1. 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
Singapore / Petronas / Petrobras, March 2010, India 2010, Brazil July 2011

2. Main simplification: Hierarchical decomposition
Dealing with complexity
Main simplification: Hierarchical decomposition
The controlled variables (CVs)
interconnect the layers
Process control
OBJECTIVE
Min J (economics); MV=y1s
RTO
cs = y1s
Follow path (+ look after other variables)
CV=y1 (+ u); MV=y2s
MPC
y2s
Stabilize + avoid drift
CV=y2; MV=u
PID
u (valves)

3. 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).

4. 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).

5. Outline Control structure design (plantwide control)
A procedure for control structure design
I Top Down
Step 1: Define operational objective (cost) and constraints
Step 2: Identify degrees of freedom and optimizate for disturbances
Step 3: What to control ? (primary CV’s) (self-optimizing control)
Step 4: Where set the production rate? (Inventory control)
II Bottom Up
Step 5: Regulatory control: What more to control (secondary CV’s) ?
Step 6: Supervisory control
Step 7: Real-time optimization
Case studies

6. Main message
1. Control for economics (Top-down steady-state arguments)
Primary controlled variables c = y1 :
Control active constraints
For remaining unconstrained degrees of freedom: Look for “self-optimizing” variables
2. Control for stabilization (Bottom-up; regulatory PID control)
Secondary controlled variables y2 (“inner cascade loops”)
Control variables which otherwise may “drift”
Both cases: Control “sensitive” variables (with a large gain)!

7. Idealized view of control (“Ph.D. control”)

8. Practice: Tennessee Eastman challenge problem (Downs, 1991) (“PID control”)

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

10. 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.

11. 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 “Ph.D” control

12. Each plant usually different – modeling expensive
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. ( ) – 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

13. 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!

14. Main objectives control system
Stabilization
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)

15. Main simplification: Hierarchical decomposition
Dealing with complexity
Main simplification: Hierarchical decomposition
The controlled variables (CVs)
interconnect the layers
Process control
OBJECTIVE
Min J (economics); MV=y1s
RTO
cs = y1s
Follow path (+ look after other variables)
CV=y1 (+ u); MV=y2s
MPC
y2s
Stabilize + avoid drift
CV=y2; MV=u
PID
u (valves)

16. Example: Bicycle riding
Hierarchical decomposition
Example: Bicycle riding
Note: 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

17. Summary: The three layers
Optimization layer (RTO; steady-state nonlinear model):
Identifies active constraints and computes optimal setpoints for primary controlled variables (y1).
Supervisory control (MPC; linear model with constraints):
Follow setpoints for y1 (usually constant) by adjusting setpoints for secondary variables (MV=y2s)
Look after other variables (e.g., avoid saturation for MV’s used in regulatory layer)
Regulatory control (PID):
Stabilizes the plant and avoids drift, in addition to following setpoints for y2. MV=valves (u).
Problem definition and overall control objectives (y1, y2) starts from the top.
Design starts from the bottom.
A good example is bicycle riding:
Regulatory control:
First you need to learn how to stabilize the bicycle (y2)
Supervisory control:
Then you need to follow the road. Usually a constant setpoint policy is OK, for example, stay y1s=0.5 m from the right hand side of the road (in this case the "magic" self-optimizing variable self-optimizing variable is y1=distance to right hand side of road)
Optimization:
Which road (route) should you follow?

18. 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
Identify regions of active constraints
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?)
Understanding and using this procedure is the most important part of this course!!!! y1 y2
MVs
Process

19. 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

20. Optimal operation distillation column
Distillation at steady state with given p and F: N=2 DOFs, e.g. L and V
Cost to be minimized (economics)
J = - P where P= pD D + pB B – pF F – pV V
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, 2) p free: pmin · p · pmax
Feed: ) F given 2) F free: F · Fmax
Optimal operation: Minimize J with respect to steady-state DOFs
cost energy (heating+ cooling)
value products
cost feed

