Outline

1
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 CVs) (self-optimizing
  control)
• Step S4 Where set the production rate?
  (Inventory control)
• II Bottom Up
• Step S5 Regulatory control What more to control
  (secondary CVs) ?
• Distillation example
• Step S6 Supervisory control
• Step S7 Real-time optimization

2
II. Bottom-up

• Determine secondary controlled variables and
  structure (configuration) of control system
  (pairing)
• A good control configuration is insensitive to
  parameter changes

3
Regulatory control layer

• Purpose Stabilize the plant using a simple
  control configuration (usually local SISO PID
  controllers simple cascades)
• Enable manual operation (by operators)
• Step S5 Regulatory / stabilizing control (PID
  layer)
• (a) What more to control (CV2y2 local CVs)?
  (Decision 2)
• (b) Pairing of inputs u2 and outputs y2
• (Decision 4)

4
u2
Degrees of freedom for optimization (usually
steady-state DOFs), MVopt CV1s Degrees of
freedom for supervisory control, MV1CV2s
unused valves Physical degrees of freedom for
stabilizing control, MV2 valves (dynamic
process inputs)
5
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

6
Details Step 5 (Structure regulatory control
layer)

• (a) What to control?
• Control CV2s (y2) that stabilizes the plant
  (stops drifting)
• Select y2 which is easy to control (favorable
  dynamics)
• Favor reliable measurements y2
• 2. 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
7
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
  measurementcontrol error
• More exact tool Partial control analysis

8
Recall maximum gain rule for selecting primary
(economic) controlled variables c
Restated for secondary controlled variables y2
Control variables y2 for which their controllable
range is large compared to their sum of optimal
variation and control error
controllable range range y2 may reach by
varying the inputs optimal variation due to
disturbances control error implementation error
n
Want large
Want small
9
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

10
2. y2 is easy to control (controllability)

• Steady state Want large gain (from u2 to y2)
• Dynamics Want small effective delay (from u2 to
  y2)
• effective delay includes
• inverse response (RHP-zeros)
• high-order lags
• Main rule y2 is easy to measure and located
  close to available manipulated variable u2
  (pairing)

11
What should we control (y2)?

• Avoid closing too many loops because it increases
  complexity

12
Details Step 5b.

• (b) Identify pairings Identify MVs (u2) to be
  used 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
  (u2), 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)
• Avoid variables u2 where (frequent) changes are
  undesirable, for example, because they disturb
  other parts of the process.
• Want tight control of important active
  constraints (to avoid back-off)
• General rule pair close (see next slide)
• Comments
• Preferably, the regulatory layer should be
  independent of the economics (operating regions
  of active constraints) - without the need to
  reassigning loops depending on disturbances,
  price changes, etc.
• The total number of theoretical pairing options
  is very large, but in practice, by following the
  above rules, the number is usually quite small
  (in some cases, there may be no feasible
  solution, so, for example, the radiating rule
  must be broken)

13
Step 5b. Further Rules for pairing of variables

• Main rule Pair close
• The response (from input to output) should be
  fast, large and in one direction. Avoid dead time
  and inverse responses!
• The input (MV) should preferably effect only one
  output (to avoid interaction between the loops)
• Try to avoid input saturation (valve fully open
  or closed) in basic control loops for level and
  pressure
• The measurement of the output y should be fast
  and accurate. It should be located close to the
  input (MV) and to important disturbances.
• Use extra measurements y and cascade control if
  this is not satisfied
• The system should be simple
• Avoid too many feedforward and cascade loops
• Obvious loops (for example, for level and
  pressure) should be closed first before you spend
  to much time on deriving process models,
  RGA-analysis, etc.

