1. Part 3: Regulatory («stabilizing») control
Wed AM
Part 3: Regulatory («stabilizing») control
Inventory (level) control structure
Location of throughput manipulator
Consistency and radiating rule
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

2. Outline Skogestad 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)
Control Active constraints + self-optimizing variables
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

3. Step S4. Where set production rate?
Very important decision that determines the structure of the rest of the inventory control system!
May also have important economic implications
Link between Top-down (economics) and Bottom-up (stabilization) parts
Inventory control is the most important part of stabilizing control
“Throughput manipulator” (TPM)
= MV for controlling throughput (production rate, network flow)
Where set the production rate = Where locate the TPM?
Traditionally: At the feed
For maximum production (with small backoff): At the bottleneck

4. TPM (Throughput manipulator)
Definition 1. TPM = MV used to control throughput (CV)
Definition 2 (Aske and Skogestad, 2009). A TPM is a degree of freedom that affects the network flow and which is not directly or indirectly determined by the control of the individual units, including their inventory control.
The TPM is the “gas pedal” of the process
Value of TPM: Usually set by the operator (manual control)
Operators are skeptical of giving up this MV to the control system (e.g. MPC)
The TPM is usually a flow (or closely related to a flow), e.g. main feedrate, but not always.
It can be a setpoint to another control loop
Reactor temperature can be a TPM, because it changes the reactor conversion,
Pressure of gas product can be a TPM, because it changes the gas product flowrate
Fuel cell: Load (current I) is usually the TPM
Usually, only one TPM for a plant, but there can be more if there are
parallel units or splits into alternative processing routes
multiple feeds that do not need to be set in a fixed ratio
If we consider only part of the plant then the TPM may be outside our control.
throughput is then a disturbance

5. TPM and link to inventory control
Liquid inventory: Level control (LC)
Sometimes pressure control (PC)
Gas inventory: Pressure control (PC)
Component inventory: Composition control (CC, XC, AC)

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

7. Production rate set at outlet: Inventory control opposite flow*
TPM
* Required to get “local-consistent” inventory control

8. Production rate set inside process*
TPM
* Required to get “local-consistent” inventory control

9. General: “Need radiating inventory control around TPM” (Georgakis)

10. Consistency of inventory control
Consistency (required property):
An inventory control system is said to be consistent if the steady-state mass balances (total, components and phases) are satisfied for any part of the process, including the individual units and the overall plant. 10

11. QUIZ 1
CONSISTENT?

12. Local-consistency rule
Rule 1. Local-consistency requires that
1. The total inventory (mass) of any part of the process must be locally regulated by its in- or outflows, which implies that at least one flow in or out of any part of the process must depend on the inventory inside that part of the process.
2. For systems with several components, the inventory of each component of any part of the process must be locally regulated by its in- or outflows or by chemical reaction.
3. For systems with several phases, the inventory of each phase of any part of the process must be locally regulated by its in- or outflows or by phase transition.
Proof: Mass balances
Note: Without the word “local” one gets the more general consistency rule

13. QUIZ 1
CONSISTENT?

14. Local concistency requirement -> “Radiation rule “(Georgakis)

15. Flow split: May give extra DOF
TPM
Split: Extra DOF (FC)
Flash: No extra DOF

16. Consistent? Local-consistent? QUIZ 2 Note: Local-consistent is
more strict as it implies
consistent

17. Closed system: Must leave one inventory uncontrolled
QUIZ 3
Closed system: Must leave one inventory uncontrolled

18. OK? (Where is production set?
QUIZ 4
OK? (Where is production set?
TPM1
TPM2
NO. Two TPMs (consider overall liquid balance).
Solution: Interchange LC and FC on last tank

19. Example: Separator control Alternative TPM locations
Compressor could be replaced by valve if p1>pG

20. Alt.1 Alt.2 Alt.4 Alt.3 Similar to original but NOT CONSISTENT
(PC not direction of flow)

21. Example: Solid oxide fuel cell
xH2??
xCH4,s CC PC
CH4
CH4 + H2O = CO + 3H2
CO + H2O = CO2 + H2
2H2 + O2- → 2H2O + 2e-
H2O
(in ratio with CH4 feed
to reduce C and CO formation)
Solid oxide electrolyte
O2- e-
TPM = current I [A] = disturbance
O2 + 4e- → 2O2-
Air
(excess O2) PC TC
Ts = 1070 K
(active constraint)

