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
1
II. Bottom-up
• Determine secondary controlled variables and structure
(configuration) of control system (pairing)
• A good control configuration is insensitive to parameter
changes
2
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 (CV2=y2; local CVs)?
(Decision 2)
(b) Pairing of inputs u2 and outputs y2
(Decision 4)
3
y1 = c
y2 = ?
Optimizer
(RTO)
Optimally constant valves
CV1s
Always active constraints
Supervisory
controller
(MPC)
y1=CV1
CV2s
Regulatory
controller
(PID)
u2
d
y2=CV2
H2
Physical
inputs (valves)
PROCESS
y
Stabilized process
4
H
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)
Objectives regulatory control layer
1.
2.
3.
4.
5.
6.
7.
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)
8. Allow for “slow” control in layer above (supervisory control)
9. Make control problem easy as seen from layer above
5
Details Step 5 (Structure regulatory control layer)
(a) What to control?
1. 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.*
6
*Comment: usually not necessary with tight control of unconstrained CVs because optimum is usually relatively flat
“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
7
“Control CV2s that stabilizes the plant (stops drifting)”
In practice, control:
1. Levels (inventory liquid)
2. Pressures (inventory gas/vapor) (note: some pressures may be left
floating)
3. 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
4. Reactor temperature
5. Distillation column profile (one temperature inside column)
• Stripper/absorber profile does not generally need to be stabilized
9
2. “y2 is easy to control” (controllability)
1. Steady state: Want large gain (from u2 to y2)
2. 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”)
10
What should we control (y2)?
•
11
Avoid closing too many loops because it increases
complexity
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)
•
•
•
•
12
Comments:
1. 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.
2. 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)
Step 5b…. Further Rules for pairing of variables
Main rule: “Pair close”
1. The response (from input to output) should be fast, large and in one direction. Avoid
dead time and inverse responses!
2. The input (MV) should preferably effect only one output (to avoid interaction
between the loops)
3. Try to avoid input saturation (valve fully open or closed) in “basic” control loops for
level and pressure
4. 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
5. The system should be simple
•
13
Avoid too many feedforward and cascade loops
6. “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.
Why simplified configurations?
Why control layers?
Why not one “big” multivariable controller?
• Fundamental: Save on modelling effort
• Other:
–
–
–
–
–
–
14
easy to understand
easy to tune and retune
insensitive to model uncertainty
possible to design for failure tolerance
fewer links
reduced computation load
Closing inner loops (cascade control):
Use of (extra) measurements (y2) as (extra) CVs
y2s
K
u2
G
y1
Primary CV
y2
Secondary CV
(control for
dynamic reasons)
Key decision: Choice of y2 (controlled variable)
Also important: Choice of u2 (“pairing”)
15
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:
y2s
New DOF
16
K
u2
G
y1
y
Original DOF
2
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:
1. 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
2. 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
17
Cascade control
distillation
ys
y
With flow loop +
T-loop in top
X
C
Ts
T
TC
Ls
L
18
X
C
FC
z
Summary step 5: Rules for selecting y2 (and u2)
Selection of y2
1. Control of y2 “stabilizes” the plant
• Control variables that “drift”
• The (scaled) gain for y2 should be large
2. Measurement of y2 should be simple and reliable
• For example, temperature or pressure
3. 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):
1. Avoid using inputs u2 that may saturate (at steady state)
•
When u2 saturates we loose control of the associated y2.
2. Avoid variables u2 where (frequent) changes are undesirable
•
19
For example, they may disturb other parts of the process.
3. The effective delay from u2 to y2 should be small (“pair close”!)
QUIZ: What are the benefits of adding a flow
controller (inner cascade)?
qs
Extra measurement y2 = q
1.
20
z
Counteracts nonlinearity in valve, f(z)
•
2.
q
With fast flow control we can assume q = qs
Eliminates effect of disturbances in p1 and p2
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:
1. Condenser level (M1)
2. Reboiler level (M2)
3. Pressure
21
E.A. Wolff and S. Skogestad, ``Temperature cascade control of distillation columns'', Ind.Eng.Chem.Res., 35, 475-484, 1996.
The dos and don’ts
of
distillation column control
Will mainly consider (indirect) composition control
Sigurd Skogestad
Norwegian University of Science and Technology – NTNU
N-7491 Trondheim, Norway
From: Plenary lecture Distillation’06, London, 05 Sep 2006
22
Studied in hundreds of research and industrial papers
over the last 60 years
23
Issues distillation control
• The “configuration” problem (level and
pressure control)
– Which are the two remaining degrees of
freedom?
