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Ro
bu
st C
on
tro
l S
yst
ems
Res
earc
h
wit
h A
pp
lica
tio
ns
1
Prof. Rama K. Yedavalli
Dep
artm
ent
of
Aer
osp
ace
Engin
eeri
ng
The
Ohio
Sta
te U
niv
ersi
ty
Colu
mb
us,
OH
Ap
ril
27, 2010
TH
AN
KS
TO
FE
RM
I-LA
BS
FO
R T
HE
INV
ITA
TIO
N A
ND
HO
SP
ITA
LIT
Y
In p
art
icu
lar
to D
r. A
see
t M
uk
he
rje
e a
nd
Dr.
In
pa
rtic
ula
r to
Dr.
Ase
et
Mu
kh
erj
ee
an
d D
r.
Ste
ve H
olm
es
2
•In
tro
du
ctio
na
nd
Pe
rsp
ect
ive
on
Co
ntr
olSys
tem
sF
ield
•U
nce
rta
inty
an
dR
ob
ust
ne
ss:
Tim
eD
om
ain
Sta
teS
pa
cea
nd
Fre
qu
en
cyD
om
ain
Tra
nsf
er
Fu
nct
ion
Vie
wp
oin
ts
•R
ob
ust
Co
ntr
olD
esi
gn
Me
tho
ds
wit
hA
pp
lica
tio
ns
•O
verv
iew
of
OS
UR
ob
ust
Co
ntr
olG
rou
pR
ese
arc
h
•Fa
ult
Dia
gn
ost
ics
an
dC
on
tro
lD
esi
gn
for
Fau
ltTo
lera
nce
Outline
3
•Fa
ult
Dia
gn
ost
ics
an
dC
on
tro
lD
esi
gn
for
Fau
ltTo
lera
nce
•D
istr
ibu
ted
Co
ntr
olw
ith
Co
mm
un
ica
tio
nC
on
stra
ints
•C
on
tro
lo
fS
up
erc
on
du
ctin
gC
avit
ies:
Re
leva
nce
an
dA
pp
lica
bil
ity
of
ou
rre
sea
rch
•C
on
clu
sio
ns
an
dF
utu
reR
ese
arc
h
•P
oss
ible
Ave
nu
es
of
Re
sea
rch
Co
lla
bo
rati
on
wit
hFe
rmiL
ab
s
Co
ntr
ol
Sy
ste
m
Fre
qu
en
cy D
om
ain
Introduction and Perspective
4
Tim
e D
om
ain
Sta
te
Sp
ace
Re
pre
sen
tati
on
Fre
qu
en
cy D
om
ain
Tra
nsf
er
Fu
nct
ion
Re
pre
sen
tati
on
Co
ntr
ol
Sy
ste
ms
Control Systems Modeling
5
Co
nti
nu
ou
s T
ime
Sy
ste
ms
Dis
cre
te T
ime
Sy
ste
ms
Sa
mp
led
Da
ta
Sy
ste
ms
Dif
fere
nti
al
eq
ua
tio
ns
Dif
fere
nce
eq
ua
tio
ns
No
nli
ne
ar
Sy
ste
m
Mo
de
l
Lin
ea
r S
yst
em
Mo
de
l
Lin
ea
riza
tio
n
Standard Controller Design
Methodologies
6
Fre
qu
en
cy D
om
ain
Ap
pro
ach
Tim
e D
om
ain
Sta
te
Sp
ace
Ap
pro
ach
PID
Co
ntr
oll
ers
Lea
d L
ag
Ne
two
rks E
ige
nst
ruct
ure
Ass
ign
me
nt
Op
tim
al
Co
ntr
ol
Me
tho
ds
(LQ
R)
Un
cert
ain
ty:
Ine
vit
ab
le i
n r
ea
l li
fe p
rob
lem
s
Acc
om
mo
da
tin
g u
nce
rta
inty
is i
mp
ort
an
t
Ro
bu
stn
ess
: A
ne
cess
ary
fe
atu
re i
n A
na
lysi
s a
nd
De
sig
n o
f
Uncertainty and Robustness
in Control Systems
7
Ro
bu
stn
ess
: A
ne
cess
ary
fe
atu
re i
n A
na
lysi
s a
nd
De
sig
n o
f
fee
db
ack
Co
ntr
ol Sys
tem
s
Ma
in t
he
me
of
ou
r re
sea
rch
PE
RT
UR
BA
TIO
N O
R M
OD
ELI
NG
ER
RO
RS
Re
al
Pa
ram
ete
r N
eg
lect
ed
Uncertainty Characterization
8
Re
al
Pa
ram
ete
r
Va
ria
tio
ns
Un
mo
de
led
Dy
na
mic
s
Ne
gle
cte
d
No
nli
ne
ari
tie
s
Ne
gle
cte
d
Ext
ern
al
Dis
turb
an
ces
Re
al P
ara
me
ter
Va
ria
tio
ns
•
Tim
e D
om
ain
(Sta
te S
pa
ce)
Ma
trix
Fre
qu
en
cy D
om
ain
(Tra
nsf
er
Fu
nct
ion
)
Po
lyn
om
ial
Uncertainty Characterization
9
)(
)(
)(
)(
0
sr
sG
sG
sG
<∆
∆+
Ma
trix
Va
ria
tio
ns
Po
lyn
om
ial
Va
ria
tio
ns
Un
mo
de
led
Dy
na
mic
s•
Tim
e D
om
ain
??
?
??
?
