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ECONOMIC PLANTWIDE CONTROL

How to design the control system for a complete

plant in a systematic manner

Sigurd Skogestad

Department 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 CV’s) (self-optimizing control)• Step S4: Where set the production rate? (Inventory control)

II Bottom Up • Step S5: Regulatory control: What more to control (secondary CV’s) ?

– 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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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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• S. Skogestad ``Plantwide control: the search for the self-optimizing control structure'', J. Proc. Control, 10, 487-507 (2000). • S. Skogestad, ``Self-optimizing control: the missing link between steady-state optimization and control'', Comp.Chem.Engng., 24, 569-

575 (2000). • I.J. Halvorsen, M. Serra and S. Skogestad, ``Evaluation of self-optimising control structures for an integrated Petlyuk distillation

column'', Hung. J. of Ind.Chem., 28, 11-15 (2000). • T. Larsson, K. Hestetun, E. Hovland, and S. Skogestad, ``Self-Optimizing Control of a Large-Scale Plant: The Tennessee Eastman Process

'', Ind. Eng. Chem. Res., 40 (22), 4889-4901 (2001). • K.L. Wu, C.C. Yu, W.L. Luyben and S. Skogestad, ``Reactor/separator processes with recycles-2. Design for composition control'', Comp.

Chem. Engng., 27 (3), 401-421 (2003). • T. Larsson, M.S. Govatsmark, S. Skogestad, and C.C. Yu, ``Control structure selection for reactor, separator and recycle processes'', Ind.

Eng. Chem. Res., 42 (6), 1225-1234 (2003). • A. Faanes and S. Skogestad, ``Buffer Tank Design for Acceptable Control Performance'', Ind. Eng. Chem. Res., 42 (10), 2198-2208 (2003). • I.J. Halvorsen, S. Skogestad, J.C. Morud and V. Alstad, ``Optimal selection of controlled variables'', Ind. Eng. Chem. Res., 42 (14), 3273-

3284 (2003). • A. Faanes and S. Skogestad, ``pH-neutralization: integrated process and control design'', Computers and Chemical Engineering, 28 (8),

1475-1487 (2004). • S. Skogestad, ``Near-optimal operation by self-optimizing control: From process control to marathon running and business systems'',

Computers and Chemical Engineering, 29 (1), 127-137 (2004). • E.S. Hori, S. Skogestad and V. Alstad, ``Perfect steady-state indirect control'', Ind.Eng.Chem.Res, 44 (4), 863-867 (2005). • M.S. Govatsmark and S. Skogestad, ``Selection of controlled variables and robust setpoints'', Ind.Eng.Chem.Res, 44 (7), 2207-2217

(2005). • V. Alstad and S. Skogestad, ``Null Space Method for Selecting Optimal Measurement Combinations as Controlled Variables'',

Ind.Eng.Chem.Res, 46 (3), 846-853 (2007). • S. Skogestad, ``The dos and don'ts of distillation columns control'', Chemical Engineering Research and Design (Trans IChemE, Part

A), 85 (A1), 13-23 (2007). • E.S. Hori and S. Skogestad, ``Selection of control structure and temperature location for two-product distillation columns'', Chemical

Engineering Research and Design (Trans IChemE, Part A), 85 (A3), 293-306 (2007). • A.C.B. Araujo, M. Govatsmark and S. Skogestad, ``Application of plantwide control to the HDA process. I Steady-state and self-

optimizing control'', Control Engineering Practice, 15, 1222-1237 (2007). • A.C.B. Araujo, E.S. Hori and S. Skogestad, ``Application of plantwide control to the HDA process. Part II Regulatory control'',

Ind.Eng.Chem.Res, 46 (15), 5159-5174 (2007). • V. Lersbamrungsuk, T. Srinophakun, S. Narasimhan and S. Skogestad, ``Control structure design for optimal operation of heat

exchanger networks'', AIChE J., 54 (1), 150-162 (2008). DOI 10.1002/aic.11366 • 990-999 (2008). T. Lid and S. Skogestad, ``Data reconciliation and optimal operation of a catalytic naphtha reformer'', Journal of

Process Control, 18, 320-331 (2008). • E.M.B. Aske, S. Strand and S. Skogestad, ``Coordinator MPC for maximizing plant throughput'', Computers and Chemical

