1 studies on plantwide control antonio carlos brandão de araújo department of chemical engineering...

1

STUDIES ON PLANTWIDE CONTROL

Antonio Carlos Brandão de Araújo

Department of Chemical EngineeringNorwegian University of Science and Tecnology (NTNU)Trondheim, Norway

January 2007

2

Outline

1. About this thesis2. Control structure design (plantwide control)3. A procedure for control structure design4. Control structure design for the HDA process5. Control structure design for the ammonia synthesis process6. Time-scale separation and self-optimizing control7. Limit cycles with imperfect valves8. Conclusion

3

About this thesis

• Motivation:– Need for more improved operation of chemical processes– More sophisticated control schemes.– However, simple enough so it can be implemented.– Lots of theory, but few large-scale case study implementations.

• Focus:– Application of Sigurd’s plantwide procedure to large-scale case studies:

HDA and ammonia synthesis.• Goal:

– First step to real-world implementation.

4

Outline


5

Quiz 1

F0

F

6

Quiz 2

yA,RyB,RyI,R

A Bk1

Ws

zf

zl

zp

yA, yB, yI

xA, xB, xI

FoyA,oyB,oyI,o

F

R

L

P

Araújo, A., Baldea, M., Skogestad, S., Daoutidis, P., Time scale separation and the link between open-loop and closed-loop dynamics, Escape/PSE 2006, Garmisch-Partenkirchen, Germany.

7

Quiz 3Araújo, A., Govatsmark, M., Skogestad, S., Application of plantwide control to large scale systems. Part I – Self-optimizing control of the HDA process, Chemical Engineering Practice.

8

Quiz 4Ammonia synthesis process

BED1

BED2

BED3

11

12

13

14

15

8

9

7

6

5

4

3

10

2HX-001

16

V4

V5

V6

V7

3029 31

1718

33

1

32

34

23

22

19 20

28

27GAS

2526

24

PURGE

21

H-502 H-583

H-501

V-502

K-402

K-401

V1

V2

V3

V8

V9

9

How we design a control system for a complete chemical plant?

• Where do we start?• What should we control? and why?• etc.• etc.

10

Control structure design

• Control structure design includes all the decisions we need to make to get (near) optimal operation.

• Large systems.• Structural issues (important):

– Implementation.– What to control in each layer?– Decentralized or multivariable control?– Do we need RTO?

11

Main simplification: Hierarchical structureObjectives and main issues

PID

RTO

MPC

Planning(months - years) Defines desired changes to the current business.

Defines the timing and volumes of the specifiedactivities needed to meet the company’s objectives.

Implements optimal (economic) policies whereDOF exist.

Guarantees safe, “stable” and smooth operation.

12

ImplementationPractical view: Separate control layer

13

Outline


14

Stepwise procedure plantwide control

I. TOP-DOWNStep 1. DEGREES OF FREEDOMStep 2. OPERATIONAL OBJECTIVES Step 3. WHAT PRIMARY VARIABLES TO CONTROL?Step 4. PRODUCTION RATE

II. BOTTOM-UP (structure control system):Step 5. REGULATORY CONTROL LAYER (PID)

What secondary variables to control?Step 6. SUPERVISORY CONTROL LAYER (MPC)

Decentralization? Step 7. OPTIMIZATION LAYER (RTO)

Can we do without it?

15

• each external feedstream: 1 (feedrate)• splitter: n-1 (split fractions) where n is the number of exit streams• mixer: 0• compressor, turbine, pump: 1 (work)• adiabatic flash tank: 1 (0 with “given” pressure) • liquid phase reactor: 1 (volume)• gas phase reactor: 1 (0 with “given” pressure) • heat exchanger: 1 (duty or net area)• distillation column excluding heat exchangers: 1 (0 with “given”

pressure) + number of sidestreams

Step 1. Degrees of Freedom

16

Step 2. Operational objectives• What are we going to use our degrees of freedom for?• Define scalar cost function J(u0,x,d)

– u0: steady-state degrees of freedom– x: states (internal variables)– d: disturbancesTypical cost function:

• Optimal operation for given d:minu0 J(u0,x,d)s. t.Model equations: f(u0,x,d) = 0Operational constraints: g(u0,x,d) < 0

J = cost feed + cost energy – value products

17

Step 3. What to control?

• Optimal solution is usually at constraints, that is, most of the degrees of freedom are used to satisfy “active constraints”, g(u0,d) = 0

• CONTROL ACTIVE CONSTRAINTS!– cs = value of active constraint– Implementation of active constraints is usually simple.

