economic plantwide1

8/13/2019 Economic Plantwide1

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ECONOMIC PLANTWIDECONTROLHow to design the control system for a complete

plant in a systematic manner

Sigurd SkogestadDepartment of Chemical Engineering

Norwegian University of Science and Tecnology (NTNU)

Trondheim, Norway

Brazil July 2011


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Outline (6 lectures)

Control structure design (plantwide control)

A procedure for control structure design

I Top Down

Step S1: Define operational objective (cost) and constraints

Step S2: Identify degrees of freedom and optimize operation for disturbances

Step S3: Implementation of optimal operation

What to control ? (primary CVs) (self-optimizing control) Step S4: Where set the production rate? (Inventory control)

II Bottom Up

Step S5: Regulatory control: What more to control (secondary CVs) ?

Distillation column control

Step S6: Supervisory control Step S7: Real-time optimization

PID tuning

(+ decentralized control if time)

*Each lecture is 2 hours with a 10 min intermediate break after about 55 min(no. of slides) + means that it most likely will continue into the next lecture

Lecture 1 (49)

Lecture 4 (62)+

Lecture 2 (71)+

Lecture 3 (36)

Lecture 5 (19)

Lecture 6 (54)

Plantwide control lectures. Sigurd Skogestad


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Plantwide control intro course: Contents

Overview of plantwide control

Top-down. Selection of primary controlled variables based on economic : The linkbetween the optimization (RTO) and the control (MPC; PID) layers

- Degrees of freedom- Optimization- Self-optimizing control- Applications

Where to set the production rate and bottleneck Bottom-up. Design of the regulatory control layer ("what more should we

control")- stabilization- secondary controlled variables (measurements)- pairing with inputs

Design of supervisory control layer- Decentralized versus centralized (MPC)- Pairing and RGA-analysis

Summary and case studies


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Main references

The following paper summarizes the procedure: S. Skogestad, ``Control structure design for complete chemical plants'',Computers and Chemical Engineering, 28 (1-2), 219-234 (2004).

There are many approaches to plantwide control as discussed in the

following review paper:

T. Larsson and S. Skogestad, ``Plantwide control: A review and a new

design procedure''Modeling, Identification and Control, 21, 209-240

(2000).

The following paper updates the procedure:

S. Skogestad, ``Economic plantwide control, Book chapter in V.Kariwala and V.P. Rangaiah (Eds), Plant-Wide Control: Recent

Developments and Applications, Wiley (late 2011).http://www.nt.ntnu.no/users/skoge/publications/2011/skogestad-plantwide-control-book-by-kariwala /

All papers available at: http://www.nt.ntnu.no/users/skoge/


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Idealized view of control(PhD control)


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How we design a control system for acomplete chemical plant?

Where do we start?

What should we control? and why?

etc.

etc.


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Alan Foss (Critique of chemical process control theory, AIChEJournal,1973):

The central issue to be resolved ... is the determination of control system

structure. Which variables should be measured, which inputs should bemanipulated and which links should be made between the two sets?

There is more than a suspicion that the work of a genius is needed here,

for without it the control configuration problem will likely remain in a

primitive, hazily stated and wholly unmanageable form. The gap is

present indeed, but contrary to the views of many, it is the theoreticianwho must close it.

Carl Nett (1989):

Minimize control system complexity subject to the achievement of accuracyspecifications in the face of uncertainty.


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Control structure design

Notthe tuning and behavior of each control loop,

But rather the control philosophy of the overall plant with emphasis on

thestructural decisions:

Selection of controlled variables (outputs)

Selection of manipulated variables (inputs)

Selection of (extra) measurements

Selection of control configuration (structure of overall controller that

interconnects the controlled, manipulated and measured variables)

Selection of controller type (LQG, H-infinity, PID, decoupler, MPC etc.).

That is: Control structure design includes all the decisions we need

make to get from ``PID control to PhD control


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Process control:

Plantwide control = Control structuredesign for complete chemical plant

Large systems

Each plant usually different modeling expensive

Slow processes no problem with computation time

Structural issues important

What to control? Extra measurements, Pairing of loops

Previous work on plantwide control:Page Buckley (1964) - Chapter on Overall process control (still industrial practice)Greg Shinskey (1967) process control systemsAlan Foss (1973) - control system structureBill Luyben et al. (1975- ) case studies ; snowball effectGeorge Stephanopoulos and Manfred Morari (1980) synthesis of control structures for chemical processesRuel Shinnar (1981- ) - dominant variables

Jim Downs (1991) - Tennessee Eastman challenge problemLarsson and Skogestad (2000): Review of plantwide control


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Control structure selection issues are identified as important also in

other industries.

