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Combination of Measurements as Controlled Variables for Self-optimizing Control

This paper explores the use of measurements as controlled variables for self-optimizing control in various applications, including oil production. It presents a simple method for selecting the optimal combination of measurements and discusses the sensitivity of these measurements to disturbances. The approach is illustrated using two examples: a toy example and gas injection in oil production.

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Combination of Measurements as Controlled Variables for Self-optimizing Control

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  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 1-4 2003 † vidaral@chemeng.ntnu.no

  2. Outline • Introduction and motivation • Formulation of operational objectives • Implementation of optimal operation • Strategies • Self-optimizing control • Introduction • Illustrating example • Optimal selection of controlled variables • Optimal linear combination of measurements • Examples • Toy example • Gas allocation in oil production Escape 13 - Lapperanta - June 1-4 - 2003

  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) Escape 13 - Lapperanta - June 1-4 - 2003

  4. Implementation • Real-time optimization • Requires detailed on-line model • Self-optimizing control (feedback control) • easy implementation Escape 13 - Lapperanta - June 1-4 - 2003

  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). Escape 13 - Lapperanta - June 1-4 - 2003

  6. 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 Escape 13 - Lapperanta - June 1-4 - 2003

  7. Controlled variables • Controlled variables c to be selected among all available measurements y, • Goal: Find the optimal linear combination (matrix H): Escape 13 - Lapperanta - June 1-4 - 2003

  8. 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 Escape 13 - Lapperanta - June 1-4 - 2003

  9. Optimal Linear Combination - • Linearized • where “sensitivity” • Want optimal value of c insensitive to disturbances: • To achieve • Always possible if: Escape 13 - Lapperanta - June 1-4 - 2003

  10. 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 Escape 13 - Lapperanta - June 1-4 - 2003

  11. Example – Toy example (cont.) • Select y2 and y3: • Gives the optimal controlled variable: • Loss Escape 13 - Lapperanta - June 1-4 - 2003

  12. 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 Escape 13 - Lapperanta - June 1-4 - 2003

  13. Example – Gas Lift Allocation (cont.) Escape 13 - Lapperanta - June 1-4 - 2003

  14. Example – Gas Lift Allocation (cont.) • Objective • Maximize profit • Constraints • Maximum gas processing capacity • Valve opening Escape 13 - Lapperanta - June 1-4 - 2003

  15. Example – Gas Lift Allocation (cont.) Escape 13 - Lapperanta - June 1-4 - 2003

  16. The loss for cLC with the combined uncertainty is due to non-linearities Example – Gas Lift Allocation (cont.) • Evaluation of loss for different control structures Escape 13 - Lapperanta - June 1-4 - 2003

  17. Choice of measurements y Escape 13 - Lapperanta - June 1-4 - 2003

  18. 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 Escape 13 - Lapperanta - June 1-4 - 2003

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