Transcript Control Structure Design: New Developments and Future Directions

Control Structure Design:
New Developments and Future Directions
Vinay Kariwala and Sigurd Skogestad
Department of Chemical Engineering
NTNU, Trondheim, Norway
[email protected]
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Control Structure Design
Challenges
Tools (partial solutions)
Case Studies
Future Directions
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Control Systems
“Ph.D. Control”
Truly Optimal
Economic
Optimizer
Optimizing
Controller
d
u
RTO
Local
(hr) Optimizer
zset
zset
ym
z
d
Process
Process
ym, zset
u
“PID Control”
Controller
MPC Supervisory
(min) Controller
y2,set
PID Regulatory
(sec) Controller
ym
u
Process
Modeling effort
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Control Structure Design: Structural Decisions
Truly Optimal
Optimizing
Controller
d
u
ym
Ph.D. Control
PID Control
Economic
Optimizer
Local
Optimizer
zset
zset
Process
Process
Supervisory
Controller
z
d
y2,set
Regulatory
Controller
ym zset
u
Controller
u
ym
Process
u
manipulated variables
ym
measured variables
z = y1 primary controlled variables
y2
secondary controlled variables (part of ym)
Decentralization of layers
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Previous Work
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Buckley (1964)
Umeda et al. (1978)
Fisher et al. (1988)
Price, Georgakis et al. (1993)
McAvoy and Ye (1994)
Luyben et al. (1997)
Ng and Stephanopolous (1998)
We want a generic approach that is mathematically
well-formulated and extends beyond process control
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Control Structure Design
Challenges
Tools (partial solutions)
Case Studies
Future Directions
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Challenges
Q1. What should be controlled?
• Choice depends on operational objectives -
Local
Optimizer
zset
usually steady-state economics
• Often the most important decision
Supervisory
Controller
y2,set
Regulatory
Controller
u
ym
Process
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Challenges
Q1. What should be controlled?
Q2. What variables should be used for
regulatory control?
• Hundreds of measurements
• Lack of precise mathematical formulation
Local
Optimizer
zset
Supervisory
Controller
y2,set
Regulatory
Controller
u
ym
Process
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Challenges
Q1. What should be controlled?
Q2. What variables should be used for
regulatory control?
Q3. To decentralize or not? If yes, how?
• Pairing selection or process decomposition
• Usually an issue for supervisory layer
Local
Optimizer
zset
Supervisory
Controller
y2,set
Regulatory
Controller
u
ym
Process
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Control Structure Design
Challenges
Tools (partial solutions)
Case Studies
Future Directions
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Q1. What should be controlled?
Self-optimizing control:
1. Control active constraints
2. Unconstrained: Control variables that give
acceptable loss when held constant
Local
Optimizer
zset
Supervisory
Controller
y2,set
• Distance to leader of race
• Speed
• Heart rate
• Level of lactate in muscles
Regulatory
Controller
u
ym
Process
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Q1. What should be controlled?
Self-optimizing control:
1. Control active constraints
2. Unconstrained: Control variables that give
acceptable loss when held constant
Local
Optimizer
zset
Supervisory
Controller
y2,set
• Distance to leader of race
• Speed
• Heart rate
• Level of lactate in muscles
Sprinter
Max Speed
Regulatory
Controller
u
ym
Process
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Q1. What should be controlled?
Self-optimizing control:
1. Control active constraints
2. Unconstrained: Control variables that give
acceptable loss when held constant
Local
Optimizer
zset
Supervisory
Controller
y2,set
Marathon
Runner
Constant
Heart Rate
• Distance to leader of race
• Speed
• Heart rate
• Level of lactate in muscles
Regulatory
Controller
u
ym
Process
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Q1. What should be controlled?