Fre
qu
en
cy D
om
ain
Tim
e D
om
ain
(Sta
te S
pa
ce)
A+
E
Fre
qu
en
cy D
om
ain
||
ΔG
(jω
)||
< r
(jω
)|
Multiplicative
ΔG
(s)
+
Unstructured Uncertainty
(Norm Bounded)
10
A0
+ E
||
E|
| <
rG
0(s
)
G(s)
= G
0(s) [I +
∆G(s) ]
+
Additive
ΔG
(s)
G0(s
)+
G(s)
= G
0(s)
+ ∆
G(s)
qE
A+⇓
0)
(
Tim
e D
om
ain
(Sta
te S
pa
ce)
Fre
qu
en
cy D
om
ain
(Tra
nsf
er
Fu
nct
ion
)
Δ1
Δ2
…
(1)
Structured Uncertainty
Re
al S
tru
ctu
red
Un
cert
ain
ty
11
i
r iii
ii
Eq
A
q
qE
A
∑=
+
⇓
<<+
10
0)
(…
Δn
(2)
K
Complex Structured Uncertainty
P(s
, q)=
N(s
, q)/
D(s
, q)
Real Structured Uncertainty
qE
A+⇓
)(
Tim
e D
om
ain
(Sta
te S
pa
ce)
E(t)
Time varying uncertainty
Lya
pu
no
vM
atr
ix
Th
eo
ry A
pp
roa
ch
Structured Uncertainty
Re
al S
tru
ctu
red
Un
cert
ain
ty
12
i
r iii
ii
Eq
A
q
qE
A
∑=
+
⇓
<<+
10
0)
(
E=constant
Time invariant uncertainty
Th
eo
ry A
pp
roa
ch
Kro
ne
cke
rM
atr
ix T
he
ory
Ap
pro
ach
STABILITY (Fundamental)
Stability Robustness
Op
en
Le
ft H
alf
Pla
ne
System Specifications
13
PERFORMANCE
Performance Robustness
Tra
nsi
en
t R
esp
on
se
Ste
ad
y S
tate
Re
spo
nse
Tra
ckin
g &
Re
gu
lati
on
Dis
turb
an
ce R
eje
ctio
nD
-sta
bil
ity
an
d
Eig
en
stru
ctu
re
Ass
ign
me
nt
Ap
pro
ach
U
nce
rta
inty
Ca
teg
ory
C
on
trib
uto
rs
(1)
µ-S
yn
the
sis
(Str
uct
ure
d S
ing
ula
r
Va
lue
, M
ult
iva
ria
ble
Sta
bil
ity
reg
ion
s)
Str
uct
ure
d a
nd
Un
stru
ctu
red
(Fre
qu
en
cy d
om
ain
)
Tit
s, S
afo
no
va
nd
Co
lle
ag
ue
s
(2)
Qu
an
tita
tive
fe
ed
ba
ck C
on
tro
lS
tru
ctu
red
fre
qu
en
cy
Ho
row
itz,
Nw
oka
h,
Wie
Major Approaches
14
(2)
Qu
an
tita
tive
fe
ed
ba
ck C
on
tro
lS
tru
ctu
red
fre
qu
en
cy
Do
ma
in
Ho
row
itz,
Nw
oka
h,
Wie
an
d C
oll
ea
gu
es
(3)
Th
eo
ry
(LQ
G/L
QR
)U
nst
ruct
ure
d
Fre
qu
en
cy D
om
ain
Ath
an
s, S
tein
,
Be
rnst
ein
, H
ad
da
d,
an
d C
oll
ea
gu
es
2H
Ap
pro
ach
U
nce
rta
inty
Ca
teg
ory
C
on
trib
uto
rs
(4)
H2/
H∞
H-i
nf
Th
eo
ryU
nst
ruct
ure
d F
req
ue
ncy
do
ma
in
Za
me
s, G
love
r, F
ran
cis,
Ten
ne
nb
au
ma
nd
Co
lle
ag
ue
s
(5)
Kh
ari
ton
ov
ba
sed
Po
lyn
om
ial
me
tho
ds
Str
uct
ure
d,
rea
l
Pa
ram
ete
r Tr
an
sfe
r
Fu
nct
ion
ba
sed
Kh
ari
ton
ov,
Ba
rmis
h,
Bh
att
ach
ary
a,
Ace
rma
nn
,
Bo
se a
nd
Co
lle
ag
ue
s
Major Approaches
15
Fu
nct
ion
ba
sed
Bo
se a
nd
Co
lle
ag
ue
s
(6)
Lya
pu
no
v K
ron
eck
er
ba
sed
Ma
trix
Me
tho
ds
Str
uct
ure
d,
rea
l
Pa
ram
ete
r, T
ime
do
ma
in
Yed
ava
lli,
Qiu
&D
av
iso
n,
Jua
ng
, H
inq
ich
&
Rit
cha
rd,
Ba
rmis
ha
nd
Co
lle
ag
ue
s
(7)
Mix
ed
H2/
H∞
Th
eo
ry
Co
mb
ine
d U
nce
rta
inty
,
Sta
te S
pa
ce
Be
rnst
ein
& H
ad
da
d,
Ba
nd
a,
Kh
arg
on
eka
r, a
nd
Co
lle
ag
ue
s
Ma
ny
con
trib
uti
on
sb
yo
the
rre
sea
rch
ers
are
cove
red
inva
rio
us
bo
oks
an
dm
on
og
rap
hs:
On
ere
leva
nt
an
du
sefu
lre
fere
nce
is
“Re
cen
tA
dva
nce
sin
Ro
bu
stC
on
tro
l”E
dit
ed
by
Pe
ter
Do
rato
an
d
R.K
.Ye
da
vall
i,IE
EE
Pre
ss,
19
90
Literature in the Field
16
R.K
.Ye
da
vall
i,IE
EE
Pre
ss,
19
90
LLRF Control Systems
17
Blo
ck d
iag
ram
of
the
LLR
F c
on
tro
l sy
ste
m.
