Ph.D. Summer school Process and Tools Integration Operability and Control for Process Integration 17. August 2005 Sten Bay Jørgensen CAPEC - Department

Ph.D. Summer schoolProcess and Tools Integration

Operability and Control forProcess Integration

17. August 2005

Sten Bay Jørgensen

CAPEC - Department of Chemical Engineering Technical University of Denmark,

DK-2800 Lyngby, Denmark

C A P E C

8/8-2/9 2005 Operability and Control for Process Integration 2

Motivation for Process and Design Integration

No recycle of information flow (arrow) – Integration possible ?

Issue 1 Issue 2

Issue 1 Issue 2

Recycle of information flow – Integration possible?

Sequential design of Heat integration Mass integrationControl

Integrated design ofHeat and mass integrationwith control

Requirement: Measures for dynamic consequences of integration to be used early in the design phase for control structuring and design


Dynamics and Control of Integrated Plants

• Process dynamics and control – a recap!

• Transfer functions, dynamics and stability

• Process integration structures

• Effects of process integration on dynamics and control

• Analysis of linear behaviour

• Implications upon control

• Nonlinear behaviour

• Dynamic consequences of optimal operation

• How to configure control?


Schedule for Operability and Control of integrated plants

Lecture 1: Process dynamics and control recap 1

Lecture 2: Process dynamics and control recap 2

Lecture 3: Control of plants with units in series

Lecture 4: Dynamics of integrated processes

Lecture 5: Control effects of recycle

Lecture 6: Effects of process integration and optimization


Lecture 1: Process Dynamics and Control recap 1

• Chemical Process Dynamics Simplified

• Material Balance Control


Chemical Process Dynamics

A → B

A + B

A

B

Heat Exchanger Reactor Separator

Standard process dynamics considers single simple standard units with linear dynamics expressed in transfer functions


Material Balance P-Control exit flow

LC

F i

Fo

oi FFdt

dV

)(0 VVKFF setcoo

)()()()()()(

)()()()()()(00

00

tVtVtrtFtFtd

tFtFtutVtVty

setii

oo

)()()(1

)()(

)()(1

)()()( sD

sGsG

sGsR

sGsG

sGsGsY

pc

pd

pc

pc

ssG

ssGKsG pdpcc

1)(

1)()(

G c(s) G p(s)SR (s) U (s) Y (s)

-

G pd(s)

S

D (s)


Material Balance P-Control simulation

LC

F i

Fo

oi FFdt

dV

)(0 VVKFF setcoo

0 2 4 6 8 104

4.5

5

V

0 2 4 6 8 102

2.5

3F

o

0.4)0(

0.30.20

set

ii

VV

FF


Material Balance PI-Control

LC

F i

Fo

oi FFdt

dV

0)0()),()(()(

))()(()(

)()(0

ItVtVT

K

dt

tdI

tVtVKtP

tItPFF

seti

c

setc

oo

)()()()()()(

)()()()()()(00

00

tVtVtrtFtFtd

tFtFtutVtVty

setii

oo

)()()(1

)()(

)()(1

)()()( sD

sGsG

sGsR

sGsG

sGsGsY

pc

pd

pc

pc

ssG

ssG

sTKsG pdp

icc

1)(

1)(

11)(

G c(s) G p(s)SR (s) U (s) Y (s)

-

G pd(s)

S

D (s)


Material Balance PI-Control simulation

LC

F i

Fo

oi FFdt

dV

0.4)0(0.30.20 setii VVFF0 2 4 6 8 10

2

2.5

3

3.5

Fo

0 2 4 6 8 103.5

4

4.5

5

V

0)0()),()(()(

))()(()(

)()(0

ItVtVT

K

dt

tdI

tVtVKtP

tItPFF

seti

c

setc

oo


Material Balance P-Control inlet flow

LC

F i

Fo

oi FFdt

dV

)( VVKF setci

0.4)0(

0.30.20

set

oo

VV

FF 0 2 4 6 8 102

2.5

3F

i

0 2 4 6 8 103

3.5

4

V


Material Balance PI-Control simulation

LC

F i

Fo

oi FFdt

dV

0.4)0(0.30.20 setoo VVFF0)0()),()((

)(

))()(()(

)()(0

ItVtVT

K

dt

tdI

tVtVKtP

tItPFF

seti

c

setc

ii

0 2 4 6 8 103.4

3.6

3.8

4

4.2

V

0 2 4 6 8 102

2.5

3

3.5

Fi


Lecture 2: Process Dynamics and Control recap!

