1. Practical plantwide process control Part 1
Sigurd Skogestad, NTNU
Thailand, April 2014

2. Part 1 (3h): Plantwide control
Introduction to plantwide control (what should we really control?)
Part 1.1 Introduction.
Objective: Put controllers on flow sheet (make P&ID)
Two main objectives for control: Longer-term economics (CV1) and shorter-term stability (CV2)
Regulatory (basic) and supervisory (advanced) control layer
Part 1.2 Optimal operation (economics)
Active constraints
Selection of economic controlled variables (CV1). Self-optimizing variables.
Part 1.3 -Inventory (level) control structure
Location of throughput manipulator
Consistency and radiating rule
Part 1.4 Structure of regulatory control layer (PID)
Selection of controlled variables (CV2) and pairing with manipulated variables (MV2)
Main rule: Control drifting variables and "pair close"
Summary: Sigurd’s rules for plantwide control

3. Course Summary
Find active constraints + self-optimizing variables (CV1). (Economic optimal operation)
Locate throughput manipulator (TPM)
“Gas pedal”
Select stabilizing CV2 + tune regulatory loops
SIMC PID rules
Design supervisory layer (control CV1)
Multi-loop (PID) ++
MPC
Difficulties:
Optimization! May need to guess active constraints (CV1)
Handling of moving active constraints
Want to avoid reconfiguration of loops

4. Summary: Sigurd’s plantwide control rules
Rules for CV1-selection:
1. Control active constraints
Purity constraint on expensive product is always active (overpurification gives loss):  
2. Unconstrained degrees of freedom (if any): Control “self-optimizing” variables (c).
The ideal variable is the gradient of J with respect to the inputs (Ju = dJ/du), which always should be zero, independent of disturbances d, but this variable is rarely available
Exception (if available!): Parallel systems (stream split, multiple feed streams/manifold) with given throughput (or given total gas flow, etc.)
Should have equal marginal costs Jiu = dJi/du, so Ju = J1u - J2u, etc.
Heat exchanger splits: equal Jächke temperatures, JT1 = (T1 – Th1)^2/(T1-T0)
In practice, one prefers to control single variables, c=Hy (where y are all available measurements and H is a selection matrix), which are easy to measure and control, and which have the following properties:
Optimal value for c is almost constant (independent of disturbances): Want small magnitude of dcopt(d)/dd.
Variable c is sensitive to changes in input: Want large magnitude of gain=dc/du (this is to reduce effect of measurement error and noise).
If the economic loss with single variables is too large, then one may use measurement combinations, c=Hy (where H is a “full” matrix).
3. Unconstrained degrees of freedom: NEVER try to control a variable that reaches max or min at the optimum (in particular, never control J)
Surprisingly, this is a very common mistake, even (especially?) with control experts
Ruke for TPM location: Locate TPM at the next constraint to become active as throughput is increased (bottleneck)
Rules for inventory control:
1. Use Radiation rule (PC, LC, FC ++)
2. Avoid having all flows in a recycle system on inventory control (this is a restatement of Luyben’s rule of “fixing a flow inside a recycle system” to avoid snowballing)
Rules for selecting stabilizing CVs (CV2): Control sensitive variablkes
Rules for pairing:
1. General: “Pair close” (large gain and small effective time delay)
2. CV1: Sigurd’s pairing rule: “Pair MV that may (optimally) saturate with CV that may be given up”
3. CV2 (stabilizing loop): Avoid MV that may saturate

5. PLANTWIDE CONTROL CASE STUDIES
Distillation: regulatory control
Distillation: Economics (CV1)
Single column
Two columns in series
Reactor/separator/recycle problem
Economics (CV1)
TPM location
Max. throughput (Bottleneck)

6. Case study: Distillation control
S. Skogestad, ``The dos and don'ts of distillation columns control'', Chemical Engineering Research and Design (Trans IChemE, Part A), 85 (A1), (2007).