•Am
pli
tud
e
Co
ntr
ol
•Ph
ase
Co
ntr
ol
•Sig
nif
ica
nt
Lit
era
ture
a
nd
In
tere
st i
n E
uro
pe
an
d
Asi
a a
nd
ou
r U
S G
ov
tLa
bs
No
min
al S
NS
RF
Co
ntr
ol
Sys
tem
•Lo
s A
lam
os
an
d O
ak
Rid
ge
la
bs
are
act
ive
in
RF
Co
ntr
ol
Sys
tem
s R
ese
arc
h
•A
Lin
ea
r K
lyst
ron
mo
de
l a
rou
nd
ea
ch
op
era
tin
g p
oin
t ca
n b
e o
bta
ine
d
op
era
tin
g p
oin
t ca
n b
e o
bta
ine
d
•A
n S
RF
Ca
vit
y l
ine
ar
mo
de
l ca
n b
e o
bta
ine
d b
y
eq
uiv
ale
nt
circ
uit
of
the
ca
vit
y (
as
an
RF
ge
ne
rato
r w
ith
a t
ran
smis
sio
n l
ine
) a
pp
roa
ch. 1
8
No
min
al
RF
Co
ntr
ol
Syst
em
Mo
de
lin
g
•S
tate
va
ria
ble
s:
Co
mp
lex
Ca
vit
y V
olt
ag
e R
ea
l
an
d I
ma
gin
ary
pa
rts
•C
on
tro
l V
ari
ab
les:
Ge
ne
rato
r C
urr
en
t R
ea
l a
nd
Ima
gin
ary
pa
rts
Ima
gin
ary
pa
rts
•M
atl
ab
an
d S
imu
lin
kca
n b
e u
sed
to
sim
ula
te
the
co
ntr
ol
syst
em
be
ha
vio
r
Imp
ort
an
t to
co
nsi
de
r P
ert
urb
ati
on
s a
nd
acc
om
mo
da
te t
he
m i
n c
on
tro
l d
esi
gn
19
Uncertainty Characterization in
LINAC LLRF Control
•U
nce
rta
inty
in R
F c
om
po
ne
nts
(l
ike
RF
sw
itch
, d
ire
ctio
na
l co
up
ler
etc
) a
nd
ca
bli
ng
: to
be
mo
de
led
as
mu
ltip
lica
tive
u
nce
rta
inty
•H
igh
Vo
lta
ge
Po
we
r su
pp
ly r
ipp
le t
o b
e m
od
ele
d a
s a
dd
itiv
e
dis
turb
an
ce
20
dis
turb
an
ce
•Lo
ren
tz f
orc
e d
etu
nin
g f
req
ue
ncy
an
d m
icro
ph
on
ics
can
be
m
od
ele
d a
s ti
me
va
ryin
g,
rea
l u
nce
rta
in p
ara
me
ters
•B
ea
m c
urr
en
t I
is m
od
ele
d a
s a
tim
e in
vari
an
t re
al
un
cert
ain
p
ara
me
ter
wit
hin
a b
ou
nd
ed
se
t.
Pe
rtu
rba
tio
n m
od
eli
ng
in
RF
Co
ntr
ol
Syst
em
s•
4 µ
se
con
d d
ela
y o
bse
rve
d i
n R
F C
on
tro
l Sys
tem
s o
f T
ES
LA T
est
Fa
cili
ty
•T
ime
de
lay
in
cre
ase
s th
e p
ha
se s
hif
t b
etw
ee
n in
pu
t a
nd
ou
tpu
t si
gn
als
an
d
thu
s li
mit
s th
e m
axi
mu
m a
llo
wa
ble
ga
in.
All
th
ese
p
ert
urb
ati
on
s ca
use
ph
ase
an
d a
mp
litu
de
dis
tort
ion
s.
We
ne
ed
to
de
sig
n c
on
tro
lle
rs w
hic
h a
re r
ob
ust
to
th
ese
We
ne
ed
to
de
sig
n c
on
tro
lle
rs w
hic
h a
re r
ob
ust
to
th
ese
Pe
rtu
rba
tio
ns.
Bo
th T
ime
Do
ma
in S
tate
Sp
ace
an
d F
req
ue
ncy
Do
ma
in
ap
pro
ach
es
ne
ed
to
be
pu
rsu
ed
.
.
