1.   Devising control structures for complete chemical plants – from art to science
Sigurd Skogestad
Department of Chemical Engineering
Norwegian University of Science and Tecnology (NTNU)
Trondheim, Norway
02 Dec. 2015
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2. Sigurd Skogestad 1955: Born in Flekkefjord, Norway
1978: MS (Siv.ing.) in chemical engineering at NTNU
: Worked at Norsk Hydro co. (process simulation)
1987: PhD from Caltech (supervisor: Manfred Morari)
1987-present: Professor of chemical engineering at NTNU
: Head of Department
2015- : Director Subsea Processing Research Center, NTNU (SUBPRO)
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)

3. Trondheim NORWAY Oslo DENMARK GERMANY UK Arctic circle SWEDEN
North Sea
Trondheim
NORWAY
SWEDEN
Oslo
DENMARK
GERMANY UK

4. Outline 1. Introduction plantwide control (control structure design)
2. Plantwide control procedure
I Top Down
Step 1: Define optimal operation
Step 2: Optimize for expected disturbances
Find active constraints
Step 3: Select primary controlled variables c=y1 (CVs)
Self-optimizing variables
Step 4: Where locate the throughput manipulator?
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
MVs
Process 7

5. How we design a control system for a complete chemical plant?
Where do we start?
What should we control? and why?
etc. 8

6. Example: Tennessee Eastman challenge problem (Downs, 1991)
Where place TC PC LC AC x
SRC ?? 9

7. In theory: Optimal control and operation
Objectives
Approach:
Model of overall system
Estimate present state
Optimize all degrees of freedom
Process control:
Excellent candidate for centralized control
CENTRALIZED
OPTIMIZER
Present state
Model of system
(Physical) Degrees of freedom

8. Optimal centralized
solution
Academic process control community fish pond
Sigurd

9. In theory: Optimal control and operation
Objectives
Approach:
Model of overall system
Estimate present state
Optimize all degrees of freedom
Process control:
Excellent candidate for centralized control
Problems:
Model not available
Objectives = ?
Optimization complex
Not robust (difficult to handle uncertainty)
Slow response time
CENTRALIZED
OPTIMIZER
Present state
Model of system
(Physical) Degrees of freedom

10. Practice: Engineering systems
Most (all?) large-scale engineering systems are controlled using hierarchies of quite simple controllers
Large-scale chemical plant (refinery)
Commercial aircraft
100’s of loops
Simple components:
PI-control + selectors + cascade + nonlinear fixes + some feedforward
Same in biological systems
But: Not well understood

11. 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. ( ) – case studies ; “snowball effect”
George Stephanopoulos and Manfred Morari (1980) – synthesis of control structures for chemical processes
Ruel Shinnar ( ) - “dominant variables”
Jim Downs (1991) - Tennessee Eastman challenge problem
Larsson and Skogestad (2000): Review of plantwide control 17

12. Main objectives control system
Economics: Implementation of acceptable (near-optimal) operation
Regulation: Stable 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)

13. Practical operation: Hierarchical structure
Our Paradigm
Practical operation: Hierarchical structure
Manager
constraints, prices
Process engineer
constraints, prices
Operator/RTO
setpoints
Operator/”Advanced control”/MPC
setpoints
PID-control
u = valves

14. Plantwide control: Objectives
Dealing with complexity
Plantwide control: Objectives
OBJECTIVE
Min J (economics)
RTO
CV1s
Follow path (+ look after other variables)
MPC
CV2s
Stabilize + avoid drift
PID
u (valves)
The controlled variables (CVs)
interconnect the layers
CV = controlled variable (with setpoint) 20

15. Control structure design procedure
I Top Down (mainly steady-state economics, y1)
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
Identify Active constraints
Step 3: Select primary “economic” controlled variables c=y1 (CV1s)
Self-optimizing variables
Step 4: Where locate the throughput manipulator (TPM)?
II Bottom Up (dynamics, y2)
Step 5: Regulatory / stabilizing control (PID layer)
What more to control (y2; local CV2s)?
Pairing of inputs and outputs
Step 6: Supervisory control (MPC layer)
Step 7: Real-time optimization (Do we need it?) y1 y2
MVs
Process
S. Skogestad, ``Control structure design for complete chemical plants'',
Computers and Chemical Engineering, 28 (1-2), (2004).

