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ECONOMIC PLANTWIDE CONTROL
How to design the control system for a complete
plant in a systematic manner
Sigurd Skogestad
Department of Chemical Engineering
Norwegian University of Science and Tecnology (NTNU)
Trondheim, Norway
Brazil, July 2011
2
Outline (6 lectures)• Control structure design (plantwide control)• A procedure for control structure design
I Top Down • Step S1: Define operational objective (cost) and constraints• Step S2: Identify degrees of freedom and optimize operation for disturbances• Step S3: Implementation of optimal operation
– What to control ? (primary CV’s) (self-optimizing control)• Step S4: Where set the production rate? (Inventory control)
II Bottom Up • Step S5: Regulatory control: What more to control (secondary CV’s) ?
– Distillation column control• Step S6: Supervisory control• Step S7: Real-time optimization
• PID tuning • (+ decentralized control if time)
*Each lecture is 2 hours with a 10 min intermediate break after about 55 min (no. of slides) + means that it most likely will continue into the next lecture
Lecture 1* (49)
Lecture 4 (62)+
Lecture 2 (71)+
Lecture 3 (36)
Lecture 5 (19)
Lecture 6 (54)
Plantwide control lectures. Sigurd Skogestad
4
Main references
• The following paper summarizes the procedure: – S. Skogestad, ``Control structure design for complete chemical plants'',
Computers and Chemical Engineering, 28 (1-2), 219-234 (2004).
• There are many approaches to plantwide control as discussed in the following review paper: – T. Larsson and S. Skogestad, ``Plantwide control: A review and a new
design procedure'' Modeling, Identification and Control, 21, 209-240 (2000).
• The following paper updates the procedure: – S. Skogestad, ``Economic plantwide control’’, Book chapter in V.
Kariwala and V.P. Rangaiah (Eds), Plant-Wide Control: Recent Developments and Applications”, Wiley (late 2011).
http://www.nt.ntnu.no/users/skoge/publications/2011/skogestad-plantwide-control-book-by-kariwala/
All papers available at: http://www.nt.ntnu.no/users/skoge/
5
• S. Skogestad ``Plantwide control: the search for the self-optimizing control structure'', J. Proc. Control, 10, 487-507 (2000). • S. Skogestad, ``Self-optimizing control: the missing link between steady-state optimization and control'', Comp.Chem.Engng., 24, 569-
575 (2000). • I.J. Halvorsen, M. Serra and S. Skogestad, ``Evaluation of self-optimising control structures for an integrated Petlyuk distillation
column'', Hung. J. of Ind.Chem., 28, 11-15 (2000). • T. Larsson, K. Hestetun, E. Hovland, and S. Skogestad, ``Self-Optimizing Control of a Large-Scale Plant: The Tennessee Eastman Process
'', Ind. Eng. Chem. Res., 40 (22), 4889-4901 (2001). • K.L. Wu, C.C. Yu, W.L. Luyben and S. Skogestad, ``Reactor/separator processes with recycles-2. Design for composition control'', Comp.
Chem. Engng., 27 (3), 401-421 (2003). • T. Larsson, M.S. Govatsmark, S. Skogestad, and C.C. Yu, ``Control structure selection for reactor, separator and recycle processes'', Ind.