14
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

15
Closing inner loops (cascade control)Use of
(extra) measurements (y2) as (extra) CVs
Primary CV
y1
G
K
y2s
u2
y2
Secondary CV (control for dynamic reasons)
Key decision Choice of y2 (controlled
variable) Also important Choice of u2
(pairing)
16
Degrees of freedom unchanged

• No degrees of freedom lost by control of
  secondary (local) variables as setpoints become
  y2s replace inputs u2 as new degrees of freedom

Cascade control
17
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

18
Cascade control distillation
ys
y
With flow loop T-loop in top
XC
Ts
T
TC
Ls
L
FC
z
XC
19
Summary step 5 Rules for selecting y2 (and u2)

• Selection of y2
• Control of y2 stabilizes the plant
• Control variables that drift
• 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.
• Avoid variables u2 where (frequent) changes are
  undesirable
• For example, they may disturb other parts of the
  process.
• The effective delay from u2 to y2 should be small
  (pair close!)

20
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

21
Example regulatory control Distillation

• Assume given feed
• 5 dynamic DOFs (L,V,D,B,VT)
• Overall objective
• Control compositions (xD and xB)
• Obvious stabilizing loops
• Condenser level (M1)
• Reboiler level (M2)
• Pressure

E.A. Wolff and S. Skogestad, Temperature
cascade control of distillation columns'',
Ind.Eng.Chem.Res., 35, 475-484, 1996.
22

• The dos and donts
• of
• distillation column control
• Sigurd Skogestad
• Norwegian University of Science and Technology
  NTNU
• N-7491 Trondheim, Norway
• From Plenary lecture Distillation06, London, 05
  Sep 2006

Will mainly consider (indirect) composition
control
23
Studied in hundreds of research and industrial
papers over the last 60 years
24
Issues distillation control

• 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?

25
Objectives of this work

• Apply general plantwide control procedure
  (Skogestad, 2004) to distillation
• From this derive (if possible) simple
  recommendations for distillation control
• Is the latter possible? Luyben (2006) has his
  doubts
• There are many different types of distillation
  columns and many different types of control
  structures. The selection of the best'' control
  structure is not as simple as some papers claim.
  Factors that influence the selection include
  volatilities, product purities, reflux ratio,
  column pressure, cost of energy, column size and
  composition of the feed prices products

He may be referring to my work...
26
2. General procedure plantwide control

• Step I. Top-down steady-state approach to
  identify primary controlled variables (y1)
• Active constraints
• Self-optimizing control
• Step II. Bottom-up identification of regulatory
  (stabilizing) control layer.
• Identify secondary controlled variables (y2)

y1s
Control of primary variables compositions (MPC)
y2s
Stabilizing control p, levels, T (PID)
27
3. Primary controlled variables distillation (y1)
Selection of primary CVs (y1)

• 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
28
Expected active constraints distillation
Selection of primary CVs (y1)

• Valueable product Purity spec. always active
• 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 ALWAYS Control valueable
  purity at spec.

29
Cheap product
Selection of primary CVs (y1)

• Over-fractionate cheap product? Trade-off
• Yes, increased recovery of valuable product (less
  loss)
• No, costs energy
• Control implications cheap product
• Energy expensive Purity spec. active
• ? Control purity at spec.
• Energy cheap Overpurify
• Unconstrained optimum given by trade-off between
  energy and recovery.
• In this case it is likely that composition
  is self-optimizing variable
• ? Possibly control purity at optimum value
  (overpurify)
• (b) Constrained optimum given by column reaching
  capacity constraint
• ? Control active capacity constraint (e.g.
  VVmax)
• Methanol water example Since methanol loss
  anyhow is low (0.1 of water), there is not much
  to gain by overpurifying. Nevertheless, with
  energy very cheap, it is probably optimal to
  operate at VVmax.

30
Conclusion primary controlled variables
Selection of primary CVs (y1)

• Product purities are very often the primary
  controlled variables (y1) for distillation
  columns
• Assume in the following two-point composition
  control
• y1 xD, xB (impurity key component)

31
4. Stabilizing control distillationSecondary
controlled variables (y2)

• 5 dynamic degrees of freedom with given feed L,
  V, D, B, VT
• To stabilize Control levels and pressure
• y2 MD, MB, p
• Choice of input u2 (to be paired with y2)
• VT is usually used to control p
• Levels (MD and MB) Many possible configurations
• Additional y2 Temperature is usually controlled
  to stabilize composition profile

32
5. Control configurations (pairing u2-y2 for
level control)
Configurations

• 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, ...

