion matrix
Kc
p
.
Appling ab
ove the method
, in the frequency
ω
= 0, we ca
n get the pre
c
om
pe
nsate
d
array of
Kc
p
for a boile
r-tu
r
bine
co
ordi
n
a
tion syste
m
.
Gershg
orin
band di
ag
ra
m of the syst
em
after com
pen
sated a
r
e carried out.
3.2. Diagona
lly
Dominant Analy
s
is of
th
e Super
c
ri
tical Unit
Co
ordinated Sy
stem
Diag
onal do
minan
ce ofcoordi
nation system
ab
out
600M
W
sup
e
rcritical on
ce-throug
h
boiler u
n
it at 100% load i
s
analyzed sho
w
n in Figu
re
3.
Figure 3. Dia
gonal d
o
mina
nce a
nalysi
s
of coordinate
d
system a
b
o
u
t 600M
W
From th
e ab
ove ch
art, we ca
n seetha
t, g
11
and g
22
in the sy
stem
have surrou
nded t
h
e
origin, so that they are non-diag
onal
dominan
ce
and their variable
s
have seri
ou
s co
upl
ing,
De
cou
p
ling n
e
tworks wo
ul
d need to be
develop
ed in
orde
r to de
sig
n
their own controlle
r.
De
cou
p
ling d
e
sig
n
of 600
MW supe
rcrit
i
ca
l on
ce
-through b
o
iler
unit at 100%
load is
sho
w
n in Fig
u
re 4. The fi
gure
sho
w
s, Gersh
w
in Go
ering
circle
s
of g11 and g
22 all have
no
longe
r su
rrou
ndedth
e
origi
n
, the system
hasal
re
a
d
y a diago
nal d
o
minan
ce, so
the system
has
achi
eved a st
atic de
cou
p
lin
g, the deco
u
p
ling matrix is
Kc
p
= [-0.0
1
1
6
-0.999
9; -0.
9951 0.0
992].
From
the abo
ve
cha
r
ts we can se
e
that the
ope
n-lo
o
p
tran
sfer fu
n
c
tion mat
r
ix o
f
boiler-
turbine
coo
r
d
i
nated syste
m
has be
co
me diago
nal
domina
n
ce matrix, thus in the next sect
ion,
we will devel
op
two subsy
s
tem
s
controll
ers
by usi
ng ADRC respectively
ac
cording to the design
method of the
single
-
loo
p
controlle
r.
-
100
-5
0
0
50
100
-
100
-5
0
0
50
100
-
5000
0
5000
10
000
-
300
-
200
-
100
0
-2
-1
0
1
0
20
40
60
-
150
-
100
-5
0
0
50
-
100
-5
0
0
50
100
g
22
g
21
g
12
g
11
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166
Figure 4. Pre
c
omp
e
n
s
ated
deco
upling
d
e
sig
n
of coo
r
dinated
syste
m
about 600
MW
4. AD
RC
Des
i
gn for Supe
rcritical
Uni
t
Coordin
a
te
d
Sy
stem
Coo
r
din
a
ted
system
can
be divided i
n
to two pa
rts,
turbine
and
boiler. Ea
ch
part is
a
compl
e
x high
-order n
onlin
ear sy
stem, and it is ve
ry difficult to
establi
s
h its
accurate mo
del.
While A
D
RC doe
s not de
mand to
kno
w
the
syst
e
m
model, we
use the
se
cond o
r
de
r lin
ear
ADRC (LA
D
RC) to de
sign t
he turbin
e co
ntrolle
r and th
e boiler
cont
roller.
4.1. The Stru
cture o
f
LADRC
LADRC controller st
ru
cture
is sho
w
n in F
i
gure 5.