Eng. Chem. Res., 42 (6), 1225-1234 (2003). • A. Faanes and S. Skogestad, ``Buffer Tank Design for Acceptable Control Performance'', Ind. Eng. Chem. Res., 42 (10), 2198-2208 (2003). • I.J. Halvorsen, S. Skogestad, J.C. Morud and V. Alstad, ``Optimal selection of controlled variables'', Ind. Eng. Chem. Res., 42 (14), 3273-
3284 (2003). • A. Faanes and S. Skogestad, ``pH-neutralization: integrated process and control design'', Computers and Chemical Engineering, 28 (8),
1475-1487 (2004). • S. Skogestad, ``Near-optimal operation by self-optimizing control: From process control to marathon running and business systems'',
Computers and Chemical Engineering, 29 (1), 127-137 (2004). • E.S. Hori, S. Skogestad and V. Alstad, ``Perfect steady-state indirect control'', Ind.Eng.Chem.Res, 44 (4), 863-867 (2005). • M.S. Govatsmark and S. Skogestad, ``Selection of controlled variables and robust setpoints'', Ind.Eng.Chem.Res, 44 (7), 2207-2217
(2005). • V. Alstad and S. Skogestad, ``Null Space Method for Selecting Optimal Measurement Combinations as Controlled Variables'',
Ind.Eng.Chem.Res, 46 (3), 846-853 (2007). • S. Skogestad, ``The dos and don'ts of distillation columns control'', Chemical Engineering Research and Design (Trans IChemE, Part
A), 85 (A1), 13-23 (2007). • E.S. Hori and S. Skogestad, ``Selection of control structure and temperature location for two-product distillation columns'', Chemical
Engineering Research and Design (Trans IChemE, Part A), 85 (A3), 293-306 (2007). • A.C.B. Araujo, M. Govatsmark and S. Skogestad, ``Application of plantwide control to the HDA process. I Steady-state and self-
optimizing control'', Control Engineering Practice, 15, 1222-1237 (2007). • A.C.B. Araujo, E.S. Hori and S. Skogestad, ``Application of plantwide control to the HDA process. Part II Regulatory control'',
Ind.Eng.Chem.Res, 46 (15), 5159-5174 (2007). • V. Lersbamrungsuk, T. Srinophakun, S. Narasimhan and S. Skogestad, ``Control structure design for optimal operation of heat
exchanger networks'', AIChE J., 54 (1), 150-162 (2008). DOI 10.1002/aic.11366 • 990-999 (2008). T. Lid and S. Skogestad, ``Data reconciliation and optimal operation of a catalytic naphtha reformer'', Journal of
Process Control, 18, 320-331 (2008). • E.M.B. Aske, S. Strand and S. Skogestad, ``Coordinator MPC for maximizing plant throughput'', Computers and Chemical
Engineering, 32, 195-204 (2008). • A. Araujo and S. Skogestad, ``Control structure design for the ammonia synthesis process'', Computers and Chemical Engineering, 32
(12), 2920-2932 (2008). • E.S. Hori and S. Skogestad, ``Selection of controlled variables: Maximum gain rule and combination of measurements'',
Ind.Eng.Chem.Res, 47 (23), 9465-9471 (2008). • V. Alstad, S. Skogestad and E.S. Hori, ``Optimal measurement combinations as controlled variables'', Journal of Process Control, 19,
138-148 (2009)
• E.M.B. Aske and S. Skogestad, ``Consistent inventory control'', Ind.Eng.Chem.Res, 48 (44), 10892-10902 (2009). + MORE
6
Idealized view of control(“PhD control”)
7
Practice: Tennessee Eastman challenge problem (Downs, 1991)
(“PID control”)
8
How we design a control system for a complete chemical plant?
• How do we get from PID control to PhD control?
• Where do we start?
• What should we control? and why?
• etc.
• etc.
9
• 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.
10
Control structure design
• Not the tuning and behavior of each control loop,
• But rather the control philosophy of the overall plant with emphasis on the structural decisions:– Selection of controlled variables (“outputs”)
– Selection of manipulated variables (“inputs”)
– Selection of (extra) measurements
– Selection of control configuration (structure of overall controller that interconnects the controlled, manipulated and measured variables)
– Selection of controller type (LQG, H-infinity, PID, decoupler, MPC etc.).
• That is: Control structure design includes all the decisions we need make to get from ``PID control’’ to “PhD” control
11
Process control:
“Plantwide control” = “Control structure design for complete chemical plant”
• Large systems
• Each plant usually different – modeling expensive
• Slow processes – no problem with computation time
• Structural issues important– What to control? Extra measurements, Pairing of loops
Previous work on plantwide control: •Page Buckley (1964) - Chapter on “Overall process control” (still industrial practice)•Greg Shinskey (1967) – process control systems•Alan Foss (1973) - control system structure•Bill Luyben et al. (1975- ) – case studies ; “snowball effect”•George Stephanopoulos and Manfred Morari (1980) – synthesis of control structures for chemical processes•Ruel Shinnar (1981- ) - “dominant variables”•Jim Downs (1991) - Tennessee Eastman challenge problem•Larsson and Skogestad (2000): Review of plantwide control
12
• Control structure selection issues are identified as important also in other industries.
Professor Gary Balas (Minnesota) at ECC’03 about flight control at Boeing:
The most important control issue has always been to select the right controlled variables --- no systematic tools used!
13
Main objectives control system
1. Stabilization2. Implementation of acceptable (near-optimal) operation
ARE THESE OBJECTIVES CONFLICTING?
