Outline
• Control structure design (plantwide control)
• A procedure for control structure design
I Top Down
•
•
•
•
Step 1: Degrees of freedom
Step 2: Operational objectives (optimal operation)
Step 3: What to control ? (self-optimzing control)
Step 4: Where set production rate?
II Bottom Up
• Step 5: Regulatory control: What more to control ?
• Step 6: Supervisory control
• Step 7: Real-time optimization
• Case studies
1
Step 4. Where set production rate?
•
•
•
•
2
Very important!
Determines structure of remaining inventory (level) control system
Set production rate at (dynamic) bottleneck
Link between Top-down and Bottom-up parts
Production rate set at inlet :
Inventory control in direction of flow
3
Production rate set at outlet:
Inventory control opposite flow
4
Production rate set inside process
5
Where set the production rate?
• Very important decision that determines the structure of the rest of the
control system!
• May also have important economic implications
6
Often optimal: Set production rate at
bottleneck!
• "A bottleneck is an extensive variable that prevents an increase in the
overall feed rate to the plant"
• If feed is cheap and available: Optimal to set production rate at
bottleneck
• If the flow for some time is not at its maximum through the
bottleneck, then this loss can never be recovered.
7
Reactor-recycle process:
Given feedrate with production rate set at inlet
8
Reactor-recycle process:
Want to maximize feedrate: reach bottleneck in column
Bottleneck: max. vapor
rate in column
9
Reactor-recycle process with production rate set at inlet
Want to maximize feedrate: reach bottleneck in column
Alt.1: Loss
Bottleneck: max. vapor
rate in column
Vs
10
FC
Vmax
V
Vmax-Vs=Back-off
= Loss
Reactor-recycle process with increased feedrate:
Optimal: Set production rate at bottleneck
Alt.2 “long loop”
MAX
11
Reactor-recycle process with increased feedrate:
Optimal: Set production rate at bottleneck
Alt.3: reconfigure
MAX
12
Reactor-recycle process:
Given feedrate with production rate set at bottleneck
Alt.3: reconfigure
(permanently)
F0s
13
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!
14
Conclusion production rate manipulator
• Think carefully about where to place it!
• Difficult to undo later
15
Outline
• Control structure design (plantwide control)
• A procedure for control structure design
I Top Down
•
•
•
•
Step 1: Degrees of freedom
Step 2: Operational objectives (optimal operation)
Step 3: What to control ? (self-optimizing control)
Step 4: Where set production rate?
II Bottom Up
• Step 5: Regulatory control: What more to control ?
• Step 6: Supervisory control
• Step 7: Real-time optimization
• Case studies
16
II. Bottom-up
• Determine secondary controlled variables and structure
(configuration) of control system (pairing)
• A good control configuration is insensitive to parameter
changes
Step 5. REGULATORY CONTROL LAYER
5.1 Stabilization (including level control)
5.2 Local disturbance rejection (inner cascades)
What more to control? (secondary variables)
Step 6. SUPERVISORY CONTROL LAYER
Decentralized or multivariable control (MPC)?
Pairing?
Step 7. OPTIMIZATION LAYER (RTO)
17
Step 5. Regulatory control layer
• Purpose: “Stabilize” the plant using local SISO PID controllers
• Enable manual operation (by operators)
• Main structural issues:
• What more should we control? (secondary cv’s, y2)
• Pairing with manipulated variables (mv’s u2)
y1 = c
y2 = ?
18
Regulatory loops
y2s
K
u2
G
y1
y
2
Key decision: Choice of y2 (controlled variable)
Also important (since we almost always use single loops in the
regulatory control layer): Choice of u2 (“pairing”)
19
Example: Distillation
• Primary controlled variable: y1 = c = xD, xB (compositions top, bottom)
• BUT: Delay in measurement of x + unreliable
• Regulatory control: For “stabilization” need control of (y2):
–
–
–
–
Liquid level condenser (MD) Unstable (Integrating) + No steady-state effect
Liquid level reboiler (MB)
Disturbs (“destabilizes”) other loops
Pressure (p)
Holdup of light component in column
(temperature profile) Almost unstable (integrating)
Ts
20
T-loop in bottom
TC
Cascade control
distillation
ys
y
With flow loop +
T-loop in top
X
C
Ts
T
TC
Ls
L
21
X
C
FC
z
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
22
K
u2
G
y1
y
Original DOF
2
Hierarchical 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
23
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
24
Implications for selection of y2:
1. Control of y2 “stabilizes the plant”
2. y2 is easy to control (favorable dynamics)
1. “Control of y2 stabilizes the plant”
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
25
B. “Practical extended stabilization” (avoid “drift” due to disturbance
sensitivity):
• Intuitive: y2 located close to important disturbance
• Or rather: Controllable range for y2 is large compared to sum of
optimal variation and control error
• More exact tool: Partial control analysis
Recall rule for selecting primary controlled variables c:
Controlled variables c for which their controllable range is large compared
to their sum of optimal variation and control error
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
Want small
control error = implementation error n
26
Want large
What should we control (y2)?