L
• e.g. LV-, DV-, DB- and L/D V/Bconfigurations
• The temperature control problem
– Which temperature (if any) should be
controlled?
• Composition control problem
– Control two, one or no compositions?
24
Ts TC
TC
V
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...
25
2. General procedure plantwide control
Step I. “Top-down” steady-state approach to
identify primary controlled variables (y1)
– Active constraints
– Self-optimizing control
y1s
Step II. Bottom-up identification of regulatory
(“stabilizing”) control layer.
– Identify secondary controlled variables (y2)
y2s
Control of primary
variables:
compositions
(MPC)
“Stabilizing” control:
p, levels, T (PID)
26
Selection of primary CVs (y1)
3. Primary controlled variables distillation (y1)
•
Cost to be minimized (economics)
J = - P where P= pD D + pB B – pF F – pV V
value products
•
cost feed
Constraints
Purity D: For example
Purity B: For example,
Flow constraints:
Column capacity (flooding):
27
cost energy (heating+ cooling)
xD, impurity · max
xB, impurity · max
0 · D, B, L etc. · max
V · Vmax, etc.
Selection of primary CVs (y1)
Expected active constraints distillation
•
Valueable product: Purity spec. always active
– Reason: Amount of valuable product (D or B)
should always be maximized
1. Avoid product “give-away”
(“Sell water as methanol”)
2. Also saves energy
• Control implications: ALWAYS
Control valueable purity at spec.
28
methanol
+ water
valuable
product
methanol
+ max. 0.5%
water
cheap product
(byproduct)
water
+ max. 0.1%
methanol
Selection of primary CVs (y1)
Cheap product
•
Over-fractionate cheap product? Trade-off:
– Yes, increased recovery of valuable product (less loss)
– No, costs energy
methanol
+ water
• Control implications cheap product:
valuable
product
methanol
+ max. 0.5%
water
1. Energy expensive: Purity spec. active
→ Control purity at spec.
2. Energy “cheap”: Overpurify
(a)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. V=Vmax)
29
–
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 V=Vmax.
cheap product
(byproduct)
water
+ max. 0.1%
methanol
Selection of primary CVs (y1)
Conclusion primary controlled variables
• 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)
30
4. Stabilizing control distillation
Secondary 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
•
31
Additional y2: Temperature is usually controlled to “stabilize”
composition profile:
Configurations
5. 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, ...
32
Configurations
Top of Column
cooling
VT
LS
LC
L+D
D
L
“Standard” :
LY-configuration
(“energy balance”)
Set manually or from
upper-layer controller
(temperature or
composition)
VT
LC
Set manually or from
upper-layer controller
DS
D
L
33
“Reversed”:
DY-configuration
(“material balance”)
Configurations
Top of Column
L
Y - configuration
D
VT
LC
D
L
D
Ls
Similar in bottom...
XV, XB, X V/B
34
x
(L/D)s
Set manually or from
upper-layer controller
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….
35
Configurations
How do the configurations differ?
•Has been a lot of discussion in the literature (Shinskey, Buckley,
Skogestad, Luyben, etc.).
•Probably over-emphasized
1. Level control by itself
(emphasized by Buckley et al., 1985)
2. Interaction of level control with composition control
•
Related to “local consistency” (Do not want inventory control to depend on
composition loops being closed)
3. “Self-regulation” in terms of disturbance rejection
(emphasized by Skogestad and Morari, 1987)
4. Remaining two-point composition control problem
(steady-state RGA - emphasized by Shinskey, 1984)
36
BUT: These comparisons are mostly without temperature control…..
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)
•
•
37
To stabilize the column we must use feedback (feedforward will give drift)
Simplest: “Profile feedback” using sensitive temperature
Stabilizing the column profile
•
Should close one “fast” loop (usually temperature) in order to
“stabilize” the column profile
–
–
–
–
–
•
P-control usually OK (no integral action)
–
38
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
Similar to control of liquid level
Stabilizing the column profile
•
Which fast loop should be closed (“pairing”)?
– Which end? Close loop in end with “most important”
product
– Which output (temperature)? Choose “sensitive” stage
– Which input (flow)? Want fast control ) “pair close”
• “Use same end” (reduces interactions for composition
control):
Btm. loop
using V
LV
Ts
TC
– Use V (or indirect by B) for temperature control in bottom
section
– Use L (or indirect by D) for temperature control in top section
• Dynamics
– L: Some delay for liquid to go down the column
– V: Vapor flow moves quickly up the column, but may take
some time before it starts changing (heat transfer dynamics)
• In general, for stabilizing loops: Avoid using an input (flow)
that can saturate
– Do not use boilup (V) if column is close to max. capacity
39
Top loop
using L
TC
TS
Bonus 1 of temp. control:
Indirect level control
TC
40
Disturbance in V, qF:
Detected by TC
and counteracted by L
-> Smaller changes
in D required to keep
Md constant!