• Usually NOT – Different time scales
• Stabilization fast time scale
– Stabilization doesn’t “use up” any degrees of freedom• Reference value (setpoint) available for layer above• But it “uses up” part of the time window (frequency range)
14
Main simplification: Hierarchical structure
Need to define objectives and identify main issues for each
layer
PID
RTO
MPC
Process control
15
cs = y1s
MPC
PID
y2s
RTO
u (valves)
Follow path (+ look after other variables)
CV=y1 (+ u); MV=y2s
Stabilize + avoid drift CV=y2; MV=u
Min J (economics); MV=y1s
OBJECTIVE
Dealing with complexity
Main simplification: Hierarchical decomposition
The controlled variables (CVs)interconnect the layers
16
Example: Bicycle ridingNote: design starts from the bottom
• Regulatory control: – First need to learn to stabilize the bicycle
• CV = y2 = tilt of bike• MV = body position
• Supervisory control: – Then need to follow the road.
• CV = y1 = distance from right hand side• MV=y2s
– Usually a constant setpoint policy is OK, e.g. y1s=0.5 m
• Optimization: – Which road should you follow? – Temporary (discrete) changes in y1s
Hierarchical decomposition
17
Plantwide control decisions
• No matter what procedure we choose to use, the following decisions must be made when designing a plantwide control strategy:
• Decision 1. Select ”economic” (primary) controlled variables (CV1) for the supervisory control layer (the setpoints CV1s link the optimization layer with the control layers).
• Decision 2. Select ”stabilizing” (secondary) controlled variables (CV2) for the regulatory control layer (the setpoints CV2s link the two control layers).
• Decision 3. Locate the throughput manipulator (TPM).
• Decision 4. Select pairings for the stabilizing layer, that is, pair inputs (valves) and controlled variables (CV2). By “valves” is here meant the original dynamic manipulated variables.
18
Skogestad plantwide control structure design procedure
I Top Down • Step S1:Step S1: Define operational objectives (optimal operation)
– Cost function J (to be minimized)– Operational constraints
• Step S2 (optimization): (a) Identify degrees of freedom (MVs). (b) Optimize for expected disturbances and find regions of active constraints
• Step S3 (implementation): Select primary controlled variables c=y1 (CVs) (Decision 1).
• Step S4: Where set the production rate? (Inventory control) (Decision 3)II Bottom Up
• Step S5: Regulatory / stabilizing control (PID layer)– What more to control (y2; local CVs)? y (Decision 2) – Pairing of inputs and outputs y (Decision 4) – Step S6: Supervisory control (MPC layer)
• Step S7: Real-time optimization (Do we need it?)
Understanding and using this procedure is the most important part of this course!!!!
y1
y2
Process
MVs
19
Comment: Luyben procedure• Step L1. Establish control objectives• Step L2. Determine control degrees of freedom• Step L3. Establish energy management system• Step L4. Set the production rate (Decision 3)• Step L5. Control product quality and handle safety, environmental and operational
constraints• Step L6. Fix a flow in every recycle loop and control inventories• Step L7. Check component balances• Step L8. Control individual unit operations• Step L9. Optimize economics and improve dynamic controllability
Notes:• “Establish control objectives” in step L1 does not lead directly to the choice of
controlled variables (Decisions 1 and 2). Thus, in Luyben’s procedure, Decisions 1, 2 and 4 are not explicit, but are included implicitly in most of the steps.
• Even though the procedure is systematic, it is still heuristic and ad hoc in the sense that it is not clear how the authors arrived at the steps or their order.
• A major weakness is that the procedure does not include economics, except as an afterthought in step L9.
20
Outline
• Skogestad procedure for control structure designI Top Down
• Step S1: Define operational objective (cost) and constraints
• Step S2: Identify degrees of freedom and optimize operation for disturbances
• Step S3: Implementation of optimal operation
– What to control ? (primary CV’s) (self-optimizing control)
• Step S4: Where set the production rate? (Inventory control)
II Bottom Up • Step S5: Regulatory control: What more to control (secondary CV’s) ?
