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ECONOMICPLANTWIDE CONTROL: Control structure design for complete processing plants

Sigurd Skogestad

Department of Chemical Engineering

Norwegian University of Science and Tecnology (NTNU)

Trondheim, Norway

Mexico, April 2012

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Trondheim, Norway

Mexico

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Trondheim

Oslo

UK

NORWAY

DENMARK

GERMANY

North Sea

SWEDEN

Arctic circle

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NTNU,Trondheim

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Outline

1. Introduction plantwide control (control structure design)

2. Plantwide control procedureI Top Down

– Step 1: Define optimal operation– Step 2: Optimize for expected disturbances– Step 3: Select primary controlled variables c=y1 (CVs) – Step 4: Where set the production rate? (Inventory control)

II Bottom Up – Step 5: Regulatory / stabilizing control (PID layer)

• What more to control (y2)?• Pairing of inputs and outputs

– Step 6: Supervisory control (MPC layer)– Step 7: Real-time optimization (Do we need it?)

y1

y2

Process

MVs

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Idealized view of control(“PhD control”)

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Practice: Tennessee Eastman challenge problem (Downs, 1991)

(“PID control”)

TC PC LC AC x SRCWhere place ??

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How do we get from PID to PhD control?How we design a control system for a complete 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”, 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.

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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Theory: Optimal operation

ALLMIGHTY GOD?

IDEAL COMMUNISM?

PROCESS CONTROL?

Objectives

Present state

Model of system

Theory:•Model of overall system•Estimate present state•Optimize all degrees of freedom

Problems: • Model not available• Optimization complex• Not robust (difficult to handle uncertainty) • Slow response time

Process control: • Excellent candidate for centralized control

(Physical) Degrees of freedom

CENTRALIZEDOPTIMIZER

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Practice: Process control

Practice:

• Hierarchical structure

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Process control: Hierarchical structure

Director

Process engineer

Operator

Logic / selectors / operator

PID control

u = valves

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cs = y1s

MPC

PID

y2s

RTO

Follow path (+ look after other variables)

Stabilize + avoid drift

Min J (economics)

u (valves)

OBJECTIVE

Dealing with complexity

Plantwide control: ObjectivesThe controlled variables (CVs)interconnect the layers

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Translate optimal operation into simple control objectives:

What should we control?

y1 = c ? (economics)

y2 = ? (stabilization)

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y1 = distance to curb (1 m)

y2 = bike tilt (stabilization)

u = muscles

Example: Bicycle riding

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Control structure design procedure

I Top Down • Step 1: Define operational objectives (optimal operation)

– Cost function J (to be minimized)

– Operational constraints

• Step 2: Identify degrees of freedom (MVs) and optimize for

expected disturbances

• Step 3: Select primary controlled variables c=y1 (CVs)

• Step 4: Where set the production rate? (Inventory control)

II Bottom Up

• Step 5: Regulatory / stabilizing control (PID layer)

– What more to control (y2; local CVs)?

– Pairing of inputs and outputs

• Step 6: Supervisory control (MPC layer)

• Step 7: Real-time optimization (Do we need it?)

y1

y2

Process

MVs

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Step 1. 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

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Step 2. Optimize

• Identify degrees of freedom (u)

• Optimize for expected disturbances (d)– Identify regions of active constraints

• Need model of system

• Time consuming, but it is offline

24(Magnus G. Jacobsen):

Example: Regions of active constraints

Control: 2 active constraints (xA, xB)

+ 2 “selfoptimizing”

3+1

1+3

Two distillation columns in series.

4 degrees of freedom + feedrate

3+1

4+0

5

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Step 3: Implementation of optimal operation

• Optimal operation for given d*:

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

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

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

→ uopt(d*)

Problem: Usally cannot keep uopt constant because disturbances d change

How should we adjust the degrees of freedom (u)?

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Implementation (in practice): Local feedback control!