• WHAT MORE SHOULD WE CONTROL?– Find variables c for remaining unconstrained degrees of freedom u.– Self-optimizing control!!! What else?

18

Self-optimizing Control

Self-optimizing control is when acceptable operation can be achieved using constant set points (cs) for the controlled variables c, without the need to re-optimizing when disturbances occur.

c=cs

19

• Constant setpoints cs give near-optimal operation, i.e., acceptable loss L for expected disturbances d and implementation errors n.

Self-optimizing Control

Acceptable loss ) self-optimizing control

20

Procedure for selecting primary CV

1. Define economics and operational constraints.2. Identify degrees of freedom and important disturbances.3. Optimize for various disturbances.4. Identify (and control) active constraints.5. Identify “self-optimizing” controlled variables for remaining degrees

of freedom:• “Brute force” evaluation of loss for promising alternatives.• Local (linear) analysis.

21

Local (linear) analysis

• It can be summarized in the maximum gain rule of Sigurd:Maximize σ(S1GJuu

-1/2)• Where:

– σ is the minimum singular value.– G is the steady-state linear matrix from u to c.– S1 is the matrix of scalings of c’s.– Juu is the Henssian of J.

• S1 takes into account optimal variation and implemetation error:

• We used a branch-and-bound algorithm to solve this problem.

1,

1{ }( )i opt i

S diagc d n

= D +

22

Step 4. Where to set production rate?

• Very important!• Related to maximizing production rate.• Determines structure of remaining inventory (level) control system.• May also have important economic implications.• Conclusion: Set production rate at (dynamic) bottleneck.

23

Modes of operation

• We distinguish between two main modes of operation.• Mode I: Given throughput:

– Feed rate is given.– Production rate is limited (e.g., market).

• Mode II: Throughput as DOF:– Mode IIa: Maximum throughput with feasible operation.– Mode IIb: Optimized throughput with maximum profit.

24

Step 5. Regulatory control layer• Purpose: “Stabilize” the plant using local SISO PID controllers. • Enable manual operation (by operators).• Main structural issues:

• What more should we control? (secondary cv’s, y2)

• Pairing with manipulated variables (mv’s u2)

y1 = c

y2 = ?

25

Objectives regulatory control layer

1. Allow for manual operation.2. Simple decentralized (local) PID controllers that can be tuned on-line.3. Take care of “fast” control.4. Avoid drift.5. Track set point changes from the layer above.6. Local disturbance rejection.7. Stabilization.8. Allow for “slow” control in layer above (supervisory control).9. Make control problem easy as seen from layer above.

26

Rules for selecting y2

1. y2 should be easy to measure.

2. Control of y2 stabilizes the plant.

3. y2 should have good controllability, that is, favorable dynamics for control.

4. y2 should be located “close” to a manipulated input (u2) (follows from rule 3) due to small “effective” delay.

5. The gain from u2 to y2 should be large.

27

Step 6. Supervisory control layer

• Purpose: Keep primary controlled outputs c=y1 at optimal setpoints cs .

• Degrees of freedom: Setpoints y2s in regulatory control layer.• Main structural issue: Decentralized or multivariable?

28

Decentralized control(single-loop controllers)

Use for: Noninteracting process and no change in active constraints.

+ Tuning may be done on-line.+ None or minimal model requirements.+ Easy to fix and change.

- Need to determine pairing.- Performance loss compared to multivariable control.- Complicated logic required for reconfiguration when active constraints

move due to disturbances.

29

Multivariable control(with explicit constraint handling = MPC)

Use for: Interacting process and changes in active constraints.

+ Easy handling of feedforward control.+ Easy handling of changing constraints.

• no need for logic.• smooth transition.

- Requires multivariable dynamic model.- Tuning may be difficult.- Less transparent.- Reliability: “Everything goes down at the same time”.

30

Step 7. Optimization layer (RTO)• Purpose: Identify active constraints and compute optimal setpoints (to be

implemented by supervisory control layer)• Main structural issue: Do we need RTO? (or is the process self-optimizing?)

• RTO not needed when– Can “easily” identify change in active constraints (operating region)– For each operating region there exists self-optimizing variables

• RTO conclusion: surely a profitable endeavor• RTO drawback: certainly difficult to design, implement, and maintain even

with today’s technology and personnel’s knowledge

Updater Model / Opt.

