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Mark
Cannon
mark
.cannon@
eng.o
x.ac.
uk
C2
1 M
od
el P
red
icti
ve C
on
tro
lL
ectu
re 1
Mic
hae
lmas
Term
2011
4 le
cture
s
C21
Mode
l P
red
ictive
Con
tro
l1
-1
Overv
iew
of
MP
C
The s
trate
gy:
1.
P
redic
tion
2.
O
nlin
e o
ptim
izatio
n
3.
R
ece
din
g h
orizo
n im
ple
me
nta
tion
1.
Pre
dic
tion
•P
lant
model:
(1)
((
),(
))x
kf
xk
uk
+=
•S
imula
te f
orw
ard
in t
ime
(|
)
(1
|)
(1
|)
uk
k
uk
k
uk
Nk
!"
#$
+#
$=#
$#
$+
!%
&
u
!F
utu
re in
put
seque
nce
:
(1
|)
(2
|)
(|
)
xk
k
xk
k
xk
Nk
+!
"#
$+
#$
=#
$#
$+
%&
x
!F
utu
re s
tate
traje
ctory
:
C21
Mode
l P
red
ictive
Con
tro
l1
-2
Overv
iew
of
MP
C
min
()
Jk
u
2.
Optim
izatio
n
•P
redic
ted c
ost
:(
)0
()
(|
),(
|)
N i
Jk
lx
ki
ku
ki
k=
=+
+'
•S
olv
e n
um
eri
cally
:optim
al i
nput
seque
nce
()
k"
u
()
k"
u
3.
Im
ple
menta
tion
•U
se f
irst
ele
ment
of
()
(|
)u
ku
kk
"=
•R
epeat
steps
1-3
at
next
sam
plin
g in
sta
nt
act
ual p
lant
inp
ut
C21
Mode
l P
red
ictive
Con
tro
l1
-3
x 0tim
e
Overv
iew
of
MP
C
pre
dic
tion h
ori
zon
kk
N+
u 0tim
epast
pre
dic
ted
(|
)
(|
)
uk
ik
xk
ik
+( )
+*
pre
dic
ted in
put/
state
at
time
usi
ng in
form
atio
n a
t tim
ek
i+
k
C21
Mode
l P
red
ictive
Con
tro
l1
-4
x 0tim
e
Overv
iew
of
MP
C
kk
N+
1k
+1
kN
++
pre
dic
tion h
ori
zon a
t tim
e
k
pre
dic
tion h
ori
zon a
t tim
e
1k
+u 0
time
C21
Mode
l P
red
ictive
Con
tro
l1
-5
Overv
iew
of
MP
C
Optim
izatio
n r
epeate
d o
nlin
e a
t sa
mplin
g in
stants
0,1
,k
="
+
Rece
din
g p
redic
tion h
orizo
n:
{}
{}
()
(|
),(
1|
)
(1)
(1
|1)
,(
|1)
ku
kk
uk
Nk
ku
kk
uk
Nk
=+
!
+=
++
++
u
u
"
"
!
•allo
ws
for
feedback
com
pensa
tes
for
model m
ism
atc
h &
dis
turb
ance
s
•co
mpensa
tes
for
finite
num
ber
of
d.o
.f.
in p
redic
tions
impro
ves
close
d-loo
p p
erf
orm
ance
C21
Mode
l P
red
ictive
Con
tro
l1
-6
Overv
iew
of
MP
C
•C
om
puta
tional o
ptim
al c
on
trol
•Lee &
Mark
us,
1963
•B
itmead,
Geve
rs&
Wert
z 1990
•A
n e
asy
wa
y to
sta
bili
ze a
sys
tem
•K
alm
an,
196
0•
Kle
inm
an,
19
70
•C
ontr
ol s
trate
gy
rein
vente
d s
eve
ral t
imes
optim
al c
ontr
ol
indust
rial p
roce
ss c
ontr
ol
const
rain
ed/n
onlin
ear
contr
ol
Deve
lopm
ent of
com
merc
ial
MP
C a
lgorith
ms:
[fro
m Q
in &
Badgw
ell
2003]
1950
’s-7
0’s
1980
’s
1990
’s
C21
Mode
l P
red
ictive
Con
tro
l1
-7
Bo
ok
s
•J.
