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AN INTRODUCTION TO PLANTWIDE CONTROL

Sigurd Skogestad

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

Bratislava, jan. 2011

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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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Plantwide control intro course: Contents

• Overview of plantwide control • Step1-3. Selection of primary controlled variables based on economic : The link

 between the optimization (RTO) and the control (MPC; PID) layers- Degrees of freedom- Optimization- Self-optimizing control- Applications- Many examples

• Step 4. Where to set the production rate and bottleneck  • Step 5. Design of the regulatory control layer ("what more should we

 control")     - stabilization    - secondary controlled variables (measurements)    - pairing with inputs    - controllability analysis    - cascade control and time scale separation.

• Step 6. Design of supervisory control layer    - Decentralized versus centralized (MPC)     - Design of decentralized controllers: Sequential and independent design    - Pairing and RGA-analysis

• Summary and case studies

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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

Process control The controlled variables (CVs)interconnect the layers

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Main message

• 1. Control for economics (Top-down steady-state arguments)– Primary controlled variables c = y1 :

• Control active constraints

• For remaining unconstrained degrees of freedom: Look for “self-optimizing” variables

• 2. Control for stabilization (Bottom-up; regulatory PID control)– Secondary controlled variables y2 (“inner cascade loops”)

• Control variables which otherwise may “drift”

• Both cases: Control “sensitive” variables (with a large gain)!

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Outline

• Control structure design (plantwide control)

• A procedure for control structure designI Top Down

• Step 1: Define optimal operation

• Step 2: Identify degrees of freedom and optimize for expected disturbances

• Step 3: What to control ? (primary CV’s) (self-optimizing control)

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

II Bottom Up • Step 5: Regulatory control: What more to control (secondary CV’s) ?

• Step 6: Supervisory control

• Step 7: Real-time optimization

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Idealized view of control(“Ph.D. 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?

• 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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Plantwide control = 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.).

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 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: Identify degrees of freedom and optimize for expected disturbances

• Optimization: Identify regions of active constraints

• Time consuming!

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3 unconstrained degrees of freedom -> Find 3 CVs

2

2

1

1

Control 3 active constraints

0

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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

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Question: What should we control (c)? (primary controlled variables y1=c)

• Introductory example: Runner

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

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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Step 3. What should we control (c)?

c = H y

y – available measurements (including u’s)

H – selection of combination matrix

What should we control?

Equivalently: What should H be?

1. Control active constraints!

2. Unconstrained variables: Control self-optimizing variables!

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Expected active constraints distillation

1. Valuable product: Purity spec. always active– Reason: Amount of valuable product (D or B) should

always be maximized• Avoid product “give-away”

(“Sell water as methanol”)• Also saves energy

• Control implications valuable product: Control purity at spec.

2. “Cheap” product. May want to over-purify! Trade-off:

– Yes, increased recovery of valuable product (less loss)– No, costs energyMay give unconstrained optimum

valuable product methanol + max. 1% water

cheap product(byproduct)water + max. 0.5%methanol

methanol+ water

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a) If constraint can be violated dynamically (only average matters)• Required Back-off = “bias” (steady-state measurement error for c)

b) If constraint cannot be violated dynamically (“hard constraint”) • Required Back-off = “bias” + maximum dynamic control error

Jopt Back-offLoss

c ≥ cconstraint

c

J

1. CONTROL ACTIVE CONSTRAINTS!

• Active input constraints: Just set at MAX or MIN• Active output constraints: Need back-off

Want tight control of hard output constraints to reduce the back-off

“Squeeze and shift”

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Example. Optimal operation = max. throughput. Want tight bottleneck control to reduce backoff!

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

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Control “self-optimizing” variables

1. 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.”

2. “Self-optimizing control” = acceptable steady-state behavior (loss) with constant CVs.

is similar to

“Self-regulation” = acceptable dynamic behavior with constant MVs.