Analysis

Control

Plant

31

Summary: Main steps

1. What should we control (y1=c)?• Must define optimal operation!

2. Where should we set the production rate?• At the bottleneck.

3. What more should we control (y2)?• Variables that “stabilize” the plant.

4. Control of primary variables:• Decentralized?• Multivariable (MPC)?• RTO?

32

Outline


33

Process Description

• Benzene production from thermal-dealkalination of toluene (high-temperature, non-catalytic process).

• Main reaction:

• Side reaction:

• Excess of hydrogen is needed to repress the side reaction and coke formation.

• References for HDA process:• McKetta (1977) – first reference on the process;• Douglas (1988) – design of the process;• Wolff (1994) – discuss the operability of the process.

• No references on the systematic application of plantwide design procedure.

CH3

+ H2 → + +CH4 Heat

H2+→2 ←

Toluene Benzene

Diphenyl

34

Mixer FEHE Furnace PFRQuench

Separator

Compressor

Cooler

StabilizerBenzeneColumn

TolueneColumn

H2 + CH4

Toluene

Toluene Benzene CH4

Diphenyl

Purge (CH4 + H2)

Process Description

35

Top-down analysis

36

Step 1 - Steady-state degrees of freedom

Process units DOF

External feed streams 2 x 1 = 2

Splitters (purge and quench) 2 x 1 = 2

Compressor duty 1 x 1 = 1

Adiabatic flash(*) (separator and quench) 2 x 0 = 0

Gas phase reactor(*) 1 x 0 = 0

Heat exchangers in recycle section(**) (furnace and cooler) 2 x 1 = 2

Heat exchangers in 3 distillation columns 3 x 2 = 6

Total 13(*) Assuming no adjustable valves for pressure control (assume fully open valve

before separator).(**) The FEHE (feed effluent heat exchanger) duty is not a degree of freedom because

there is no adjustable bypass.

37

Mixer FEHE

Furnace

Reactor

Quencher

Separator

Compressor

Cooler


TolueneColumn

H2 + CH4

Toluene

Toluene Benzene CH4

Diphenyl

Purge (H2 + CH4)

1

2

3

64

7

5

1113

12 10 8

9

Step 1 - Steady-state degrees of freedom

38

Step 2 - Definition of optimal operation

• The following profit is to be maximized:

-J = pbenDben + pfuelQfuel – ptolFtol – pgasFgas – pfuelQfur – pcwQcw – ppowerWpower - psteamQsteam

• Constraints during operation:– Production rate: Dben ≥ 265 lbmol/h.– Hydrogen excess in reactor inlet: Fhyd / (Fben + Ftol + Fdiph) ≥ 5.– Reactor inlet pressure: Preactor,in ≤ 500 psia.– Reactor inlet temperature: Treactor,in ≥ 1150 °F.– Reactor outlet temperature: Treactor,out ≤ 1300 °F.– Quencher outlet temperature: Tquencher,out ≤ 1150 °F.– Product purity: xDben ≥ 0.9997.– Separator inlet temperature: 95 °F ≤ Tseparator ≤ 105 °F.– Compressor power: WS ≤ 545 hp– Furnace heat duty: Qfur ≤ 24 MBtu– Cooler heat duty: Qcool ≤ 33 MBtu– + Distillation heat duties (condensers and reboilers).

39

Operation with given flow rateMode I

40

Step 3 - Disturbances

D1 Fresh toluene feed rate [lbmol/h] 300 285

D2 Fresh toluene feed rate [lbmol/h] 300 315

D3 Fresh gas feed rate methane mole fraction 0.03 0.08

D4 Hydrogen to aromatic ratio in reactor inlet 5.0 5.5

D5 Reactor inlet pressure [psi] 500 520D6 Quencher outlet temperature [oF] 1150 1170

D7 Product purity in the benzene column distillate 0.9997 0.9960

D8 Benzene mole fraction in stabilizer distillate 1 · 10−4 3 · 10−4

D9 Methane mole fraction in stabilizer bottoms 1 · 10−6 5 · 10−6

D10 Benzene mole fraction in benzene column bottoms

1.3 · 10−3 2 · 10−3

D11 Diphenyl mole fraction in toluene column distillate

0.5 · 10−3 1 · 10−3

D12 Toluene mole fraction in toluene column bottoms 0.4 · 10−3 1 · 10−3

41

Step 4 - Optimization• Optimization of the distillation train:

– We used a simplified recovery model for the distillation columns when optimizing the entire plant.