16. 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) = 0
Operational constraints: g(u,x,d) < 0
J = cost feed + cost energy – value products

17. Step S2. Optimize (a) Identify degrees of freedom (b) Optimize for expected disturbances
Need good model, usually steady-state
Optimization is time consuming! But it is offline
Main goal: Identify ACTIVE CONSTRAINTS
A good engineer can often guess the active constraints

18. Step S3: Implementation of optimal operation
Have found the optimal way of operation. How should it be implemented?
What to control ? (primary CV’s).
Active constraints
Self-optimizing variables (for unconstrained degrees of freedom)

19. Optimal operation of runner
Optimal operation - Runner
Optimal operation of runner
Cost to be minimized, J=T
One degree of freedom (u=power)
What should we control?

20. 1. Optimal operation of Sprinter
Optimal operation - Runner
1. Optimal operation of Sprinter
100m. J=T
Active constraint control:
Maximum speed (”no thinking required”)
CV = power (at max)

21. 2. Optimal operation of Marathon runner
Optimal operation - Runner
2. Optimal operation of Marathon runner
40 km. J=T
What should we control? CV=?
Unconstrained optimum
u=power
J=T
uopt

22. Optimal operation - Runner
Self-optimizing control: Marathon (40 km)
Any self-optimizing variable (to control at constant setpoint)?
c1 = distance to leader of race
c2 = speed
c3 = heart rate
c4 = level of lactate in muscles

23. Conclusion Marathon runner
Optimal operation - Runner
Conclusion Marathon runner
c=heart rate
J=T
copt
select one measurement
c = heart rate
CV = heart rate is good “self-optimizing” variable
Simple and robust implementation
Disturbances are indirectly handled by keeping a constant heart rate
May have infrequent adjustment of setpoint (cs)

24. Step 3. What should we control (c)?
Selection of primary controlled variables y1=c
Control active constraints!
Unconstrained variables: 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.”

25. 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

26. Production rate set at inlet : Inventory control in direction of flow*
TPM
* Required to get “local-consistent” inventory control

27. Production rate set at outlet: Inventory control opposite flow
TPM

28. Production rate set inside process
TPM
Radiating inventory control around TPM (Georgakis et al.)

29. QUIZ. Are these structures workable? Yes or No?
TPM
TPM

30. Example: Tennessee Eastman
TPM ?
TPM ? 40

31. 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

32. Control structure design procedure
I Top Down (mainly steady-state economics)
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
Identify Active constraints
Step 3: Select primary “economic” controlled variables c=y1 (CVs)
Self-optimizing variables
Step 4: Where locate the throughput manipulator (TPM)?
II Bottom Up (dynamics)
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
MVs
Process
S. Skogestad, ``Control structure design for complete chemical plants'',
Computers and Chemical Engineering, 28 (1-2), (2004).

33. Example/Quiz: Optimal operation of two distillation columns in series
D1,A
D2,B
Feed: Components A, B and C
Three products D1, D2, B2 (>95% purity)
Most valuable: B
Energy is cheap
Cost (J) = - Profit = pF F + pV(V1+V2) – pD1D1 – pD2D2 – pB2B2
Constraints: 3 purity constraints, 2 capacity constraints (max V)
Steady-state degrees of freedom (given pressure, given feed): 2 +2 = 4
Need to find 4 variables to control / keep constant
B2,C

34. Expected active constraints distillation
Selection of CV1
Expected active constraints distillation
valuable
product
methanol
+ max. 0.5%
water
cheap product
(byproduct)
+ max. 2%
+ water
Both products (D,B) generally have purity specs
Optimal operation. Control implications:
To avoid product give-away ALWAYS Control valuable product at spec. (active constraint).
May overpurify (not control) cheap product

35. Control of Distillation columns in seriesPC PC LC LC
Given LC LC
4 steady-state degrees of freedom
Red: Basic regulatory loops 46