Self-optimizing control:
1. Control active constraints
2. Unconstrained: Control variables that give
acceptable loss when held constant
Brute force evaluation
Locally optimal methods
Maximum gain rule: max
Combination of measurements
Local
Optimizer
zset
Supervisory
Controller
y2,set
Regulatory
Controller
u
ym
Process
Skogestad. J. Proc. Control, 2000
Halvorsen, Morud, Skogestad and Alstad. Ind. Eng. Chem. Res. 2003
Ph.D. Thesis of M. Govatsmark and V. Alstad, NTNU, Norway
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Regulatory layer
Local
Optimizer
zset
Supervisory
Controller
Prevent the runner from falling
(Separation of tasks)
y2,set
Objectives – regulatory control:
a. Stabilization
b. Disturbance rejection
u
Regulatory
Controller
ym
Process
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Q2a. Variables for stabilization?
Choose variables that minimize input usage
• Reduced likelihood of input saturation
• Least disturbing effect on stabilized system
Achievable input performance
d
u
Minimal Hankel singular value
y2
Unstable part of G
Havre and Skogestad, IEEE TAC, 2003 (pole-vector approach)
Kariwala, Skogestad, Forbes and Meadows. Intl. J. Control, 2005.
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Q2b. Variables for Disturbance Rejection
Local
Disturbance
Rejection
- u2
+
+
+
u1
n
y2
Stabilized
System
d
r
z
With y2 controlled:
Choose variables to reduce disturbance sensitivity
Minimize
Maximize
Skogestad and Postlethwaite. Multivariable Feedback Control, 2e, 2005
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Sequential Approach
1.
u
2. u1
y2,set
3.
u1
y2,set
K
u2
System
z
Primary CVs
Economically self-optimizing
System
z
y2
Secondary CVs and
pairing with MVs
Stabilization,
Disturbance rejection
Stabilized
System
z
Pairing selection
Integrity, Interactions
Kariwala, Forbes and Meadows, Automatica, 2005 (Integrity)
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Control Structure Design
Challenges
Tools (partial solutions)
Case Studies
Future Directions
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Applications
Traditional:
• Chemical plants
• Aerospace and mechanical systems
Emerging:
• Fuel cells
• Bioreactors
• Systems biology
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Example: Binary Distillation Column
LC
K1
xD
F
zF
V
LR
xD
D
L
D
L
F
zF
LC
V
LR
K2
B
xB
1. Primary CVs (self-optimizing)
z: Top and Bottom compositions
B
xB
2a. Stabilization
y2: Holdups
u2: External flows
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Example: Binary Distillation Column
LC
LC
K1
L
K1
L
xD
D
F
zF
T15
K3
V
F
zF
r
K4
T15
K3
V
LR
K2
D
xD
r
LR
K5
K2
B
xB
xB
B
2b. Disturbance rejection
y2: Temperature on Tray 15
u2: Vapor Boilup
3. Pairings
xD – Reflux
xB – Temperature setpoint
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Example: Solid Oxide Fuel Cell
• Track changes in power demand
• Avoid large temperature variations in SOFC
Kandepu et al., Proceedings of SIMS, Trondheim, Norway, 2005
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Extra Manipulated Variables
Fuel Bypass
Air Bypass
Air Blow-Off
Disturbance sensitivity – Fresh fuel, Air Bypass
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Performance Evalution
Inputs are also within bounds
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Control Structure Design
Challenges
Tools (partial solutions)
Case Studies
Future Directions
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Controller Complexity
´´Minimize controller complexity subject to the
achievement of accuracy specifications in the face
of uncertainty. (Nett, 1990)´´
• How to define controller complexity?
– Number of non-zero elements of controller
– Number of tuning parameters
• How to consider it during structure selection?
Nobakhti, Proceedings of ISIC MED, 2005
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Alternatives
Computational Aspects
Problem size
Millions of Alternatives
How to avoid combinatorial issues?
– Integer variables, Non-convexity, Multi-objective
– NP-hardness (Integrity problem)
Cao and Saha, Chem. Eng. Sci., 2005
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Conclusions: Remaining Challenges
• Controller complexity
– Definition, inclusion in selection procedure
• Computational aspects
– Integer variables, Non-convexity, Multi-objective
– NP-hardness (Integrity problem)
• Non-linear systems
– Most of theory – Linear systems
• Time-scale separation
– Speeds of layers
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Control Structure Design:
New Developments and Future Directions
Vinay Kariwala and Sigurd Skogestad
Department of Chemical Engineering
NTNU, Trondheim, Norway
[email protected]