– The distillation section was optimized separately using detailed models.– It is always optimal to have the most valuable product at its constraint.– For the distillation columns we have:

StabilizerxD,benzene 1 · 10-4

xB,methane 1 · 10-6

Benzene columnxD,benzene 0.9997

xB,benzene 1.3 · 10-3

Toluene columnxD,diphenyl 0.5 · 10-3

xB,toluene 0.4 · 10-3

42

Step 4 - Optimization

• Entire process:

43

• 5 constraints are optimally active in all operating points:

1. Toluene feed rate (UB)2. Reactor inlet hydrogen-aromatics ratio (LB)3. Separator temperature (LB)4. Quencher outlet temperature (LB)5. Reactor pressure (UB)

• In addition, we have the distillation specifications

6. Methane mole fraction in stabilizer bottom7. Benzene mole fraction in stabilizer distillate8. Toluene mole fraction in benzene column bottom9. Benzene mole fraction in benzene column distillate10. Diphenyl mole fraction in toluene column bottom11. Toluene mole fraction in toluene column distillate

• 2 remaining unconstrained degrees of freedom.

Step 4 - Optimization

44

Step 4 - Optimization (Active Constraints)

Mixer FEHE

Furnace

Reactor

Quencher

Separator

Compressor

Cooler


TolueneColumn

H2 + CH4

Toluene

Toluene Benzene CH4

Diphenyl

Purge (H2 + CH4)

8

1

4

2

7

6

9

10

11

4

3

5

45

Candidate Controlled Variables• Candidate controlled variables:

– Pressure differences;– Temperatures;– Compositions;– Heat duties;– Flow rates.

• 70 candidate controlled variables are selected for 13 DOF.• Number of different sets of controlled variables:

• With 11 active constraints there are 2 DOF left:

• What should we do with the remaining 2 DOF?– Self-optimizing control!!! Surely!!!

1370 70! 4.75 1013 57!13!

æ ö÷ç ÷= = ×ç ÷ç ÷çè ø

59 59! 17112 57!2!

æ ö÷ç ÷= =ç ÷ç ÷çè ø

46

Step 5 - Analysis of the linear model

• Consider maximizing σ(S1·G2x2·Juu-1/2).

• Scale variables properly (find S1), linearize to find G2x2 and calculate Juu.

• Use a branch-and-bound algorithm.

47

σ(S1·G2x2·Juu-1/2) = 2.33·10-3 Average Loss

(k$/year)Mixer outlet inert (methane) mole fractionQuencher outlet toluene mole fraction

15.39


(k$/year)Mixer outlet inert (methane) mole fractionToluene conversion at reactor outlet

26.55


(k$/year)Mixer outlet inert (methane) mole fractionSeparator liquid benzene mole fraction

31.39

a. All measurements: σ(S1Gfull·Juu-1/2) = 6.34·10-3

III

Step 5 - Analysis of the linear model

48

Step 6 - Final selection

I II

Mixer FEHE

Furnace

Reactor

Quencher

Separator

Compressor

Cooler


TolueneColumn

H2 + CH4

Toluene

Toluene Benzene CH4

Diphenyl

Purge (H2 + CH4)

8

1

4

2

7

6

9

10

11

4

3

5

49

Operation with maximum throughputMode II

50

Step 7 - Bottleneck location

• Optimize the operation for each step increase in Ftol.• We found the same active constraints as in Mode I.• At about Ftol = 380 lbmol/h, constraint at compressor power becomes

active.• Above Ftol = 393 lbmol/h the operation becomes infeasible: Furnace

heat duty reaches its maximum – BOTTLENECK.

300 310 320 330 340 350 360 370 380 3904600

4800

5000

5200

5400

5600

5800

6000

6200

Toluene feed rate (Ftol) [lbmol/h]

Prof

it [k

$/ye

ar]

Linear base line (constant ratio Profit/Ftol)

51

Step 8 - Controlled variable selection

• With WS and Qfur active, there is 1 DOF left (Ftol).• We need to find a self-optimizing controlled variable for this DOF.• In order to mitigate the need for reconfiguration we select mixer

outlet inert (methane) mole fraction, xmix,met, for which the average loss is 68.74 k$/year.

• The throughput manipulator is then Qfur = Qfur,max.

52

Bottom-up design

53

Regulatory layer - Stabilization• Control reactor temperature and liquid levels in separator and

distillation columns (LV configuration).