Rule: Maximize the scaled gain
•
•
General case: Maximize minimum singular value of scaled G
Scalar case: |Gs| = |G| / span
•
|G|: gain from independent variable (u2) to candidate controlled variable
(y2)
–
IMPORTANT: The gain |G| should be evaluated at the (bandwidth)
frequency of the layer above in the control hierarchy!
•
•
•
span (of y2) = optimal variation in y2 + control error for y2
–
–
27
If the layer above is slow: OK with steady-state gain as used for selecting
primary controlled variables (y1=c)
BUT: In general, gain can be very different
Note optimal variation: This is often the same as the optimal variation used for selecting primary
controlled variables (c).
Exception: If we at the “fast” regulatory time scale have some yet unused “slower” inputs (u1)
which are constant then we may want find a more suitable optimal variation for the fast time
scale.
Minimize state drift by controlling y2
• Problem in some cases: “optimal variation” for y2 depends on overall
control objectives which may change
• Therefore: May want to “decouple” tasks of stabilization (y2) and
optimal operation (y1)
• One way of achieving this: Choose y2 such that “state drift” dw/dd is
minimized
• w = Wx – weighted average of all states
• d – disturbances
• Some tools developed:
– Optimal measurement combination y2=Hy that minimizes state drift
(Hori) – see Skogestad and Postlethwaite (Wiley, 2005) p. 418
– Distillation column application: Control average temperature column
28
2. “y2 is easy to control” (controllability)
1. Statics: Want large gain (from u2 to y2)
2. Main rule: y2 is easy to measure and located
close to available manipulated variable u2
(“pairing”)
3. Dynamics: Want small effective delay (from u2 to y2)
•
“effective delay” includes
•
•
29
inverse response (RHP-zeros)
+ high-order lags
Rules for selecting u2 (to be paired with y2)
1. Avoid using variable u2 that may saturate (especially in loops at the
bottom of the control hieararchy)
•
Alternatively: Need to use “input resetting” in higher layer
•
Example: Stabilize reactor with bypass flow (e.g. if bypass may saturate, then
reset in higher layer using cooling flow)
2. “Pair close”: The controllability, for example in terms a small effective
delay from u2 to y2, should be good.
30
Effective delay and tunings
• θ = effective delay
• PI-tunings from “SIMC rule”
• Use half rule to obtain first-order model
– Effective delay θ = “True” delay + inverse response time constant + half of
second time constant + all smaller time constants
– Time constant τ1 = original time constant + half of second time constant
– NOTE: The first (largest) time constant is NOT important for controllability!
31
Summary: Rules for selecting y2 (and u2)
Selection of y2
1. Control of y2 “stabilizes” the plant
•
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
•
Should generally avoid failures, including saturation, in lower layers
2. “Pair close”!
•
32
The effective delay from u2 to y2 should be small
Example regulatory control: Distillation
(see separate slides)
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
33
E.A. Wolff and S. Skogestad, ``Temperature cascade control of distillation columns'', Ind.Eng.Chem.Res., 35, 475-484, 1996.
Selecting measurements and inputs for
stabilization: Pole vectors
• Maximum gain rule is good for integrating (drifting) modes
• For “fast” unstable modes (e.g. reactor): Pole vectors useful for
determining which input (valve) and output (measurement) to use for
stabilizing unstable modes
• Assumes input usage (avoiding saturation) may be a problem
• Compute pole vectors from eigenvectors of A-matrix
34
35
36
Example: Tennessee Eastman challenge
problem
37
38
39
40
41
42
43
Control configuration elements
• Control configuration. The restrictions imposed on the overall
controller by decomposing it into a set of local controllers
(subcontrollers, units, elements, blocks) with predetermined links and
with a possibly predetermined design sequence where subcontrollers
are designed locally.