• Transfer functions and single loop control

• Internal model based control

• Performance limitations in single loop control

• Control of Production Rate in Chemical Plant

• Front end control (Push)

• On demand control (Pull)


Transfer functions

Local Transfer Function • zi a zero in left half plane gives overshoot• pj a pole in left half plane gives exponential decay

Initially single variable transferfunctions are considered, i.e. all signals are scalars: gi(s) = ni(s)/di(s)

Transfer functions will also be divided into g(s)=ga(s)gm(s)where gm(s) is the minimum phase partand ga(s) is the allpass part,which contains all nonminimumphase components:

n

1j j

m

1i iprod

)ps(

)zs()s(G

)s(F

)s(X

*i

isTa

zs

zse)s(G


Single Control Loop

u

d

y

gd

g

u y

gd

gcg

-1

d

r

Standard single variable open loop process:

y = g u + gd d

• Significantly reduces sensitivity to disturbances at low frequences

• For high gain control the sensitivity to model uncertainty is significantly reduced

• Control performance is limited for RHP zeros, i.e. Nonminimumphase behaviour

rgg

ggd

gg

gy

c

c

c

d

11

Standard single loop control:


Internal Model Based Control Design

dGrGy

sGsG

VGVGsG

sVsVsVsG

sGsGsGsG

aa

mcIMC

mammcIMC

mam

ma

)^1(^

)(^)( :esdisturbanc stepFor

^^)(

:controller IMC by theerror integral minimum with controlled is

)()()( edisturbanc theand stable, is )(^ where

)(^)(^)(^ model with the)( process The

1

1

mammcIMC

mam

ma

VGVGsG

sVsVsVsG

sGsGsGsG

1ˆˆ)(

:controller-IMC by theerror integral minimum with controlled is

)()()( edisturbanc theand stable, is )(ˆ where

)(ˆ)(ˆ)(ˆ model with the)( process The

1

)(ˆ)( :esdisturbanc stepFor 1 sGsG mcIMC

u y

gd

gcIMCg

-1

d

r

-ĝm

The IMC regulator gives the closed loop:

dGrGy aa )ˆ1(ˆ

Thus the nonminimum phase inĜa limits achievable performance!


Control Performance Reducing DynamicsControl Performance Reducing Dynamics

TimeX

prod

• Local Transfer FunctionLocal Transfer Function

n

1j j

m

1i iprod

)ps(

)zs()s(G

)s(F

)s(X

• Zero Dynamics Zero Dynamics – Real zero in right half planeReal zero in right half plane

• Singularities Singularities (due to sensitivity to uncertainty)(due to sensitivity to uncertainty)

– Real pole into right half planeReal pole into right half plane

– Complex pole pair into right half planeComplex pole pair into right half plane

Time

Xpr

od

Time

Xpr

od


Material Balance P-Control

LC

F i

Fo

oi FFdt

dV

)(0 VVKFF setcoo

)()()()()()(

)()()()()()(00

00

tVtVtrtFtFtd

tFtFtutVtVty

setii

oo

)(1

)(

)()()(1

)()(

)()(1

)()()(

sDKs

sRKs

K

sDsGsG

sGsR

sGsG

sGsGsY

cc

c

pc

pd

pc

pc

ssG

ssGKsG pdpcc

1)(

1)()(

Gc(s) Gp(s)SR(s) U(s) Y(s)

-

Gpd(s)

S

D(s)