LC01

LC11LC21LC31

LC32 LC22 LC12

TC01

54

Regulatory layer - Avoiding drift I: Pressure control

LC01

LC11LC21LC31

LC32 LC22 LC12

PC01

PC11PC22PC33

TC01

55

Regulatory layer - Avoiding drift II: Temperature control

LC01

LC11LC21LC31

LC32 LC22 LC12

PC01

PC11PC22PC33

TC02

TC03

TC22

TC11

#20

#3#5

TC33

TC01

56

Regulatory layer - Avoiding drift III: Flow control

LC01

LC11LC21LC31

LC32 LC22 LC12

PC01

PC11PC22PC33

TC02

TC03

TC22

TC11

#20

#3#5

TC33

FC01

FC02

TC01

57

Regulatory layer - “Intermediate” regulatory layer

LC01

LC11LC21LC31

LC32 LC22 LC12

PC01

PC11PC22PC33

TC02

TC03

TC22

TC11

#20

#3#5

TC33

FC01

FC02

• No need since control of the secondary controlled variables indirectly results in “acceptable” control of the primary variables.

TC01

58

Supervisory layer – Mode I

LC01

LC11LC21LC31

LC32 LC22 LC12

TC01

PC01

PC11PC22PC33

TC02

TC03

TC22

TC11

#20

#3#5

TC33

FC01

FC02

RC01

CC01

CC02

CC21

CC22

CC32

CC31

CC12

CC11

59

Supervisory layer – Mode II

LC01

LC11LC21LC31

LC32 LC22 LC12

TC01

PC01

PC11PC22PC33

TC02

TC03

TC22

TC11

#20

#3#5

TC33

FC01

FC02

RC01

CC01

CC21

CC22

CC32

CC31

CC12

CC11

Fixed

60

Dynamic simulations – Mode I: 10% increase in Ftol.

R e a c to r S e c tio n

T im e [H o u rs ]

Xm

ix.m

et [lb

mo

l/lbm

ol]

rH2

[lbm

ol/lb

mo

l]

Prin

[ps

i]

0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 3 .5 4 .0 4 .5 5 .0

0.5

60

.57

0.5

80

.59

0.6

4.0

4.5

5.0

5.5

6.0

49

5.0

50

0.0

50

5.0

51

0.0

B e n z e n e P ro d u c t

T im e [H o u rs ]

Xb

en

[lbm

ol/lb

mo

l]

Fb

en

[lbm

ol/h

r]

0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 3 .5 4 .0 4 .5 5 .0

0.9

99

60

.99

97

0.9

99

8

24

0.0

26

0.0

28

0.0

30

0.0

32

0.0


T im e [H o u rs ]

Xm

ix,m

et [lb

mo

l/lbm

ol]

rH2

[lbm

ol/lb

mo

l]

Prin

[ps

i]

0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 3 .5 4 .0 4 .5 5 .0

0.5

60

.57

0.5

80

.59

0.6

4.0

4.5

5.0

5.5

6.0

49

5.0

50

0.0

50

5.0

51

0.0


T im e [H o u rs ]

Xb

en

[lbm

ol/lb

mo

l]

Fb

en

[lbm

ol/h

r]

0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 3 .5 4 .0 4 .5 5 .0

0.9

99

60

.99

97

0.9

99

8

24

0.0

26

0.0

28

0.0

30

0.0

32

0.0

M a n ip u la tio n s

T im e [H o u rs ]

Ws

[hp

]

Qfu

r [MM

Btu

/hr]

Fg

as

[lbm

ol/h

r]

Fto

l [lbm

ol/h

r]

0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 3 .5 4 .0 4 .5 5 .0

40

0.0

48

0.0

56

0.0

64

0.0

8.0

12

.01

6.0

20

.02

4.0

39

0.0

42

0.0

45

0.0

48

0.0

51

0.0

26

0.0

28

0.0

30

0.0

32

0.0

34

0.0

Configuration in this work Luyben’s configuration

61

Dynamic simulations – Mode I: 10% reduction in Ftol.