Professor Gary Balas (Minnesota) at ECC03 about flight control at Boeing:

The most important control issue has always been to select the right

controlled variables --- no systematic tools used!


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Main objectives control system

1. Stabilization

2. Implementation of acceptable (near-optimal) operation

ARE THESE OBJECTIVES CONFLICTING?

Usually NOT

Different time scales

Stabilization fast time scale

Stabilization doesnt use up any degrees of freedom Reference value (setpoint) available for layer above

But it uses up part of the time window (frequency range)


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cs = y1s

MPC

PID

y2s

RTO

u (valves)

Follow path (+ look afterother variables)

CV=y1 (+ u); MV=y2s

Stabilize + avoid drift

CV=y2; MV=u

Min J (economics);

MV=y1s

OBJECTIVE

Dealing with complexity

Main simplification: Hierarchical decomposition

Process control The controlled variables (CVsinterconnect the layers


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Plantwide control decisions

No matter what procedure we choose to use, the following decisions

must be made when designing a plantwide control strategy:

Decision 1. Select economic (primary) controlled variables (CV1)

for the supervisory control layer (the setpoints CV1s link the

optimization layer with the control layers).

Decision 2. Select stabilizing (secondary) controlled variables

(CV2) for the regulatory control layer (the setpoints CV2s link the two

control layers).

Decision 3. Locate the throughput manipulator (TPM).

Decision 4. Select pairings for the stabilizing layer, that is, pair inputs

(valves) and controlled variables (CV2). By valves is here meant the

original dynamic manipulated variables.


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Skogestad plantwide control structure design

procedure

I Top Down Step S1:Step S1: Define operational objectives (optimal operation)

Cost function J (to be minimized)

Operational constraints

Step S2 (optimization): (a) Identify degrees of freedom (MVs). (b)Optimize for expected disturbances and find regions of active constraints

Step S3 (implementation): Select primary controlled variables c=y1 (CVs)(Decision 1).

Step S4: Where set the production rate? (Inventory control) (Decision 3)

II Bottom Up Step S5: Regulatory / stabilizing control (PID layer)

What more to control (y2; local CVs)? y (Decision 2) Pairing of inputs and outputs y (Decision 4)

Step S6: Supervisory control (MPC layer)

Step S7: Real-time optimization (Do we need it?)

Understanding and using this procedure is the most important part ofthis course!!!!

y1

y2

Process

MVs


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Comment: Luyben procedure

Step L1.Establish control objectives

Step L2. Determine control degrees of freedom

Step L3. Establish energy management system Step L4. Set the production rate (Decision 3)

Step L5. Control product quality and handle safety, environmental and operationalconstraints

Step L6. Fix a flow in every recycle loop and control inventories

Step L7. Check component balances

Step L8. Control individual unit operations Step L9. Optimize economics and improve dynamic controllability

Notes:

Establish control objectives in step L1 does not lead directly to the choice of

controlled variables (Decisions 1 and 2). Thus, in Luybens procedure, Decisions 1, 2and 4 are not explicit, but are included implicitly in most of the steps.

Even though the procedure is systematic, it is still heuristic and ad hoc in the sense thatit is not clear how the authors arrived at the steps or their order.

A major weakness is that the procedure does not include economics, except as anafterthought in step L9.


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Outline

Skogestad procedure for control structure design

I Top Down





II Bottom Up




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Step S1. Define optimal operation (economics)

What are we going to use our degrees of freedom u (MVs) for?

Define scalar cost function J(u,x,d)

u: degrees of freedom (usually steady-state)

d: disturbances

x: states (internal variables)

Typical cost function:

Optimize operation with respect to u for given d (usually steady-state):

minu J(u,x,d)

subject to:Model equations: f(u,x,d) = 0

Operational constraints: g(u,x,d) < 0

J = cost feed + cost energy value products


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Optimal operation

Mode 1. Given feedrate

Amount of products is then usually indirectly given and J = cost energy.Optimal operation is then usually unconstrained:

Mode 2. Maximum productionProducts usually much more valuable than feed + energy costs small.

With feedrate as a degree of freedom, optimal operation is then usuallyconstrained by bottleneck.

minimize J = cost feed + cost energy value products

maximize efficiency (energy)

Two main cases (modes) depending on marked conditions:

Control: Focus on tight control of

bottleneck (obvious what to control)

Control: Operate at optimal

trade-off (not obvious what to

control to achieve this)


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Outline

Skogestad procedure for control structure design

I Top Down





II Bottom Up




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Step S2 (Optimize operation):

(a) Identify degrees of freedom

(b) Optimize for expected disturbances Need good steady-state model

Goal: Identify regions of active constraints

Time consuming!