21. Optimal operation
minimize J = cost feed + cost energy – value products
Two main cases (modes) depending on marked conditions:
Given feed
Amount of products is then usually indirectly given and J = cost energy. Optimal operation is then usually unconstrained:
Feed free
Products usually much more valuable than feed + energy costs small.
Optimal operation is then usually constrained:
“maximize efficiency (energy)”
Control: Operate at optimal trade-off (not obvious what to control to achieve this)
“maximize production”
Control: Operate at bottleneck
(“obvious what to control”)

22. Comments optimal operation
Do not forget to include feedrate as a degree of freedom!!
For LNG plant it may be optimal to have max. compressor power or max. compressor speed, and adjust feedrate of LNG
For paper machine it may be optimal to have max. drying and adjust the feedrate of paper (speed of the paper machine) to meet spec!
Control at bottleneck
see later: “Where to set the production rate”

23. Step 2: (a) Identify degrees of freedom and (b) optimize for expected disturbances
Optimization: Identify regions of active constraints
Time consuming! 3
3 unconstrained degrees of freedom -> Find 3 CVs 2 1
Control 3 active constraints

24. Active constraint regions for two distillation columns in series

25. Step 2a: 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

26. Optimizer (RTO) TPM H1 H2 d PROCESS y Stabilized process ny CV1s CV1
Optimally constant valves
TPM
CV1s
Supervisory controller (MPC)
CV1
unused valves
CV2s
CV2
Regulatory controller (PID) H1 H2
Physical
inputs (valves) d
PROCESS y
Stabilized process ny
Degrees of freedom for optimization (usually steady-state DOFs), MVopt = CV1s
Degrees of freedom for supervisory control, MV1=CV2s + unused valves
Physical degrees of freedom for stabilizing control, MV2 = valves (dynamic process inputs)

27. Steady-state degrees of freedom (DOFs)
IMPORTANT! DETERMINES THE NUMBER OF VARIABLES TO CONTROL!
No. of primary CVs = No. of steady-state DOFs
Methods to obtain no. of steady-state degrees of freedom (Nss):
Equation-counting
Nss = no. of variables – no. of equations/specifications
Very difficult in practice
Valve-counting (easier!)
Nss = Nvalves – N0ss – Nspecs
N0ss = variables with no steady-state effect
Potential number for some units (useful for checking!)
Correct answer: Will eventually it when we perform optimization
CV = controlled variable (c)

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)

29. Typical Distillation column4 5 3 1
With given feed and pressure:
NEED TO IDENTIFY 2 more CV’s
- Typical: Top and btm composition 6 2
Nvalves = 6 , N0y = 2 ,
NDOF,SS = = 4 (including feed and pressure as DOFs)
N0y : no. controlled variables (liquid levels) with no steady-state effect

30. Heat-integrated distillation process

31. Heat-integrated distillation process

32. Heat exchanger with bypasses

33. Heat exchanger with bypasses

34. Steady-state degrees of freedom (Nss): 3
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

35. Heat exchanger with bypasses

36. Distillation column (with feed and pressure as DOFs)
split
“Potential number”,
Nss= 0 (distillation) + 1 (feed) + 2*1 (heat exchangers) + 1 (split) = 4
With given feed and pressure: N’ss = 4 – 2 = 2

37. Heat-integrated distillation process

38. HDA process Mixer FEHE Furnace PFR Quench Separator Compressor Cooler
Stabilizer
Benzene
Column
Toluene
H2 + CH4
CH4
Diphenyl
Purge (H2 + CH4)

39. HDA process: steady-state degrees of freedom8 7
feed:1.2
hex: 3, 4, 6
splitter 5, 7
compressor: 8
distillation: 2 each column 3 1 2 4 5 6 13 11 9 14 12 10
Conclusion: 14 steady-state DOFs
Assume given column pressures

40. Otherwise: Need to add equipment
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

41. QUIZ Degrees of freedom (Dynamic, steady-state)?
Heating
Cooling
Feed
51%A, 49%B
Purge (mostly A, some B, trace C)
Liquid Product (C)
Flash
Gas phase process
(e.g. ammonia, methanol)
Degrees of freedom (Dynamic, steady-state)?
Expected active constraints?
Proposed control structure?

42. 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)?
What should we control?