36. Operation of Distillation columns in series 4 steady-state DOFs
Example /QUIZ 1
Operation of Distillation columns in series 4 steady-state DOFs =
N=41
αAB=1.33
N=41
αBC=1.5
> 95% B
pD2=2 $/mol
> 95% A
pD1=1 $/mol
F ~ 1.2mol/s
pF=1 $/mol = =
< 4 mol/s
< 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)
QUIZ: What are the expected active constraints?
1. Always. 2. For low energy prices.
DOF = Degree Of Freedom
Ref.: M.G. Jacobsen and S. Skogestad (2011) 47

37. Control of Distillation columns in series
SOLUTION QUIZ1 + new QUIZ2
Control of Distillation columns in series PC PC LC LC CC xB
xBS=95%
UNCONSTRAINED
CV=?
Given
MAX V2
MAX V1 LC LC
Red: Basic regulatory loops 49

38. Control of Distillation columns. Cheap energy
Quiz 2.
Control of Distillation columns. Cheap energy PC PC LC LC CC xB
xBS=95%
What is a good CV?
Given
MAX V2
MAX V1 LC LC

39. Control of Distillation columns. Cheap energy
Solution.
Control of Distillation columns. Cheap energy PC PC LC LC CC xB
xBS=95% CC xB
xAS=2.1%
Given
MAX V2
MAX V1 LC LC 52

40. Active constraint regions for two distillation columns in series
Steay-state optimization
Active constraint regions for two distillation columns in series 1
Mode 1 (expensive energy)
Energy
price 1
Mode 2: operate at BOTTLENECK
Higher F infeasible because
all 5 constraints reached
[$/mol] 2 3 2 1
[mol/s]
Mode 1, Cheap energy: 1 remaining unconstrained DOF (L1)
-> Need to find 1 additional CV
CV = Controlled Variable

41. Unconstrained optimum: What variable should be control?
Often not obvious
“Self-optimizing control”: Constant setpoint gives optimal operation for changing disturbances
Idea: Move optimization into faster control layer

42. The ideal “self-optimizing” variable is the gradient, Ju
Unconstrained degrees of freedom
The ideal “self-optimizing” variable is the gradient, Ju
c =  J/ u = Ju
Keep gradient at zero for all disturbances (c = Ju=0)
Problem: Usually no measurement of gradient u
cost J
Ju=0
Ju<0
uopt Ju 68

43. u J J>Jmin ? Jmin J<Jmin Infeasible
Never try to control the cost function J (or any other variable that reaches a maximum or minimum at the optimum) u J
J>Jmin ?
Jmin
J<Jmin
Infeasible
Better: control its gradient, Ju.

44. Parallel heat exchangers What should we control?
m [kg/s]
Th2, UA2 T2 T1 T α
1-α
Th1, UA1
1 Degree of freedom (u=split ®)
Objective: maximize J=T (= maximize total heat transfer Q)
What should we control?
Here: No active constraint.
Control T?
NO!
Optimal: Control Ju=0

45. c = Ju = TJ1 – TJ2
TJ = JÄSCHKE TEMPERATURE

46. H
Ideal: c = Ju
In practise: c = H y.
Task: Determine H!

47. Optimal linear measurement combination
Candidate measurements (y): Include also inputs u H

48. Optimal linear measurement combination: Nullspace method
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

49. Nullspace method
Proof. Appendix B in: Jäschke and Skogestad, ”NCO tracking and self-optimizing control in the context of real-time optimization”, Journal of Process Control, (2011) .

50. Example. Nullspace Method for Marathon runner
u = power, d = slope [degrees]
y1 = hr [beat/min], y2 = v [m/s]
F = dyopt/dd = [ ]’
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 v
Control c = constant -> hr increases when v decreases (OK uphill!)

