Post on 26-Feb-2018
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CHE517CHE517
AdvancedAdvancedProcess ControlProcess ControlProf. Shi-Shang JangProf. Shi-Shang Jang
Chemical Engineering DepartmentChemical Engineering Departmentational !sing-H"a #niversit$ational !sing-H"a #niversit$
Hsin Ch"% !ai&anHsin Ch"% !ai&an
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Course DescriptionCourse Description Course: CHE517 Advanced Process Control Instructor: Professor Shi-Shan !an "e#t: Se$or% D&E&% Process D'na(ics and
Control% )nd Ed&% *ile'% +SA% ),,& Course .$/ective: "o stud' the application ofadvanced control (ethods to che(ical andelectronic (anufacturin processes
Course Policies: .ne E#a(0,23% a finalpro/ect 0,23 and $i4eel' ho(e4or0,23
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Course .utlineCourse .utline
1& 6evie4 of eed$ac Control S'ste()& D'na(ic Si(ulation +sin 8A"9A
and Si(u-lin& eedfor4ard Control and Cascade
Control& Selective Control S'ste(
5& "i(e Dela' Co(pensation;& 8ultivaria$le Control
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Course .utline - ContinuedCourse .utline - Continued
7& Co(puter Process Control
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eed$ac Controleed$ac Control
E#a(ples: 6oo( te(perature control Auto(atic cruise control Steerin an auto(o$ile Suppl' and de(and of che(ical enineers
Controller
Transmitter
Set point
stream
Temp
sensorHeat loss
condensate
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eed$ac Control-$loceed$ac Control-$locdiara(diara(
"er(inolo':
Set point 8anipulated varia$le 08?3 Controlled varia$le 0C?3 Distur$ance or load 0D?3 Process controller
Controller process
Sensor +
transmitter
+
-Set point
Measured value
error
Manipulated
variable
Controlled variable
disturbance
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Instru(entationInstru(entation
Sinal "rans(ission: Pneu(atic -15psi% safe loner ti(e las% relia$le Electronic -),(A% current% fast% eas' to interface 4ith co(puters% (a' $e sensitive to
(anetic and@or electric fields "ransducers: to transfor( the sinals $et4een t4o t'pes of sinals% I@P: current to
pneu(atic% P@I% pneu(atic to current
Controller
Transmitter
Set point
stream
Temp
sensorHeat loss
condensate
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8odelin8odelin
6ate of accu(ulation Input output B eneration consu(ption
At stead' state : let " "S and S , S+A0"S- ",S3
Deviation varia$les : let " "SB"d% SBd% ", ",sB",d
"hen :
If s'ste( is at stead' state initiall' "d0,3 ,
)()( 0TTUAQTMCdt
dP =
Mass M
Cp
T
QQ=UA(T-T!
)()( 0ddddP TTUAQTdt
dMC =
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!ransfer '"nctions!ransfer '"nctions(aplace !ransforming)(aplace !ransforming)
M Cp S Td(S! = "d(S! - U A (Td(S! Tod(S!!
#r
( ) ( ) ( )
UASMC
SUAT
UASMC
SqST
p
od
p
dd
++
+=
UAMsC
UA
p+
UAMsCp+
1
$Td(S!
+
+
"d(S!
Tod(S!
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on-isother(al CS"6on-isother(al CS"6
"otal (ass $alance:
8ass $alance :
Ener' $alance :
Initial conditions : ?0t,3 ?i% "0t,3 "i% CA0t,3 CAi
Input varia$les : ,% CA,% ",%
FFVdt
d= 0)(
condensate
T % & CAC'
&
CAT
&
CAT
steam
A'
rA= - )CA mol*t,
) = e-.*/T
VKCCFCFCVdt
dAAAA )()( 00 =
)())(()( 00 TTsUAKCHrTCFTCFTCVdt
dAPPP ++=
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9ineariation of a unction9ineariation of a unction
00 - 0+
-
(0!
0
a0+b
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9ineariation9ineariation
( ) ( ) ( )
( ) ( ) ( )
( )
0 0
0 0
0 0
0 0
,
( , )
0
Laplace Transform
( )
1
x x x xu u u u
dd d
d d d
d
d
dx f f f x u x x u u
dt x u
f x u
dxax bu
dt
sx s ax s bu s
or
x s b K
u s s a s
= == =
= +
+
= + +
= +
= = +
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9ineariation of on-9ineariation of on-isother(al CS"6isother(al CS"6
12
12
11 0 ,
,
21 22 , 11 0,
31 32 , 33 31 0, 32 , 33
11 12
, 21 22 , 21 22 23
31 32 33 31 32 3
. .