21
MIM
O F
req
ue
ncy
Do
ma
in
Me
tho
ds
Robust Control Design Methods
22
_
∆ ∆∆∆P(s)
C(s)
G(s)
+
∆1
C
G1
G2
rz 1
uz 4
w2
w1z 2
z 3w3
y
MIM
O T
ime
Do
ma
in S
tate
Sp
ace
Me
tho
ds
Lin
ea
r P
ara
me
ter
Va
ryin
g
Ric
cati
ba
sed
Ro
bu
st C
on
tro
l Ly
ap
un
ov
ba
sed
LM
I
Robust Control Design Methods
23
Lin
ea
r P
ara
me
ter
Va
ryin
g
Me
tho
d
Ric
cati
ba
sed
Ro
bu
st C
on
tro
l
De
sig
n M
eth
od
s
Lya
pu
no
vb
ase
d L
MI
me
tho
ds
Ro
bu
st C
on
tro
l fo
r Li
ne
ar
Inte
rva
l P
ara
me
ter
Ma
trix
-
fam
ilie
s
Gu
ara
nte
ed
Co
st C
on
tro
lR
ob
ust
Co
ntr
ol
for
Ult
ima
te
Bo
un
de
dn
ess
Ro
bu
st C
on
tro
l o
f Li
ne
ar
Inte
rva
l P
ara
me
ter
Sy
ste
ms
in S
tate
Sp
ace
fra
me
wo
rk
24
PE
RT
UR
BA
TIO
N O
R M
OD
ELI
NG
ER
RO
RS
Ne
gle
cte
d
Uncertainty Characterization
Pa
ram
ete
r
25
Un
mo
de
led
Dy
na
mic
s
Ne
gle
cte
d
No
nli
ne
ari
tie
s
Ne
gle
cte
d
Ext
ern
al
Dis
turb
an
ces
Pa
ram
ete
r
Va
ria
tio
ns
Cx
y
Bu
Ax
x
=
+=
&
Co
nsi
de
r th
e s
yste
m
wit
h t
he
co
ntr
ol la
w g
ive
n b
y
Linear State Feedback Control Design
Using Perturbation Bound Analysis
26
Gx
u=
wit
h t
he
co
ntr
ol la
w g
ive
n b
y
Let
us
ass
um
e t
ha
t w
e c
an
de
term
ine
a G
su
ch t
ha
t th
e
no
min
al c
lose
d l
oo
p s
yste
m m
atr
ix A
+B
G is
sta
ble
.
ebb
eaa
UB
UA
=∈∆
=∈∆
the
capture
and
matrices
the
and
B,
and
A
matrices
the
in
expected
deviations
absolute
maximum
the
denote
and
,
where
UU
ba
∈∈
Let
us
ass
um
e p
ert
urb
ati
on
s in
th
e A
an
d B
ma
tric
es
wit
h t
he
foll
ow
ing
str
uct
ure
:
Perturbation Bound Analysis
27
meb
bea
am
GU
UBG
A∈
+=∈
∆+
∆=
∆
by
given
is
of
control
nominal
with
system
the
of
matrix
system
loop
closed
linear
onin
perturbati
Total
y.
uncertaint
the
of
structure
the
capture
and
matrices
the
and
B,
and
A
matrices
the
in
Gx
u
UU
ebea
=
1
ifan
dby
bounded
ons
per
turb
ati
al
lfo
r
stab
le
is sy
stem
linea
r
per
turb
ed
The
:T
heo
rem
ba
µ=
<∈
∈∈
Perturbation Bound Analysis
28
equat
ion
mat
rix
L
yap
unov
t
he
of
solu
tion
t
he
is
wher
e
and
)](
[
1
max
P
GU
UP
b
sm
ebea
ma
µ
µσ
µ∈<
∈
=∈
+<
∈
02
)(
)(
=+
++
+n
TI
PBG
ABG
AP
De
fin
e
Sta
bil
ity
Ro
bu
stn
ess
In
de
x β
SR
as
foll
ow
s:
Ca
se a
) C
he
ckin
g s
tab
ilit
y f
or
giv
en
pe
rtu
rba
tio
n r
an
ge
:
For
this
c
ase
Stability Robustness Index and Control
Design Algorithm
29
aSR
∈−
=∆
µβ
µβ
∆ =SR
For
this
c
ase
Ca
se b
) S
pe
cify
ing
th
e b
ou
nd
: Fo
r th
is c
ase
KB
RG
T
c
1
0
1−
−=
ρ
01
0=
+−
+−
QK
BR
KB
KA
KA
T
c
T
ρ
Bu
ild
a c
on
tro
l ga
in v
ia L
QR
me
tho
d:
Let
the
co
ntr
ol
ga
in G
be
va
rie
d v
ia a
sca
lar
me
asu
re g
ive
n b
y
Stability Robustness Index and Control
Design Algorithm
30
2/
1
0
2/
1
0
max
])
([
])
([
or
)(
dt
Gx
Gx
dt
uu
J
GG
J
TT
Ten
sen
∫∫
∞∞
==
==
σ
Let
the
co
ntr
ol
ga
in G
be
va
rie
d v
ia a
sca
lar
me
asu
re g
ive
n b
y
Plo
t β
SR
v.s.
Je
n a
nd
se
lect
a g
ain
wh
ich
ke
ep
s β
SR
po
siti
ve
an
d/o
r m
ax
imu
m
0)
0()
()
(x
xu
BB
xA
Ax
=∆
++
∆+
=
&
by
given
are
vector
control
and
vector
state
of
components
The
→
→2
4R
uR
x
Ap
pli
cati
on
to
Ve
rtic
al Ta
keo
ff a
nd
La
nd
ing
Air
cra
ft
Application to Flight Control
31
control
pitch
cyclic"
al
longitudin
"
control
pitch
"collective
ees)
angle(degr
pitch
e/second)
rate(degre
pitch
nots)
velocity(k
vertical
nots)
velocity(k
horizontal
by
given
are
vector
control
and
→→→→→→
→
214321
24
"
uuxxxx
Ru
R
−
−−
−−
=
01
00
42
00
.1
707
.0
36
81
.0
10
02
.0
02
08
.4
00
24
.0
01
.1
04
82
.0
45
55
.0
01
88
.0
02
71
.0
03
66
.0
A
17
61
.0
44
22
.0
Application to Flight Control
32
]0
5.
