CAPE FORUM Vezprem, Hungary 14-15 February 2004

Towards Integration of Design and Control

Sten Bay Jørgensen

CAPEC Department of Chemical Engineering,

Technical University of Denmark,DK-2800 Lyngby, Denmark

http://www.capec.kt.dtu.dk

C A P E C

CAPE FORUM Vezprem, Hungary14-15 February 2004

13-14 February 2004

CAPE FORUM, Vezprem, Hungary 2

OUTLINE

• Introduction & objectives

• Plantwide Control Problem

• Decision problems in Control design

• Towards Integration of Process and Control design

• Model analysis

• Application examples

• Conclusions

13-14 February 2004


The plantwide control problem• A chemical process plant

Consits of several processes connected in parallel and sequence which must be executed in a coordinated manner to provide the required product amounts at the specified yields and qualities. The different processes may be continuous and/or batch. The production objective is specified in terms of a specific number of batches or operating periods for the continuous parts.

• The plant operations modelThere are many feasible operations and paths which may lead to the desired production rate at the specified quality given availability contraints, hence optimisation is required to provide an optimal solution

• Disturbancesin market or process conditions introduces uncertainty into the execution of the the plant operations model, hence control is required to reduce their influence.

• The plantwide control problemImplementation of the optimal plant operations model is referred to as the ”plantwide control problem”

13-14 February 2004


Hierarchical Plantwide Control Structure

Market

Setpointtrajectories

Local optimisation(hour)

Supervisory control(minutes)

Regulatory control(seconds)

Scheduling(days to weeks)

Site-wide Optimisation(day)

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Implementation of the optimal plant operations model I

1. Determine the optimal operations model

2. Investigate possible complex behaviours near the optimal operation region (Ideally with the basic control structure implemented, since more behaviours may be generated by the control structure, however stabilizing control has to be implemented).

3. Select measurements that provide information about the process/product state, eg. quality. Select actuators with significant effect upon the process/product peformance quality.

4. Combine actuators to minimize actuator interactions!

5. Pair combined actuators and measurements into a decentralised control structure. If the basic control strucure

– can be made selfoptimizing then SISO control layer is sufficient below the optimizing layer.

13-14 February 2004


Closed loop implementation – SISO Control layer

(Business) OptimisationMarket

Process Monitoring(State assessment)

Single Loop Controls

Process

Enabling signals

Measurements

Setpointtrajectory

May work if a ”self-optimising control structure” exists!

Disturbances

13-14 February 2004


Implementation of the optimal plant operations model II

1. Determine the optimal operations model

2. Investigate possible behaviours near the optimal operation region (Ideally with the basic control structure implemented, since more behaviours may be generated by the control structure, but stabilizing control has to be implemented).

3. Select measurements that provide information about the process/product state, eg. quality. Select actuators with significant effect upon the process/product peformance quality.

4. Combine actuators to minimize actuator interaction!

5. Pair combined actuators and measurements into a decentralised control structure. If the basic control strucure

– can be made selfoptimizing then SISO control layer is sufficient below optimizing layer.

– can not be made selfoptimizing then determine size of multivariable control problem, and implement a multivariable layer

13-14 February 2004


Closed loop implementation – with MIMO and SISO Control layers

(Business) OptimisationMarket

Process Monitoring(State assessment)

Single loop Controls

Process

Enabling signals

Measurements

Setpointtrajectory

MP (& IL) Control

Disturbances

13-14 February 2004


Loop pairringSelect loops by pairring ”combined actuators” with measurements to:1. achieve as direct an action as possible2. Stabilize unstable states, including to:3. handle nonlinear behaviours, e.g. a. Fold bifurcations by closing loops around them to achieve stabilizing control on (some) unstable branch(es)

b. Hopf bifurcations by suitable non-linear control design. b. Movement of zeros into the RHP by plant redesign, thereby

reducing (eliminating) nonminimum phase behaviour4. Track constraints

Ideally the developed decentralised control structure should be ”selfoptimizing”: Reject disturbances with constant setpoints, i.e. maintain profit - if sufficient degrees of freedom are available!

13-14 February 2004


Integration of Design & Control

• Is the plant operable?– Can disturbances be tolerated?– Can the plant be started-up– …….

Where during plant design may the above control related issues be handled?