)()()( sYsRKsU c


Plant Production Rate – Front End 1Raw

MaterialStorage

Purchasing

FinalProductStorage

LC LC LC

F i Fo

Management or ProductionSupervision

oP

i

FFdt

dV

FFdt

dV

FFdt

dV

FFdt

dV

3

323

212

11

)(

)(

)(

3,330

33

2,220

22

1,110

11

VVKFF

VVKFF

VVKFF

setc

setc

setc



MaterialStorage

Purchasing

FinalProductStorage

LC LC LC

F i Fo


)()(1

)(

)()(1

)(

)(1

)(

23

22

33

12

11

22

01

1

sYKs

KsU

KssY

sYKs

KsU

KssY

sUKs

sY

c

c

c

c

c

c

c

)()(

)()(

)()(

333

222

111

sYKsU

sYKsU

sYKsU

c

c

c

)(1

)()()(

)( 333 sD

ssY

s

K

s

sDsUsY c

P



MaterialStorage

Purchasing

FinalProductStorage

LC LC LC

F i Fo


)(1

)(1

)( 012

1

3

23 sDs

sUKsKs

K

Ks

K

s

KsY

cc

c

c

ccP

Simple strategy )()()()( 00 sDsUtdtu


Plant Production Rate - On Demand Raw

MaterialStorage

Purchasing

FinalProductStorage

LC LC LC LC

F i Fo

oP

i

FFdt

dV

FFdt

dV

FFdt

dV

FFdt

dV

3

323

212

11

)(

)(

)(

)(

,0

33

3,330

22

2,220

11

1,110

PsetPcP

setc

setc

setcii

VVKFF

VVKFF

VVKFF

VVKFF


Lecture 3: Control of Plants with units in series

• Units in Series

• Disturbance effects

• Production rate – front end

• Production rate – on demand

• How to achieve changes in production rate

• Partial control

• Reactor control

• Examples of Production rate control


Units in Series - No Recycle

• The plantwide control problem is greatly simplified when there is no recycle of mass or energy.

• The control system of each unit is configured individually to handle load disturbances.

C

A B CA

B C

B

• Separation ExampleVolatility order: A > B > C

Direct Sequence: The lightest component is taken out of the top of the first column.


Production Rate - Front End

PC

CCLC

CC

LC

C

PC

CCLC

CC

LC

FC

A B CA

B C

B

Disturbances propagate in the direction of mass flow


Production Rate - On Demand

PC

CCLC

CC

LC

C

PC

CCLC

CC

LC

A B CA

B C

B

FC

Disturbances propagate in the opposite direction of mass flow


Production Plant without recycles Production Plant without recycles

Raw MaterialPurification

ProductPurification

ReactorRaw Material Product

An ideal abstraction since energy and rawmaterials are not used very efficiently!


Production Rate

• Changes in production rate can be achieved only by changing the conditions in the reactor.

• Some variable that affects the reaction in the reactor must vary.

Liquid Phase Reactors• Hold-up• Temperature• Concentrations

Gas Phase Reactors• Pressure• Temperature• Concentrations


Partial Control

• Often for reactors (and other units) the number of control objectives exceed the number of manipulated variables.

• We must assign manipulated variables to achieve the control objectives, which must be important for the operation of the plant and leave the rest of the variables uncontrolled.


Plantwide Production Rate Control

• Production rate changes should be achieved by modifying the setpoint of a partial control loop in the reaction section.

• Separation section will not be significantly disturbed.


Reactor Control

• Managing energy (temperature control)• Keeping as constant as possible the composition

and flow rate of the total reactor feed stream (Fresh feed and recycle).


Units in Series - Production Rate

A

A BA

B

TR

EATkxTkVR

BA

g

aA exp)()( 0

• How do we specify and control the plant-wide production rate of B, when there is a reactor in the plant?

• Reaction kinetics has to be considered!

AAg

a

x

R

x

R

TR

E

T

R

T

R

V

R

V

R

Sensitivities:


A

A BA

B

CCLC

CCLC

PC

CC

LC


AxTkVR

BA

)(

• The production rate is controlled through partial control of the reaction rate.V controlledxA controlledT controlled (by ass.)

• Production rate may be changed by changing the setpoint to the reactor CC or the reactor LC.

• Reactor LC change will not change the composition fed to the distillation col.

All three dominant reaction rate variables controlled => SMALL variance.