22. LOCATION OF SENSORS
Location flow sensor (before or after valve or pump): Does not matter from consistency point of view
Locate to get best flow measurement
Before pump: Beware of cavitation
After pump: Beware of noisy measurement
Location of pressure sensor (before or after valve, pump or compressor): Important from consistency point of view

23. Where should we place TPM?
TPM = MV used to control throughput
Traditionally: TPM = Main feed valve (or pump/compressor)
Gives inventory control “in direction of flow”
Consider moving TPM if:
There is an important CV that could otherwise not be well controlled
Dynamic reasons
Special case: Max. production important: Locate TPM at process bottleneck* !
TPM can then be used to achieve tight bottleneck control (= achieve max. production)
Economics: Max. production is very favorable in “sellers marked”
If placing it at the feed may yield infeasible operation (“overfeeding”)
If “snowballing” is a problem (accumulation in recycle loop), then consider placing TPM inside recycle loop
BUT: Avoid a variable that may (optimally) saturate as TPM (unless it is at bottleneck)
Reason: To keep controlling CV=throughput, we would need to reconfigure (move TPM)**
*Bottleneck: Last constraint to become active as we increase throughput -> TPM must be used for bottleneck control
**Sigurd’s general pairing rule (to reduce need for reassigning loops): “Pair MV that may (optimally) saturate with CV that may be given up”

24. QUIZ. Distillation. OK?
LV-configuration
TPM

25. DB-configuration OK???
TPM

26. DB-configuration: Level control NOT consistent by itself, but can still work* if we add one (or preferably two) composition/temperature loops cc
TPM cc
*But DB-configuration is not recommended!

27. QUIZ * **
* Keep p ¸ pmin
** Keep valve fully open

29. QUIZ

30. LOCATION OF SENSORS
Location flow sensor (before or after valve or pump): Does not matter from consistency point of view
Locate to get best flow measurement
Before pump: Beware of cavitation
After pump: Beware of noise
Etc.
Location of pressure sensor (before or after valve, pump or compressor): Important from consistency point of view

31. Often optimal: Locate TPM at bottleneck!
"A bottleneck is a unit where we reach a constraints which makes further increase in throughput infeasible"
If feed is cheap and available: Located TPM at bottleneck (dynamic reasons)
If the flow for some time is not at its maximum through the bottleneck, then this loss can never be recovered.

32. Single-loop alternatives for bottleneck control
Want max flow here
Traditional: Manual control of feed rate
TPM
Alt.1. Feedrate controls bottleneck flow (“long loop”…): FC
Fmax
TPM
Alt. 2: Feedrate controls lost task (another “long loop”…):
Fmax
TPM
Alt. 3: Reconfigure all upstream inventory loops:
Fmax
TPM

33. May move TPM to inside recycle loop to avoid snowballing
Example: Eastman esterification process
Alcohol recycle
Reach max mass transfer
rate: R increases sharply
(“snowballing”)
Ester product
Alcohol + water + extractive agent (e)

34. First improvement: Located closer to bottleneck

35. Final improvement: Located “at” bottleneck + TPM is inside “snowballing” loop
Follows Luyben’s law 1 to avoid snowballing(modified): “Avoid having all streams in a recycle system on inventory control”

36. Where should we place TPM?
TPM = MV used to control throughput
Traditionally: TPM = Main feed valve (or pump/compressor)
Operators like it. Gives inventory control “in direction of flow”
Consider moving TPM if:
There is an important CV that could otherwise not be well controlled
Dynamic reasons
Special case: Max. production important: Locate TPM at process bottleneck* !
Because max. production is very favorable in “sellers marked”
TPM can then be used to achieve tight bottleneck control (= achieve max. flow)
If placing it at the feed may yield infeasible operation (“overfeeding”)
If “snowballing” is a problem (accumulation in recycle loop), then consider placing TPM inside recycle loop
BUT: Avoid a variable that may (optimally) saturate as TPM (unless it is at bottleneck)
Reason: To keep controlling CV=throughput, we would need to reconfigure (move TPM)**
*Bottleneck: Last constraint to become active as we increase throughput -> TPM must be used for bottleneck control
**Sigurd’s general pairing rule (to reduce need for reassigning loops): “Pair MV that may (optimally) saturate with CV that may be given up”

