ECONOMIC
PLANTWIDE 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
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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
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160 journal publications
Book: Multivariable Feedback Control (Wiley 1996; 2005)
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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)
Trondheim, Norway
Teheran
4
Arctic circle
North Sea
Trondheim
NORWAY
SWEDEN
Oslo
DENMARK
GERMANY
UK
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NTNU,
Trondheim
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Outline
1. Introduction plantwide control (control structure design)
2. Plantwide control procedure
I Top Down
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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?)
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y1
y2
MVs
Process
How we design a control system for a
complete chemical plant?
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Where do we start?
What should we control? and why?
etc.
etc.
Example: Tennessee Eastman challenge
problem (Downs, 1991)
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Where place
TC
PC
LC
AC
x
SRC
??
• 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:
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•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
Theory: Optimal operation
Objectives
Present state
Model of system
Theory:
CENTRALIZED
OPTIMIZER
•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
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(Physical) Degrees of freedom
Practice: Process control
Practice:
• Hierarchical structure
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Process control: Hierarchical structure
Director
Process engineer
Operator
Logic / selectors / operator
PID control
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u = valves
Dealing with complexity
Plantwide control: Objectives
The controlled variables (CVs)
interconnect the layers
OBJECTIVE
Min J (economics)
RTO
cs = y1s
MPC
other variables)
y2s
PID
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Follow path (+ look after
Stabilize + avoid drift
u (valves)
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?)
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y1
y2
MVs
Process
Step 1. Define optimal operation (economics)
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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:
J = cost feed + cost energy – value products
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Optimize operation with respect to u for given d (usually steady-state):
minu J(u,x,d)
subject to:
Model equations:
Operational constraints:
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f(u,x,d) = 0
g(u,x,d) < 0
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:
Operational constraints:
→ uopt(d*)
f(u,x,d) = 0
g(u,x,d) < 0
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!
y
“Self-optimizing
control:” Constant
setpoints for c gives
acceptable loss
Main issue:
What should we
control?
d
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Local feedback:
Control c (CV)
Optimizing control
Feedforward
Optimal operation - Runner
Example: Optimal operation of runner
– Cost to be minimized, J=T
– One degree of freedom (u=power)
– What should we control?
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Optimal operation - Runner
Sprinter (100m)
• 1. Optimal operation of Sprinter, J=T
– Active constraint control:
• Maximum speed (”no thinking required”)
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Optimal operation - Runner
Marathon (40 km)
• 2. Optimal operation of Marathon runner, J=T
– Unconstrained optimum!
– Any ”self-optimizing” variable c (to control at
constant setpoint)?
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c1 = distance to leader of race
c2 = speed
c3 = heart rate
c4 = level of lactate in muscles
Optimal operation - Runner
Conclusion Marathon runner
select one measurement
c = heart rate
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• Simple and robust implementation
• Disturbances are indirectly handled by keeping a constant heart rate
• May have infrequent adjustment of setpoint (heart rate)
Further examples
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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 spending
Optimal values obtained by ”benchmarking”
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Investment (portofolio management). J = profit. c = Fraction of
investment in shares (50%)
Biological systems:
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”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
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 /QUIZ 1
Operation of Distillation columns in series
With given F (disturbance): 4 steady-state DOFs (e.g., L and V in each column)
N=41
αAB=1.33
F ~ 1.2mol/s
pF=1 $/mol
> 95% A
pD1=1 $/mol
= 4 mol/s
<
=> 95% B
N=41
αBC=1.
5
pD2=2 $/mol
<=2.4 mol/s
> 95% C
pB2=1 $/mol
Cost (J) = - Profit = pF F + pV(V1+V2) – pD1D1 – pD2D2 – pB2B2
Energy price: pV=0-0.2 $/mol (varies)
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DOF = Degree Of Freedom
Ref.: M.G. Jacobsen and S. Skogestad (2011)
QUIZ: What are the expected active constraints?
1. Always. 2. For low energy prices.
QUIZ 2
Control of Distillation columns in series
PC
PC
LC
LC
Given
LC
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Red: Basic regulatory loops
LC
QUIZ. Assume low energy prices (pV=0.01 $/mol).
How should we control the columns?
HINT: CONTROL ACTIVE CONSTRAINTS
SOLUTION QUIZ 2
Control of Distillation columns in series
PC
PC
LC
LC
xB
UNCONSTRAINED
CV=?