B.
Ra
wlin
gs
and D
.Q.
Mayn
e
•J.
M.
Maci
ejo
wsk
i
Chapte
rs 1
, 2,
3,
6,
8,
10
Pre
ntic
e H
all,
2002
Pre
dic
tive C
ontr
ol w
ith C
onst
rain
ts
Model P
redic
tive C
ontr
ol:
Theory
and D
esi
gn
Nob H
ill P
ub
lishin
g,
20
09
C21
Mode
l P
red
ictive
Con
tro
l1
-8
1 0
()
(|
)(
|)
(|
)(
|)
(|
)(
|)
NT
T
i
T
Jk
xk
ik
Qx
ki
ku
ki
kR
uk
ik
xk
Nk
Qx
kN
k
! =
=!
++
++
+"
%&
++
+
'
Exam
ple
•Lin
ear
pla
nt
model
•Q
uadra
tic c
ost
•e.g
. P
redic
tion h
orizo
n:
Degre
es
of
freedom
in p
redic
tions:
(d.o
.f.)
TQ
CC
=
[]
(1)
()
()
()
1.1
20
,,
11
00
.95
0.0
78
7
xk
Ax
kB
uk
yC
xk
AB
C
+=
+=
!"
!"
==
=!
#$
#$
%&
%&
3N
=(
|)
()
(1
|)
(2
|)
uk
k
ku
kk
uk
k
!"
#$
=+
#$
#$
+%
&
u
C21
Mode
l P
red
ictive
Con
tro
l1
-9
01
23
45
67
89
10
-4-20246
input
01
23
45
67
89
10
-1
-0.50
0.51
output
sa
mp
le
pre
dic
ted
cu
rre
nt
pre
dic
ted
cu
rre
nt
sam
ple
0k
=
Exam
ple
C21
Mode
l P
red
ictive
Con
tro
l1
-10
01
23
45
67
89
10
-4-20246
input
01
23
45
67
89
10
-1
-0.50
0.51
output
sa
mp
le
pre
dic
ted
cu
rre
nt
pa
st
pre
dic
ted
cu
rre
nt
pa
st
sam
ple
1
k=
Exam
ple
C21
Mode
l P
red
ictive
Con
tro
l1
-11
01
23
45
67
89
10
-4-20246
input
01
23
45
67
89
10
-1
-0.50
0.51
output
sa
mp
le
pre
dic
ted
pa
st
pre
dic
ted
cu
rre
nt
pa
st
sam
ple
2k
=01
23
45
67
89
10
-4-20246
input
01
23
45
67
89
10
-1
-0.50
0.51
output
sa
mp
le
pre
dic
ted
cu
rre
nt
pa
st
pre
dic
ted
cu
rre
nt
pa
st
sam
ple
7k
=
Exam
ple
C21
Mode
l P
red
ictive
Con
tro
l1
-12
Mo
tivati
on
Adva
nta
ges:
•F
lexi
ble
pla
nt
model
e.g
. m
ulti
varia
ble
linear
or
nonlin
ear
dete
rmin
istic
, st
och
ast
ic o
r fu
zzy
•In
put
and s
tate
const
rain
ts a
ccom
mod
ate
d
e.g
. act
uato
r lim
itatio
ns
safe
ty,
en
viro
nm
enta
l an
d e
conom
ic c
onst
rain
ts
•A
ppro
xim
ate
ly o
ptim
al c
lose
d-lo
op p
erf
orm
ance
(depe
nde
nt
on h
orizo
n,
cost
and d
.o.f
.)