51. More general (“exact local method”)
With measurement noise
More general (“exact local method”)
No measurement error: HF=0 (nullspace method)
With measuremeng error: Minimize GFc
Maximum gain rule

52. Control structure design procedure
I Top Down (mainly steady-state economics)
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
Identify Active constraints
Step 3: Select primary “economic” controlled variables c=y1 (CVs)
Self-optimizing variables
Step 4: Where locate the throughput manipulator (TPM)?
II Bottom Up (dynamics)
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
MVs
Process
S. Skogestad, ``Control structure design for complete chemical plants'',
Computers and Chemical Engineering, 28 (1-2), (2004).

53. Optimal centralized
solution
Academic process control community fish pond
Sigurd

54. Example: CO2 refrigeration cyclepH
J = Ws (work supplied)
DOF = u (valve opening, z)
Main disturbances:
d1 = TH
d2 = TCs (setpoint)
d3 = UAloss
What should we control?

55. 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 = bar/K
Nonlinear evaluation of loss: OK!

56. Refrigeration cycle: Proposed control structure
Control c= “temperature-corrected high pressure”. k = -8.5 bar/K

57. 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:
stripper top pressure
condenser temperature
pump pressure of recycle amine
cooler temperature
CO2 recovery ≥ 80%
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.
*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, (2011).

58. Proposed control structure with given feed

59. 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

60. Production rate set at inlet : Inventory control in direction of flow*
TPM
* Required to get “local-consistent” inventory controlC

61. Production rate set at outlet: Inventory control opposite flow
TPM

62. Production rate set inside process
TPM
Radiating inventory control around TPM (Georgakis et al.)

63. “Sellers marked” = high product prices:
Optimal operation = max. throughput (active constraints)
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
100

64. 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

65. 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 = ?
102

66. “Control CV2s that stabilizes the plant (stops drifting)” In practice, control:
Levels (inventory liquid)
Pressures (inventory gas/vapor) (note: some pressures may be left floating)
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
Reactor temperature
Distillation column profile (one temperature inside column)
Stripper/absorber profile does not generally need to be stabilized
103

67. Main objectives control system
Implementation of acceptable (near-optimal) operation
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)
105

68. Example: Exothermic reactor (unstable)
Active constraints (economics): Product composition c + level (max)
u = cooling flow (q)
y1 = composition (c)
y2 = temperature (T)
feed CC
y1=c
y1s
Ls=max TC
y2=T
y2s LC
product u
cooling
106

69. ”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

70. Why simplified configurations. Why control layers
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
110

71. 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

72. Rule 4: Locate the TPM close to the process bottleneck
Rules for Step S4: Location of throughput manipulator (TPM)
Rule 4: Locate the TPM close to the process bottleneck .
The justification for this rule is to take advantage of the large economic benefits of maximizing production in times when product prices are high relative to feed and energy costs (Mode 2). To maximize the production rate, one needs to achieve tight control of the active constraints, in particular, of the bottleneck, which is defined as the last constraint to become active when increasing the throughput rate (Jagtap et al., 2013).

73. Rule 5: (for processes with recycle) Locate the TPM inside the recycle loop.
The point is to avoid “overfeeding” the recycle loop which may easily occur if we operate close to the throughput where “snowballing” in the recycle loop occurs. This is a restatement of Luyben’s rule “Fix a Flow in Every Recycle Loop” (Luyben et al., 1997). From this perspective, snowballing can be thought of as the dynamic consequence of operating close to a bottleneck which is within a recycle system.
In many cases, the process bottleneck is located inside the recycle loop and Rules 4 and 5 give the same result.

74. Rules for Step S5: Structure of regulatory control layer.
Rule 6: Arrange the inventory control loops (for level, pressures, etc.) around the TPM location according to the radiation rule.
The radiation rule (Price et al., 1994), says that, the inventory loops upstream of the TPM location must be arranged opposite of flow direction. For flow downstream of TPM location it must be arranged in the same direction. This ensures “local consistency” i.e. all inventories are controlled by their local in or outflows.

75. Rule 7: Select “sensitive/drifting” variables as controlled variables CV2 for regulatory control.
This will generally include inventories (levels and pressures), plus certain other drifting (integrating) variables, for example,
a reactor temperature
a sensitive temperature/composition in a distillation column.
This ensures “stable operation, as seen from an operator’s point of view.
Some component inventories may also need to be controlled, especially for recycle systems. For example, according to “Down’s drill” one must make sure that all component inventories are “self-regulated” by flows out of the system or by removal by reactions, otherwise their composition may need to be controlled (Luyben, 1999).