T im e [H o u rs ]

Xm

ix.m

et [lb

mo

l/lbm

ol]

rH2

[lbm

ol/lb

mo

l]

Prin

[ps

i]

0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 3 .5 4 .0 4 .5 5 .0

0.5

60

.57

0.5

80

.59

0.6

4.0

4.5

5.0

5.5

6.0

49

5.0

50

0.0

50

5.0

51

0.0


T im e [H o u rs ]

Xb

en

[lbm

ol/lb

mo

l]

Fb

en

[lbm

ol/h

r]

0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 3 .5 4 .0 4 .5 5 .0

0.9

99

60

.99

97

0.9

99

8

24

0.0

26

0.0

28

0.0

30

0.0

32

0.0


T im e [H o u rs ]

Xm

ix,m

et [lb

mo

l/lbm

ol]

rH2

[lbm

ol/lb

mo

l]

Prin

[ps

i]

0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 3 .5 4 .0 4 .5 5 .0

0.5

60

.57

0.5

80

.59

0.6

4.0

4.5

5.0

5.5

6.0

49

5.0

50

0.0

50

5.0

51

0.0


T im e [H o u rs ]

Xb

en

[lbm

ol/lb

mo

l]

Fb

en

[lbm

ol/h

r]

0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 3 .5 4 .0 4 .5 5 .0

0.9

99

60

.99

97

0.9

99

8

24

0.0

26

0.0

28

0.0

30

0.0

32

0.0

M a n ip u la tio n s

T im e [H o u rs ]

Ws

[hp

]

Qfu

r [MM

Btu

/hr]

Fg

as

[lbm

ol/h

r]

Fto

l [lbm

ol/h

r]

0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 3 .5 4 .0 4 .5 5 .0

40

0.0

48

0.0

56

0.0

64

0.0

8.0

12

.01

6.0

20

.02

4.0

39

0.0

42

0.0

45

0.0

48

0.0

51

0.0

26

0.0

28

0.0

30

0.0

32

0.0

34

0.0

Configuration in this work Luyben’s configuration

xmet,mix

62

Summary

• Lots of possible candidate controlled variables make this a challenging process.

• But self-optimizing technology reduces the solution space so that (near) optimal operation is achieved.

• This process has a physical bottleneck on the furnace heat duty which limits the operation at +30% of nominal feed rate.

• The designed regulatory control layer assures good dynamic performance for the configurations in both modes of operation.

63

Outline


64

Process Description

• This is an interesting case study for it has an “optimized throughput” that is hit before any physical limitation make it infeasible.

• The reaction taking place isN2 + 3H2 ↔ 2NH3

• The kinetics are represented by the Temkin-Pyzhev equation:

• Where

65

Process Description

BED1

BED2

BED3

11

12

13

14

15

8

9

7

6

5

4

3

10

2HX-001

16

V4

V5

V6

V7

3029 31

1718

33

1

32

34

23

22

19 20

28

27GAS

2526

24

PURGE

21

H-502 H-583

H-501

V-502

K-402

K-401

V1

V2

V3

V8

V9

97% NH3

66

Degree of freedom analysis

67

Optimal operation• We then maximize

• Subject to

68

Mode I – given feed rate• Important disturbances:

• Optimization: 2 active constraints leaves 3 unconstrained DOFu = [WK-401 WK-402 Fpurge]

69

Mode I – given feed rate• Local analysis gives maximized gain for:

y = [WK-401 WK-402 Fpurge]

• Loss evaluation for y = [WK-401 WK-402 Fpurge]:

y

70

Mode II – variable feed rate• Maximum throughput:

71

Mode II – variable feed rate• At the optimized throughput the compressors are at their constriants.• This leaves 2 steady-state DOF: u = [Fgas Fpurge].• Disturbances:

• Optimization:

72

• Local analysis gives maximized gain for:y = [PRIN yCH4,purge]

• Loss evaluation for y = [PRIN yCH4,purge]:

Mode II – variable feed rate

73

Regulatory layer

BED1

BED2

BED3

11

12

13

14

15

8

9

7

6

5

4

3

10

2HX-001

16

V4

V5

V6

V7

3029 31

1718

33

1

32

34

23

22

19 20

28

27GAS

2526

24

PURGE

21

H-502 H-583

H-501

V-502

K-402

K-401

V1

V2

V3

V8

V9

FC1

LC1

FC2

TC1

74

Supervisory layer - Mode I

BED1

BED2

BED3

11

12

13

14

15

8

9

7

6

5

4

3

10

2HX-001

16

V4

V5

V6

V7

3029 31

1718

33

1

32

34

23

22

19 20

28

27GAS

2526

24

PURGE

21

H-502 H-583

H-501

V-502

K-402

K-401

V1

V2

V3

V8

V9

FC1

LC1

FC2

TC1

75

Supervisory layer - Mode II

Maximum

Maximum

BED1

BED2

BED3

11

12

13

14

15

8

9

7

6

5

4

3

10

2HX-001

16

V4

V5

V6

V7

3029 31

1718

33

1

32

34

23

22

19 20

28

27GAS

2526

24

PURGE

21

H-502 H-583

H-501

V-502

K-402

K-401

V1

V2

V3

V8

V9

FC1

LC1

FC2

TC1

CC1

PC1

76

Simulations – 5oC increase in cooling water to H-583Mode I

Mode II

77

Summary

• This is an interesting case study where the economic bottleneck comes first.