37. Moving TPM
A purely top-down approach: Start by controlling all active constaints at max. throughput (may give moving TPM)
Economic Plantwide Control Over a Wide Throughput Range: A Systematic Design Procedure
Rahul Jagtap, Nitin Kaistha*and Sigurd Skogestad
Step 0: Obtain active constraint regions for the wide throughput range
Step 1: Pair loops for tight control of economic CVs at maximum throughput
Most important point economically
Most active constraints
Step 2: Design the inventory (regulatory) control system
Step 3: Design loops for ‘taking up’ additional economic CV control at lower throughputs along with appropriate throughput manipulation strategy
Warning: May get complicated, but good economically because of tight control of active constraints

38. TPM for < max throughput
Figure 5. Plantwide control structure for maximum throughput operation of recycle process (Case Study I)
A + B  C
B + C  D
Stripper
Column
A, B Recycle B A C D FC PC LC TC X RC
CCD
CCB
V1MAX
V2MAX
0.98%
0.02%
LVLRxrMAX
TPM for < max throughput
165 °C
xBRxr Opt
HS3
TRxrOpt
HS2
LS1
SP1
SP3
LC2
SP2
SP1 > SP2 > SP3
LC1
LC3
LS2
TRxrMAX

39. Conclusion TPM (production rate manipulator)
Think carefully about where to place it!
Difficult to undo later

40. Outline Skogestad 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 example
Step S6: Supervisory control
Step S7: Real-time optimization

41. 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

42. Regulatory layer
II. Bottom-up
Determine secondary controlled variables (CV2) and structure (configuration) of control system (pairing, CV2-MV2)
A good control configuration is insensitive to parameter changes

43. Step 5. Regulatory control layer
Regulatory layer
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, CV2, use of extra measurements)
Pairing with manipulated variables (mv’s u2)
CV1
CV2 = ?

44. Objectives regulatory control layer
Regulatory layer
Objectives regulatory control layer
Allow for manual operation
Simple decentralized (local) PID controllers that can be tuned on-line
Take care of “fast” control
Track setpoint changes from the layer above
Local disturbance rejection
Stabilization (mathematical sense)
Avoid “drift” (due to disturbances) so system stays in “linear region”
“stabilization” (practical sense)
Allow for “slow” control in layer above (supervisory control)
Make control problem easy as seen from layer above
Use “easy” and “robust” measurements (pressure, temperature)
Simple structure
Contribute to overall economic objective (“indirect” control)
Should not need to be changed during operation

45. Regulatory layer
Stabilizing control: Use inputs MV2=u2 to control “drifting” variables CV2
Primary CV
CV1
CV2s K u2 G
CV2
Secondary CV
(control for
dynamic reasons)
Key decision: Choice of CV2 (controlled variable)
Also important: Choice of MV2=u2 (“pairing”)
Process control: Typical «drifting» variables (CV2) are
Liquid inventories (level)
Vapor inventories (pressure)
Some temperatures (reactor, distillation column profile)

46. Degrees of freedom unchanged
Regulatory layer
Degrees of freedom unchanged
No degrees of freedom lost as setpoints y2s replace inputs u2 as new degrees of freedom for control of y1
Cascade control: G K
CV2s u2
CV2
CV1
Original DOF
New DOF

47. Example: Exothermic reactor (unstable)
Regulatory layer
Example: Exothermic reactor (unstable)
Active constraints (economics): Product composition c + level (max)
u = cooling flow (q)
CV1 = composition (c)
CV2 = temperature (T)
feed CC
CV1=c
CV1s
Ls=max TC
CV2=T
CV2s LC
product u
cooling

49. Optimizer (RTO) PROCESS H2 H y ny d Stabilized process u1 u2 CV1s
Supervisory controller (MPC)
Regulatory controller (PID) H2 H
y1=CV1
CV2s y ny d
Stabilized process
CV1s
y2=CV2
Physical
inputs (valves)
Optimally constant valves
Always active constraints u1 u2
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)