“Self-optimizing control:” Constant setpoints for c gives acceptable loss

y

FeedforwardOptimizing controlLocal feedback: Control c (CV)

d

Main issue:What should we control?

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– Cost to be minimized, J=T

– One degree of freedom (u=power)

– What should we control?

Optimal operation - Runner

Example: Optimal operation of runner

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Sprinter (100m)

• 1. Optimal operation of Sprinter, J=T– Active constraint control:

• Maximum speed (”no thinking required”)

Optimal operation - Runner

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• 2. Optimal operation of Marathon runner, J=T– Unconstrained optimum!

– Any ”self-optimizing” variable c (to control at constant setpoint)?

• c1 = distance to leader of race

• c2 = speed

• c3 = heart rate

• c4 = level of lactate in muscles

Optimal operation - Runner

Marathon (40 km)

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Conclusion Marathon runner

c = heart rate

select one measurement

• Simple and robust implementation• Disturbances are indirectly handled by keeping a constant heart rate• May have infrequent adjustment of setpoint (heart rate)

Optimal operation - Runner

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Further examples

• Central bank. J = welfare. c=inflation rate (2.5%)• Cake baking. J = nice taste, c = Temperature (200C)• Business, J = profit. c = ”Key performance indicator (KPI), e.g.

– Response time to order– Energy consumption pr. kg or unit– Number of employees– Research spendingOptimal values obtained by ”benchmarking”

• Investment (portofolio management). J = profit. c = Fraction of investment in shares (50%)

• Biological systems:– ”Self-optimizing” controlled variables c have been found by natural selection– Need to do ”reverse engineering” :

• Find the controlled variables used in nature• From this identify what overall objective J the biological system has been

attempting to optimize

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Step 3. What should we control (c)? (primary controlled variables y1=c)

Selection of controlled variables c

1. Control active constraints!

2. Unconstrained variables: Control self-optimizing variables!

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Example active constraintOptimal operation = max. throughput (active constraint)

Time

Back-off= Lost production

Rule for control of hard output constraints: “Squeeze and shift”! Reduce variance (“Squeeze”) and “shift” setpoint cs to reduce backoff

Want tight bottleneck control to reduce backoff!

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Control “self-optimizing” variables

• Old idea (Morari et al., 1980):

“We want to find a function c of the process variables which when held constant, leads automatically to the optimal adjustments of the manipulated variables, and with it, the optimal operating conditions.”

• The ideal self-optimizing variable c is the gradient (c = J/ u = Ju)

– Keep gradient at zero for all disturbances (c = Ju=0)

– Problem: no measurement of gradient

Unconstrained degrees of freedom

u

cost J

Ju=0Ju

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H

Ideal: c = Ju

In practise: c = H y. Task: Determine H!

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Systematic approach: What to control?

• Define optimal operation: Minimize cost function J

• Each candidate c = Hy:

”Brute force approach”: With constant setpoints cs compute loss L for expected disturbances d and implementation errors n

• Select variable c with smallest loss

Acceptable loss ) self-optimizing control

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Example recycle plant. 3 steady-state degrees of freedom (u)

Minimize J=V (energy)

Active constraintMr = Mrmax

Active constraintxB = xBmin

L/F constant: Easier than “two-point” control

Self-optimizing

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Optimal operation

Cost J

Controlled variable cccoptopt

JJoptopt

Unconstrained optimum

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Optimal operation

Cost J

Controlled variable cccoptopt

JJoptopt

Two problems:

• 1. Optimum moves because of disturbances d: copt(d)

• 2. Implementation error, c = copt + n

d

n

Unconstrained optimum

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Good candidate controlled variables c (for self-optimizing control)

1. The optimal value of c should be insensitive to disturbances

• Small Fc = dcopt/dd

2. c should be easy to measure and control

3. Want “flat” optimum -> The value of c should be sensitive to changes in the degrees of freedom (“large gain”)

• Large G = dc/du = HGy

BADGoodGood

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Optimizer

Controller thatadjusts u to keep

cm = cs

Plant

cs

cm = c + n

u

y nyd

u

c

J

cs=copt

uopt

n

) Want c sensitive to u (”large gain”)