0 0 0 0
0
dd d
A d
d A d d d
dd A d d d A d d
d d
A d A d
d d
dVb F b F
dt
dCa V a C b F b F
dt
dTa V a C a T b F b C b Ts
dti e
V V b bd
C a a C b b bdt
T a a a T b b b
= +
= + + +
= + + + + +
= +
[ ] [ ]
( ) { }( ) ( ) ( ) ( ) ( )
0,
3 ,
0,
,
,
1
0,
( ) ( )
0 0 1 0 0 0
( ) ( )
( ) '
d
d
s d
d d
A d d
d s d
d
p d L d L d
F
F AX s BU s
T
V F
y C F CX DU
T T
T s C sI A B D U s
G s Ts s G s F s G s F s
= +
= + = +
= + = + +
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Co((on "ransfer unctionsCo((on "ransfer unctionsFGain ti(e constantFGain ti(e constant
Jda(pin factor Ddela'Jda(pin factor Ddela'
irst .rder S'ste(
Second .rder S'ste(
irst .rder Plus "i(e Dela'
Second .rder Plus "i(e Dela'
( ) 1
)(
+=
s
K
sMV
sCV
( )Dse
ss
K
sMV
sCV
++=
12
)(22
( )Dse
s
K
sMV
sCV
+=
1
)(
( ) 12
)(
22 ++=
ss
K
sMV
sCV
" f i f" f i f
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"ransfer unctions of"ransfer unctions ofControllersControllers
Proportional Control 0P3
Proportional Interal Control 0PI3
Proportional-Interal-Derivative Control 0PID3
m(s! = )c1 e(s! 2
e = Tspt- T)c
e(s! m(s!
+=
t
0
c dt)t(e
1
)t(e!)t(m
+= )s(e
s
1)s(e!)s(m
c
e(s! m(s!)s
11(!
c
+
e(s! m(s!)ss
11(! "
c ++
+
+=
t
0 "
cdt
dedt)t(e
1)t(e!)t(m
[ ]
+
+= ss
11)s(e!)s(m "
c
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"he Sta$ilit' of a 9inear"he Sta$ilit' of a 9inearS'ste(S'ste(
Given a linear s'ste( '0s3@u0s3
G0s30s3@D0s3 4here % D arepol'no(ials
A linear s'ste( is sta$le if and onl' ifall the roots of D0s3 is at 9HS% i&e&%the real parts of the roots of D0s3 areneative&
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Sta$ilit' in a Co(ple# Plane
/e
3m
4urd5 oscillator5
4urd5 oscillator5
ast 6eca5 Slo7 6eca5
.8ponential 6eca5
.8ponential 6eca5
7it9 oscillator5
Slo7 :ro7t9
ast .8ponential
:ro7t9
.8ponential :ro7t9
7it9 oscillator5
Stable (;H4! Unstable (/H4!
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Partial Proof of the "heor'Partial Proof of the "heor'
or e#a(ple: y(s)/u(s)=K/(s+1)
"he root of D(s)=-1/
In ti(e do(ain: y+y=ku(t) "he solution of this .DE can $ederived $' y(t)=e-t/ [e1/ku(t)dt+c]
It is clear that if K,% li(t L
' L&
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"ransfer functions in parallel"ransfer functions in parallel
M0S3 G10S3N+10S3 B G)0S3N+)0S3
U(S!
0
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"ransfer function loc"ransfer function locdiara(diara(
)c+
-
Tset
control
QS
process
c (S! e(s! = >c e
0< = >p m = >p >c e
0 = >; ; + 0; ; + >p >c e
0m= >m 0 = >m >; ; + >p >c e
0 = >; ; + >p >c10s 0m2
= >; ; + >p >c 10s2 >p >c 10m2
=>; ; + >p >c 0s >p >c >m 0
s
mcp
cp
mcp
L #$$$1
$$L
$$$1
$#
++
+=
$ 0(S!
+
+
>;(S!
>4(S!
>m(S!
;(S!
m>c(S!$
+
-0s
0m
0uation :
1BGc0s3Gp0s3G(0s3,
are all in 9HP
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9evel S'ste(9evel S'ste(
( ) ( )
( ) ( )
( )
( ) ( ) 11%%11
Laplac&n
2
,po&ntreferencea$&en
.
,
0
,00
00
+=
+=
+=
=+
=+
==
s
K
saA
a
aAssF
s!or
sFsa!"s#As!
!!