7. Typical “LV”-regulatory control
Assume given feed
5 dynamic DOFs (L,V,D,B,VT)
Overall objective (CV1):
Control compositions (xD and xB)
“Obvious” stabilizing loops (CV2):
Condenser level (M1)
Reboiler level (M2)
Pressure (p)
+ “non-obvious” CV2
Column temperature (T)

8. Issues distillation controlTC Ts L V
The “configuration” problem (level and pressure control)
Which are the two remaining degrees of freedom?
e.g. LV-, DV-, DB- and L/D V/B-configurations
The temperature control problem
Which temperature (if any) should be controlled?
Composition control problem
Control two, one or no compositions?
Always control valuable product at spec

9. Control “configurations” (pairing u2-y2 for level control)
“XY-configuration”
X: remaining input in top after controlling top level (MD):
X= L (reflux), D, L/D,…
Y: remaining input in bottom after controlling MB:
Y = V (boilup, energy input), B, V/B, ...

10. Top of Column “Standard” : LY-configuration (“energy balance”)
Configurations
Top of Column
cooling LC VT LS
“Standard” :
LY-configuration
(“energy balance”)
L+D D L
Set manually or from upper-layer controller (temperature or composition)
Set manually or from upper-layer controller VT LC DS
“Reversed”:
DY-configuration
(“material balance”) D L

11. Top of Column x Similar in bottom... XV, XB, X V/B Configurations VT DLC D L D Ls
Set manually or from upper-layer controller x
(L/D)s
Similar in bottom...
XV, XB, X V/B

12. How do the configurations differ?
Has been a lot of discussion in the literature (Shinskey, Buckley, Skogestad, Luyben, etc.).
Probably over-emphasized, but let us look at it
Level control by itself
(emphasized by Buckley et al., 1985)
Interaction of level control with composition control
Related to “local consistency” (Do not want inventory control to depend on composition loops being closed)
“Self-regulation” in terms of disturbance rejection
(emphasized by Skogestad and Morari, 1987)
Remaining two-point composition control problem
(steady-state RGA - emphasized by Shinskey, 1984)

13. LV-configuration (most common)
D and B for levels (“local consistent”)
L and V remain as degrees of freedom
after level loops are closed
Other possibilities:
DB, L/D V/B, etc….

14. BUT: To avoid strong sensitivity to disturbances:
Temperature profile must also be “stabilized” D
feedback using e.g. D,L,V or B
LIGHT F TC
HEAVY B
Even with the level and pressure loops closed the column is practically unstable - either close
to integrating or even truly unstable ( e.g. with mass reflux: Jacobsen and Skogestad, 1991)
To stabilize the column we must use feedback (feedforward will give drift)
Simplest: “Profile feedback” using sensitive temperature

15. Stabilizing the column profile
Should close one “fast” loop (usually temperature) in order to “stabilize” the column profile
Makes column behave more linearly
Strongly reduces disturbance sensitivity
Keeps disturbances within column
Reduces the need for level control
Makes it possible to have good dual composition control
P-control usually OK (no integral action)
Similar to control of liquid level

16. Stabilizing the column profile (T)
Regulatory layer
Stabilizing the column profile (T) LV TC T s
. loop TC TS
(a) Common: Control T using V
(b) If V may saturate: Use L
T at which end? Prefer “important” end with tightest purity spec,
T at which stage? Choose “sensitive” stage (sensitive to MV change)
Pair T with which input (MV)? Generally “pair close”
But avoid input that may saturate
Dynamics: V has immediate effect, whereas L has delay
Prefer “same end” (L for Ttop, V for Tbtm) to reduce interactions
Note: may not be possible to satisfy all these rules

17. Bonus 1 of temp. control: Indirect level controlTC
Disturbance in V, qF:
Detected by TC
and counteracted by L
-> Smaller changes
in D required to keep
Md constant!

18. Bonus 2 of temp. control: Less interactive
Setpoint T:
New “handle”
instead of L Ts TC

19. Less interactive: RGA with temperature loop closed

20. Less interactive: Closed-loop response with decentralized PID-composition control
Interactions much smaller with “stabilizing” temperature loop closed
… and also disturbance sensitivity is expected smaller %

21. Integral action in inner temperature loop has little effect%

22. Note: No need to close two inner temperature loops%
Would be even better
with V/F

23. Would be even better with V/F:Ts TC F
(V/F)s x V

24. A “winner”: L/F-T-congurationx Ts
(L/F)s
Only caution: V should not saturate

25. Temperature control: Which stage?TC

26. Binary distillation: Steady-state gain G0 = ΔT/ΔL for small change in L
BTM
TOP

27. Summary: Which temperature to control?
Rule 1. Avoid temperatures close to column ends (especially at end where impurity is small)
Rule 2. Control temperature at important end (expensive product)
Rule 3. To achieve indirect composition control: Control temperature where the steady-state sensitivity is large (“maximum gain rule”).
Rule 4. For dynamic reasons, control temperature where the temperature change is large (avoid “flat” temperature profile). (Binary column: same as Rule 3)
Rule 5. Use an input (flow) in the same end as the temperature sensor.
Rule 6. Avoid using an input (flow) that may saturate.