A

A BA

B

FC

LC

CCLC

PC

CC

LC

AxTkVR

BA

)(

• One dominant variable, xA, of the reaction rate is uncontrolled because reactor composition measurement is not possible.

• Reaction rate and production rate may fluctuate.

• Production rate may be changed by changing the setpoint to the reactor FC or the reactor LC.

• Rate set at front end.

xA not controlled directly. This leads to larger variance in the production rate than

in the previous configuration.



A

A B

A

B

LC

CCLC

PC

CC

LC

FCAxTkVR

BA

)(

• On-Demand:The production rate is specified by setting the FC of the bottom product in the distillation column.

• The disturbances propagates in the opposite direction of the mass flow.

xA not controlled directly. This leads to larger variance in the production rate than

in the first configuration.


Lecture 4: Process Integration and Dynamics

• Process Integration Structures

• Series – has been covered

• Parallel

• Recycle

• Example Recycle Plant models

• Disturbance Sensitivity of Recycle plant


Generic Production Plant Generic Production Plant

Raw MaterialPurification

ProductPurification

Reactor

Energy Recycle

Reactant Recycle

Raw Material Product

Process integration is mandatory for energy and rawmaterial efficiency!


Dynamic consequences of process integration

g1(s) g2(s) g3(s)

g4(s)

• Plant as an integration of different unit processes • Relate behaviour of integrated plant to

• behaviour of individual units• structure of interconnections

• Thereby existing knowledge of unit behaviour can be exploited, for the analysis of linear behaviour

Hangos (1991) and Jacobsen (1999)


Interconnection Structures

g1(s) g2(s)g1(s)

g2(s)

Series Parallel

g2(s)

g1(s)

Recycle

Zeroes and poles are the union of those of units

Zeroes are movedPoles are the union of those of units

Zeroes are the union of those of n1 and poles of d2

Poles are moved!

21

1221

21 )()()(

dd

dndn

sgsgsg

2121

21

21

1

)()(1

)()(

nndd

dn

sgsg

sgsg

21

21

21 )()()(

dd

nn

sgsgsg


Summary: Process Integration Structures

• Series and parallel interconnections:

Realtively simple to deduce overall behaviour from unit behaviours (only zeros are affected in parallel interconnections).

• Recycle interconnections:

More complicated relation between overall behaviour and unit behaviours (poles are moved).


Simple Recycle Example (1)

SeparationSection

Reactor Section

Recycle

Feed

Product

ReactorEffluent

1222222

2111111

xuubxadt

dx

xuuubxadt

dx



SeparationSection

Reactor Section

Recycle

Feed

Product

ReactorEffluent

1222222

2111111

xuubxadt

dx

xuuubxadt

dx

Laplace Transformation

ii

i

ii aa

bK

sXs

KsX

sUs

KsX

1

)(1

)(

)(1

)(

12

22

11

11

SU

X2

X1

++

G 2(s)

G 1(s)U1



SU

X2

X1

++

G 2(s)