• Step S6: Supervisory control
• Step S7: Real-time optimization
21
Step S1. Define optimal operation (economics)
• What are we going to use our degrees of freedom u (MVs) for?• Define scalar cost function J(u,x,d)
– u: degrees of freedom (usually steady-state)– d: disturbances– x: states (internal variables)Typical cost function*:
• Optimize operation with respect to u for given d (usually steady-state):
minu J(u,x,d)subject to:
Model equations: f(u,x,d) = 0Operational constraints: g(u,x,d) < 0
J = cost feed + cost energy – value products
*No need to include fixed costs (capital costs, operators, maintainance) at ”our” time scale (hours)Note: Operational profit P = -J.
22
Optimal operation distillation column
• Distillation at steady state with given p and F: N=2 DOFs, e.g. L and V (u)
• Cost to be minimized (economics)
J = - P where P= pD D + pB B – pF F – pV
• Constraints
Purity D: For example xD, impurity · max
Purity B: For example, xB, impurity · max
Flow constraints: min · D, B, L etc. · max
Column capacity (flooding): V · Vmax, etc.
Pressure: 1) p given (d) 2) p free (u): pmin · p · pmax
Feed: 1) F given (d) 2) F free (u): F · Fmax
• Optimal operation: Minimize J with respect to steady-state DOFs (u)
value products
cost energy (heating+ cooling)
cost feed
23
Outline
• Skogestad procedure for control structure designI Top Down
• Step S1: Define operational objective (cost) and constraints
• Step S2: Identify degrees of freedom and optimize operation for disturbances
• Step S3: Implementation of optimal operation
– What to control ? (primary CV’s) (self-optimizing control)
• Step S4: Where set the production rate? (Inventory control)
II Bottom Up • Step S5: Regulatory control: What more to control (secondary CV’s) ?
• Step S6: Supervisory control
• Step S7: Real-time optimization
24
Step S2 (Optimize operation):
(a) Identify degrees of freedom (b) Optimize for expected disturbances
• Need good steady-state model
• Goal: Identify regions of active constraints
• Time consuming!
25
Plans for next lectures
• Step 2 (Find optimal operation using offline calculations):– Step 2a : DOF analysis (steady-state) (12 slides)
– Step 2b: Optimize for expected disturbances (1 slide)
– QUIZ’s
• Step 3 (Implementation of optimal operation) (Lecture 2, many slides!)Identify primary (“economic”) controlled variables (CVs):
1. Control active constraints. Backoff
2. Remaining unconstrained: Find “self-optimizing” CVs
Will use a lot of time on this!
26
Step S2a: Degrees of freedom (DOFs) for operation
NOT as simple as one may think!
To find all operational (dynamic) degrees of freedom:
• Count valves! (Nvalves)
• “Valves” also includes adjustable compressor power, etc.
Anything we can manipulate!
BUT: not all these have a (steady-state) effect on the economics
Steady-state DOFs
27
Steady-state degrees of freedom (DOFs)
IMPORTANT!
DETERMINES THE NUMBER OF VARIABLES TO CONTROL!
• No. of primary CVs = No. of steady-state DOFs
CV = controlled variable (c)
Methods to obtain no. of steady-state degrees of freedom (Nss):
1. Equation-counting • Nss = no. of variables – no. of equations/specifications • Very difficult in practice
2. Valve-counting (easier!)• Nss = Nvalves – N0ss – Nspecs
• N0ss = variables with no steady-state effect3. Potential number for some units (useful for checking!)
4. Correct answer: Will eventually find it when we perform optimization
Steady-state DOFs
28
Steady-state degrees of freedom (Nss): 2. Valve-counting
• Nvalves = no. of dynamic (control) DOFs (valves)
• Nss = Nvalves – N0ss – Nspecs : no. of steady-state DOFs • N0ss = N0y + N0,valves : no. of variables with no steady-state effect
– N0,valves : no. purely dynamic control DOFs
– N0y : no. controlled variables (liquid levels) with no steady-state effect
• Nspecs: No of equality specifications (e.g., given pressure)
Steady-state DOFs
29
Nvalves = 6 , N0y = 2* , NDOF,SS = 6 -2 = 4 (including feed and pressure as DOFs)
Typical Distillation column
*N0y : no. controlled variables (liquid levels) with no steady-state effect
With given feed and pressure:NEED TO IDENTIFY 2 more CV’s - Typical: Top and btm composition
1
2
3
4
5
6
Steady-state DOFs
30
Heat-integrated distillation process
Nvalves = 11 (w/feed), N0y = 4 (levels), Nss = 11 – 4 = 7 (with feed and 2 pressures) Need to find 7 CVs!