50. Details Step 5 (Structure regulatory control layer)
Regulatory layer
(a) What to control (CV2)?
Control CV2 that “stabilizes the plant” (stops drifting)
Select CV2 which is easy to control (favorable dynamics)
In addition, active constraints (CV1) that require tight control (small backoff) may be assigned to the regulatory layer.*
*Comment: usually not necessary with tight control of unconstrained CVs because
optimum is usually relatively flat

51. “Control CV2s that stabilizes the plant (stops drifting)”
A. “Mathematical stabilization” (e.g. reactor):
Unstable mode is “quickly” detected (state observability) in the measurement (y2) and is easily affected (state controllability) by the input (u2).
Tool for selecting input/output: Pole vectors
y2: Want large element in output pole vector: Instability easily detected relative to noise
u2: Want large element in input pole vector: Small input usage required for stabilization
B. “Practical extended stabilization” (avoid “drift” due to disturbance sensitivity):
Intuitive: y2 located close to important disturbance
Maximum gain rule: Controllable range for y2 is large compared to sum of optimal variation and measurement+control error
More exact tool: Partial control analysis

52. Regulatory layer
“Control CV2 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., amine/water depletes in recycle loop in CO2 capture plant
E.g., butanol accumulates in methanol-water distillation column
E.g., 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

53. Identify MVs (u2) to control CV2, taking into account:
Details Step 5b….
Regulatory layer
(b) Identify pairings =
Identify MVs (u2) to control CV2, taking into account:
Want “local consistency” for the inventory control
Implies radiating inventory control around given flow
Avoid selecting as MVs in the regulatory layer, variables that may optimally saturate at steady-state (active constraint on some region), because this would require either
reassigning the regulatory loop (complication penalty), or
requiring back-off for the MV variable (economic penalty)
Want tight control of important active constraints (to avoid back-off)
General rule: ”pair close” (see next slide)

54. Step 5b…. Main rule: “Pair close”
Regulatory layer
Step 5b…. Main rule: “Pair close”
The response (from input to output) should be fast, large and in one direction.
Avoid dead time and inverse responses!

55. Regulatory layer
Sigurd’s pairing rule: “Pair MV that may (optimally) saturate with CV that may be given up”
Main reason: Minimizes need for reassigning loops
Important: Always feasible (and optimal) to give up a CV when optimal MV saturation occurs.
Proof (DOF analysis): When one MV disappears (saturates), then we have one less optimal CV.
Failing to follow this rule: Need some “fix” when MV saturates to remain optimal, like
reconfiguration (logic)
backoff (loss of optimality)
BUT: Rule may be in conflict with other criteria
Dynamics (“pair close” rule)
Interactions (“avoid negative steady-state RGA” rule)
If conflict: Use reconfiguration (logic) or go for multivariable constraint control (MPC which may provide “built-in” logic) LV TC T s
. loop TC TS
(a) Normal: Control T using V
(b) If V may saturate: Use L

56. Regulatory layer
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

57. Hierarchical/cascade control: Time scale separation
With a “reasonable” time scale separation between the layers
(typically by a factor 5 or more in terms of closed-loop response time)
we have the following advantages:
The stability and performance of the lower (faster) layer (involving y2) is not much influenced by the presence of the upper (slow) layers (involving y1)
Reason: The frequency of the “disturbance” from the upper layer is well inside the bandwidth of the lower layers
With the lower (faster) layer in place, the stability and performance of the upper (slower) layers do not depend much on the specific controller settings used in the lower layers
Reason: The lower layers only effect frequencies outside the bandwidth of the upper layers

58. Cascade control distillation ys y Ts T Ls L z With flow loop +
T-loop in top y XC Ts T TC Ls L FC z XC

59. QUIZ: What are the benefits of adding a flow controller (inner cascade)?qs
Extra measurement y2 = q q z
Counteracts nonlinearity in valve, f(z)
With fast flow control we can assume q = qs
Eliminates effect of disturbances in p1 and p2

60. Summary: Sigurd’s plantwide control rules
Rules for CV-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 (is 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
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)
A special case is a closed system
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

61. 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

62. 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:

63. PC TC