G 1(s)U1

)()()()()(

))()()(()(

1211

211

sXsGsGsUsG

sXsUsGsX

)(1

11

1

1

)()1)(1(

)1(

)(

111

1

)()()(1

)()(

21

212

21

21

2

21

1

2121

21

2

2

1

1

1

1

21

11

sUs

KKs

KK

s

KK

K

sUKKss

sK

sU

sK

sK

sK

sUsGsG

sGsX

1

)(1

)(2

22

1

11

s

KsG

s

KsG

)(

1

1)(

:1

21

21

2

21

11

21

sU

ss

sKsX

KK

:121 KK



:121 KK

)(12

1

)(1

11

1

1)(

222

21

212

21

21

2

21

11

sUss

sK

sUs

KKs

KK

s

KK

KsX

)1(

)(

2

1

11 2121

221

21

21

21

1

KKKKKK

KK

:10 21 KK 1)1(

)(

2

1

2121

221

KK

)()1)(1(

1)( 2

1 sUss

sKsX

BA

1

1

2

2

B

A



)()1)(1(

1)( 2

1 sUss

sKsX

BA

0 0.5 10

5

10

15

20

0 0.5 10.5

0.6

0.7

0.8

0.9

1

0 0.5 10

20

40

60

80

100

)1(

)(

2

1

11 2121

221

21

21

21

1

KKKKKK

KK

11 22 BA

blue

redK

4

111 212

1K .vsK 1A K .vs 1B K .vs



)()1)(1(

1)( 2

1 sUss

sKsX

BA

0 20 40 60 80 1000

2

4

6

8

10

K1=0.4

K1=0.8

K1=0.9

time

X 1

1

1

1

2

1

2

K

Both the time constant and the steady-state gain has been dramatically changed by the recycle stream

Unit Step Response


Snowball Effect

• Observation: Recycle systems has a large tendency to exhibit large variations in the magnitude of the recycle flow.

SU

X2

X1

++

G 2(s)

G 1(s)U1

)()1)(1(

1)( 2

1 sUss

sKsX

BA

)()1)(1(

)(1

)(

2

12

22

sUss

KK

sXs

KsX

BA

21

1

1 KK

KK

• Snowball effect: sensitivity of recycle flow rates to small disturbances


Snowball Effect – Static analysis• Snowball effect: sensitivity of recycle flow rates to small disturbances

F, xF

A=>B

R, xR

V

B , xB

L

D

Only show composition of reactant A, i.e. xAll A is removed in Distillate, i.e. xB=0 and xD=1:

Total balance:RB VkxBxFx

F

Component balance around reactor:

RRDF VkxRxxFRFx )(

Dax

FxDa

FDa

FxVk

VkF

xx

BxFxxxF

xx

VkxxxFR

FFF

RD

BFFD

RD

RFD

1

1

)()(

Thus if Da = Vk/F approaches xF then R can become very large!


Control Implications of the Snowball Effect

• Set the production rate at the front end, I.e. by setting U.

• If the snowball effect is dominant, K2*K >> 1, small changes in U lead to large changes in X2.

• Large changes in X2 implies that the recycle valve goes either fully open or closed.

• As X2 is large, X1 is also large and this may overload the separation section.

SU

X2

X1

++

G 2(s)

G 1(s)U1

SeparationSection

Reactor Section

Recycle

Feed

Product

ReactorEffluent

Production rate can typically NOT be set at the front end for mass recycle systems.


Snowball Effect - Example

AxTkVR

BA

)(

A

A

B

BA,

• Isothermal reactor operation (perfect temperature control)

• Produce pure B

• Be able to manipulate the production rate of B

• Select a control structure that will meet these objectives



• All flows in recycle loop set by level controllers

• A small change in the production rate set front-end leads to large changes in the recycle loop flow rates.

• No plantwide control of inventory of A.

LC

FC

PC

CCLC

CC

LC

SMALL flexibility index regarding production rate.

AxTkVR

BA

)(


Snowball Effect - Example• We cannot manipulate production rate directly by manipulating the fresh feed flow

• The setpoint to the reactor LC is used to control production rate

• No snowball effect due to FC in recycle loop

System inventory of A is controlled by the reactor LC. This improves the flexibility index.

FC

LC

PC

CCLC

CC

LC

AxTkVR

BA

)(



• To prevent the snowball effect, the mass recycle loop must have a flow controller.

• The plant inventory of A must be controlled. It is not sufficient to control the individual unit inventories of A.

• In the upper flow sheet any disturbance that increase the total inventory of A in the process will produce large increases in the flowrates around the recycle loop.

LC

FC

PC

CCLC

CC

LC

FC

LC

PC

CCLC

CC

LC



• Consider a 20% production rate increase of B.

• In the first control structure the separation section must handle the entire load, as xA must change with 20%. The feed to the distillation column changes, as well as the feed rate.

• In the second control structure both reactor composition and volume changes. So the separation section sees a smaller load disturbance

• Production rate can only be changed by changing the conditions in the reactor!