QUIZ 3 Steady-state DOFs
31
Heat exchanger with bypasses
CW
Nvalves = 3, N0valves = 2 (of 3), Nss = 3 – 2 = 1
Steady-state DOFs
32
Steady-state degrees of freedom (Nss): 3. Potential number for some process units• each external feedstream: 1 (feedrate)
• splitter: n-1 (split fractions) where n is the number of exit streams
• mixer: 0
• compressor, turbine, pump: 1 (work/speed)
• adiabatic flash tank: 0*
• liquid phase reactor: 1 (holdup reactant)
• gas phase reactor: 0*
• heat exchanger: 1 (bypass or flow)
• column (e.g. distillation) excluding heat exchangers: 0* + no. of sidestreams
• pressure* : add 1DOF at each extra place you set pressure (using an extra valve, compressor or pump), e.g. in adiabatic flash tank, gas phase reactor or absorption column
• *Pressure is normally assumed to be given by the surrounding process and is then not a degree of freedom
• Ref: Araujo, Govatsmark and Skogestad (2007)
• Extension to closed cycles: Jensen and Skogestad (2009)
• Real number may be less, for example, if there is no bypass valve
Steady-state DOFs
33
Heat exchanger with bypasses
CW
“Potential number heat exchanger” Nss = 1
Steady-state DOFs
34
“Potential number”, Nss= 0 (column distillation) + 1 (feed) + 2*1 (heat exchangers) + 1 (split) = 4With given feed and pressure: N’ss = 4 – 2 = 2
Distillation column (with feed and pressure as DOFs)
split
Steady-state DOFs
35
Heat-integrated distillation process
Potential number, Nss = 1 (feed) + 2*0 (columns) + 2*1 (splits) + 1 (sidestream) + 3 (hex) = 7
Steady-state DOFs
36
HDA process
Mixer FEHE Furnace PFR Quench
Separator
Compressor
Cooler
StabilizerBenzeneColumn
TolueneColumn
H2 + CH4
Toluene
Toluene Benzene CH4
Diphenyl
Purge (H2 + CH4)
QUIZ 4 Steady-state DOFs
37
HDA process: steady-state degrees of freedom
1
2
3
8 7
4
6
5
9
10
11
12
13
14 Conclusion: 14 steady-state DOFs
Assume given column pressures
feed:1.2
hex: 3, 4, 6
splitter 5, 7
compressor: 8
distillation: 2 each column
QUIZ 4 solution
Hm….. Consider-Feeds-Heat exchangers-Splitters-Compressors-Distillation columns
Steady-state DOFs
38
• Check that there are enough manipulated variables (DOFs) - both dynamically and at steady-state (step 2)
• Otherwise: Need to add equipment– extra heat exchanger
– bypass
– surge tank
Steady-state DOFs
39
Step S2b: Optimize with respects to DOFS (u) for expected disturbances (d) …….. and identify regions of active constraints
minu J(u,x,d)subject to:
Model equations: f(u,x,d) = 0Operational constraints: g(u,x,d) < 0
• Idea: Prepare operation for expected future disturbances, incl. price changes• In principle: simple• In practise: very time consuming
– Commercial simulators (Aspen, Unisim/Hysys) are set up in “design mode” and often work poorly in “operation (rating) mode”.
• Example Heat exchanger• Easy (Design mode): Given streams (and temperatures), find UA • Difficult (Operation mode): Given UA, find outlet temperatures
– Optimization methods in commercial simulators often poor• We use Matlab or even Excel “on top”• Heat exchanger: Let Matlab/Excel vary temperatures to match given UA
– Focus on most important disturbances and range. Whole picture is complicated
d1 = feedrate
d2 = energyprice
Ref. Jacobsen and Skogestad, ESCAPE’21, Greece, 2011
40
Optimal operation
Mode 1. Given feedrate
Mode 2. Maximum production
minimize J = cost feed + cost energy – value products
Two main cases (modes) depending on marked conditions:
41
Amount of products is then usually indirectly given and
Optimal operation is then usually unconstrained
“maximize efficiency (energy)” Control: Operate at optimal trade-off (not obvious what to control to achieve this)
Mode 1. Given feedrate
J = cost feed– value products + cost energy
c
J = energy
copt
constant
42
• Assume feedrate is degree of freedom
• Assume products much more valuable than feed
• Optimal operation is then to maximize product rate– But must remain feasible
– constrained by bottleneck
Mode 2. Maximum production
Control: Focus on tight control of bottleneck (“obvious what to control”)
c
J
copt
Infeasibleregion
J = cost feed + cost energy – value products
43
Example with Quiz:Optimal operation of two distillation columns in series
44
Operation of Distillation columns in seriesWith given F (disturbance): 4 steady-state DOFs (e.g., L and V in each column)
DOF = Degree Of FreedomRef.: M.G. Jacobsen and S. Skogestad (2011)
Energy price: pV=0-0.2 $/mol (varies)Cost (J) = - Profit = pF F + pV(V1+V2) – pD1D1 – pD2D2 – pB2B2
> 95% BpD2=2 $/mol
F ~ 1.2mol/spF=1 $/mol < 4 mol/s < 2.4 mol/s
> 95% CpB2=1 $/mol
N=41αAB=1.33
N=41αBC=1.5
> 95% ApD1=1 $/mol
QUIZ: What are the expected active constraints?1. Always. 2. For low energy prices.