00
15
.0
85
.0[
)0(
00
49
.4
52
.5
59
22
.7
54
46
.3
17
61
.0
44
22
.0
−=
−
−=
Tx
B
is condition
initial
The
702
.3
544
.3
39
.3
53
.1
42
.1
31
.1
3817
.0
3681
.0
3545
.0
213432
≤=
≤
≤=
≤
≤=
≤ baa
Example
33
157
.0
11
.0
0136
.0
21
34
32
=∆
=∆
=∆
ba
a
5674
.1
106
.1
1363
.0
21
34
32
=∆
=∆
=∆
ba
a
Case I I
Case I
Example
34
OSU Robust Control Group Research
OSU Research
Activities
Goodrich Engine
Control
NASA
Dryden
US Army
Uncertain
Systems
Research
NSF
35
AFRL/PR
CCCS
Flow Control
NASA
Glenn / GEAE
Cu
rre
nt
Gra
du
ate
Stu
de
nts
•W
en
fei
Li (
M.S
./P
h.D
.)
•H
sun
-Hsu
nH
ua
ng
(P
h.D
.)
•N
ag
ini
De
vara
kon
da
(Ph
.D.)
•R
oh
itB
ela
pu
rka
r (M
.S./
Ph
.D)
•H
-In
fco
ntr
ol
wit
hR
eg
ion
al
Sta
bil
ity
Co
nst
rain
ts(L
iua
nd
Yed
ava
lli)
•T
ime
resp
on
seb
ou
nd
sfo
rLi
ne
ar
Un
cert
ain
syst
em
s(C
RA
sho
kK
um
ar
an
dYe
da
vall
i)
•S
tab
ilit
ya
nd
Ro
bu
stn
ess
for
Ma
trix
Se
con
dO
rde
rSys
tem
sw
ith
sma
rtst
ruct
ure
con
tro
la
pp
lica
tio
ns
(An
jali
Diw
eka
ra
nd
OSU Robust Control Group Research
36
wit
hsm
art
stru
ctu
reco
ntr
ol
ap
pli
cati
on
s(A
nja
liD
iwe
kar
an
dYe
da
vall
i)
•C
on
tro
lD
esi
gn
inR
eci
pro
cal
Sta
teS
pa
ceF
ram
ew
ork
(Tse
ng
an
dYe
da
vall
i)
•S
ma
rtD
efo
rma
ble
Win
gst
ruct
ure
sfo
rIm
pro
ved
Air
cra
ftR
oll
Ove
rm
an
eu
vers
(Kw
ak
an
dYe
da
vall
i)
•N
eu
ral
ne
two
rkb
ase
dn
on
lin
ea
rco
ntr
oll
ers
for
flig
ht
veh
icle
ap
pli
cati
on
s(S
ha
nka
ra
nd
Yed
ava
lli)
•Fa
ult
de
tect
ion
usi
ng
dy
na
mic
thre
sho
lda
pp
roa
chw
ith
air
cra
fte
ng
ine
ap
pli
cati
on
s(L
ia
nd
Yed
ava
lli)
•R
ob
ust
sta
bil
ity
an
dco
ntr
ol
of
mu
lti-
bo
dy
gro
un
dve
hic
les
OSU Robust Control Group Research
37
•R
ob
ust
sta
bil
ity
an
dco
ntr
ol
of
mu
lti-
bo
dy
gro
un
dve
hic
les
un
de
ru
nce
rta
inty
an
dfa
ilu
res
(Hu
an
ga
nd
Yed
ava
lli)
•E
colo
gic
al
sig
nst
ab
ilit
ya
nd
its
use
inro
bu
ste
ng
ine
eri
ng
syst
em
s(D
eva
rako
nd
aa
nd
Yed
ava
lli)
•D
istr
ibu
ted
en
gin
eco
ntr
ol
un
de
rco
mm
un
ica
tio
nco
nst
rain
ts(B
ela
pu
rka
ra
nd
Yed
ava
lli)
Dynamic
Inversion
Control
Allocation
SDRE
X-40 Dynamic Inversion Controller
Pra
ve
en
Sh
an
kar
38
•R
ob
ust
ne
ss A
na
lysi
s o
f th
e X
-40
A D
yn
am
ic I
nve
rsio
n C
on
tro
lle
r
•Im
ple
me
nta
tio
n o
f co
mb
ine
d D
yn
am
ic I
nve
rsio
n -
Sta
te
De
pe
nd
en
t R
icca
ti E
qu
ati
on
Te
chn
iqu
e
•S
tab
ilit
y D
om
ain
Est
ima
tio
n (
Re
gio
n o
f A
ttra
ctio
n)
•M
eth
od
of
Ve
cto
r N
orm
s
•S
um
of
Sq
ua
res
Pro
gra
mm
ing
SDRE
Redesign
Reference
Model
PI
Controller
Neural
Network
Dynamic
Inversion
Control
Allocator
δω
ωdes
F-1
5
A Neural Network Based Adaptive Observer
for Turbine Engine Parameter Estimation
Pra
ve
en
Sh
an
kar
39
•Im
ple
me
nta
tio
n o
f G
row
ing
Ra
dia
l Ba
sis
Fu
nct
ion
Ne
ura
l
Ne
two
rk t
o m
inim
ize
err
or
du
e t
o m
od
eli
ng
an
d f
ail
ure
s in
con
tro
l su
rfa
ces
•S
ucc
ess
full
y im
ple
me
nte
d f
or
F-1
5 D
yn
am
ic I
nve
rsio
n
Co
ntr
oll