LC

FC

PC

CCLC

CC

LC

FC

LC

PC

CCLC

CC

LC

AxTkVRBA )(


Disturbance Sensitivity of single loop control

u

d

y

gd

g

Standard single variable process: y = g u + gd d

u y

gd

gcg

-1

Standard single loop control: gd g gc

y = ----------d + ----------- r 1 + g gc 1 + g gc

Significantly reduces sensitivity to disturbances at low frequences

What happens with process integration?

d


Disturbance Sensitivity with process recycle

ydgd

grec

g = gd/(1 – gd grec) = S gd

• The Sensitivity function S = 1/ (1 – gd grec) catches the effect of recycle upon disturbance sensitivity.

• Instability is induced by recycle if gd grec is stable and

| gd grec (iωc)| > 1 and φ(gd grec (iωc)) = n 2π

where ωc is the critical frequency

• Note feedback may be positive or negative• Control is based upon negative feedback• Recycle introduces positive feedback


Feedback effects on Disturbance Sensitivity

• Negative feedback if | gd grec (0)| < 0

• Static Sensitivity |S(0)| < 1 Hence disturbance sensitivity is reduced at low frequences • The critical frequency ωc > 0 – Increasing the loop gain will yield a pair of complex poles crossing the imaginary axis.• The closed loop response usually is faster

• Positive feedback if | gd grec (0)| > 0 • Static Sensitivity |S(0)| > 1 Hence disturbance sensitivity is increased at low frequencies

• The critical frequency may be at ωc = 0 – thus a real pole crosses the imaginary axis for | gd grec (0)| > 1, i.e. static multiplicity. Or at ωc = n 2π where a complex pair crosses.• Thus the recycle loop response usually is slower if not unstable


Example Plant

Mixer Reactor SeparatorF, xFi xF

A+R=>2R

xR

V

B =R, xB

L

D=F, yD

Note autocatalytic reaction, e.g. bioreactor

Main disturbance: xFi

Objective:Maintain yD constant


Example Plant – Unit models

M

Mixer – static:

Reactor:

Separator:

FrFR xgxs

x

110

6.0

R

DRB

D

x

LG

x

L

sx

y

2.203.0

4.003.0

130

1

FBFi xFRRxFx )( )/()1( FRRkxkkxx FiBF


Example Plant – Block Diagram

1-k gr

GD

k

L yD

xF xR

xB

xFi


Example Plant: Disturbance Sensitivity

1-k gr

k

yD

xF zF

xB

xFi

gD12

gD22

Effect of xFi on yD:

• Sensitivity S = 1/(1-kgrgD22)

Static loop gain: kgr(0) gD22(0) = 1.32 k thus positive feedback

Unstable for k > 0.76 (R/F > 3.1)


Summary on Sensitivity effects of Recycle

• Recycle of material or energy introduces positive feedback which

• increases low frequency disturbance sensitivity

• induces slower dynamics or instability

• Thus recycle implies a stronger need for control to reduce the effect of disturbances and also to stabilize the plant

• How to handle the increased disturbance sensitivity?


Lecture 5: Control of Recycle Plants

• Feedback Control of Recycle Plants

• Control of variable in recycle path

• Control of variable not in recycle path

• Summary of control effects of recycle

• Conclusions on linear dynamics and control of Process Integrated Plants


Feedback Control SISO versus recycle variable

d y

g

gd

Standard single variable process: y = g u + gd d

Perfect rejection of disturbance requires:

u = - (gd / g ) d

u

d y

g

gd

Control of variable in recycle loop:

y = (gu + gdd)/(1-gdgrec)= S(gu +gdd)

Perfect rejection of disturbance requires: u = - (gd / g ) d

• Thus required input unaffected by recycle

u

grec


Feedback Control of variable not in recycle 1

d

x

g21

g22

Control of variable not in recycle loop:u

grec

yg11

g12

22221

1211

u

u

gg

gg

x

y

Thus the transfer function from u to y is affected by recycle!But how?

xgdu rec2u2

122 )1( recggSdgSugSx 2221

dgg

gu

gg

ggg

SdguSgggg

xgdgugy

recrec

rec

rec

rec

22

12

22

112211

12211211

1211

11

/1


Feedback Control of variable not in recycle 2

ugg

gggy

rec

rec

22

112211

1

/1

Recycle affetcs the static behaviour such that: 1. It will have more poles in the RHP than g11 if

g22(0)grec(0) >1 and λ11(0) ≠1 2. It will have more zeros in the RHP than g11 if g22(0)grec(0)/λ11(0) >1 and

λ11(0) ≠1.The above two conditions are sufficient for moving a real pole or zero into the RHP. Thus if g11 is stable and nonminimum phase the above two conditions imply that the

recycle system has RHP poles and RHP zeros respectively.