CC
Given
MAX V1
LC
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Red: Basic regulatory loops
MAX V2
LC
xBS=95%
SOLUTION QUIZ 1 (more details)
Active constraint regions for two
distillation columns in series
Energy
price
[$/mol]
BOTTLENECK
Higher F infeasible because
all 5 constraints reached
[mol/s]
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CV = Controlled Variable
Unconstrained degrees of freedom
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
cost J
Ju
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Ju=0
u
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
PC
PC
LC
LC
xB
xB
CC
CC
xAS=2.1%
Given
MAX V1
LC
MAX V2
LC
Cost (J) = - Profit = pF F + pV(V1+V2) – pD1D1 – pD2D2 – pB2B2
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Red: Basic regulatory loops
xBS=95%
Unconstrained optimum
Optimal operation
Cost J
Jopt
copt
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Controlled variable c
Unconstrained optimum
Optimal operation
d
Cost J
Jopt
n
copt
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Controlled variable c
Two problems:
• 1. Optimum moves because of disturbances d: copt(d)
• 2. Implementation error, c = copt + n
Good candidate controlled variables c
(for self-optimizing control)
1. The optimal value of c should be insensitive to disturbances
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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”)
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Large G = dc/du = HGy
Good
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Good
BAD
Optimal measurement combination
•Candidate measurements (y): Include also inputs u
H
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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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With measurement noise
Optimal measurement combination,
c = Hy
n
d
y'
'
Wd
cs = constant
+
-
K
u
Gdy
Wn
+
Gy
+
c
+
y
+
H
“=0” in nullspace method (no noise)
“Minimize” in Maximum gain rule
( maximize S1 G Juu-1/2 , G=HGy )
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“Scaling” S1
Example: CO2 refrigeration cycle
J = Ws (work supplied)
DOF = u (valve opening, z)
Main disturbances:
d 1 = TH
d2 = TCs (setpoint)
d3 = UAloss
What should we control?
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pH
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
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Control c= “temperature-corrected high pressure”. k = -8.5 bar/K
Case study
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
4 equality and 2 inequality constraints:
1. stripper top pressure
2. condenser temperature
3. pump pressure of recycle amine
4. cooler temperature
5. CO2 recovery ≥ 80%
6. Reboiler duty < 1393 kW (nominal +20%)
Step S2.
(a) 10 degrees of freedom: 8 valves + 2 pumps
4 levels without steady state effect:
absorber 1,stripper 2,make up tank 1
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
Step S3 (Identify CVs). 1. Control the 4 equality constraints
2. Identify 2 self-optimizing CVs. Use Exact Local method and select CV set with minimum loss.
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*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).
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
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Very important!
Determines structure of remaining inventory (level) control system
Set production rate at (dynamic) bottleneck
Link between Top-down and Bottom-up parts
Production rate set at inlet :
Inventory control in direction of flow*
TPM
* Required to get “local-consistent” inventory controlC
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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)
Want tight bottleneck
control to reduce
backoff!
Back-off
= Lost
production
Time
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Rule for control of hard output constraints: “Squeeze and shift”!
Reduce variance (“Squeeze”) and “shift” setpoint cs to reduce backoff
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) operation
2. Stabilization
ARE THESE OBJECTIVES CONFLICTING?
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Usually NOT
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Different time scales
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Stabilization doesn’t “use up” any degrees of freedom
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Stabilization fast time scale
Reference value (setpoint) available for layer above
But it “uses up” part of the time window (frequency range)
Example: Exothermic reactor (unstable)
Active constraints (economics):
Product composition c + level (max)
• u = cooling flow (q)
• y1 = composition (c)
• y2 = temperature (T)
feed
y1s
CC
y2s
TC
y1=c
LC
y2=T
u
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Ls=max
product
cooling
”Advanced control”
STEP 6. SUPERVISORY LAYER
Objectives of supervisory layer:
1. Switch control structures (CV1) depending on operating region
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Active constraints
self-optimizing variables
2. Perform “advanced” economic/coordination control tasks.
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Control primary variables CV1 at setpoint using as degrees of freedom (MV):
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Keep an eye on stabilizing layer
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Avoid saturation in stabilizing layer
Feedforward from disturbances
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Setpoints to the regulatory layer (CV2s)
”unused” degrees of freedom (valves)
If helpful
Make use of extra inputs
Make use of extra measurements
Implementation:
• Alternative 1: Advanced control based on ”simple elements”
• Alternative 2: MPC
Why simplified configurations?
Why control layers?
Why not one “big” multivariable controller?
• Fundamental: Save on modelling effort
• Other:
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–
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easy to understand
easy to tune and retune
insensitive to model uncertainty
possible to design for failure tolerance
fewer links
reduced computation load
Summary.
Systematic procedure for plantwide control
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Start “top-down” with economics:
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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)
cs
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Regulatory control I: Decide on how to move mass through the plant:
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Regulatory control II: “Bottom-up” stabilization of the plant
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Step 5A: Propose “local-consistent” inventory (level) control structure.
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”.
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Step 6: “Advanced/supervisory control” system (MPC):
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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
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, 569575 (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 selfoptimizing 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).
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138-148 (2009)
E.M.B. Aske and S. Skogestad, ``Consistent inventory control'', Ind.Eng.Chem.Res, 48 (44), 10892-10902 (2009).