er
an
d F
-18
Ro
bu
st L
QR
Tra
cke
r
•To
be
im
ple
me
nte
d o
n p
ilo
ted
sim
ula
tio
n a
t N
AS
A D
ryd
en
•R
ob
ust
Sta
bil
ity
an
d C
on
tro
l o
f
Mu
lti-
bo
dy
Gro
un
d V
eh
icle
s
un
de
r U
nce
rta
inty
an
d F
ail
ure
s
•G
rou
nd
Ve
hic
le D
yn
am
ics
–R
oll
ove
r st
ab
ilit
y
Robust Stability and Control of
Multi-body Ground Vehicles
Hsu
n-H
sun
Hu
an
g
–R
oll
ove
r st
ab
ilit
y
–R
ide
an
d H
an
dli
ng
Pe
rfo
rma
nce
–S
tab
ilit
y u
nd
er
fail
ure
s
•E
ffo
rts
to C
oll
ab
ora
te w
ith
TAR
DE
C in
Wa
rre
n,
MI
4/2
9/2
01
0
•A
pp
lica
tio
n o
f co
nce
pts
of
bio
log
y a
nd
lif
e s
cie
nce
to
en
gin
ee
rin
g s
yste
ms:
Qu
ali
tati
ve (
sig
n)
sta
bil
ity
an
d
Ro
bu
st s
tab
ilit
y
Qualitative (Sign) Stability of Ecology
Na
gin
iD
eva
rako
nd
a
4/2
9/2
01
0
•A
pp
lica
tio
n o
f m
od
el
ba
sed
co
ntr
ol
stra
teg
ies
for
en
gin
e
con
tro
l
•A
pp
lica
tio
n o
f m
od
el
ba
sed
dia
gn
ost
ic t
ech
niq
ue
s
–S
en
sor
fau
lt d
ete
ctio
n a
nd
iso
lati
on
in
Tu
rbin
e E
ng
ine
si
mu
lati
on
mo
de
l u
sin
g N
eu
ral
Ne
two
rks
an
d b
an
k o
f
Fault Diagnostics for Aircraft Engines
With Uncertain Model Data
We
nfe
iLi
sim
ula
tio
n m
od
el
usi
ng
Ne
ura
l N
etw
ork
s a
nd
ba
nk
of
Ka
lma
n F
ilte
rs
•A
pp
lica
tio
n o
f m
od
el
ba
sed
pro
gn
ost
ic t
ech
niq
ue
s to
Tu
rbin
e
En
gin
e s
imu
lati
on
mo
de
l
4/2
9/2
01
0
•T
he
Ka
lma
n f
ilte
r is
co
mp
ose
d o
f a
no
nli
ne
ar
on
-bo
ard
en
gin
e m
od
el (O
BE
M)
an
d l
ine
ar
sta
te-s
pa
ce m
od
el.
•T
he
OB
EM
is
to g
en
era
te t
he
sta
te v
ari
ab
les
an
d s
en
sor
ou
tpu
ts,
run
nin
g i
n p
ara
lle
l w
ith
th
e a
ctu
al e
ng
ine
at
Kalman Filter Approach
ou
tpu
ts,
run
nin
g i
n p
ara
lle
l w
ith
th
e a
ctu
al e
ng
ine
at
the
est
ima
ted
he
alt
h c
on
dit
ion
.
4/2
9/2
01
0
Dy
na
mic
(A
da
pti
ve)
Th
resh
old
•C
urr
en
t a
pp
roa
che
s u
se C
on
sta
nt
Th
resh
old
–La
ckin
g g
uid
eli
ne
s fo
r o
pti
ma
l th
resh
old
se
lect
ion
–In
ap
pro
pri
ate
Th
resh
old
se
lect
ion
le
ad
s to
mo
re F
als
e
Ala
rms
an
d M
isse
d D
ete
ctio
ns
•D
yn
am
ic (
Ad
ap
tive
) T
hre
sho
ld A
pp
roa
ch•
Dy
na
mic
(A
da
pti
ve)
Th
resh
old
Ap
pro
ach
–A
cco
mm
od
ate
s u
nce
rta
inty
in
th
e M
od
els
–H
elp
s in
Re
du
cin
g F
als
e A
larm
s a
nd
Mis
sed
De
tect
ion
s
–Id
ea
alr
ea
dy
use
d i
n A
uto
mo
tive
ap
pli
cati
on
s
4/2
9/2
01
0
OBEM
Nonlinear/Linear
(CLM)
ucmd
zOBEM
xOBEM
Fault Detection System using
Dynamic Threshold Approach
4/2
9/2
01
0
Kalman Filter
zest
xest
Real Engine
(Component Level Model)
z
Residual/
Threshold
R=Z-Zest
Th=Zo-Zest
fault exists
or not
Engine Fault Detection System Scheme
+=
+=
vu
hx
gz
wu
hx
fx
),
,(
),
,(
&
•A
n a
ircr
aft
en
gin
e is
a n
on
lin
ea
r m
od
el:
Engine System Model
4/2
9/2
01
0
+
=v
uh
xg
z)
,,
(
wh
ere
x,
h,
u a
nd
z r
ep
rese
nt
sta
te v
ari
ab
les,
he
alt
h
pa
ram
ete
rs,
con
tro
l co
mm
an
d in
pu
ts,
an
d s
en
sor
ou
tpu
ts.
w
is t
he
pro
cess
no
ise
an
d v
is
the
se
nso
r n
ois
e.