In Conclusion: Closing a control loop from y to u will most certainly be affected by the dynamics introduced through recycle!

G

gg

Det

2211

The recycle

transfer function:


Plantwide Control Structure Design Procedure (Luyben et al.)

• Establish control objectives

• Determine control degrees of freedom

• Establish energy management system

• Set production rate

• Control production quality and handle safety, environmental and operational constraints

• Fix a flow in every recycle loop and control inventories

• Check component balances

• Control individual unit operations

• Optimize economics and improve dynamic controllability


Summary on control effects of recycle

• Control of variables within the recycle loop • Input required to reject a disturbance is unaffected by recycle

• Control of variable not within the recycle loop

• Input required to reject a disturbance is affected by recycle

in fact the effect of control inputs relative to disturbance may decrease significantly.

• Recycle may introduce RHP zeros

If acceptable control is not possible then redesign such that recycle loop gain decreases


Conlusions on linear dynamics and control

• Plant dynamics may be strongly affected by recycles

• Recycle usually gives positive feedback• increases low freqency sensitivity• renders response slower or causes instability

• Controllability for variables outside the recycle loop may be severely reduced by recycle, i.e. reduced efffect of control inputs possibly combined with RHP zeros• Recycle may significantly increase model uncertainty for units in plant compared to that of individual units (not shown).

• Remedy: Redesign loop to decrease loop gain. Often that means modify reactor design!


Lecture 6: Effects of Process Integration on nonlinear behaviour

• The Control Hierachy and degrees of freedom

• Profit Optimizing Control

• Operational Implications

• Example: Continuous cultivation of yeast

• Analysis

• Experiment

• Example with Optimal operation of process integrated plant

• Ammonia reactor with feed-effluent heat exchange


Profit Optimizing Control Profit Optimizing Control

• Productivity in Continuous Process:Productivity in Continuous Process:

• Optimality requires : Max JOptimality requires : Max J

rawprod xFcxFJ

RHSF

xxc

F

x prodrawprod

RHSF

xprod

RHSF

xprod

RHSF

xprod


Gain Changes for XGain Changes for Xprodprod vs. F vs. F

• Output MultiplicityOutput Multiplicity– Dynamic Consequence:Dynamic Consequence:

Instability when (dXInstability when (dXprodprod/dF)<0/dF)<0

• Input MultiplicityInput Multiplicity– Dynamic Consequence:Dynamic Consequence:

May be a zero in RHP, i.e. May be a zero in RHP, i.e. unstable zero dynamics.unstable zero dynamics.


Control Performance Reducing DynamicsControl Performance Reducing Dynamics

TimeX

prod

• Local Transfer FunctionLocal Transfer Function

n

1j j

m

1i iprod

)ps(

)zs()s(G

)s(F

)s(X

• Zero Dynamics - input multiplicityZero Dynamics - input multiplicity– Real zero in right half planeReal zero in right half plane

• Singularities - output multiplicitySingularities - output multiplicity– Real pole into right half planeReal pole into right half plane

– Complex pole pair into right half planeComplex pole pair into right half plane Time

Xpr

od

Time

Xpr

od


Process Analysis: Operational Implications of Optimality

• Complex behaviour may be encountered near an optimal operating point

• Optimised process integrated design increases the likelihood of complex behaviour

Theorems based upon induction:


Continuous Cultivation of Yeast

• Bifurcation analysis reveals:

– Hysteresis curve, multiple steady-states at maximal biomass productivity!

f

0.3 0.32 0.34 0.36 0.38 0.45

10

15

Bio

mas

s [

g/L

]

Dilution rate [1/hr]