Engineering, 32, 195-204 (2008). • A. Araujo and S. Skogestad, ``Control structure design for the ammonia synthesis process'', Computers and Chemical Engineering, 32

(12), 2920-2932 (2008). • E.S. Hori and S. Skogestad, ``Selection of controlled variables: Maximum gain rule and combination of measurements'',

Ind.Eng.Chem.Res, 47 (23), 9465-9471 (2008). • V. Alstad, S. Skogestad and E.S. Hori, ``Optimal measurement combinations as controlled variables'', Journal of Process Control, 19,

138-148 (2009)

• E.M.B. Aske and S. Skogestad, ``Consistent inventory control'', Ind.Eng.Chem.Res, 48 (44), 10892-10902 (2009). + MORE

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Idealized view of control(“PhD control”)

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Practice: Tennessee Eastman challenge problem (Downs, 1991)

(“PID control”)

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

• How do we get from PID control to PhD control?

• Where do we start?

• What should we control? and why?

• etc.

• etc.

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• Alan Foss (“Critique of chemical process control theory”, AIChE Journal,1973):

The central issue to be resolved ... is the determination of control system structure. Which variables should be measured, which inputs should be manipulated 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 theoretician who must close it.

• Carl Nett (1989):Minimize control system complexity subject to the achievement of accuracy

specifications in the face of uncertainty.

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Control structure design

• Not the tuning and behavior of each control loop,

• But rather the control philosophy of the overall plant with emphasis on the structural 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 structure design 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 systems•Alan Foss (1973) - control system structure•Bill Luyben et al. (1975- ) – case studies ; “snowball effect”•George Stephanopoulos and Manfred Morari (1980) – synthesis of control structures for chemical processes•Ruel Shinnar (1981- ) - “dominant variables”•Jim Downs (1991) - Tennessee Eastman challenge problem•Larsson 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 ECC’03 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. Stabilization2. Implementation of acceptable (near-optimal) operation

ARE THESE OBJECTIVES CONFLICTING?

• Usually NOT – Different time scales

• Stabilization fast time scale

– Stabilization doesn’t “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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Main simplification: Hierarchical structure

Need to define objectives and identify main issues for each

layer

PID

RTO

MPC

Process control

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cs = y1s

MPC

PID

y2s

RTO

u (valves)

Follow path (+ look after other 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

The controlled variables (CVs)interconnect the layers

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Example: Bicycle ridingNote: design starts from the bottom

• Regulatory control: – First need to learn to stabilize the bicycle

• CV = y2 = tilt of bike• MV = body position

• Supervisory control: – Then need to follow the road.

• CV = y1 = distance from right hand side• MV=y2s

– Usually a constant setpoint policy is OK, e.g. y1s=0.5 m

• Optimization: – Which road should you follow? – Temporary (discrete) changes in y1s

Hierarchical decomposition

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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 of this 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 operational

constraints• 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 Luyben’s procedure, Decisions 1, 2 and 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 that it 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 an afterthought in step L9.

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Outline

• Skogestad procedure for control structure designI 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 CV’s) (self-optimizing control)

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

II Bottom Up • Step S5: Regulatory control: What more to control (secondary CV’s) ?

• Step S6: Supervisory control

• Step S7: Real-time optimization

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

J = cost feed + cost energy – value products

*No need to include fixed costs (capital costs, operators, maintainance) at ”our” time scale (hours)Note: Operational profit P = -J.

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Optimal operation distillation column

• Distillation at steady state with given p and F: N=2 DOFs, e.g. L and V (u)

• Cost to be minimized (economics)

J = - P where P= pD D + pB B – pF F – pV

• Constraints

Purity D: For example xD, impurity · max

Purity B: For example, xB, impurity · max

Flow constraints: min · D, B, L etc. · max

Column capacity (flooding): V · Vmax, etc.

Pressure: 1) p given (d) 2) p free (u): pmin · p · pmax

Feed: 1) F given (d) 2) F free (u): F · Fmax

• Optimal operation: Minimize J with respect to steady-state DOFs (u)

value products

cost energy (heating+ cooling)

cost feed

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Outline

• Skogestad procedure for control structure designI 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 CV’s) (self-optimizing control)

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

II Bottom Up • Step S5: Regulatory control: What more to control (secondary CV’s) ?