$F!!!fFF
Ff
dtd!A
!F
!$FFFdt
d!A
di%
d
di%dd
ddi%i%i%
i%
d
i%
i%outi%
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h l dA i h l ! d CS"6
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A onisother(al !aceted CS"6A onisother(al !aceted CS"6 i/ 0aterial alance of species A
ii/ Energ$ alance of the ,ac+et
iii/ Energ$ alance for the reactor
iv/ Dependence of the rate constant ontemperat"re
2)(A
AAA $CV
CC&dt
dC f =
P
A
P
'f
C
H$C
VC
TTA
V
TT&
dt
dT
2)()(
=
'
(''
P'
''
M
TT&
CM
TTA
dt
dT )(
'
)(
=
)
23
e*p(0
+
=
T
QA$
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9ineariation of9ineariation ofonisother(al CS"6onisother(al CS"6
C?"0t3
8?*c0t3
It can $e sho4n that
( )
( ) 123,
+++=
'sbsas
K
s&
sT
d'
d
A P ti l E lA Practical E#a(ple " t"e(perature
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A Practical E#a(pleA Practical E#a(ple "e(perature"e(peratureControl of a CS"6Control of a CS"6
8ethod of 6eaction Curve8ethod of 6eaction Curve
6
6ead time
Ma8imum slope
C
4rocess
output
Time constant time
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Oieler-ichols 6eaction CurveOieler-ichols 6eaction Curve
"unin 6ule"unin 6ule+ onl + +"
!c %"!p 0.-%"!p 1.2%"!p
n.a. "%0.3 "%0.
"
n.a. n.a. 0."
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C
6
m
6= uenc' Do(ainAnal'sisAnal'sis
Definitions: Given a transfer functionG0s3'0s3@#0s3 Given #0t3AsinRt4e have '0t3 sin0RtBU3
*e denote A(plitude 6atioA60R3@A Phase AnleU0R3
oth A6 and U are function of
fre>uenc' R 4e hence define A6and U is the fre>uenc' response ofs'ste( G0s3
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An E2ampleAn E2ample
( )( ) ( )3211
+++ sssA sin(t! ' = sin(t+!
6 f e> enc 6esponse of a
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re>uenc' 6esponse of are>uenc' 6esponse of afirst order s'ste(first order s'ste(
( )
1
22
1
22
22
22
tan
1
tan)s&n(1
)(
1)(
)(s&n)(1
)()(
)(
=+
=
=++
++=
+==
+==
KA*
tKA
ty
s
K
s
Asy
s
AsxtAtx
s
KsG
sx
sy
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asic "heore(asic "heore( Given a process 4ith transfer function
G0s3
A60R3 G0iR3
V0R3 G0iR3 asicall'% G0iR3aBi$
( )ab
baA*
%tan 1
22
=
+=
E l i t . dE#a(ple: irst .rder
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E#a(ple: irst .rderE#a(ple: irst .rderS'ste(S'ste(
( )
( )
-0l&m
0l&m
tatote
tantan
1
11
)(
1
1
1
)(1
1
1
1
1)(
11
22
22
222222
=
=
=
=
+=+=
+=
+
+
+
=
+
=
+
=
+=
A*
a
b
baA*
ibaii
i
iG
ssG
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Corollar'Corollar'
If G0s3G10s3G)0s3G-0s3
"hen A60G3A60G13 A60G)3 A60G-3
V0G3V 0G13 BV 0G)3BV 0G-3
Proof: .(itted
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E#a(pleE#a(ple
( ) ( ) ( ) ( )
( ) ( )
( ) ( )211121
22
2
2
22
1
121
212
2
1
1
tantan
11
11)(
=+=
++==
=++
=
KKA*A*A*
sGsGKK
sG
ode Plot: An e#a(pleode Plot: An e#a(ple
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ode Plot: An e#a(pleode Plot: An e#a(pleG0s31@0sB130sB)30sB3G0s31@0sB130sB)30sB3
4here d$),lo4here d$),lo1,1,0A630A63
'>uist Plot'>uist Plot
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'>uist Plot'>uist Plots'stf0nu(%den3s'stf0nu(%den3
W+IS"0s's%X4(in%4(a#Y33W+IS"0s's%X4(in%4(a#Y33
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'>uist Sta$ilit' Criteria'>uist Sta$ilit' Criteria
Given G0iR3% assu(e that at afre>uenc' Ru% such that V-1
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"he E#tension of '>uist"he E#tension of '>uistSta$ilit' CriteriaSta$ilit' Criteria
Given plant open loop transferfunction G0s3% such that at afre>uenc' Ru% the phase anle
V0Ru3-1
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Si(ulin E#a(pleSi(ulin E#a(ple
ti(e
6espo
nse
D1& &7-1&)&
s
P es
G .0
1.2
14.0
+
Si(ulin E#a(pleSi(ulin E#a(ple
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Si(ulin E#a(ple -Si(ulin E#a(ple -ContinuedContinued
\\ s'stf01%]1 ; 11 ;^3
"ransfer function:
1
----------------------
s_ B ; s_) B 11 s B ;
\\ $ode0s's3
u&5A6u-
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Si(ulin E#a(ple -Si(ulin E#a(ple -ContinuedContinued
1& 6eaction Curve Approach:FC1&)@DFp1&)N)&5@0,&5N,&1;53;ID@,&51DDN,&5,&)5
0 1 2 3 4 5 6 7 8 9 100
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Si(ulin E#a(pleSi(ulin E#a(ple
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Si(ulin E#a(ple -Si(ulin E#a(ple -ContinuedContinued
1& +lti(ate properties Approach:Fu@1&7