Chemostat, Sf = 28g/L

StableUnstable


Adaptive Model Predictive Control Adaptive Model Predictive Control

Controller Bioreactor

Parameter EstimationControl Design

-1

uy ref y

Controller Parameters


Response to Etanol Setpoint ChangesResponse to Etanol Setpoint Changes


Ethanol Concentration vs. Dilution Rate Ethanol Concentration vs. Dilution Rate


Ammonia Reactors

Operating point:Feed temperatureFeed concentrationFeed flow ratePressure

No automatic control of inlet temperature

Feed

By-pass

3-bed quench reactor simple reactor


Energy Integrated Ammonia Reactor

0 1 2 3

5

10

15

20

Inlet Ammonia Mole Fraction [%]

Ou

tlet A

mm

on

ia M

ass

Fra

ctio

n [%

]

Stable Steady StateUnstable Steady StateHopf Bifurcation

Stable Limit CycleUnstable Limit Cycle

Subcritical Hopf bifurcation from the upper steady state

Stable limit cycle coexists with the upper stable steady state

! Safer to operate in region with no stable limit cycle

!

I II III IV V VI I


Dynamic SimulationIn

let A

mm

oni

a M

ole

Fra

ctio

n [%

] • Operate at ignited steady state and increase inlet concentration:– Passing Hopf at 2.3

mole%

– Large amplitude oscillations

• Decrease inlet concentration– Passing cyclic fold at

2.1 mole%

– Stable steady state

0 50 100 150 2001.8

2.0

2.2

2.4

2.6

2.8

Dimensionless time

300

350

400

450

500

550

Be

d O

utle

t te

mp

era

ture

[C]

Hopf

Cyclic fold


Conclusions on nonlinear analysis

• New process design tools should be developed to account for possible nonlinear behaviours

• To operate near optimal operating points reliable model identification and nonlinear control is desirable - a profit margin of 3% has been estimated!

• Is a combined process and nonlinear control design optimization formulation solvable - to exploit the nonlinearity?


General Plantwide Control Structure Design Procedure

• Top down analysis– Define operational objectives– Manipulated variables and degrees of freedom for control– Select primary controlled variables (given ¨via design goal)– Production rate: determine where to set this in the plant, often at some interior

position– Investigate possible nonlinear complex behavioours near optimal operation

• Bottom up design– Regulatory control layer

• Stabilization• Local disturbance rejection

– Supervisory control layer• Keep controlled outputs at optimal setpoints

– Optimization layer• identify active constraints and determine optimal setpoints

– Validation simulations

Extention of Skogestad (2004)


Conclusions on Dynamics and Control of Process Integrated Plants

• Linear Analysis explains large sensitivity of recycle plants especially for control of variables not in recycle path.

• Optimizing Operation exploits nonlinearities, therefore nonlinear analysis is recommendable.

• Nonlinear Analysis explains specific cases – it is therefore difficult to generalise. It is however important to understand how to avoid occurrence of potentially serious problems.


References and Further Reading

• Luyben, Tyreus, Luyben: Plantwide Process Control, McGraw-Hill (1998), chap. 1-3

• Jacobsen, E.W.: On the dynamics of integrated plants – non-minimum phase behaviour. Journal of Process Control 9 (1999) 439-451

• Skogestad, S. : Plantwide control: the search for the self-optimizing control structure: Journal of Process Control 10 (2000) 487-507

• Skogestad, S.: Control structure design for complete chemical plants. Comp. and Chem. Engineering 28(2004)219-234.


Monographs

• Buckley: Techniques of Process Control, Wiley (1964)

• Shinskey: Process Control Systems, McGraw-Hill (1988)

• Rijnsdorp: Integrated Process Control and Automation, Elsevier (1991)

• Luyben, Tyreus, Luyben: Plantwide Process Control, McGraw-Hill (1999)

• Ng, Stephanopoulos: Plant-wide control structures and strategies, Academic Press (2000)

Documents

Ph.D. Summer school Process and Tools Integration Operability and Control for Process Integration 17. August 2005 Sten Bay Jørgensen CAPEC - Department