+
+=
wu
BAx
x)
(&
•O
bta
inin
g a
lin
ea
r st
ate
-sp
ace
mo
de
l a
t t
he
de
sire
d s
tea
dy
-sta
te p
oin
t:
Engine System Model
4/2
9/2
01
0
+
=v
Cx
z
•D
iscr
eti
zin
g t
he
lin
ea
r co
nti
nu
ou
s-ti
me
sys
tem
fo
r
de
sig
nin
g t
he
Ka
lma
n f
ilte
r:
++
+=
+
++
Ψ+
+Φ
=+
)1(
)1(
)1(
)(
)(
),1
()
()
,1(
)1(
kv
xk
Ck
z
kw
ku
kk
kx
kk
kx
d
020
4060
80100
120140
160180
200306
4
3064.53065
3065.53066
input W
F36
time
WF36
u(1) uengine
(1)
248249250inpu
t AE24
AE24
u(2) uengine
(2)
2468
10
12
Fault Dectection Using Dynamic Threshold
residual XN2
residual threshold XN2 (z1)
constant threshold
5
10
15
20
residual XN25
residual threshold XN25 (z2)
constant threshold
No Fault
4/2
9/2
01
0
020
4060
80100
120140
160180
200247
time
020
4060
80100
120140
160180
20033343536
input ST
P25
time
STP25
u(3) uen
gine(3)
050
100
150
200
-20
0
50
100
150
200
0
010
20
30
40
50
60
70
80
90
0
0.51
1.5
010
20
30
40
50
60
70
80
90
0
0.51
1.5
020
4060
80100
120
140
160
180
200
3065
3070
3075
input WF36
time
WF36
u(1)
uengine(1)
248
249
250
input AE24
AE24
u(2)
uengine(2)
2468
10
Fault Dectection Using Dynamic Threshold
residual XN2
residual threshold XN2 (z1)
constant threshold
5
10
15
20
residual XN25
residual threshold XN25 (z2)
constant threshold
Fault in First Actuator
4/2
9/2
01
0
020
4060
80100
120
140
160
180
200
247
time
020
4060
80100
120
140
160
180
200
33343536input STP25
time
STP25
u(3)
uengine(3)
050
100
150
200
0
050
100
150
200
0
010
20
30
40
50
60
70
80
90
0
0.51
1.5
010
20
30
40
50
60
70
80
90
0
0.51
1.5
020
4060
80100
120
140
160
180
200
3064
3064.5
3065
3065.5
3066
input WF36
time
WF36
u(1)
uengine(1)
250
260
270
280
input AE24
AE24
u(2)
uengine(2)
02468
10
Fault Dectection Using Dynamic Threshold
residual XN2
residual threshold XN2 (z1)
constant threshold
05
10
15
20
residual XN25
residual threshold XN25 (z2)
constant threshold
Fault in Second Actuator
4/2
9/2
01
0
020
4060
80100
120
140
160
180
200
240
time
020
4060
80100
120
140
160
180
200
33343536input STP25
time
STP25
u(3)
uengine(3)
050
100
150
200
-2
050
100
150
200
-5
010
20
30
40
50
60
70
80
90
0
0.51
1.5
010
20
30
40
50
60
70
80
90
0
0.51
1.5
020
4060
80100
120
140160
180
200306
4
3064.5
3065
3065.5
3066
input WF
36
time
WF36
u(1)
uengine(1)
248
249
250
input AE24
AE24
u(2)
uengine(2)
2468
10
Fault Dectection Using Dynamic Threshold
residual XN2
residual threshold XN2 (z1)
constant threshold
5
10
15
20
25
residual XN25
residual threshold XN25 (z2)
constant threshold
Fault in Third Actuator
4/2
9/2
01
0
020
4060
80100
120
140160
180
200247
time
020
4060
80100
120
140160
180
20034.83535.2
35.4
35.6
input STP25
time
STP25
u(3)
uengine(3)
050
100
150
200
0
050
100
150
200
0
010
20
30
40
50
60
70
80
90
0
0.51
1.5
010
20
30
40
50
60
70
80
90
0
0.51
1.5
•D
yn
am
ic T
hre
sho
ld w
ork
s w
ell
•F
irst
an
d t
hir
d a
ctu
ato
r fa
ult
s e
asi
er
to d
ete
ct;
seco
nd
Fau
lt D
ete
ctio
n R
esu
lts
Fault Detection Summary
•F
irst
an
d t
hir
d a
ctu
ato
r fa
ult
s e
asi
er
to d
ete
ct;
seco
nd
act
ua
tor
fau
lt h
ard
er
to d
ete
ct.
•T
he
est
ima
tio
n e
rro
r in
th
e t
ran
sie
nt
ph
ase
re
lati
vely
larg
e.
Be
tte
r tu
nin
g o
f K
alm
an
fil
ter
ga
in d
esi
rab
le.
4/2
9/2
01
0
Dis
trib
ute
d E
ng
ine
Co
ntr
ol
Syst
em
(D
EC
)
•E
ach
se
nso
r/a
ctu
ato
r re
pla
ced
by
sma
rt s
en
sor/
act
ua
tor.
•S
ign
al p
roce
ssin
g d
on
e b
y s
ma
rt
mo
du
les.
•In
form
ati
on
tra
nsf
er
t
hro
ug
h
Ro
hit
Be
lap
urk
ar
53
•In
form
ati
on
tra
nsf
er
t
hro
ug
h
seri
al c
om
mu
nic
ati
on
.
•S
ma
rt m
od
ule
s in
clu
de
pro
cess
ing
cap
ab
ilit
y t
o p
erf
orm
he
alt
h
dia
gn
ost
ics
an
d m
an
ag
em
en
t
fun
ctio
ns.
•C
an
be
mo
de
led
as
Ne
two
rke
d
Co
ntr
ol S
yste
ms
FADEC based on Distributed Architecture
Ne
two
rke
d C
on
tro
l Sy
ste
ms
(NC
S)
Ba
sic
ele
me
nts
of
NC
S
1.
Se
nso
rs
2.
Act
ua
tors
3.
Co
mm
un
ica
tio
n n
etw
ork
4.
Co
ntr
oll
er
Ne
two
rk
Act
ua
tors
Pla
nt
Se
nso
rs 54
4.