Bonus 2 of temp. control:
Less interactive
TC
41
Ts
Setpoint T:
New “handle”
instead of L
Less interactive:
RGA with temperature loop closed
42
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
%
43
Integral action in inner temperature loop has
little effect
%
44
Note: No need to close two inner temperature
loops
%
45
Would be even better
with V/F
Would be even better with V/F:
TC
F
(V/F)s
x
V
46
Ts
A “winner”: L/F-T-conguration
x
Ts
47
(L/F)s
TC
Only caution: V should not saturate
Temperature control: Which stage?
TC
48
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
49
Binary distillation: Unscaled steady-state gain
G0 = ΔT/ΔL for small change in L
T/L
BTM
50
TOP
Procedure scaling
1.
Nominal simulation
2.
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
3.
Obtain scalings (“optimal variation for various disturbances”)
Find Ti,opt for the following disturbances
1.
2.
F (from 1 to 1.2)
zF from 0.5 to 0.6
yoptf
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 yoptf=0)
4.
5.
Control (implementation) error. Assume=0.5 K on all stages
Find
scaled-gain = gain/span
where span = abs(yoptf)+abs(yoptz)+0.5
“Maximize gain rule”: Prefer stage where scaled-gain is large
51
Implementation error used , n = 0.5C
Scaling 2: Not used
BTM
52
TOP
Conclusion:
•Control in middle of section (not
at column ends or around feed)
•Scalings not so important here
8. Indirect composition control
Which temperature to control?
•
Evaluate relative steady-state composition deviation (”exact local method”):
def
DX =
•
53
Lmax
æx H - x H ÷
ö2
ç top
top,s ÷
= max çç
+
÷
H
÷
¢
ec 2 £ 1 ç
÷
è xtop,s
ø
2
æx L - x L ö
çç btm
btm,s ÷
÷
÷
çç
L
÷
÷
x
è
ø
btm,s
ec includes:
- disturbances (F, zF, qF)
- implementation measurement error (0.5 for T)
•
•
Have looked at 15 binary columns and 5
multicomponent (Hori, Skogestad, 2007)
Main focus on “column A”
–
–
–
–
–
54
40 theoretical stages
Feed in middle
1% impurity in each product
Relative volatility: 1.5
Boiling point difference: 10K
Table: Binary mixture - Steady-state relative composition deviations ( D X )for binary column A
Fixed variables
X
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.
55
BAD
Table: Binary mixture - Steady-state relative composition deviations ( D X )for binary column A
Fixed variables
X
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.
56
BEST
Table: Binary mixture - Steady-state relative composition deviations ( D X )for binary column A
Fixed variables
X
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.
57
Good
Table: Binary mixture - Steady-state relative composition deviations ( D X )for binary column A
Fixed variables
X
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.
58
Simple
Table: Binary mixture - Steady-state relative composition deviations ( D X )for binary column A
Fixed variables
X
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.
59
Simple
Table: Binary mixture - Steady-state relative composition deviations ( D X )for binary column A
Fixed variables
X
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
Bad
* Temperature optimally located
** Optimal temperature in opposite section.
Conclusion: Fix L and a temperature
60
Avoid controlling temperature at column ends
column A
X
•
61
Composition deviation:
1- L/F and one temperature
2- V/F and one temperature
3- Two temperatures symmetrically located
Which temperature should we control?
•
•
•
•
•
•
62
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.
Conclusion stabilizing control:
Remaining supervisory control problem
Ls
Would be even better with L/F
Ts
TC
With V for T-control
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+ may adjust setpoints for p, M1 and M2 (MPC)
Summary step 5: Rules for selecting y2 (and u2)
Selection of y2
1. Control of y2 “stabilizes” the plant
• Control variables that “drift”
• The (scaled) gain for y2 should be large
2. Measurement of y2 should be simple and reliable
• For example, temperature or pressure
3. 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):
1. Avoid using inputs u2 that may saturate (at steady state)
•
When u2 saturates we loose control of the associated y2.
2. Avoid variables u2 where (frequent) changes are undesirable
•
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For example, they may disturb other parts of the process.
3. The effective delay from u2 to y2 should be small (“pair close”!)