Some control configuration elements:
• Cascade controllers
• Decentralized controllers
• Feedforward elements
• Decoupling elements
44
•
•
•
45
Cascade control arises when the output from one controller is the input to
another. This is broader than the conventional definition of cascade control
which is that the output from one controller is the reference command
(setpoint) to another. In addition, in cascade control, it is usually assumed that
the inner loop K2 is much faster than the outer loop K1.
Feedforward elements link measured disturbances to manipulated inputs.
Decoupling elements link one set of manipulated inputs (“measurements”)
with another set of manipulated inputs. They are used to improve the
performance of decentralized control systems, and are often viewed as
feedforward elements (although this is not correct when we view the control
system as a whole) where the “measured disturbance” is the manipulated
input computed by another decentralized controller.
Why simplified configurations?
• Fundamental: Save on modelling effort
• Other:
–
–
–
–
–
–
46
easy to understand
easy to tune and retune
insensitive to model uncertainty
possible to design for failure tolerance
fewer links
reduced computation load
Cascade control
(conventional; with extra measurement)
The reference r2 is an output from another controller
General case (“parallel cascade”)
Special common case (“series cascade”)
47
Series cascade
1.
2.
3.
Disturbances arising within the secondary loop (before y2) are corrected by the
secondary controller before they can influence the primary variable y1
Phase lag existing in the secondary part of the process (G2) is reduced by the secondary
loop. This improves the speed of response of the primary loop.
Gain variations in G2 are overcome within its own loop.
Thus, use cascade control (with an extra secondary measurement y2) when:
•
The disturbance d2 is significant and G1 has an effective delay
•
The plant G2 is uncertain (varies) or n onlinear
48
Design:
•
First design K2 (“fast loop”) to deal with d2
•
Then design K1 to deal with d1
Tuning cascade
•
•
Use SIMC tuning rules
K2 is designed based on G2 (which has effective delay 2)
–
then y2 = T2 r2 + S2 d2 where S2 ¼ 0 and T2 ¼ 1 ¢ e-(2+c2)s
•
•
•
•
T2: gain = 1 and effective delay = 2+c2
SIMC-rule: c2 ¸ 2
Time scale separation: c2 · c1/5 (approximately)
K1 is designed based on G1T2
•
49
y2 = T2 r2 + S2d2
same as G1 but with an additional delay 2+c2
Exercise: Tuning cascade
1. (without cascade, i.e. no feedback from y2).
Design a controller based on G1G2
2. (with cascade)
Design K2 and then K1
50
Tuning cascade control
51
Extra inputs
• Exercise: Explain how “valve position control” fits into this
framework. As en example consider a heat exchanger with bypass
52
Exercise
•
Exercise:
(a) In what order would you tune the controllers?
(b) Give a practical example of a process that fits into this block diagram
53
Partial control
• Cascade control: y2 not important in itself, and setpoint (r2) is available
for control of y1
• Decentralized control (using sequential design): y2 important in itself
54
Partial control analysis
Primary controlled
variable y1 = c
(supervisory control layer)
Local control of y2
using u2
(regulatory control layer)
Setpoint y2s : new DOF
for supervisory control
y1 = P1 u1 + Pr1 (y2s-n2) + Pd1 d
P1 = G11 – G12 G22-1 G21
Pd1 = Gd1 – G12 G22-1 Gd2 - WANT SMALL
Pr1 = G12 G22-1
55
Partial control: Distillation
Supervisory control:
u1 = V
Primary controlled
variables y1 = c = (xD xB)T
Regulatory control:
Control of y2=T
using u2 = L (original DOF)
Setpoint y2s = Ts : new DOF
for supervisory control
y1 = P1 u1 + Pr1 (y2s-n2) + Pd1 d
P1 = G11 – G12 G22-1 G21
Pd1 = Gd1 – G12 G22-1 Gd2 - WANT SMALL
Pr1 = G12 G22-1
56
Limitations of partial control?
• Cascade control: Closing of secondary loops does not by itself impose
new problems
– Theorem 10.2 (SP, 2005). The partially controlled system [P1 Pr1]
from [u1 r2] to y1
has no new RHP-zeros that are not present in the open-loop system [G11 G12]
from [u1 u2] to y1
provided
• r2 is available for control of y1
• K2 has no RHP-zeros
• Decentralized control (sequential design): Can introduce limitations.
– Avoid pairing on negative RGA for u2/y2 – otherwise Pu likely has a RHPzero
57
BREAK
Outline
• Control structure design (plantwide control)
• A procedure for control structure design
I Top Down
•
•
•
•
Step 1: Degrees of freedom
Step 2: Operational objectives (optimal operation)
Step 3: What to control ? (primary CV’s) (self-optimizing control)
Step 4: Where set production rate?