Operability: The ability to achieve acceptable control performance, ie., to keep the controlled outputs and manipulated inputs within specified bounds - subject to signal uncertainty (disturbances, noise), model

uncertainty, etc., using available inputs and measurements. Note any unstable state must be both state controllable and state observable

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Definition of Integration

Integration

Off-line

Tools

On-line

Process

Simultaneously solve more than one problem, or, simultaneously perform more than one operation !

Process Integration is about Operation/Control !

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Difference Between Process & Tools Integration

Tools Integration:

Combines tools/algorithms in order to determine optimal operation model & optimal design subject to constraints

Process Integration

Links more than one operation and/or equipment together in order to achieve an integrated condition of operation & design. But reduces degrees of freedom.

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Tools Integration: Basis for Integration

design control

synthesis

To simultaneously consider aspects of synthesis, design and control. What is “common” information to the three problems:

Intensive variables such as T, P, x are “common” but have

different “functions”

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Functions of Intensive Variables T, P, x

Synthesis: Determine effects of T, P, x on the process model (properties) to generate the process flowsheet/configuration

Design: Determine T, P, x such that the process satisfies the specified objectives

Energy: Determine H(T, P, x) to compute the energy requirements

Control: Determine the sensitivities of T, P, x in order to design the control system

Environmental Impact: Identify environmental problems through x

Economy: Cost of operation & equipment are functions of T, P, x

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Introduction - II: Objectives

Perform model analysis (before rigorous solution) so that

– Infeasible alternatives can be rejected– Information on the control structure can be generated– Sub-problems related to design & control can be identified and solved.....

leading to a better understanding of design & control and thereby, an improved formulation of the integrated design& control problem

13-14 February 2004


Constraint Equations

0 = g2 (x, y, p, d)

Balance Equations

dx/dt = f(x, y, p, d, t)

Constitutive Equations/ Phenomena Models

0 = g1 (x, y) -

Constitutive equations (not rigorous) relate conceptual variables to measurable variables & species

parameters. i = f i(T, P, x; m)

T, P, x; Ñ, species

Intensive variables - can be measured

Conceptual variables - cannot be measured directly

Model Analysis - I: Process Models

13-14 February 2004


Model Analysis - II: Role of Intensive Variables

Synthesis/Design: Determine T, P, x such that the process satisfies the specified objectives

Control: Determine the sensitivities of T, P, x in order to design the control system

Intensive Variables (s)

Process Variables Measured Variables

Design Control

= f(p, d, s) d/ ds control structure

13-14 February 2004


Model Analysis - III

* Starting point - model plus assumptions– Identify important constitutive equations and their dependent intensive and the corresponding derivative information– Identify non-linear terms and their effects– Investigate how to decouple the balance equations

* Provides information related to process sensitivity, process feasibility, design constraints and solutions for design & control sub-problems

* Helps to formulate an integrated design & control problem

13-14 February 2004


Application Examples

• Control of Fermentor – nonlinear issue

• Control of Ammonia reactor - nonlinear issue

• Heat integrated distillation pilot plant - actuator

Objective is to highlight the use of model analyses rather than to find the optimal

integrated solution

13-14 February 2004


Continuous Cultivation of Yeast

Bifurcation analysis reveals:

– Hysteresis curve, multiple steady-states at maximal biomass productivity! Sf=28 g/L

– Optimal biomass productivity is achieved when operating very close to the turning point - which requires control!

f

0.3 0.32 0.34 0.36 0.38 0.45

10

15

Bio

mas

s [

g/l

]

Dilution rate [1/h]

Stable

Unstable

13-14 February 2004


Yeast metabolism

glucose

pyruvate

TCA

CO2

glycolysis

acetaldehyde

acetate

ethanol

biomass

Growth on glucose – at high D (Dcrit) – Crabtree effect: Overflow metabolism

r1

r7

r2

r3

r4

r5

r6

Thus a selfoptimizing controller could be based upon measurement of ethanol and manipulation of dilution rate:A productostat

13-14 February 2004


Productostat results- Biomass and ethanol

Steady-state multiplicity were observed at dilution rates below Dcrit when operating in closed loop !

