process control ppt

7/25/2019 process control ppt

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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$


27/55

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


29/55

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."


30/55

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


42/55

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


44/55

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


45/55

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


46/55

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


48/55

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


49/55

'>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


50/55

'>uist Sta$ilit' Criteria'>uist Sta$ilit' Criteria

Given G0iR3% assu(e that at afre>uenc' Ru% such that V-1


51/55

"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


52/55

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

+



53/55

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-


54/55


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



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1& +lti(ate properties Approach:Fu@1&7

process control ppt

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