• Step S6: Supervisory control

• Step S7: Real-time optimization

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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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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)

– QUIZ’s

• Step 3 (Implementation of optimal operation) (Lecture 2, many slides!)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!

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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

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 effect3. 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 CV’s - Typical: Top and btm composition

1

2

3

4

5

6

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!

QUIZ 3 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 extra valve, 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 (column distillation) + 1 (feed) + 2*1 (heat exchangers) + 1 (split) = 4With given feed and pressure: N’ss = 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

Steady-state DOFs

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HDA process

Mixer FEHE Furnace PFR Quench

Separator

Compressor

Cooler

StabilizerBenzeneColumn

TolueneColumn

H2 + CH4

Toluene

Toluene Benzene CH4

Diphenyl

Purge (H2 + CH4)

QUIZ 4 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: 14 steady-state DOFs

Assume given column pressures

feed:1.2

hex: 3, 4, 6

splitter 5, 7

compressor: 8

distillation: 2 each column

QUIZ 4 solution

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

Steady-state DOFs

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Step S2b: Optimize with respects to DOFS (u) for expected disturbances (d) …….. and identify regions of active constraints

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

Model equations: f(u,x,d) = 0Operational 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” and often 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, ESCAPE’21, Greece, 2011

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Optimal operation

Mode 1. Given feedrate

Mode 2. Maximum production

minimize J = cost feed + cost energy – value products

Two main cases (modes) depending on marked conditions:

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Amount of products is then usually indirectly given and

Optimal operation is then usually unconstrained

“maximize efficiency (energy)” Control: Operate at optimal trade-off (not obvious what to control to achieve this)

Mode 1. Given feedrate

J = cost feed– value products + cost energy

c

J = energy

copt

constant

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• Assume feedrate is degree of freedom

• Assume products much more valuable than feed

• Optimal operation is then to maximize product rate– But must remain feasible

– constrained by bottleneck

Mode 2. Maximum production

Control: Focus on tight control of bottleneck (“obvious what to control”)

c

J

copt

Infeasibleregion

J = cost feed + cost energy – value products

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Example with Quiz:Optimal operation of two distillation columns in series

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

DOF = Degree Of FreedomRef.: M.G. Jacobsen and S. Skogestad (2011)

Energy price: pV=0-0.2 $/mol (varies)Cost (J) = - Profit = pF F + pV(V1+V2) – pD1D1 – pD2D2 – pB2B2

> 95% BpD2=2 $/mol

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

> 95% CpB2=1 $/mol

N=41αAB=1.33

N=41αBC=1.5

> 95% ApD1=1 $/mol

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

QUIZ 1

45 DOF = Degree Of Freedom

Ref.: M.G. Jacobsen and S. Skogestad (2011)

Energy price: pV=0-0.2 $/mol (varies)Cost (J) = - Profit = pF F + pV(V1+V2) – pD1D1 – pD2D2 – pB2B2

> 95% BpD2=2 $/mol

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

> 95% CpB2=1 $/mol

1. xB = 95% BSpec. valuable product (B): Always active!Why? “Avoid product give-away”

N=41αAB=1.33

N=41αBC=1.5

> 95% ApD1=1 $/mol

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

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Active constraint regions for two distillation columns in series

[mol/s]

[$/mol]

CV = Controlled Variable

Energyprice

SOLUTION QUIZ 1 (more details)

BOTTLENECKHigher F infeasible because all 5 constraints reached

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Active constraint regions for two distillation columns in series

[mol/s]

[$/mol]

CV = Controlled Variable

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

Energyprice

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? HINT: CONTROL ACTIVE CONSTRAINTSRed: Basic regulatory loops

QUIZ 2

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Control of Distillation columns in series

Given

LC LC

LC LC

PCPC

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!

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

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In practise

• New figure, that is, update the one fom next slide

• Column with T-loops, column 1 with T btm

• V1 and V2 max repøaced by dp-contrpø

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Control of Distillation columns in series

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. T1S and T2S would then replace L1 and L2 as DOFs…… but leave this out for now..

Red: Basic regulatory loops

TC TCT1s T2s

T1 T2

Comment

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Active constraint regions for two distillation columns in series

CV = Controlled Variable

3 2

01

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

SOLUTION QUIZ 2 (more details)