3. 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

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H

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H

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Guidelines for selecting single measurements as CVs

• Rule 1: The optimal value for CV (c=Hy) should be insensitive to disturbances d (minimizes effect of setpoint error)

• Rule 2: c should be easy to measure and control (small implementation error n)

• Rule 3: “Maximum gain rule”: c should be sensitive to changes in u (large gain |G| from u to c) or equivalently the optimum Jopt should be flat with respect to c (minimizes effect of implementation error n)

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

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Optimal measurement combination

H

•Candidate measurements (y): Include also inputs u

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Nullspace method

No measurement noise (n=0)

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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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Example: CO2 refrigeration cycle

J = Ws (work supplied)DOF = u (valve opening, z)Main disturbances:

d1 = TH

d2 = TCs (setpoint) d3 = UAloss

What should we control?

pH

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CO2 refrigeration cycle

Step 1. One (remaining) degree of freedom (u=z)

Step 2. Objective function. J = Ws (compressor work)

Step 3. Optimize operation for disturbances (d1=TC, d2=TH, d3=UA)• Optimum always unconstrained

Step 4. Implementation of optimal operation• No good single measurements (all give large losses):

– ph, Th, z, …

• Nullspace method: Need to combine nu+nd=1+3=4 measurements to have zero disturbance loss

• Simpler: Try combining two measurements. Exact local method:

– c = h1 ph + h2 Th = ph + k Th; k = -8.53 bar/K

• Nonlinear evaluation of loss: OK!

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CO2 cycle: Maximum gain rule

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Refrigeration cycle: Proposed control structure

Control c= “temperature-corrected high pressure”

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Step 4. Where set production rate?

• Where locale the TPM (throughput manipulator)?

• 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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TPM (Throughput manipulator)

• TPM (Throughput manipulator) = ”Unused” degree of freedom that affects the throughput.

• Definition (Aske and Skogestad, 2009). A TPM is a degree of freedom that affects the network flow and which is not directly or indirectly determined by the control of the individual units, including their inventory control.

• Usually set by the operator (manual control), often the main feedrate

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

* Required to get “local-consistent” inventory control

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

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Step 5: Regulatory control layer

Step 5. Choose structure of regulatory (stabilizing) layer (a) Identify “stabilizing” CV2s (levels, pressures, reactor temperature,one

temperature in each column, etc.). In addition, active constraints (CV1) that require tight control (small backoff) may be assigned to the regulatory layer. (Comment: usually not necessary with tight control of unconstrained CVs because optimum is usually relatively flat)

(b) Identify pairings (MVs to be used to control CV2), taking into account – Want “local consistency” for the inventory control– Want tight control of important active constraints– Avoid MVs that may saturate in the regulatory layer, because this would

require either• reassigning the regulatory loop (complication penalty), or • requiring back-off for the MV variable (economic penalty)

Preferably, the same regulatory layer should be used for all operating regions without the need for reassigning inputs or outputs.

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Rules for pairing of variables and choice of control structure

Main rule: “Pair close”1. The response (from input to output) should be fast, large and in one direction. Avoid

dead time and inverse responses! 2. The input (MV) should preferably effect only one output (to avoid interaction

between the loops)3. Try to avoid input saturation (valve fully open or closed) in “basic” control loops for

level and pressure4. The measurement of the output y should be fast and accurate. It should be located

close to the input (MV) and to important disturbances.• Use extra measurements y’ and cascade control if this is not satisfied

5. The system should be simple• Avoid too many feedforward and cascade loops

6. “Obvious” loops (for example, for level and pressure) should be closed first before you spend to much time on deriving process matrices etc.

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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):

– Liquid level condenser (MD)

– Liquid level reboiler (MB)

– Pressure (p)

– Holdup of light component in column (temperature profile)

Unstable (Integrating) + No steady-state effect

Variations in p disturb other loops

Almost unstable (integrating)

TCTs

T-loop in bottom

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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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Degrees of freedom unchanged

• No degrees of freedom lost by control of secondary (local) variables as setpoints become y2s replace inputs u2 as new degrees of freedom

GKy2s u2

y2

y1

Original DOFNew DOF

Cascade control:

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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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Control configuration elements

• Control configuration. The restrictions imposed on the overall controller by decomposing it into a set of local controllers (subcontrollers, units, elements, blocks) with predetermined links and with a possibly predetermined design sequence where subcontrollers are designed locally.

Some control configuration elements:

• Cascade controllers

• Decentralized controllers

• Feedforward elements

• Decoupling elements

• Selectors

• Split-range control

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Summary. Systematic procedure for plantwide control

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

maximize profit) – Step 3B: For remaining unconstrained degrees of freedom: Select CV1s c based on

self-optimizing control.

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

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

3. Regulatory control II: “Bottom-up” stabilization of the plant• Step 5B: Control variables CV2 to stop “drift” (sensitive temperatures, pressures, ....)

– Pair variables to avoid interaction and saturation

4. Finally: make link between “top-down” and “bottom up”. • Step 6: “Advanced 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

CV2

CV1

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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).

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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).