Figure 5. LADRC cont
roll
er st
r
u
ct
u
r
e
In gen
eral,
when th
e
controller i
s
de
sig
ned, the
pa
rt
whi
c
h i
s
high
er tha
n
the
th
ird-ord
e
r
(incl
udin
g
thi
r
d-o
r
de
r) in th
e obj
ect
ca
n
be
see
n
a
s
u
n
ce
rtain pa
rt of
t
he
dy
n
a
mi
c sy
st
em,
so
t
h
e
system
can b
e
simplified a
s
the followi
n
g
form:
0
(,
,
)
y
fy
y
w
b
u
(9)
Whe
r
e,
u
i
s
the
system
input,
y
i
s
the sy
stem
output,
w
i
s
the
system
un
kno
w
n
disturban
ce,
f
represents the system
to
tal disturb
a
n
c
e,
b
0
is the controlle
r gain
,
and the state
equatio
n of the system
can
be expre
s
se
d as the follo
wing:
12
23
0
3
1
xx
x
xb
u
xh
yx
(10
)
-1
0
1
2
-6
0
-4
0
-2
0
0
20
-6
-4
-2
0
2
-1
0
1
2
3
-0
.
8
-0
.
6
-0
.
4
-0
.
2
0
0
0.
2
0.
4
0.
6
0.
8
-
10000
-5
0
0
0
0
5
000
0
100
200
300
z3
z2
z1
1
u1
S
c
ope
2
x
'
= A
x
+B
u
y
= C
x
+D
u
LESO
1
1/
b0
1
Gai
n
2
kd
_
1
Ga
i
n
1
kp
_
1
Ga
i
n
A
dd3
Add
1
Ad
d
2
r1
1
y1
g
22
g
21
g
11
g
12
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TELKOM
NIKA
ISSN:
1693-6
930
Active
Distu
r
ban
ce Reje
ction Co
ntrol of Therm
a
l Power Unit Coo
r
d
i
nated… (Rui
qing Zha
n
g
)
167
Whe
r
e
x
1
,
x
2
,
x
3
rep
r
e
s
ent
s the system state variable
s
，
and
h
LESO is the
extended
sta
t
e ob
se
rver
of
LADRC. T
he in
puts of
the ob
se
rver incl
ude
output u of
the co
ntrolle
r and o
u
tput
y of t
he system. The
outputs
of the ob
se
rver are
z
=[
z
1
,
z
2
,
z
3
]
T
, where
z
3
is t
he expan
sio
n
of the state, rep
r
e
s
ent
s the sy
stem to
tal disturban
ce,
whi
c
h i
n
cl
ud
es th
e
syst
em of
external di
st
urba
nce
s
and
u
n
ce
rtainty wi
thin the
system
disturban
ce
s.
Match the ri
g
h
t obse
r
ver g
a
in, so that e
a
ch o
b
serve
r
ed valueof L
ESO can tra
ck e
a
ch
state of the system, i.e.
→
,
→
,
→
,
,
. z
3
just dynami
c
ally estim
a
te
s value
f
. The
coeffici
ent matrix of the observe
r can be
written re
sp
e
c
tively.
11
0
20
1
300
A
，
01
02
03
Bb
，
10
0
01
0
00
1
C
，
00
00
00
D
(11
)
Assu
ming
all
the pole
s
of t
he ob
se
rver
are a
r
rang
ed
with
ω
0
, the chara
c
te
risti
c
equatio
n
for LESO is
following.
3
32
12
3
0
||
sI
A
s
s
s
s
(12
)
So we ca
n ob
tain the following relate
d eq
uation
s
,
23
10
2
0
3
0
3,
3
,
(13
)
Whe
r
e
ω
0
is
calle
d the ob
serve
r
ba
nd
width and it is the only nee
d
tuning pa
ra
meters in
LESO.
If the variable
u
is sele
cted
as the follo
wi
ng,
0
0
(,
,
)
f
yy
w
u
u
b
(14
)
Then, the no
nlinea
r syste
m
will becom
e an
integral seri
es type sy
stem, namely
.
y
,
,
̂
(
1
5
)
So we
can
u
s
e the
"linea
r
state erro
r fee
dba
ck
(LSEF)" lawto
de
sig
n
the
ideal
co
ntrolle
r.
State feedba
ck
cont
rol law can be d
e
si
g
ned the follo
wing.
(
1
6
)
Whe
r
e,
v
i
s
the set value.
