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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
Shiraz, Jan. 2013
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Sigurd Skogestad
• 1955: Born in Flekkefjord, Norway• 1978: MS (Siv.ing.) in chemical engineering at NTNU• 1979-1983: Worked at Norsk Hydro co. (process simulation)• 1987: PhD from Caltech (supervisor: Manfred Morari)• 1987-present: Professor of chemical engineering at NTNU• 1999-2009: Head of Department
• 160 journal publications• Book: Multivariable Feedback Control (Wiley 1996; 2005)
– 1989: Ted Peterson Best Paper Award by the CAST division of AIChE – 1990: George S. Axelby Outstanding Paper Award by the Control System Society of IEEE – 1992: O. Hugo Schuck Best Paper Award by the American Automatic Control Council– 2006: Best paper award for paper published in 2004 in Computers and chemical engineering. – 2011: Process Automation Hall of Fame (US)
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Trondheim, Norway
Teheran
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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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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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Example: Tennessee Eastman challenge problem (Downs, 1991)
TC PC LC AC x SRCWhere place ??
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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
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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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
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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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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.
Example /QUIZ 1
=
= =
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Control of Distillation columns in series
Given
LC LC
LC LC
PCPC
QUIZ. Assume low energy prices (pV=0.01 $/mol).How should we control the columns? HINT: CONTROL ACTIVE CONSTRAINTSRed: Basic regulatory loops
QUIZ 2
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Control of Distillation columns in series
Given
LC LC
LC LC
PCPC
Red: Basic regulatory loops
CC
xB
xBS=95%
MAX V1 MAX V2
SOLUTION QUIZ 2
UNCONSTRAINEDCV=?
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Active constraint regions for two distillation columns in series
[mol/s]
[$/mol]
CV = Controlled Variable
Energyprice
SOLUTION QUIZ 1 (more details)
BOTTLENECKHigher F infeasible because all 5 constraints reached
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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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Control of Distillation columns in series
Given
LC LC
LC LC
PCPC
Red: Basic regulatory loops
CC
xB
xBS=95%
MAX V1 MAX V2
CC
xB
xAS=2.1%
Cost (J) = - Profit = pF F + pV(V1+V2) – pD1D1 – pD2D2 – pB2B2
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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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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 Δcopt = 0 ∙Δ d
• Find optimal solution as a function of d: uopt(d), yopt(d)
• Linearize this relationship: Δyopt = F ∙Δd • F – optimal sensitivity matrix
• Want:
• To achieve this for all values of Δd (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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'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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Refrigeration cycle: Proposed control structure
Control c= “temperature-corrected high pressure”. k = -8.5 bar/K
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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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“Sellers marked” = high product prices:Optimal 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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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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“Control CV2s that stabilizes the plant (stops drifting)” In practice, control:
1. Levels (inventory liquid)
2. Pressures (inventory gas/vapor) (note: some pressures may be left floating)
3. Inventories of components that may accumulate/deplete inside plant
• E.g., amount of amine/water (deplete) in recycle loop in CO2 capture plant
• E.g., amount of butanol (accumulates) in methanol-water distillation column
• E.g., amount of inert N2 (accumulates) in ammonia reactor recycle
4. Reactor temperature
5. Distillation column profile (one temperature inside column)
• Stripper/absorber profile does not generally need to be stabilized
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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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”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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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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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. – Step 3B: Remaining unconstrained DOFs: Self-optimizing CVs c. – 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).