• The proposed control structures are in accordance with the actual industrial practice.

• They give good dynamic performance.

• However, one can think of implementing an MPC solution since the loss is not so small.

78

Outline


79

Time scale separation – singular perturbation

• Design of regulatory control layer.• Daoutidis et al. (2002, 2006) have shown that material streams with vastly different

magnitudes leads to time scale separation:– Fast time scales are in the order of magnitude of process units: Large flow rates as

manipulations.– Slow time scales captures the evolution of the network (upper layer control): Small

flow rates as manipulations.• Implementation:

– Nonlinear model equations are available.– Rearrange and decompose the model according to ul large flows and us small flows

using singular perturbation analysis. Quite complicated operation when dealing with large flowsheets.

– 3 almost decoupled layers will appear naturally: fast (ul), intermediate (us), and slow (purge flow).

• Drawback:– No economics is considered!!!

80

Case study – reactor-separator with recycle

yA,RyB,RyI,R

A Bk1

Ws

zf

zl

zp

yA, yB, yI

xA, xB, xI

FoyA,oyB,oyI,o F

R

L

P

ML

MV

SeparatorReactor

81

Economics by self-optimizing control

• Degrees of freedom:

• Disturbances:

82


• Optimal operation:Max (-J) = (pL – pP)L – pWWs

s.t.Preactor ≤ 2.0 MPa

xB ≥ 0.8711Ws ≤ 20 kWzF, zP [0,1]

• Optimization:

Preactor and xB are active.

• Unconstrained variables:

Only one DOF left!

83


• Loss evaluation:

84


• Final selection by self-optimizing control:

y = [Preactor xB Ws ] with u = [zF zP Ws]

85

Regulatory design by singular perturbation

• Selection by singular perturbation:

86

Control configuration arrangements

• By singular perturbation: • By self-optimizing control:

87

Control configuration arrangements

• By combining both:

88

Simulations

Singular perturbation:

• Disturbance: 10% increase in Fo at t = 0h followed by 5% increase in xB,sp at t = 50h

Infeasible!

89

Simulations

Self-optimizing control:


Bad dynamics!

90

Simulations

Combination of both:


Optimal and with good dynamic!

91

Summary• Time scale separation via singular perturbation analysis seems to be a very good technique to the systematic design of regulatory layers.

• Regulatory design: This method is simple compared to optimization approaches but it is more systematic than the empiricism used so far.

92

Outline


93

• Are large process gains a problem in terms of input-output controllability?

• We consider two kinds of input errors:

– Input load disturbances.

– Limited input resolution.

The problem

94

• The keyword in this presentation is CONTROLLABILITY.

• Skogestad and Postlethwaite (1996) describe (input-output) controllability as the ability to achieve acceptable control performance for all expected plant variations regardless of the controller.

• In this context, one factor to be considered is the magnitude of the process gains,

max(G) and min(G).

• Morari (1983) states that min(G) ≥ 1 in order to get acceptable control.

• But how about max(G)?

• Skogestad and Postlethwaite (1996) state that large max(G) is not necessarily a problem.

Previous Work

95

• In a recent paper McAvoy and Braatz (2003) claim that max(G) < 50.

• If correct, it has important implications for design of many processes.

• Consider the control of liquid level: It has infinite steady state gain due to integrator, however is easily controllable.

• Nevertheless, high process gains may pose a problem at higher frequencies when input errors are considered…

Previous Work

96

• Limited input resolution is represented by a quantizer in whichuq = qround(u / q), q is the quantization step

• The block diagram is given by

• In general, with a quantizer, limit cycles are inevitable if the controller has integral action - independent of the controller tuning.