Dis
adva
nta
ges:
•R
equires
on
line o
ptim
izatio
n
nonlin
ear/
unce
rtain
pla
nts
com
puta
tion
ally
exp
ensi
ve
C21
Mode
l P
red
ictive
Con
tro
l1
-13
Ap
plic
ati
on
s:
Pro
ces
s c
on
tro
l
Ste
el h
ot
rolli
ng m
ill
C21
Mode
l P
red
ictive
Con
tro
l1
-14
Ap
plic
ati
on
s:
Pro
ces
s c
on
tro
l
#
G
$%
tH
G
Inputs
:,
,,
GH
$%
Outp
uts
:,t
#
Obje
ctiv
e:
con
trol r
esi
du
al s
tress
es
#
Ste
el h
ot
rolli
ng m
ill
C21
Mode
l P
red
ictive
Con
tro
l1
-15
Ap
plic
ati
on
s:
Ch
em
ica
l p
roc
ess
co
ntr
ol
•M
PC
is u
sed t
o c
ontr
ol m
ore
than 4
50
0 c
hem
ica
l pro
cess
es
(2006)
•B
reakd
ow
n o
f M
PC
applic
atio
ns
in t
he c
he
mic
al i
ndust
ry [fro
m N
ag
y, I
JRN
C 2
006]
C21
Mode
l P
red
ictive
Con
tro
l1
-16
Ap
plic
ati
on
s:
Ele
ctr
o-m
ec
ha
nic
al s
ys
tem
s
Pre
dic
tive s
win
g-u
p &
bala
nci
ng c
ontr
olle
rs
C21
Mode
l P
red
ictive
Con
tro
l1
-17
Ap
plic
ati
on
s:
Ele
ctr
o-m
ec
ha
nic
al s
ys
tem
s
Win
d-t
urb
ine b
lade p
itch
C21
Mode
l P
red
ictive
Con
tro
l1
-18
inst
rum
ents
(in
puts
)
Su
sta
inab
le D
evelo
pm
en
t P
olic
y A
ssessm
en
t
!"#
$%&'("
)"*+
'(")
"*,-
#.(
/"%
,$
0.*1$.2.,%
/"%
,$
31-
.*.4,#
MP
C
indic
ato
rs(o
utp
uts
)
pre
dic
ted
outp
uts
pre
dic
ted
outp
uts
C21
Mode
l P
red
ictive
Con
tro
l1
-19
Pre
dic
tio
n m
od
el
Lin
ear
pla
nt
model
•pre
dic
tions
d
epend li
nearl
y o
n(
)k
x(
)k
u
+quadra
tic c
ost
:(
)(
)(
)2
()
TT
Jk
kH
kf
kg
=+
+u
uu
(wh
ere
a
re f
unct
ions
of
)
,f
g(
)x
k
line
ar
const
rain
ts:
()
cc
Ak
b&
u
(wh
ere
is
a funct
ion o
f
)cb
()
xk
•onlin
e o
ptim
izatio
n:
min
2
s.t.
TT
cc
Hf
Ab+
&
u
uu
u
u
conve
xQ
P(q
uadra
tic p
rogra
m)
eff
icie
ntly
& r
elia
bly
solv
able
C21
Mode
l P
red
ictive
Con
tro
l1
-20
Pre
dic
tio
n m
od
el
•nonlin
ear
de
pend
ence
of
pre
dic
tions
o
n
Nonlin
ear
pla
nt
model
()
kx
()
ku
+co
st:
()
((
),(
))
Jk
Jx
kk
=u
const
rain
ts:
((
),(
))
0c
gx
kk
&u
nonco
nve
xin
genera
l( ) *
man
y lin
ear
ap
plic
atio
ns
but
few
non
linear
MP
C a
pplic
atio
ns
•onlin
e o
ptim
izatio
n:
min
((
),)
s.t.
((
),)
0c
Jx
k
gx
k&
u
u
u
nonco
nve
xN
LP
•lo
cal m
inim
a
•so
lvers
unre
liab
le:
(genera
l no
nlin
ear
pro
gra
m)
conve
rgence
?co
mputa
tional l
oad?