28. Conclusion stabilizing control: Remaining supervisory control problemTC Ts Ls
Would be even better with L/F
With V for T-control
+ may adjust setpoints for p, M1 and M2 (MPC)

29. Summary step 5: Rules for selecting y2 (and u2)
Selection of y2
Control of y2 “stabilizes” the plant
The (scaled) gain for y2 should be large
Measurement of y2 should be simple and reliable
For example, temperature or pressure
y2 should have good controllability
small effective delay
favorable dynamics for control
y2 should be located “close” to a manipulated input (u2)
Selection of u2 (to be paired with y2):
Avoid using inputs u2 that may saturate (at steady state)
When u2 saturates we loose control of the associated y2.
“Pair close”!
The effective delay from u2 to y2 should be small

30. CASE STUDIES

31. Example (TPM location): Evaporator (with liquid feed, liquid heat medium, vapor product)
Present structure has feed pump as TPM: May risk “overfeeding”
PROBLEM:
Objective: “Keep p=ps (or T=Ts) if possible, but main priority is to evaporate a given feed”
CVs in order of priority:
CV1 = level, CV2 = throughput, CV3 = p
MV1 = feed pump, MV2 = heat fluid valve, MV3= vapor product valve
Constraints on MVs (in order of becoming active as throughput is increased):
Max heat (MV2), Fully open product valve (MV3), Max pump speed (MV1)
Where locate TPM? Pairings?

32. Note: Fully open gas product valve (MV3) is also the bottleneck
Pairing based on Sigurd’s general pairing rule**:
CV1=level with MV1 (top-priority CV is paired with MV that is least likely to saturate)
CV2=throughput with MV3 (so TPM =gas product valve)
CV3=p with MV2 (MV2 may saturate and p may be given up)
Note: Fully open gas product valve (MV3) is also the bottleneck
Rules agree because bottleneck is last constraints to become active as we increase throughput
* General: Do not need a FC on the TPM
**Sigurd’s general pairing rule: “Pair MV that may (optimally) saturate with CV that may be given up”

33. CASE STUDY: Recycle plant (Luyben, Yu, etc.) Part 1 -3
Recycle of unreacted A (+ some B) 5
Feed of A 4 1 2
Assume constant reactor temperature.
Given feedrate F0 and column pressure: 3
Dynamic DOFs: Nm = 5
Column levels: N0y = 2
Steady-state DOFs: N0 = = 3
Product (98.5% B)

34. Recycle plant: Optimal operation
Part 1: Economics (Given feed)
Recycle plant: Optimal operation mT
1 remaining unconstrained degree of freedom, CV=?

35. J=V as a function of reflux L
Optimum
= Nominal point
With fixed active constraints:
Mr = 2800 kmol (max), xB= 1.5% A (max)

36. Control of recycle plant: Conventional structure (“Two-point”: CV=xD)LC
TPM LC xD XC XC xB LC
Control active constraints (Mr=max and xB=0.015) + xD

37. Luyben law no. 1 (to avoid snowballing):
“Fix a stream in the recycle loop” (CV=F or D)

38. Luyben rule: CV=D (constant)LC LC XC LC

39. “Brute force” loss evaluation:Disturbance in F0
Luyben rule:
Conventional
Loss with nominally optimal setpoints for Mr, xB and c

40. Loss evaluation: Implementation error
Luyben rule:
Loss with nominally optimal setpoints for Mr, xB and c

41. Conclusion: Control of recycle plant
Active constraint
Mr = Mrmax
Self-optimizing
L/F constant: Easier than “two-point” control
Assumption: Minimize energy (V)
Active constraint
xB = xBmin

42. Modified Luyben’s law to avoid snowballing
Luyben law no. 1 (“Plantwide process control”, 1998, pp. 57): “A stream somewhere in all recycle loops must be flow controlled”
Luyben rule is OK dynamically (short time scale),
BUT economically (steady-state): Recycle should increase with throughput
Modified Luyben’s law 1 (by Sigurd): “Avoid having all streams in a recycle system on inventory control”
Good economic control may then require that the stream which is not on inventory control is chosen as the TPM (throughput manipulator).