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
58
Step 6. Supervisory control layer
• Purpose: Keep primary controlled outputs c=y1 at optimal setpoints cs
• Degrees of freedom: Setpoints y2s in reg.control layer
• Main structural issue: Decentralized or multivariable?
59
Decentralized control
(single-loop controllers)
Use for: Noninteracting process and no change in active constraints
+ Tuning may be done on-line
+ No or minimal model requirements
+ Easy to fix and change
- Need to determine pairing
- Performance loss compared to multivariable control
- Complicated logic required for reconfiguration when active constraints
move
60
Multivariable control
(with explicit constraint handling = MPC)
Use for: Interacting process and changes in active constraints
+ Easy handling of feedforward control
+ Easy handling of changing constraints
• no need for logic
• smooth transition
-
61
Requires multivariable dynamic model
Tuning may be difficult
Less transparent
“Everything goes down at the same time”
Outline
• Control structure design (plantwide control)
• A procedure for control structure design
I Top Down
•
•
•
•
Step 1: Degrees of freedom
Step 2: Operational objectives (optimal operation)
Step 3: What to control ? (self-optimizing control)
Step 4: Where set production rate?
II Bottom Up
• Step 5: Regulatory control: What more to control ?
• Step 6: Supervisory control
• Step 7: Real-time optimization
• Case studies
62
Step 7. Optimization layer (RTO)
• Purpose: Identify active constraints and compute optimal setpoints (to
be implemented by supervisory control layer)
• Main structural issue: Do we need RTO? (or is process selfoptimizing)
• RTO not needed when
– Can “easily” identify change in active constraints (operating region)
– For each operating region there exists self-optimizing var
63
Outline
• Control structure design (plantwide control)
• A procedure for control structure design
I Top Down
•
•
•
•
Step 1: Degrees of freedom
Step 2: Operational objectives (optimal operation)
Step 3: What to control ? (self-optimizing control)
Step 4: Where set production rate?
II Bottom Up
• Step 5: Regulatory control: What more to control ?
• Step 6: Supervisory control
• Step 7: Real-time optimization
• Conclusion / References
64
Summary: Main steps
1. What should we control (y1=c=z)?
•
Must define optimal operation!
2. Where should we set the production rate?
•
At bottleneck
3. What more should we control (y2)?
•
Variables that “stabilize” the plant
4. Control of primary variables
•
•
65
Decentralized?
Multivariable (MPC)?
Conclusion
Procedure plantwide control:
I. Top-down analysis to identify degrees of freedom and
primary controlled variables (look for self-optimizing
variables)
II. Bottom-up analysis to determine secondary controlled
variables and structure of control system (pairing).
66
More examples and case studies
•
•
•
•
67
HDA process
Cooling cycle
Distillation (C3-splitter)
Blending
References
•
•
•
•
•
Halvorsen, I.J, Skogestad, S., Morud, J.C., Alstad, V. (2003), “Optimal selection of controlled
variables”, Ind.Eng.Chem.Res., 42, 3273-3284.
Larsson, T. and S. Skogestad (2000), “Plantwide control: A review and a new design
procedure”, Modeling, Identification and Control, 21, 209-240.
Larsson, T., K. Hestetun, E. Hovland and S. Skogestad (2001), “Self-optimizing control of a
large-scale plant: The Tennessee Eastman process’’, Ind.Eng.Chem.Res., 40, 4889-4901.
Larsson, T., M.S. Govatsmark, S. Skogestad and C.C. Yu (2003), “Control of reactor,
separator and recycle process’’, Ind.Eng.Chem.Res., 42, 1225-1234
Skogestad, S. and Postlethwaite, I. (1996, 2005), Multivariable feedback control, Wiley
•
Skogestad, S. (2000). “Plantwide control: The search for the self-optimizing control
structure”. J. Proc. Control 10, 487-507.
•
Skogestad, S. (2003), ”Simple analytic rules for model reduction and PID controller tuning”,
J. Proc. Control, 13, 291-309.
•
Skogestad, S. (2004), “Control structure design for complete chemical plants”, Computers
and Chemical Engineering, 28, 219-234. (Special issue from ESCAPE’12 Symposium, Haag,
May 2002).
… + more…..
•
See home page of S. Skogestad:
68
http://www.nt.ntnu.no/users/skoge/