C21
Mode
l P
red
ictive
Con
tro
l1
-21
Pre
dic
tio
n m
od
el
Dis
crete
-tim
ep
redic
tion m
ode
l
(1)
[(
1|
)(
2|
)(
|)]
Tk
uk
ku
kk
uk
Nk
+=
++
+u
#is
poss
ible
•if
f
or
inte
ger
/sa
mp
TT
n=
n=
then
(
allo
ws
for
guara
nte
ed s
tabili
ty)
(1)
()
kk
"+
=u
u
u 0
tT
=2
tT
=
t0
pre
dic
ted a
t2
tT
=
pre
dic
ted a
tt
T=
sam
pT
•P
redic
tions
optim
ize
d p
eri
odic
ally
at
,0
,1,
tkT
k=
="
sam
pT
typic
ally
in
teger
multi
ple
of
model s
am
ple
inte
rval
T=
C21
Mode
l P
red
ictive
Con
tro
l1
-22
Pre
dic
tio
n m
od
el
Contin
uous-
time
pre
dic
tion m
odel
use
ful i
f no d
iscr
ete
-tim
e m
od
el a
vaila
ble
•C
ontin
uous-
time p
redic
tion m
odel c
an b
e in
tegra
ted o
nlin
e
(e.g
. usi
ng R
un
ge-K
utt
a)
This
cours
e: dis
crete
-tim
e m
odel w
ithsa
mp
TT
=
•1st
-ord
er
hold
(
pie
cew
ise
linear
in
):
tu
u 0
tT
=2
tT
=
t0
pre
dic
ted a
tt
T=
hig
her
ord
er
ho
ld a
lso p
oss
ible
(
pie
cew
ise
quadra
tic,
cub
ic e
tc)
u
C21
Mode
l P
red
ictive
Con
tro
l1
-23
Co
ns
tra
ints
Const
rain
ts a
re p
rese
nt
in e
very
contr
ol p
rob
lem
•In
put
const
rain
ts:
()
uu
ku
&&
()
(1)
uu
ku
ku
'&
!!
&'
(abso
lute
)
(rate
)
•ty
pic
ally
act
ive d
urin
g t
ransi
ents
e.g
. va
lve s
atu
ratio
n,
d.c
. m
oto
r sa
tura
tion
•S
tate
const
rain
ts:
()
xx
kx
&&
•or
act
ive in
ste
ad
y st
ate
e.g
. pro
cess
indust
ry e
conom
ic c
onst
rain
ts
•ca
n b
e a
ctiv
e d
urin
g t
ransi
ents
e.g
. aircr
aft
sta
ll sp
ee
d
(lin
ear)
C21
Mode
l P
red
ictive
Con
tro
l1
-24
Co
ns
tra
ints
Cla
ssify
const
rain
ts a
s eith
er
hard
or
soft
:
•H
ard
const
rain
ts m
ust
be s
atis
fied a
t all
times
oth
erw
ise t
he p
roble
m is
infe
asi
ble
•S
oft
const
rain
ts c
an b
e v
iola
ted t
o a
void
infe
asi
bili
ty
This
cours
e:
only
hard
co
nst
rain
ts c
onsi
dere
d
•re
move
least
critic
al c
onst
rain
t until
optim
izatio
n is
feasi
ble
stra
tegie
s fo
r h
andlin
g s
oft
co
nst
rain
ts:
•im
pose
hard
const
rain
ts o
n t
he p
roba
bili
ty o
f vi
ola
ting e
ach so
ft c
onst
rain
t
C21
Mode
l P
red
ictive
Con
tro
l1
-25
Co
ns
tra
int
ha
nd
lin
g
Suboptim
al m
eth
ods
for
hand
ling in
put
const
rain
ts:
•S
atu
rate
unco
nst
rain
ed c
ontr
ol l
aw
(const
rain
ts u
sually
ignore
d in
contr
olle
r d
esi
gn)
•“D
e-t
une”
un
const
rain
ed c
ontr
ol l
aw
incr
ease
pen
alty
on
in
optim
al c
ontr
ol p
erf
orm
ance
ob
ject
ive
u
•A
nti-
win
dup s
trate
gie
s
limit
state
of
dyn
am
ic c
ontr
olle
r
e.g
. in
tegra
l term
of
PI
or
PID
C21
Mode
l P
red
ictive
Con
tro
l1
-26
Co
ns
tra
int
ha
nd
lin
g
Eff
ect
s of
input
satu
ratio
n:
()
uu
ku
&&
unco
nst
rain
ed c
ontr
ol l
aw
:fr
eeu
satu
rate
d c
ontr
ol l
aw
:m
in{
,}
0
max
{,
}0
free
free
free
free
uu
uu
uu
u
,(
=-
<.