Thus th
e clo
s
ed-lo
op tra
n
sf
er functio
n
is
descri
bed a
s
followin
g
.
1
2
()
p
c
dp
k
Gs
s
ks
k
(17
)
To
simplify the p
a
ra
mete
rs in th
e
con
t
roller to b
e
tuning, a
n
d
ω
c
is
a
s
s
u
me
d a
s
the
band
width
of
the
co
ntrolle
r, so the
cha
r
acte
ri
stic
pol
ynomial of
th
e controller repre
s
e
n
ts a
s
a
function of
ω
c
, i.e:
2
2
dp
c
sk
s
k
s
(18
)
W
h
er
e
k
p
=
ω
c
2
，
k
d
=2
ω
c
，
th
en
ω
c
is the
only ne
ed tu
n
i
ng p
a
ra
mete
rs in li
nea
r
state e
rro
r
feedba
ck (LS
E
F).
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016 : 162 – 1
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168
4.2. The desi
gn of ADRC
controller of Coordina
te
d Sy
stem
Based
on p
s
eu
do dia
g
o
nal de
cou
p
li
ng co
mpe
n
sation, adrc
controlle
r of above
c
o
ordinated sys
tem
is
built in
s
i
mulink
of matlab
environment.In order to
c
o
mpare the
c
ontrolled
result, PID controlle
rof th
e co
ordi
nate
d
syste
m
is
setcomm
only. The two cont
rolle
rs
abo
ut the
controlled
system are sho
w
n in Figure 6. In whic
h, the
adrc co
ntroll
er of
the co
ordinated
syste
m
are in the up
e
r
blue dotted
box, and the PID contro
ller of the plant is in the lower pink box.
Figur
e 6. The
control
sy
ste
m
diagr
ams o
f
LADRC a
n
d
PID
4.3. ADRC Si
mulation Experiment for Coordin
a
te
d
Sy
stem
For a
600M
W sup
e
rcriti
cal
unit co
ordi
nat
ed sy
stem at
100% loa
d
, lo
ad di
sturb
a
n
c
e and
the main ste
a
m pre
s
sure
disturb
a
n
c
e
exper
iment
s are ca
rri
ed
out under
LADRC an
d
PID
control respectively.
In whic
h, ADRC
contr
o
lle
r para
m
eter
s a
r
e:
01
1
0
1
1
.
89
,
0
.018
,
0
.0
023
3
c
b
,
02
2
0
2
0.31
,
0
.029
,
0
.00
019
c
b
PID controller param
eters are:
11
0.625
,
70.1
pi
KT
,
21
2
.
2
751
,
8
50
pi
KT
The
comp
ari
s
on
s of
syst
em ste
p
re
sp
onse cu
rve
s
for loa
d
di
stu
r
ban
ce
are shown in
Figure 7.
Evaluation Warning : The document was created with Spire.PDF for Python.
TELKOM
NIKA
ISSN:
1693-6
930
Active
Distu
r
ban
ce Reje
ction Co
ntrol of Therm
a
l Power Unit Coo
r
d
i
nated… (Rui
qing Zha
n
g
)
169
Figure 7. Co
mpari
s
o
n
s of
system
step resp
on
se curv
es un
der LA
DRC a
nd PID
In Figu
re 7, l
oad
step
distu
r
ban
ce
expe
ri
mentis
co
ndu
cted at
50
s. The
figu
re (a
)
is
lo
ad
respon
se
curve, and figu
re
(b
) is the m
a
in ste
a
m p
r
e
s
sure
re
spon
se curve. T
he
blue h
eavy li
ne
in the
figures is und
er the
co
ntrol
of L
A
DRC
re
spo
n
se
curve, th
e em
ergi
ng
g
r
een
line
i
s
PID
control u
nde
r the
re
spon
se curve,
and
the
red
da
shed li
ne i
s
t
he ta
rget
of
the sy
stem.
The
figure
s
sho
w
that
theplant is
can be see
n
as
a
singl
e
variabl
e afte
r the p
s
e
udo
diago
nalizatio
n
and de
co
uple
d
by ADR
C
, and the effect of LADRC
c
ontrol i
s
much better than
the effect of the
PID.