“Flat optimum is same as large gain”

H

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Optimal measurement combination

H

•Candidate measurements (y): Include also inputs u

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Optimal measurement combination: Nullspace method

• Want optimal value of c independent of disturbances ) copt = 0 ¢ d

• Find optimal solution as a function of d: uopt(d), yopt(d)

• Linearize this relationship: yopt = F d • F – optimal sensitivity matrix

• Want:

• To achieve this for all values of d (Nullspace method):

• Always possible if

• Comment: Nullspace method is equivalent to Ju=0

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Example. Nullspace Method for Marathon runner

u = power, d = slope [degrees]

y1 = hr [beat/min], y2 = v [m/s]

F = dyopt/dd = [0.25 -0.2]’

H = [h1 h2]]

HF = 0 -> h1 f1 + h2 f2 = 0.25 h1 – 0.2 h2 = 0

Choose h1 = 1 -> h2 = 0.25/0.2 = 1.25

Conclusion: c = hr + 1.25 v

Control c = constant -> hr increases when v decreases (OK uphill!)

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Refrigeration cycle: Proposed control structure

Control c= “temperature-corrected high pressure”. k = -8.5 bar/K

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'd

ydG

cs = constant +

+

+

+

+

- K

H

yG y

'yn

c

u

dW nW

“Minimize” in Maximum gain rule( maximize S1 G Juu

-1/2 , G=HGy )

“Scaling” S1

“=0” in nullspace method (no noise)

Optimal measurement combination, c = HyWith measurement noise

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Control structure design using self-optimizing control for economically optimal CO2 recovery*

Step S1. Objective function= J = energy cost + cost (tax) of released CO2 to air

Step S3 (Identify CVs). 1. Control the 4 equality constraints2. Identify 2 self-optimizing CVs. Use Exact Local method and select CV set with minimum loss.

4 equality and 2 inequality constraints:

1. stripper top pressure2. condenser temperature3. pump pressure of recycle amine4. cooler temperature

5. CO2 recovery ≥ 80%6. Reboiler duty < 1393 kW (nominal +20%)

4 levels without steady state effect: absorber 1,stripper 2,make up tank 1

*M. Panahi and S. Skogestad, ``Economically efficient operation of CO2 capturing process, part I: Self-optimizing procedure for selecting the best controlled variables'', Chemical Engineering and Processing, 50, 247-253 (2011).

Step S2. (a) 10 degrees of freedom: 8 valves + 2 pumps

Disturbances: flue gas flowrate, CO2 composition in flue gas + active constraints

(b) Optimization using Unisim steady-state simulator. Region I (nominal feedrate): No inequality constraints active 2 unconstrained degrees of freedom =10-4-4

Case study

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Proposed control structure with given feed

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Step 4. Where set production rate?

• Where locale the TPM (throughput manipulator)?

– The ”gas pedal” of the process• Very important!

• Determines structure of remaining inventory (level) control system

• Set production rate at (dynamic) bottleneck

• Link between Top-down and Bottom-up parts

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Production rate set at inlet :Inventory control in direction of flow*

* Required to get “local-consistent” inventory controlC

TPM

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Production rate set at outlet:Inventory control opposite flow

TPM

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Production rate set inside process

TPM

Radiating inventory control around TPM (Georgakis et al.)

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LOCATE TPM?

• Conventional choice: Feedrate• Consider moving if there is an important active

constraint that could otherwise not be well controlled

• Good choice: Locate at bottleneck

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Step 5. Regulatory control layer

• Purpose: “Stabilize” the plant using a simple control configuration (usually: local SISO PID controllers + simple cascades)

• Enable manual operation (by operators)

• Main structural decisions:• What more should we control?

(secondary CV’s, y2, use of extra measurements)

• Pairing with manipulated variables (MV’s u2)

y1 = c

y2 = ?