33
Top of Column
Configurations
cooling
VT
LS
Standard LY-configuration (energy balance)
LD
D
L
Set manually or from upper-layer controller
(temperature or composition)
Set manually or from upper-layer controller
VT
DS
LC
Reversed DY-configuration (material balance)
D
L
34
Top of Column
Configurations
VT
LC
D
L
D
Ls
Set manually or from upper-layer controller
(L/D)s
x
Similar in bottom... XV, XB, X V/B
35
LV-configuration (most common)

• LV-configuration
• 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.

36
How do the configurations differ?
Configurations

• Has been a lot of discussion in the literature
  (Shinskey, Buckley, Skogestad, Luyben, etc.).
• Probably over-emphasized

• 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)

BUT These comparisons are mostly without
temperature control..
37
BUT To avoid strong sensitivity to disturbances
Temperature profile must also be stabilized
D
feedback using e.g. D,L,V or B
LIGHT
TC
F
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

38
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

39
Stabilizing the column profile
40
Bonus 1 of temp. control Indirect level control
Disturbance in V, qF Detected by TC and
counteracted by L -gt Smaller changes in D
required to keep Md constant!
41
Bonus 2 of temp. control Less interactive
Setpoint T New handle instead of L
Ts
TC
42
Less interactive RGA with temperature loop
closed
43
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

44
Integral action in inner temperature loop has
little effect

45
Note No need to close two inner temperature loops

Would be even better with V/F
46
Would be even better with V/F
Ts
TC
F
(V/F)s
x
V
47
A winner L/F-T-conguration
Only caution V should not saturate
48
Temperature control Which stage?
49
Which temperature?Rule Maximize the scaled gain

• Scalar case. Minimum singular value gain G
• Maximize scaled gain G G0 / span
• G0 gain from independent variable (u) to
  candidate controlled variable (c)
• span (of c) variation (of c) optimal
  variation in c control error for c

50
Binary distillation Unscaled steady-state gain
G0 ?T/?L for small change in L
? T / ? L
BTM
TOP
51

• Procedure scaling
• Nominal simulation
• Unscaled gains (steady-state sensitivity)
• Make small change in input (L) with the other
  inputs (V) constant.
• Find gain ? Ti/? L
• Do the same for change in V
• Obtain scalings (optimal variation for various
  disturbances)
• Find ?Ti,opt for the following disturbances
• F (from 1 to 1.2) yoptf
• zF from 0.5 to 0.6 yoptz
• Optimal variation yopt to disturbances Keep
  constant xD and xB by changing both L and V
  (disturbance in F has no effect in this case, so
  yoptf0)
• Control (implementation) error. Assume0.5 K on
  all stages
• Find
• scaled-gain gain/span

52
Implementation error used , n 0.5C
Scaling 2 Not used
BTM
TOP

• Conclusion
• Control in middle of section (not at column ends
  or around feed)
• Scalings not so important here

53
8. Indirect composition controlWhich temperature
to control?

• Evaluate relative steady-state composition
  deviation (exact local method)
• ec includes
• - disturbances (F, zF, qF)
• - implementation measurement error (0.5 for T)

54

• Have looked at 15 binary columns and 5
  multicomponent (Hori, Skogestad, 2007)
• Main focus on column A
• 40 theoretical stages
• Feed in middle
• 1 impurity in each product
• Relative volatility 1.5
• Boiling point difference 10K