QUIZ 1
45 DOF = Degree Of Freedom
Ref.: M.G. Jacobsen and S. Skogestad (2011)
Energy price: pV=0-0.2 $/mol (varies)Cost (J) = - Profit = pF F + pV(V1+V2) – pD1D1 – pD2D2 – pB2B2
> 95% BpD2=2 $/mol
F ~ 1.2mol/spF=1 $/mol < 4 mol/s < 2.4 mol/s
> 95% CpB2=1 $/mol
1. xB = 95% BSpec. valuable product (B): Always active!Why? “Avoid product give-away”
N=41αAB=1.33
N=41αBC=1.5
> 95% ApD1=1 $/mol
2. Cheap energy: V1=4 mol/s, V2=2.4 mol/sMax. column capacity constraints active!Why? Overpurify A & C to recover more B
QUIZ: What are the expected active constraints?1. Always. 2. For low energy prices.
Hm….?
Operation of Distillation columns in seriesWith given F (disturbance): 4 steady-state DOFs (e.g., L and V in each column)
SOLUTION QUIZ 1
46
Active constraint regions for two distillation columns in series
[mol/s]
[$/mol]
CV = Controlled Variable
Energyprice
SOLUTION QUIZ 1 (more details)
BOTTLENECKHigher F infeasible because all 5 constraints reached
47
Active constraint regions for two distillation columns in series
[mol/s]
[$/mol]
CV = Controlled Variable
QUIZ. Assume low energy prices (pV=0.01 $/mol).How should we control the columns?
Energyprice
QUIZ 2
48
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
49
Control of Distillation columns in series
Given
LC LC
LC LC
PCPC
Red: Basic regulatory loops
CC
xB
xBS=95%
MAX V1 MAX V2
1 unconstrained DOF (L1):Use for what?? CV=? •Not: CV= xA in D1! (why? xA should vary with F!) •Maybe: constant L1? (CV=L1)•Better: CV= xA in B1? Self-optimizing?
General for remaining unconstrained DOFs: LOOK FOR “SELF-OPTIMIZING” CVs = Variables we can keep constantWILL GET BACK TO THIS!
SOLUTION QUIZ 2
Hm…….HINT: CONTROL ACTIVE CONSTRAINTS!
QUIZ. Assume low energy prices (pV=0.01 $/mol).How should we control the columns? HINT: CONTROL ACTIVE CONSTRAINTS
50
In practise
• New figure, that is, update the one fom next slide
• Column with T-loops, column 1 with T btm
• V1 and V2 max repøaced by dp-contrpø
51
Control of Distillation columns in series
Given
LC LC
LC LC
PCPC
Comment: Should normally stabilize column profiles with temperature control,Should use reflux (L) in this case because boilup (V) may saturate. T1S and T2S would then replace L1 and L2 as DOFs…… but leave this out for now..
Red: Basic regulatory loops
TC TCT1s T2s
T1 T2
Comment
52
Active constraint regions for two distillation columns in series
CV = Controlled Variable
3 2
01
1
0
2
[mol/s]
[$/mol]
1
Cheap energy: 1 remaining unconstrained DOF (L1) -> Need to find 1 additional CVs (“self-optimizing”)
More expensive energy: 3 remaining unconstrained DOFs -> Need to find 3 additional CVs (“self-optimizing”)
Energyprice
SOLUTION QUIZ 2 (more details)