43. Part 2: TPM location
Example Reactor-recycle process: Given feedrate (production rate set at inlet)
TPM

44. Part 2: TPM location PC TC D L F0 F V B
Note: Temperature and pressure controllers shown;
Otherwise as before

45. Alt.1 Alt.2 Alt.3 Alt.4 More? Alt. 5? Alt.6? Alt. 7?
T fixed in reactor
Alt.1
Alt.2
Follows Luyben law 1:
TPM inside recycle
Alt.3
Alt.4
More?
Alt. 5?
Alt.6?
Alt. 7?
Not really comparable
since T is not fixed
Unconventional TPM

46. What about TPM=D (Luyben rule)?
Alt. 5
What about TPM=D (Luyben rule)?
Control xB, xD, Md
Not so simple with liquid feed….. PC TC
TPM LC LC ? XC LC XC

47. What about TPM=D (Luyben rule)?
Alt. 5
What about TPM=D (Luyben rule)?
Another alternative:
Top level control by boilup
Get extra DOF in top
OK! PC TC
TPM LC LC XC LC XC

48. NOTE: There are actually two recycles
One through the reactor (D or F)
One through the column (L)
One flow inside both recycle loops: V
Alt.6: TPM=V if we want to break both recycle loops! PC TC

49. TPM = V Alt. 6 PC LC LC L XC F TC TPM XC LC
L and F for composition control: OK!

50. What about keeping V constant?
Alt. 7
What about keeping V constant? PC TC LC
TPM L LC F0 F V LC XC
With feedrate F0 fixed (TPM)
L for compostion control in bottom (xB)
Top composition floating
NO! Never control cost J=V

51. Bottleneck: max. vapor rate in column
Reactor-recycle process: Want to maximize feedrate: reach bottleneck in column
Bottleneck: max. vapor rate in column
TPM

52. Bottleneck: max. vapor rate in column
Reactor-recycle process with max. feedrate Alt.A: Feedrate controls bottleneck flow
Bottleneck: max. vapor rate in column
TPM Vs FC
Vmax V
Vmax-Vs=Back-off
= Loss
Get “long loop”: Need back-off in V

53. Bottleneck: max. vapor rate in column
Reactor-recycle process with max. feedrate: Alt. B Move TPM to bottleneck (MAX). Use feedrate for lost task (xB)
Bottleneck: max. vapor rate in column
MAX
TPM
=Alt.6 TPM
Get “long loop”: May need back-off in xB instead…

54. Reactor-recycle process with max. feedrate: Alt
Reactor-recycle process with max. feedrate: Alt. C: Best economically: Move TPM to bottleneck (MAX) + Reconfigure upstream loops
MAX LC
TPM
OK, but reconfiguration undesirable…
=Alt.6 TPM

55. Reactor-recycle process: Alt.C’: Move TPM + reconfigure (permanently!)LC CC
TPM
F0s
=Alt.6 TPM
For cases with given feedrate: Get “long loop” but no associated loss

56. Alt.4: Multivariable control (MPC)
Can reduce loss
BUT: Is generally placed on top of the regulatory control system (including level loops), so it still important where the production rate is set!
One approach: Put MPC on top that coordinates flows through plant
By manipulating feed rate and other ”unused” degrees of freedom (including level setpoints):
E.M.B. Aske, S. Strand and S. Skogestad,
``Coordinator MPC for maximizing plant throughput'',
Computers and Chemical Engineering, 32, (2008).

57. Comments on case study Operate with L=0 (column is a flash).
Not optimal nominally, but good enough?
Many papers, a lot of confusion
Stupid recommendations of “balanced schemes” with reactor level not at maximum (Luyben , Yu)
Gives economic loss
Not understood: Distillation column itself is also a recycle
Recommended reading:
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).

58. Plantwide control. Main 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:
All papers available at:

59. PC TC