43. Solution I (“obvious”): Optimal feedforward
Problem: UNREALISTIC!
Lack of measurements of d
Sensitive to model error

44. Solution II (”obvious”): Optimizing controly
Estimate d from measurements y
and recompute uopt(d)
Problem:
COMPLICATED!
Requires detailed model and description of uncertainty

45. Solution III (in practice): FEEDBACK with hierarchical decompositiony
CVs: link optimization and control layers
When disturbance d:
Degrees of freedom (u) are updated indirectly to keep CVs at setpoints

46. “Self-Optimizing Control” = Solution III with constant setpointsy
Self-optimizing control: Constant setpoints give acceptable loss
Issue:
What should we control?

47. self-optimizing control
Formal Definition
Controller
Process d
u(d)
c = f(y) cs e - + n cm
Acceptable loss )
self-optimizing control
Self-optimizing control is said to occur when we can achieve an acceptable loss (in comparison with truly optimal operation) with constant setpoint values for the controlled variables without the need to reoptimize when disturbances occur.
Reference: S. Skogestad, “Plantwide control: The search for the self-optimizing control structure'', Journal of Process Control, 10, (2000).

48. How does self-optimizing control (solution III) work?
When disturbances d occur, controlled variable c deviates from setpoint cs
Feedback controller changes degree of freedom u to uFB(d) to keep c at cs
Near-optimal operation / acceptable loss (self-optimizing control) is achieved if
uFB(d) ≈ uopt(d)
or more generally, J(uFB(d)) ≈ J(uopt(d))
Of course, variation of uFB(d) is different for different CVs c.
We need to look for variables, for which J(uFB(d)) ≈ J(uopt(d)) or Loss = J(uFB(d)) - J(uopt(d)) is small

49. Remarks “self-optimizing control”
1. Old idea (Morari et al., 1980):
“We want to find a function c of the process variables which when held constant, leads automatically to the optimal adjustments of the manipulated variables, and with it, the optimal operating conditions.”
2. “Self-optimizing control” = acceptable steady-state behavior (loss) with constant CVs.
is similar to
“Self-regulation” = acceptable dynamic behavior with constant MVs.
3. The ideal self-optimizing variable c is the gradient (c =  J/ u = Ju)
Keep gradient at zero for all disturbances (c = Ju=0)
Problem: no measurement of gradient

50. Step 3. What should we control (c)? Simple examples

51. 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?

52. Self-optimizing control: Sprinter (100m)
Optimal operation - Runner
Self-optimizing control: Sprinter (100m)
1. Optimal operation of Sprinter, J=T
Active constraint control:
Maximum speed (”no thinking required”)

53. Self-optimizing control: Marathon (40 km)
Optimal operation - Runner
Self-optimizing control: Marathon (40 km)
2. Optimal operation of Marathon runner, J=T

54. Solution 1 Marathon: Optimizing control
Optimal operation - Runner
Solution 1 Marathon: Optimizing control
Even getting a reasonable model requires > 10 PhD’s  … and the model has to be fitted to each individual….
Clearly impractical!

55. Solution 2 Marathon – Feedback (Self-optimizing control)
Optimal operation - Runner
Solution 2 Marathon – Feedback (Self-optimizing control)
What should we control?

56. Self-optimizing control: Marathon (40 km)
Optimal operation - Runner
Self-optimizing control: Marathon (40 km)
Optimal operation of Marathon runner, J=T
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

57. Conclusion Marathon runner
Optimal operation - Runner
Conclusion Marathon runner
select one measurement
c = heart rate
Simple and robust implementation
Disturbances are indirectly handled by keeping a constant heart rate
May have infrequent adjustment of setpoint (heart rate)

58. Example: Cake Baking Disturbances Measurements Degrees of Freedom
Objective: Nice tasting cake with good texture
Disturbances
Measurements
d1 = oven specifications
y1 = oven temperature
d2 = oven door opening
y2 = cake temperature
d3 = ambient temperature
y3 = cake color
d4 = initial temperature
u1 = Heat input
u2 = Final time
Degrees of Freedom

59. Further examples self-optimizing control
Marathon runner
Central bank
Cake baking
Business systems (KPIs)
Investment portifolio
Biology
Chemical process plants: Optimal blending of gasoline
Define optimal operation (J) and look for ”magic” variable (c) which when kept constant gives acceptable loss (self-optimizing control)

60. More on further examples
Central bank. J = welfare. u = interest rate. c=inflation rate (2.5%)
Cake baking. J = nice taste, u = heat input. 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”
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 possibly identify what overall objective J the biological system has been attempting to optimize

61. Summary Step 3. What should we control (c)?
c = H y
y – available measurements (including u’s)
H – selection of combination matrix
What should we control?
Equivalently: What should H be?
Control active constraints!
Unconstrained variables: Control self-optimizing variables!