The comp
ari
s
on
s of
syst
em step
re
spon
se
c
u
r
v
es
fo
r
th
e
ma
in
s
t
ea
m pr
e
s
s
u
r
e
disturban
ce
are sho
w
n in Fi
gure 8.
Figure 8. Main steam p
r
e
s
sure
step di
st
urba
nce expe
riment
In Figure 8, the step di
stu
r
ban
ce exp
e
riment
of the main stea
m pre
s
sure is condu
cte
d
at 50s. Th
e figure
(a
) is l
oad respon
se cu
rve,
and
the figure
(b
) is the m
a
in
steam p
r
e
ssure
respon
se
cu
rve. The blue
heavy line in the fi
gure
s
is unde
r the
control of L
A
DRC re
sp
o
n
se
curve, the em
ergin
g
green l
i
ne is PID co
ntrol und
er th
e re
spon
se
curve, and the
red da
sh
ed li
ne
is the
targ
et
of the
system
. The figu
re
s
sho
w
th
at
th
e p
l
a
n
t
is
c
a
n
b
e
s
e
en
as
a s
i
ng
le
var
i
a
b
le
after the p
s
e
udo dia
gon
ali
z
ation
and d
e
co
uple
d
by
ADRC, and t
he effect of L
A
DRC contro
l is
much b
e
tter than the effect
of the PID.
As we
can
se
e from
the fig
u
re
8, the
re
s
pond
index
of load
andm
ain
steam
p
r
e
s
sure
with
LADRCs is o
b
viously supe
rior to that ofPID.
5. Conclusio
n
In this pap
e
r
, for co
ordi
nated sy
ste
m
of a sup
e
rcritical on
ce-throug
h bo
iler unit,
freque
ncy do
main analy
s
i
s
is pe
rform
e
d, steady
co
mpen
sation
matrix is de
si
gned, an
d ADRC
0
20
0
40
0
60
0
800
1
000
1
200
140
0
160
0
18
00
2
000
0
0.
5
1
1.
5
0
20
0
40
0
60
0
800
1
000
1
200
140
0
160
0
18
00
2
000
0
0.
1
0.
2
0.
3
0.
4
0
200
400
600
800
1000
1200
1400
1600
1800
2000
-2
.
5
-2
-1
.
5
-1
-0
.
5
0
0.5
(
a
)
T
i
m
e
s
Loa
d R
e
s
p
o
n
s
e
0
200
400
600
800
1000
1200
1400
1600
1800
2000
0
0.2
0.4
0.6
0.8
1
1.2
1.4
(
b
)
T
i
m
e
s
P
r
es
s
u
r
e
R
e
s
pon
s
e
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016 : 162 – 1
7
0
170
control
strate
gy of coo
r
din
a
ted b
o
iler-tu
rbine
sy
stem
is e
s
tabli
s
h
e
d
.
Steady state
de
cou
p
ling
a
n
d
dynamic com
pen
sation co
ntrol
of
the system a
r
e realized. Loa
d step di
sturban
ce test
s
are
carrie
d out u
nder PI
D co
n
t
rol strategy
and LA
DRCs
control st
rat
egy re
spe
c
tively. The re
su
lts
sho
w
th
at th
e re
sp
on
se
curve
cont
rolle
d by LA
DRCsis si
gnificant
ly better tha
n
thatof the PI
D
controlle
r. Th
is st
rategy
combine
d
the
frequ
en
cy d
o
main
analy
s
is with
di
sturban
ce
reje
cti
o
n
control te
chn
o
logy to the
coo
r
din
a
ted
system
i
n
th
ermal
po
we
r
units, is a n
e
w b
o
ile
r-tu
r
bine
coo
r
din
a
tion
control sch
e
m
e, and its
controlle
r
can
be de
sign
ed
quickly and
e
fficiently, and has
less tuning p
a
ram
e
ters, is
easy to be ap
plied in engi
n
eerin
g.
Ackn
o
w
l
e
dg
ements
This work wa
s su
ppo
rted b
y
NSF6117
41
11.
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