76. Rule 8: Economically important active constraints (a subset of CV1), should be selected as controlled variables CV2 in the regulatory layer.
Economic variables, CV1, are generally controlled in the supervisory layer. Moving them to the faster regulatory layer may ensure tighter control with a smaller backoff.
Backoff: difference between the actual average value (setpoint) and the optimal value (constraint).

77. Rule 9: “Pair-close” rule: The pairings should be selected such that, effective delays and loop interactions are minimal.

78. Rule 10: : Avoid using MVs that may optimally saturate (at steady state) to control CVs in the regulatory layer (CV2)
The reason is that we want to avoid re-configuring the regulatory control layer. To follow this rule, one needs to consider also other regions of operation than the nominal, for example, operating at maximum capacity (Mode 2) where we usually have more active constraints.

79. Rules for Step S6: Structure of supervisory control layer.
Rule 11: MVs that may optimally saturate (at steady state) should be paired with the subset of CV11 that may be given up.
This rule applies for cases when we use decentralized control in the supervisory layer and we want to avoid reconfiguration of loops.
The rule follows because when a MV optimally saturates, then there will be one less degree of freedom, so there will be a CV1 which may be given up without any economic loss. The rule should be considered together with rule 10.

80. 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

81. 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), (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, (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:

82. S. Skogestad ``Plantwide control: the search for the self-optimizing control structure'', J. Proc. Control, 10, (2000).
S. Skogestad, ``Self-optimizing control: the missing link between steady-state optimization and control'', Comp.Chem.Engng., 24, (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, (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), (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), (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), (2003).
A. Faanes and S. Skogestad, ``Buffer Tank Design for Acceptable Control Performance'', Ind. Eng. Chem. Res., 42 (10), (2003).
I.J. Halvorsen, S. Skogestad, J.C. Morud and V. Alstad, ``Optimal selection of controlled variables'', Ind. Eng. Chem. Res., 42 (14), (2003).
A. Faanes and S. Skogestad, ``pH-neutralization: integrated process and control design'', Computers and Chemical Engineering, 28 (8), (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), (2004).
E.S. Hori, S. Skogestad and V. Alstad, ``Perfect steady-state indirect control'', Ind.Eng.Chem.Res, 44 (4), (2005).
M.S. Govatsmark and S. Skogestad, ``Selection of controlled variables and robust setpoints'', Ind.Eng.Chem.Res, 44 (7), (2005).
V. Alstad and S. Skogestad, ``Null Space Method for Selecting Optimal Measurement Combinations as Controlled Variables'', Ind.Eng.Chem.Res, 46 (3), (2007).
S. Skogestad, ``The dos and don'ts of distillation columns control'', Chemical Engineering Research and Design (Trans IChemE, Part A), 85 (A1), (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), (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, (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), (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), (2008). DOI /aic.11366
T. Lid and S. Skogestad, ``Scaled steady state models for effective on-line applications'', Computers and Chemical Engineering, 32, (2008). T. Lid and S. Skogestad, ``Data reconciliation and optimal operation of a catalytic naphtha reformer'', Journal of Process Control, 18, (2008).
E.M.B. Aske, S. Strand and S. Skogestad, ``Coordinator MPC for maximizing plant throughput'', Computers and Chemical Engineering, 32, (2008).
A. Araujo and S. Skogestad, ``Control structure design for the ammonia synthesis process'', Computers and Chemical Engineering, 32 (12), (2008).
E.S. Hori and S. Skogestad, ``Selection of controlled variables: Maximum gain rule and combination of measurements'', Ind.Eng.Chem.Res, 47 (23), (2008).
V. Alstad, S. Skogestad and E.S. Hori, ``Optimal measurement combinations as controlled variables'', Journal of Process Control, 19, (2009)
E.M.B. Aske and S. Skogestad, ``Consistent inventory control'', Ind.Eng.Chem.Res, 48 (44), (2009).