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Example with Quiz:

Optimal operation of two distillation columnsin series


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SOLUTION QUIZ 1


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Energy price: pV=0-0.2 $/mol (varies)

Cost (J) = - Profit = pF F + pV(V1+V2) pAD1 pBD2 pCB2

> 95% BpB=2 $/mol

F ~ 1.2mol/spF=1 $/mol < 4 mol/s < 2.4 mol/s

> 95% CpC=1 $/mol

1. xB = 95% BSpec. valuable product (B): Always active!

Why? Avoid product give-away

N=41AB=1.33

N=41BC=1.5

> 95% ApA=1 $/mol

2. Cheap energy: V1=4 mol/s, V2=2.4 mol/s

Max. column capacity constraints active!Why? Overpurify A & C to recover more B

QUIZ: What are the expected active constraints?1. Always. 2. For low energy prices.

Hm.?

Operation of Distillation columns in seriesWith given F (disturbance): 4 steady-state DOFs (e.g., L and V in each column)

SOLUTION QUIZ 1

SOLUTION QUIZ 1 (more details)


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Active constraint regions for two

distillation columns in series

[mol/s]

[$/mol]

CV = Controlled Variable

Energyprice


BOTTLENECKHigher F infeasible becauseall 5 constraints reached

QUIZ 2


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[mol/s]

[$/mol]


QUIZ. Assume low energy prices (pV=0.01 $/mol).How should we control the columns?

Energyprice

QUIZ 2

QUIZ 2


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Control of Distillation columns in series

Given

LC LC

LC LC

PCPC

QUIZ. Assume low energy prices (pV=0.01 $/mol).How should we control the columns?Red: Basic regulatory loops

QUIZ 2

Comment


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Given

LC LC

LC LC

PCPC

Comment: Should normally stabilize column profiles with temperature control,Should use reflux (L) in this case because boilup (V) may saturate.T1

Sand T2

Swould then replace L1 and L2 as DOFs but leave this out for now..

Red: Basic regulatory loops

TC TCT1s T2sT1 T2

Comment


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SOLUTION QUIZ 2


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Given

LC LC

LC LC

PCPC

QUIZ. Assume low energy prices (pV=0.01 $/mol).How should we control the columns?Red: Basic regulatory loops

CC

xB

xBS=95%

MAX V1 MAX V2

1 unconstrained DOF (L1):Use for what?? CV=?Not: CV= xA in D1! (why? xA should vary with F!)Maybe: constant L1? (CV=L1)

Better: CV= xA in B1? Self-optimizing?

General for remaining unconstrained DOFs:LOOK FOR SELF-OPTIMIZING CVs = Variables we can keep constantWILL GET BACK TO THIS!

SOLUTION QUIZ 2

Hm.HINT: CONTROL ACTIVE CONSTRAINTS!



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3 2

0

1

1

0

2

[mol/s]

[$/mol]

1

Cheap energy: 1 remaining unconstrained DOF (L1)-> Need to find 1 additional CVs (self-optimizing)

More expensive energy: 3 remaining unconstrained DOFs-> Need to find 3 additional CVs (self-optimizing)

Energyprice

Q ( )


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Plans for next lectures

Step 2 (Find optimal operation using offline calculations):

Step 2a : DOF analysis (steady-state) (12 slides)

Step 2b: Optimize for expected disturbances (1 slide)

Step 3 (Implementation of optimal operation) (Lecture 2)

Identify primary (economic) controlled variables (CVs):

1. Control active constraints. Backoff

2. Remaining unconstrained: Find self-optimizing CVs

Will use a lot of time on this!

Steady-state DOFs


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Step S2a: Degrees of freedom (DOFs)for operation

NOT as simple as one may think!

To find all operational (dynamic) degrees of freedom:

Count valves! (Nvalves)

Valves also includes adjustable compressor power, etc.

Anything we can manipulate!

BUT: not all these have a (steady-state) effect on the economics

y

Steady-state DOFs


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Steady-state degrees of freedom (DOFs)

IMPORTANT! DETERMINES THE NUMBER OF VARIABLES TO

CONTROL!