Model is a FEPPhM

0.2 0.25 0.3 0.350

2

4

6

8

10

12

14

16

18

20

Bio

mas

s [g

/l]

D [h-1]

Dcrit

Biomass - open loop Biomass - closed loopEthanol - open loop Ethanol - closed loopModel

0.2 0.25 0.3 0.350

2

4

6

8

10

12

14

16

18

20

Eth

ano

l [g

/l]

0.2 0.25 0.3 0.350

2

4

6

8

10

12

14

16

18

20

0.2 0.25 0.3 0.350

2

4

6

8

10

12

14

16

18

20

0.2 0.25 0.3 0.350

2

4

6

8

10

12

14

16

18

20

0.2 0.25 0.3 0.350

2

4

6

8

10

12

14

16

18

20

13-14 February 2004


Nonlinear issuesNonlinear issuesProfit Optimising Control Profit Optimising 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

RHS

F

xprod

RHS

F

xprod

13-14 February 2004


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.

13-14 February 2004


Process Analysis: Operational Implications of Optimality

• Complex behaviour may be encountered near an optimal operating point

• Optimised process integrated design increases the likelihood of performance reducing complex behaviour

Theorems based upon induction:

Jørgensen & Jørgensen (1998)

13-14 February 2004


Ammonia Reactors

Operating point:Feed temperatureFeed concentrationFeed flow ratePressure

No automatic control of inlet temperature

Feed

By-pass3-bed quench reactorsimple reactor

Open Loop: Andersen and Jørgensen (1999)

Closed Loop: Recke, Andersen & Jørgensen (2000)

13-14 February 2004


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

Recke, Andersen & Jørgensen (2000)

13-14 February 2004


Ammonia Reactor: Bifurcation Diagram for Open/Closed Loop

Stable steady state Unstable steady state Stable periodic solution Unstable periodic solutionCi Cyclic fold bifurcationFi Fold bifurcationHi Hopf bifurcation

Open LoopClosed Loop= o.5 rad/h

G=5

13-14 February 2004


Feed Flowrate step changes

κ= 0.025 κ= -0.025 κ= -0.05 κ= 0.025 κ= -0.025

Open LoopClosed Loop= o.5 rad/h

G=5

κ= -0.05

13-14 February 2004


Energy integrated distillation pilot plant

Decanter

Reboiler

SecondaryCondenser

Air coolers

Receiver

Compressors

Superheating

Condenser

Dis

tilla

tion

colu

mn

D, XD

B, XB

F, XF

Expansion valve

9CV

8CV

PH

PL

13-14 February 2004


Model analysis for heat integrated plant

But, QB, QC can not be manipulated directly

QB=h1(T(PH), PL)

QC=h2(T(PL), PH)

Thus, actuator variables: L/D, PH, PL

Control variables: XD, XB, P

1) What is the operation region for actuators: PH , PL?

2) How to use actuators to cover the operating region?

For heat integrated plant three static degrees of freedom:

Sten Bay Jørgensen

Qb and Qc can be manipulatred independently, but they are highly correlated. Where does your analysis show this?

Sten Bay Jørgensen

How did you reach this result? You MUST show the analysis.....which leads you to this result!

13-14 February 2004


A feasible rangeof operation is:

T: 320 – 370 (K)P: 406 –1321(kPa)

Question: How to use actuators to move the operating point? PLQCP

PHQBVXB ?

Determination of the operation range From pure component properties

0

10000

20000

30000

40000

50000

60000

150 200 250 300 350 400 450 500 550 600 650

Temperature (K)

Ent

halp

y (k

J / k

mol

)

0

10

20

30

40

50

60

70

80

90

100

Vap

our

pres

sure

(b

ar)

Freon

Methanol Isopropanol

0

10000

20000

30000

40000

50000

60000

150 200 250 300 350 400 450 500 550 600 650

Temperature (K)

Ent

halp

y (k

J / k

mol

)

0

10

20

30

40

50

60

70

80

90

100

Vap

our

pres

sure

(b

ar)

Freon

Methanol Isopropanol

13-14 February 2004


Model analysis for actuator combinations

))P(TT(UA)T)P(T(UAHV L4CCCBH1BB1

)(20 CC TfP

PP)T(fP CB21B

Simple Steady state energy balance of the heatintegrated distillation column (total reflux operation, no heat loss):

13-14 February 2004


PH has positive gain to column pressure P and

positive gain to vapour flow rate V PL has positive gain to column pressure P but

negative gain to vapour flow rate V THUS: Column pressure P may be controlled by PH+ PL

Column vapor flow rate V may be controlled by PH- PL

Model Analysis: Actuator combination

13-14 February 2004


Model analysis for actuator selection & combination

0.25

0.45

0.65

0.85

1.05

1.25

1.45

1.65

1.85

2.05

2.25

35 55 75 95 115

Column pressure (KPa)

Vapour

flow

rate

(m3

/h)

81

5

4

B

9

27

63

A PL, PH both strongly affect V, P

Operation points movement Branch A: Constant PL=500kPa, 25kPa steps decrease in PH

Branch B: Constant PH=1075kPa, 25 kPa steps decrease in PL.