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Degrees of freedom for optimization (usually steady-state DOFs), MVopt = CV1sDegrees of freedom for supervisory control, MV1=CV2s + unused valvesPhysical degrees of freedom for stabilizing control, MV2 = valves (dynamic process inputs)

Optimizer (RTO)

PROCESS

Supervisory controller (MPC)

Regulatory controller (PID) H2 H

CV1

CV2s

y

ny

d

Stabilized process

CV1s

CV2

Physicalinputs (valves)

Optimally constant valves

Always active constraints

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Main objectives control system

1. Implementation of acceptable (near-optimal) operation2. Stabilization

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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Example: Exothermic reactor (unstable)

• u = cooling flow (q)

• y1 = composition (c)

• y2 = temperature (T)

u

TCy2=T

y2s

CCy1=c

y1s

feed

product

cooling

LC

Ls=max

Active constraints (economics):Product composition c + level (max)

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Example: Distillation

• Primary controlled variable: y1 = c = xD, xB (compositions top, bottom)

• BUT: Delay in measurement of x + unreliable

• Regulatory control: For “stabilization” need control of (y2):

1. Liquid level condenser (MD)

2. Liquid level reboiler (MB)

3. Pressure (p)

4. Holdup of light component in column (temperature profile)

Unstable (Integrating) + No steady-state effect

Variations in p disturb other loops

Almost unstable (integrating)

TCTs

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Why simplified configurations?Why control layers?Why not one “big” multivariable controller?• Fundamental: Save on modelling effort

• Other: – easy to understand

– easy to tune and retune

– insensitive to model uncertainty

– possible to design for failure tolerance

– fewer links

– reduced computation load

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”Advanced control” STEP 6. SUPERVISORY LAYER

Objectives of supervisory layer:1. Switch control structures (CV1) depending on operating region

• Active constraints• self-optimizing variables

2. Perform “advanced” economic/coordination control tasks.– Control primary variables CV1 at setpoint using as degrees of freedom (MV):

• Setpoints to the regulatory layer (CV2s)• ”unused” degrees of freedom (valves)

– Keep an eye on stabilizing layer• Avoid saturation in stabilizing layer

– Feedforward from disturbances• If helpful

– Make use of extra inputs– Make use of extra measurements

Implementation:• Alternative 1: Advanced control based on ”simple elements”• Alternative 2: MPC

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Summary. Systematic procedure for plantwide control

• Start “top-down” with economics: – Step 1: Define operational objectives and identify degrees of freeedom– Step 2: Optimize steady-state operation. – Step 3A: Identify active constraints = primary CVs c. Should controlled to

maximize profit) – Step 3B: For remaining unconstrained degrees of freedom: Select CVs c based

on self-optimizing control.

– Step 4: Where to set the throughput (usually: feed)

• Regulatory control I: Decide on how to move mass through the plant:• Step 5A: Propose “local-consistent” inventory (level) control structure.

• Regulatory control II: “Bottom-up” stabilization of the plant• Step 5B: Control variables to stop “drift” (sensitive temperatures, pressures, ....)

– Pair variables to avoid interaction and saturation

• Finally: make link between “top-down” and “bottom up”. • Step 6: “Advanced/supervisory control” system (MPC):

• CVs: Active constraints and self-optimizing economic variables +• look after variables in layer below (e.g.,

avoid saturation)• MVs: Setpoints to regulatory control layer.• Coordinates within units and possibly between units

cs

http://www.nt.ntnu.no/users/skoge/plantwide

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Summary and 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 (2012).

• More information:

http://www.nt.ntnu.no/users/skoge/plantwide

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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. Kariwala, S. Skogestad and J.F. Forbes, ``Reply to ``Further Theoretical results on Relative Gain Array for Norn-Bounded

Uncertain systems'''' Ind.Eng.Chem.Res, 46 (24), 8290 (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 • T. Lid and S. Skogestad, ``Scaled steady state models for effective on-line applications'', Computers and Chemical Engineering, 32,

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).