No. of primary CVs = No. of steady-state DOFs

CV = controlled variable (c)

Methods to obtain no. of steady-state degrees of freedom (Nss):

1. Equation-counting Nss = no. of variables no. of equations/specifications

Very difficult in practice

2. Valve-counting (easier!) Nss = Nvalves N0ss Nspecs N0ss = variables with no steady-state effect

3. Potential number for some units (useful for checking!)

4. Correct answer: Will eventually find it when we perform optimization

Steady-state DOFs


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Steady-state degrees of freedom (Nss):2. Valve-counting

Nvalves = no. of dynamic (control) DOFs (valves)

Nss = Nvalves N0ss Nspecs : no. of steady-state DOFs

N0ss = N0y + N0,valves : no. of variables with no steady-state effect

N0,valves : no. purely dynamic control DOFs

N0y : no. controlled variables (liquid levels) with no steady-state effect

Nspecs: No of equality specifications (e.g., given pressure)

Steady-state DOFs


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Nvalves = 6 , N0y = 2 ,

NDOF,SS

= 6 -2 = 4 (including feed and pressure as DOFs)

Typical Distillation column

N0y : no. controlled variables (liquid levels) with no steady-state effect

With given feed and pressure:NEED TO IDENTIFY 2 more CVs- Typical: Top and btm composition

1

2

3

4

5

6

QUIZ 3

Steady-state DOFs


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Heat-integrated distillation process

Nvalves = 11 (w/feed), N0y = 4 (levels),

Nss= 11 4= 7 (with feed and 2 pressures)

Need to find 7 CVs!

Steady-state DOFs


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Heat exchanger with bypasses

CW

Nvalves = 3, N0valves = 2 (of 3), Nss= 3 2 = 1

Steady-state DOFs


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Steady-state degrees of freedom (Nss

):

3. Potential number for some process units

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/speed)

adiabatic flash tank: 0*

liquid phase reactor: 1 (holdup reactant) gas phase reactor: 0*

heat exchanger: 1 (bypass or flow)

column (e.g. distillation) excluding heat exchangers: 0* + no. of sidestreams

pressure*

: add 1DOF at each extra place you set pressure (using an extravalve, compressor or pump), e.g. in adiabatic flash tank, gas phase reactor or

absorption column

*Pressure is normally assumed to be given by the surrounding process and is then not a degree of freedom

Ref: Araujo, Govatsmark and Skogestad (2007)

Extension to closed cycles: Jensen and Skogestad (2009)

Real number may be less, for example, if there is no bypass valve

Steady-state DOFs


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Heat exchanger with bypasses

CW

Potential number heat exchanger Nss= 1

Steady-state DOFs


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Potential number,Nss= 0 (distillation) + 1 (feed) + 2*1 (heat exchangers) + 1 (split) = 4

With given feed and pressure: Nss = 4 2 = 2

Distillation column (with feed and pressure as DOFs)

split

Steady-state DOFs


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Heat-integrated distillation process

Potential number, Nss= 1 (feed) + 2*0 (columns) + 2*1

(splits) + 1 (sidestream) + 3 (hex) = 7

QUIZ 4 Steady-state DOFs


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HDA process

Mixer FEHE Furnace PFRQuench

Separator

Compressor

Cooler

StabilizerBenzene

Column

Toluene

Column

H2 + CH4

Toluene

Toluene Benzene CH4

Diphenyl

Purge (H2 + CH4)

QUIZ 4 solution

Steady-state DOFs


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HDA process: steady-state degrees of freedom

1

2

3

8 7

4

6

5

9

10

11

12

13

14 Conclusion: 14steady-stateDOFs

Assume given column pressures

feed:1.2

hex: 3, 4, 6

splitter 5, 7

compressor: 8

distillation: 2 each

column

Hm.. Consider-Feeds-Heat exchangers

-Splitters-Compressors-Distillation columns

Steady-state DOFs


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Check that there are enough manipulated variables (DOFs) - both

dynamically and at steady-state (step 2)

Otherwise: Need to add equipment

extra heat exchanger

bypass

surge tank

Step S2b: Optimize with respects to DOFS


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(u) for expected disturbances (d) ..

and identify regions of active constraints

minu J(u,x,d)subject to:

Model equations: f(u,x,d) = 0

Operational constraints: g(u,x,d) < 0

Idea: Prepare operation for expected future disturbances, incl. price changes

In principle: simple

In practise: very time consuming

Commercial simulators (Aspen, Unisim/Hysys) are set up in design mode andoften work poorly in operation (rating) mode.

Example Heat exchanger

Easy (Design mode): Given streams (and temperatures), find UA

Difficult (Operation mode): Given UA, find outlet temperatures

Optimization methods in commercial simulators often poor

We use Matlab or even Excel on top

Heat exchanger: Let Matlab/Excel vary temperatures to match given UA

Focus on most important disturbances and range. Whole picture is complicated

d1 = feedrate

d2

= energyprice

Ref. Jacobsen and Skogestad, ESCAPE21, Greece, 2011

economic plantwide1

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