05
10
15
20
25
30
35
40
-202468
u
05
10
15
20
25
30
35
40
-505
y
sa
mp
le
sa
tura
ted
lq
ru
nco
nstr
ain
ed
lq
r
Exa
mple
:
input
satu
ratio
n
+
•poss
ible
inst
abili
ty
•poor
perf
orm
ance
(unst
able
ope
n-loo
p p
lant)
1,1
uu
=!
=fr
ee
LQ
uK
x=
as
befo
re(
,,
)A
BC
C21
Mode
l P
red
ictive
Con
tro
l1
-27
Co
ns
tra
int
ha
nd
lin
g
De-t
unin
g o
f o
ptim
al c
ontr
ol l
aw
:
LQ
K=
optim
al f
/bgain
for
LQ
cost
0
TT
k
Jx
Qx
uR
u)
)
=
=+
'In
crease
until
satis
fies
const
rain
ts t
hro
ughout
opera
ting r
egio
n
RL
Qu
Kx
=
01
02
03
04
05
06
07
0-20246
y
sa
mp
le
01
02
03
04
05
06
07
0-202468
u
lqr,
R=
10
00
lqr,
R=
0.0
1
Exa
mple
:
31
0R
=2
10
R!
=
+
6se
ttle
T=
40
sett
leT
=
•sl
ow
outp
ut
conve
rgence
•but
stabili
ty g
uara
nte
ed
as
befo
re(
,,
)A
BC
C21
Mode
l P
red
ictive
Con
tro
l1
-28
Co
ns
tra
int
ha
nd
lin
g
Anti-
win
dup: a
void
s in
stabili
ty in
co
ntr
olle
r w
hen c
onst
rain
ts a
re a
ctiv
e
•poor
perf
orm
ance
or
inst
abili
ty is
poss
ible
uu
=or
or
exp
one
ntia
lly
u(
)v
tu
*u
/
uu
u&
&1
()
i
uK
ee
dt
T=
+0
/
+u
is n
o lo
nger
satu
rate
d w
hen
c
hanges
sign
e
•M
an
y poss
ible
appro
ach
es,
e.g
. P
I co
ntr
olle
r:
1
1i
sT+
Ke
u
v
sat(
)
i
uK
ev
Tv
vu
=+
+=
$u
u
C21
Mode
l P
red
ictive
Con
tro
l1
-29
Co
ns
tra
int
ha
nd
lin
g
•A
nti-
win
dup is
base
d o
n p
ast
behavi
our
of
pla
nt
alo
ne
•N
eed t
o a
ntic
ipate
futu
re c
onst
rain
t vi
ola
tion
MP
C o
ptim
izes
futu
re p
erf
orm
ance
05
10
15
20
25
30
35
40
-10123
u
05
10
15
20
25
30
35
40
-505
y
sa
mp
le
mp
c, N
=1
6sa
tura
ted
lq
r
Exa
mple
:
const
rain
ed M
PC
vs.
satu
rate
d L
Q f
eedb
ack
as
befo
re(
,,
)A
BC
(both
base
d o
n c
ost
)J
)
sett
leT
•re
duce
d t
o 2
0 w
ith M
PC
•st
abili
ty g
uara
nte
ed
C21
Mode
l P
red
ictive
Con
tro
l1
-30
Su
mm
ary
•P
redic
t perf
orm
ance
usi
ng
pla
nt
mode
l
•lin
ear
or
non
line
ar,
dis
crete
or
contin
uous
time
•O
ptim
ize f
utu
re in
puts
•co
mputa
tion
ally
easi
er
than
optim
izin
g c
lose
d-lo
op
•Im
ple
ment
first
sam
ple
, th
en
repeat
optim
izatio
n
•pro
vides
fee
dback
to r
educe
eff
ect
of
unce
rtain
ty
•H
andlin
g s
yste
m c
onst
rain
ts:
•S
atu
ratio
n,
anti-
win
du
p,
de
-tunin
g
•M
PC