55
Table Binary mixture - Steady-state relative
composition deviations ( )for binary column A
Fixed variables
Tb,55 Tt,55 0.530
Tb,70 L/F 0.916
Tb,50 L/F 0.975
Tb,75 - V/F 1.148
Tb,90 L 1.223
Tb,70 L/D 1.321
Tb,50 L 1.386
Tt,95 V 1.470
L/D V/B 15.84
L/F V/B 18.59
L B 21.06
D V 21.22
L V 63.42
D B infeasible
Temperature optimally located Optimal temperature in opposite section. Temperature optimally located Optimal temperature in opposite section.
BAD
56
Table Binary mixture - Steady-state relative
composition deviations ( )for binary column A
Fixed variables
Tb,55 Tt,55 0.530
Tb,70 L/F 0.916
Tb,50 L/F 0.975
Tb,75 - V/F 1.148
Tb,90 L 1.223
Tb,70 L/D 1.321
Tb,50 L 1.386
Tt,95 V 1.470
L/D V/B 15.84
L/F V/B 18.59
L B 21.06
D V 21.22
L V 63.42
D B infeasible
Temperature optimally located Optimal temperature in opposite section. Temperature optimally located Optimal temperature in opposite section.
BEST
57
Table Binary mixture - Steady-state relative
composition deviations ( )for binary column A
Fixed variables
Tb,55 Tt,55 0.530
Tb,70 L/F 0.916
Tb,50 L/F 0.975
Tb,75 - V/F 1.148
Tb,90 L 1.223
Tb,70 L/D 1.321
Tb,50 L 1.386
Tt,95 V 1.470
L/D V/B 15.84
L/F V/B 18.59
L B 21.06
D V 21.22
L V 63.42
D B infeasible
Temperature optimally located Optimal temperature in opposite section. Temperature optimally located Optimal temperature in opposite section.
Good
58
Table Binary mixture - Steady-state relative
composition deviations ( )for binary column A
Fixed variables
Tb,55 Tt,55 0.530
Tb,70 L/F 0.916
Tb,50 L/F 0.975
Tb,75 - V/F 1.148
Tb,90 L 1.223
Tb,70 L/D 1.321
Tb,50 L 1.386
Tt,95 V 1.470
L/D V/B 15.84
L/F V/B 18.59
L B 21.06
D V 21.22
L V 63.42
D B infeasible
Temperature optimally located Optimal temperature in opposite section. Temperature optimally located Optimal temperature in opposite section.
Simple
59
Table Binary mixture - Steady-state relative
composition deviations ( )for binary column A
Fixed variables
Tb,55 Tt,55 0.530
Tb,70 L/F 0.916
Tb,50 L/F 0.975
Tb,75 - V/F 1.148
Tb,90 L 1.223
Tb,70 L/D 1.321
Tb,50 L 1.386
Tt,95 V 1.470
L/D V/B 15.84
L/F V/B 18.59
L B 21.06
D V 21.22
L V 63.42
D B infeasible
Temperature optimally located Optimal temperature in opposite section. Temperature optimally located Optimal temperature in opposite section.
Simple
60
Table Binary mixture - Steady-state relative
composition deviations ( )for binary column A
Fixed variables
Tb,55 Tt,55 0.530
Tb,70 L/F 0.916
Tb,50 L/F 0.975
Tb,75 - V/F 1.148
Tb,90 L 1.223
Tb,70 L/D 1.321
Tb,50 L 1.386
Tt,95 V 1.470
L/D V/B 15.84
L/F V/B 18.59
L B 21.06
D V 21.22
L V 63.42
D B infeasible
Temperature optimally located Optimal temperature in opposite section. Temperature optimally located Optimal temperature in opposite section.
Bad
Conclusion Fix L and a temperature
61
Avoid controlling temperature at column ends
column A

• Composition deviation
• 1- L/F and one temperature
• 2- V/F and one temperature
• 3- Two temperatures symmetrically located

62
Which temperature should we 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.

63
Conclusion stabilizing controlRemaining
supervisory control problem
Would be even better with L/F
With V for T-control
may adjust setpoints for p, M1 and M2 (MPC)
64
Summary step 5 Rules for selecting y2 (and u2)

• Selection of y2
• Control of y2 stabilizes the plant
• Control variables that drift
• 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.
• Avoid variables u2 where (frequent) changes are
  undesirable
• For example, they may disturb other parts of the
  process.
• The effective delay from u2 to y2 should be small
  (pair close!)