K Gy -+r

Quantizer

u uqe

Process

q

uq

u

Limit cycles

97

• 3rd order process with PI-controller:– G(s) = 100 / [(10s + 1)(s + 1)2]– K(s) = 0.04(10s + 1) / 10s– q = 0.03 and r0 = 1

• Oscillations:– a = 0.189– T = 6.72s

0 20 40 60 80 1000

0.5

1

1.5

y

0 20 40 60 80 1000

0.01

0.02

0.03

Time

u q

a

T

Limit cycles

• FOD-process with PI-control – G(s) = 100e-s / (10s + 1)– K(s) = 0.04(10s + 1) / 10s– q = 0.03 and r0 = 0.2

• Oscillations:– a = 0.3– T = 16.07s

0 20 40 60 80 1000

0.2

0.4

y

0 20 40 60 80 1000

0.01

0.02

0.03

Time

u q

98

Limit cycles - Describing function• Assume the established limit cycle can be regarded as a relay.

• Assume (quasi) sinusoid response.

• Use Describing Function analysis.

• The describing function is given by

N(a) = 4q / (a).

• The condition for oscillations is

N(a)L(j) = −1.

• After some manipulations:

a (4q/) |G(jL,180)| and T = 2π/ωL,180

99

• Consider the first-order plus delay (FOD) processG(s) = k e-s / (s + 1)

• With the PI-controllerK(s) = Kc (Is + 1) / (Is); I =

• The exact expression for the amplitude isa = k q (1 - e-/ + e-T/ – e-(T-)/) / (1 - e-T/).

With:– T = [1 / (1 - f) + 1 / f], T [4, [. = / (1 - f).– f is computed from uss = uq1f + uq2(1 - f).

0 20 40 60 80 1000

0.2

0.4

y

0 20 40 60 80 1000

0.01

0.02

0.03

Time

u qf = 7%

Limit cycles - Exact FOD prediction

100

• Describing function applied to FOD:

• The exact expression for the amplitude isa = k q (1 - e-/ + e-T/ – e-(T-)/) / (1 - e-T/).

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.2

0.4

0.6

0.8

1

1.2 1.27

/

a / (

k q

)

f = 0 or 1

f = 0.1 or 0.9

f = 0.2 or 0.8

f = 0.3 or 0.7

f = 0.5

Using DF (3) 4 /

a / (

k q)

/

Describing function

æ ö÷ç ÷ç ÷çè ø2

4 kqa =π π τ +1

2 θ

Limit cycles - Comparison

101

• Let amax denote the maximum allowed amplitude of oscillations in y.

• The controllability requirement is

|G(jL,180)| < amax / 4q, L,180 1.5/ (L,180 3S)

Controllability requirement

102

1. Change the actuator (smaller q).2. Redesign the process (smaller effective delay ).3. Introduce fast, forced cycling (may wear out the valve).4. Valve positioner.

Mitigating Oscillations

0 10 20 30 40 50 60 70 80 90 1000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Time

y

Without valve positioner With valve positioner

0 10 20 30 40 50 60 70 80 90 1000

0.01

0.02

0.03

Without valve positioner

Time

u q

0 10 20 30 40 50 60 70 80 90 1000

0.01

0.02

0.03

With valve positioner

u q

103

• With feedback control, “large disturbances” are not necessarily a problem, but they impose limitations on the minimum bandwidth.

• Some known facts:

– No control:|y()| = |Gd(j)| |du()|.

– Control objective:|y()| < ymax.

– Immediate conclusion: Control is not needed if |Gd(j)du| < ymax.

Input Load Disturbance

K G y-

+r

-e

du

++

G

u

Gd

K G y-

+r

u-e ++

du

+ +

104

– With control [S=(1+GK)-1]:

|y()| = |S(j)| |Gd(j)| d()

– … and the requirement is then:

|S(j)| |Gd(j)| du < ymax, .

– Generally, |S(0)| is small, thus |Gd(0)| may be large.

– At the bandwidth frequency, defined as |S(jS)| = 1 (S 0.5 / , where = effective delay) with Gd(s) = G(s):

|G(jS)| < ymax / |du(ωS)|

Input Load Disturbance

106

Outline


107

Conclusion

• The plantwide control design procedure of Sigurd was successfully applied to two large-scale case studies.

• This may be seen as a first step for future real-world implementation of this technology in process industries worldwide.

• However, a word on practical optimization techniques is worthwhile: There is still work to be done in this area.

• A bit more of research should be devoted to improve the systematic procedure for regulatory control design: Perhaps time-scale separation from singular perturbation analysis gives a good hint.

• Actuators may cause control problems that can impact on the design of the regulatory layer and thus should be taken into account in the design procedure, at least in the final evaluation (validation) of the proposed structure.

1 studies on plantwide control antonio carlos brandão de araújo department of chemical engineering...

Documents