1. Combination of Measurements as Controlled Variables for Self-optimizing Control
Vidar Alstad†
and
Sigurd Skogestad
Department of Chemical Engineering,
Norwegian University of Science and Technology,
Trondheim, Norway
Presented at ESCAPE 13, Lappeenranta,
Finland, June †

2. Outline Introduction optimal operation
Implementation of optimal operation
Strategies
Self-optimizing control
Introduction
Illustrating example
Selection of controlled variables
Optimal linear combination of measurements
Examples
Toy example
Gas allocation in oil production
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3. Introduction and Motivation
Optimal operation for a given disturbance d
Generally two classes of problems
Constrained: All DOF (u’s) optimally constrained → Implementation easy by active constraint control
Unconstrained: Some DOF (u’s) unconstrained (Focus here)
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4. Implementation Real-time optimization
Requires detailed on-line model
Self-optimizing control (feedback control)
easy implementation
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5. Self-optimizing Control
Define loss:
Self-optimizing Control
Self-optimizing control is when acceptable loss can be achieved using constant set points (cs) for the controlled variables c (without re-optimizing when disturbances occur).
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6. Self-optimizing Control – Illustrating Example
Optimal operation of Marathon runner, J=T
Any self-optimizing variable c (to control at constant setpoint)?
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7. Self-optimizing Control – Illustrating Example
Optimal operation of Marathon runner, J=T
Any self-optimizing variable c (to control at constant setpoint)?
c1 = distance to leader of race
c2 = speed
c3 = heart rate
c4 = level of lactate in muscles
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8. Controlled variables
Controlled variables c to be selected among all available measurements y,
Goal: Find the optimal linear combination (matrix H):
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9. Candidate Controlled Variables: Guidelines
Requirements for good candidate controlled variables (Skogestad & Postlethwaite, 1996)
Its optimal value copt(d) is insensitive to disturbances
It should be easy to measure and control accurately
The variables c should be sensitive to change in inputs
The selected variables should be independent
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10. Optimal Linear Combination -
Linearized
where “sensitivity”
Want optimal value of c insensitive to disturbances:
To achieve
Always possible if:
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11. Example – Toy example Consider the scalar unconstrained problem
The following measurements are available
Controlling y1 gives perfect self-optimizing control.
Is there a combination of y2 and y3 with the same properties?
(Yes, should be because we have
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12. Example – Toy example (cont.)
Select y2 and y3:
Gives the optimal controlled variable:
Loss
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13. Example – Gas Lift Allocation - Introduction
Wells produce gas and oil from sub-sea reservoirs
Gas injection:
used to increase production
Additional cost of compressing gas
Limited gas processing capacity top-side
Limits the rate of gas from the reservoirs and injection
Case studied
2 production wells
Gas injection into each well
1 transportation line
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14. Example – Gas Lift Allocation (cont.)
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15. Example – Gas Lift Allocation (cont.)
Objective
Maximize profit
Constraints
Maximum gas processing capacity
Valve opening
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16. Example – Gas Lift Allocation (cont.)
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17. Example – Gas Lift Allocation (cont.)
Evaluation of loss for different control structures
The loss for cLC with the combined uncertainty is due to non-linearities
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18. Choice of measurements y
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19. Conlusion
Controlled variables: Derived simple method for optimal measurement combination
Find sensitivity of optimal value of measurements to disturbances
Select the controlled variables as:
Illustrated on two examples
Toy example
Gas injection in oil production
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