Co
ntr
oll
er
Generic NCS Architecture
Co
mm
un
ica
tio
n C
on
stra
ints
to
co
nsi
de
r fo
r a
na
lysi
s
of
NC
S
•P
ack
et
Dro
po
ut
•N
etw
ork
in
du
ced
Tim
e D
ela
y
•C
ha
nn
el
Ba
nd
wid
th
Co
ntr
oll
er
Time Delay Systems
55
Decentralized Control System for
Multiple Klystrons
56
AP
T L
LRF
Co
ntr
ol
Sys
tem
Fu
nct
ion
ali
ty a
nd
arc
hit
ect
ure
-A
.H.
Re
ga
n,
A.S
. R
oh
lev,
C.D
. Z
iom
ek
Blo
ck d
iag
ram
of
fee
db
ack
co
ntr
ol sy
ste
m f
or
mu
ltip
le k
lyst
ron
s
Fau
lt T
ole
ran
t A
cce
lera
tor
57
Re
f:E
nh
an
cin
g A
cce
lera
tor
Re
lia
bil
ity
wit
h L
LRF
Dig
ita
l Te
chn
olo
gy
-Lu
cija
Lu
kova
c
Fa
ult
to
lera
nt
acc
ele
rato
r d
em
on
stra
ted
fro
m b
ea
m
dyn
am
ics
po
int
of
vie
w
Pro
po
sed
OS
U R
ese
arc
h T
op
ics
of
Re
leva
nce
to
Fe
rmi-
Lab
s
•LL
RF
Co
ntr
ol S
yste
ms:
No
min
al a
nd
Pe
rtu
rba
tio
n M
od
eli
ng
an
d a
pp
rop
ria
te R
ob
ust
Co
ntr
ol D
esi
gn
•Fa
ult
De
tect
ion
, I
sola
tio
n a
nd
Acc
om
mo
da
tio
n
58
•D
ece
ntr
ali
zed
, D
istr
ibu
ted
Co
ntr
ol w
ith
co
mm
un
ica
tio
n
con
stra
ints
/fa
ilu
res
take
n in
to c
on
sid
era
tio
n
Of
cou
rse
, e
ach
of
the
se t
op
ics
is o
f im
me
nse
sco
pe
an
d
use
fuln
ess
an
d r
eq
uir
e l
on
g t
erm
su
pp
ort
an
d c
oll
ab
ora
tio
n
RO
BU
ST
EN
GIN
EE
RIN
G
SY
ST
EM
S,
LLC
•Fo
un
de
d i
n 2
00
8 b
y P
rof.
R.
K.
Yed
ava
lli
•W
e u
nd
ert
ake
co
nsu
ltin
g p
roje
cts
in t
he
re
late
d f
ield
s o
f:
•R
ob
ust
Co
ntr
ol Sys
tem
s A
na
lysi
s a
nd
De
sig
n f
or
Un
cert
ain
Dy
na
mic
Sys
tem
s
•O
pti
miz
ati
on
of
Dy
na
mic
Sys
tem
s
•D
istr
ibu
ted
Co
ntr
ol Sys
tem
s
59
Co
ntr
oll
ing
Un
cert
ain
Sy
ste
ms
Wit
h C
ert
ain
ty
•D
istr
ibu
ted
Co
ntr
ol Sys
tem
s
•C
on
tro
l Ap
pli
cati
on
s in
V
ari
ou
s Sys
tem
s
•E
ma
il:
con
tact
@ro
bu
ste
ng
sys.
com
•W
eb
site
: w
ww
.ro
bu
ste
ng
sys.
com
Po
ssib
le A
ven
ue
s o
f C
oll
ab
ora
tio
n
Ve
ry m
uch
in
tere
ste
d i
n e
xplo
rin
g p
oss
ible
ave
nu
es
of
coll
ab
ora
tio
n w
ith
Ferm
i-La
bs
Th
ese
po
ten
tia
lly
ma
y i
ncl
ud
e
•P
I R
ese
arc
h s
po
nso
rsh
ip f
or
Re
sea
rch
to
be
ca
rrie
d o
ut
at
OS
U w
ith
mo
nit
ori
ng
of
pro
gre
ss b
y F
erm
i-La
bs
pe
rso
nn
el
•R
ese
arc
h S
po
nso
rsh
ip c
an
be
div
ide
d b
etw
ee
n R
ob
ust
En
gin
ee
rin
g
Sys
tem
s a
nd
OS
U
•P
oss
ible
In
tera
ctio
n w
ith
Oth
er
Go
vt.
La
bs
such
as
Los
Ala
mo
s a
nd
Oa
k
Rid
ge
•E
xch
an
ge
of
tech
nic
al
info
rma
tio
n t
hro
ug
h
sem
ina
rs
•O
the
rs?
60
Su
mm
ary
an
d C
on
clu
sio
ns
•M
od
ern
Ro
bu
st C
on
tro
l Sys
tem
s T
he
ory
ha
s
mu
ch t
o o
ffe
r in
th
e C
on
tro
l o
f
Su
pe
rco
nd
uct
ing
C
av
ity
ap
pli
cati
on
•A
mu
ltid
isci
pli
na
ry t
ea
m c
oll
ab
ora
tio
n a
•
A m
ult
idis
cip
lin
ary
te
am
co
lla
bo
rati
on
a
ne
cess
ity
fo
r a
co
mp
lex
pro
ject
su
ch a
s
AD
S/P
roje
ct X
•O
SU
/RE
S v
ery
mu
ch i
nte
rest
ed
in
co
ntr
ibu
tin
g
to A
DS
/Pro
ject
X
61
•T
ha
nk
yo
u v
ery
mu
ch f
or
you
r a
tte
nti
on
•Q
ue
stio
ns?
62
•Q
ue
stio
ns?
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