62. 1. CONTROL ACTIVE CONSTRAINTS!

63. Example: Optimal operation distillation
Cost to be minimized (economics)
J = - P where P= pD D + pB B – pF F – pV V
Constraints
Purity D: For example xD, impurity · max
Purity B: For example, xB, impurity · max
Flow constraints: 0 · D, B, L etc. · max
Column capacity (flooding): V · Vmax, etc.
cost energy (heating+ cooling)
value products
cost feed

64. Expected active constraints distillation
valuable
product
methanol
+ max. 5%
water
cheap product
(byproduct)
+ max. 2%
+ water
Valuable product: Purity spec. always active
(if we get paid for impurity)
Reason: Amount of valuable product (D or B) should always be maximized
Avoid product “give-away”
(“Sell water as methanol”)
Also saves energy
Control implications valuable product: Control purity at spec.
2. “Cheap” product. May want to over-purify!
Trade-off:
Yes, increased recovery of valuable product (less loss)
No, costs energy
May give unconstrained optimum

65. Active constraint regions distillation
No pay for impurity (pD=x*PD0): Can have no active constraints F pV
Infeas.
xDmax
xBmax,
Vmax
(-1)
No constraints.
Overpurify
D and B
(2)
xDmax (1)
xDmax,
xBmax
(0)
Vmax,
(1)
Region below here does not exist if pD is constant (“expensive product purity constraint xDmax always active”)
pV=0

66. 1. CONTROL ACTIVE CONSTRAINTS!
Active input constraints: Just set at MAX or MIN
Active output constraints: Need back-off
Back-off
Loss
c ≥ cconstraint c J
Jopt
If constraint can be violated dynamically (only average matters)
Required Back-off = “bias” (steady-state measurement error for c)
If constraint cannot be violated dynamically (“hard constraint”)
Required Back-off = “bias” + maximum dynamic control error
Want tight control of hard output constraints to reduce the back-off
“Squeeze and shift”

67. Example. Optimal operation = max. throughput
Example. Optimal operation = max. throughput. Want tight bottleneck control to reduce backoff!
Time
Back-off
= Lost production
Rule for control of hard output constraints: “Squeeze and shift”!
Reduce variance (“Squeeze”) and “shift” setpoint cs to reduce backoff

68. Hard Constraints: «SQUEEZE AND SHIFT»
© Richalet

69. SUMMARY ACTIVE CONSTRAINTS
cconstraint = value of active constraint
Implementation of active constraints is usually “obvious”, but may need “back-off” (safety limit) for hard output constraints
Cs = Cconstraint - backoff
Want tight control of hard output constraints to reduce the back-off
“Squeeze and shift”

70. QUIZ (again) Degrees of freedom (Dynamic, steady-state)?
Heating
Cooling
Feed
51%A, 49%B
Purge (mostly A, some B, trace C)
Liquid Product (C)
Flash
Gas phase process
(e.g. ammonia, methanol)
Degrees of freedom (Dynamic, steady-state)?
Expected active constraints? (1. Feed given; 2. Feed free)
Proposed control structure?

71. 2. UNCONSTRAINED VARIABLES: - WHAT MORE SHOULD WE CONTROL
2. UNCONSTRAINED VARIABLES: - WHAT MORE SHOULD WE CONTROL? - WHAT ARE GOOD “SELF-OPTIMIZING” VARIABLES?
Intuition: “Dominant variables” (Shinnar)
Is there any systematic procedure?
A. Sensitive variables: “Max. gain rule” (Gain= Minimum singular value)
B. “Brute force” loss evaluation
C. Optimal linear combination of measurements, c = Hy