13-14 February 2004


Simulation validation of Actuator selection

0.25

0.45

0.65

0.85

1.05

1.25

1.45

1.65

1.85

2.05

2.25

40 60 80 100 120Column pressure (Kpa)

Va

po

ur

flow

ra

te (

m3 /h)

1

2

3

4 A

B

A curve: PH+PL is constant, PH-PL increases B curve: PH-PL is constant, PH+PL decreases

0.25

0.45

0.65

0.85

1.05

1.25

1.45

1.65

1.85

2.05

2.25

40 60 80 100 120Column pressure (Kpa)

Va

po

ur

flow

ra

te (

m3 /h)

1

2

3

4 A

B

A curve: PH+PL is constant, PH-PL increases B curve: PH-PL is constant, PH+PL decreases

13-14 February 2004


• Model analysis provides insights to the integration of design & control (e.g. helps to define and solve the control structure problem)

• Variables for integrating design and control for the energy integrated distillation column can be defined properly and consistently for subsequent model analysis

• Nonlinear analysis is required to reveal different aspects of complex behaviours

• Control structuring has multiple objectives

• Process design does affect controlled behaviour

• Several issues in proper control design remain open. Thus integrated process and control design is also still an open issue!

Conclusions

13-14 February 2004


References - needs a couple more..– Andersen, M.Y.; N.H. Pedersen, H. Brabrand, L. Hallager, S.B. Jørgensen, (1997): 'Regulation of a Continuous

yeast Bioreactor near the Critical Dilution rate using a Productostat', Journal of Biotechnology, 54, pp. 1-14 – Bonné, D.; S.B. Jørgensen (2001): Batch to Batch Improving Control of Yeast Fermentation, Computer Aided

Chemical Engineering, 9, Elsevier, pp. 621-626. – Bonné, D.; S.B. Jørgensen (2003): Data-Driven Modelling of Batch Processes. ADCHEM, Hongkong, China.

pp.663-668. – Jørgensen, J.B.; Jørgensen, S.B. (1998): 'Operational Implications of Optimality', AIChE Symposium Series, 94

issue 320, pp. 308-314– Lee, J.S.; K.S. Lee; W.C: Kim (2000): Model-base iterative learning control with a qudratic criterion for time-

varying linear systems. Automatica 36, pp. 641-657.– Lei, F; Olsson, L.; Jorgensen, S.B.(2003): 'Experimental investigations of state multiplicity in aerobic

continuous cultivations of Saccharomyces cerevisiae', J. Bioeng. Biotech, J. Bioeng. Biotech, 82, pp. 766-777 – Li, H.W.; Gani, R.; Jorgensen, S.B.(2003): Process Insights Based Control Structuring of an Integrated

Distillation Pilot Plant, Ind.Engng.Chem. Research 42(20), pp. 4620-4627 – Mönnigmann, M; J. Hahn, W. Marquardt (2003):Towards constructive nonlinear dynamics- Case studies in

chemical process design. In G. Radons, R. Neugenbauer (eds.), Nonlinear Dynamics of Production Systems. Viley-VCH, Weinheim.

– Papaeconomou, I.; Jørgensen, S.B.; Gani, R..(2003): A Conceptual “Design” Based Method for Generation of Batch Recipes. Proceedings of FOCAPO 2003, Florida, USA, pp. 473-476.

– Recke, B.R. Andersen, S.B. Jørgensen, (2001), 'Bifurcation Control of Sample Chemical Reaction Systems, "Advanced Control of Chemichal Processes", ed. L. Bigler et af, Elsevier Science. pp.

– Russel, B.M.; Henriksen, J.P.; Jørgensen, S. Bay; & Gani, R.: ”Integration of design and control through model analysis” Comp. Chem Engng 26(2002) 213-225

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

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CAPE FORUM Vezprem, Hungary 14-15 February 2004

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