1. Control Structure Design: New Developments and Future Directions Vinay Kariwala and Sigurd Skogestad Department of Chemical Engineering NTNU, Trondheim, Norway skoge@chemeng.ntnu.no

2. 2 Control Structure Design Challenges Tools (partial solutions) Case Studies Future Directions

3. 3 Control Systems Optimizing Controller Process uymym d Truly Optimal Economic Optimizer Process Controller d u y m, z set z z set “Ph.D. Control” Modeling effort “PID Control” Local Optimizer Supervisory Controller Regulatory Controller Process z set y 2,set ymym u PID (sec) MPC (min) RTO (hr)

4. 4 Decentralization of layers Control Structure Design: Structural Decisions d Optimizing Controller Process Economic Optimizer Process Controller d z set Local Optimizer Supervisory Controller Regulatory Controller Process Truly Optimal Ph.D. ControlPID Control z set z z = y 1 primary controlled variables y 2,set y 2 secondary controlled variables (part of y m ) ymym ymym ymym y m measured variables u u u u manipulated variables

5. 5 Previous Work 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

6. 6 Control Structure Design Challenges Tools (partial solutions) Case Studies Future Directions

7. 7 Challenges Q1. What should be controlled? Choice depends on operational objectives - usually steady-state economics Often the most important decision Local Optimizer Supervisory Controller Regulatory Controller Process z set y 2,set ymym u

8. 8 Challenges Q2. What variables should be used for regulatory control? Hundreds of measurements Lack of precise mathematical formulation Local Optimizer Supervisory Controller Regulatory Controller Process z set y 2,set ymym u Q1. What should be controlled?

9. 9 Challenges Q3. To decentralize or not? If yes, how? Pairing selection or process decomposition Usually an issue for supervisory layer Local Optimizer Supervisory Controller Regulatory Controller Process z set y 2,set ymym u Q2. What variables should be used for regulatory control? Q1. What should be controlled?

10. 10 Control Structure Design Challenges Tools (partial solutions) Case Studies Future Directions

11. 11 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 Supervisory Controller Regulatory Controller Process z set y 2,set ymym u Distance to leader of race Speed Heart rate Level of lactate in muscles

12. 12 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 Supervisory Controller Regulatory Controller Process z set y 2,set ymym u Sprinter Max Speed Distance to leader of race Speed Heart rate Level of lactate in muscles

13. 13 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 Supervisory Controller Regulatory Controller Process z set y 2,set ymym u Marathon Runner Constant Heart Rate Distance to leader of race Speed Heart rate Level of lactate in muscles

14. 14 Q1. What should be controlled? 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  Brute force evaluation  Locally optimal methods Maximum gain rule: max Combination of measurements Local Optimizer Supervisory Controller Regulatory Controller Process z set y 2,set ymym u Self-optimizing control: 1.Control active constraints 2.Unconstrained: Control variables that give acceptable loss when held constant

15. 15 Regulatory layer Local Optimizer Supervisory Controller Regulatory Controller Process z set y 2,set ymym u Prevent the runner from falling (Separation of tasks) Objectives – regulatory control: a.Stabilization b.Disturbance rejection

16. 16 Q2a. Variables for stabilization? Choose variables that minimize input usage Reduced likelihood of input saturation Least disturbing effect on stabilized system Havre and Skogestad, IEEE TAC, 2003 (pole-vector approach) Kariwala, Skogestad, Forbes and Meadows. Intl. J. Control, 2005. Minimal Hankel singular value Unstable part of G Achievable input performance uy2y2 d

17. 17 Q2b. Variables for Disturbance Rejection Choose variables to reduce disturbance sensitivity Minimize Maximize Skogestad and Postlethwaite. Multivariable Feedback Control, 2e, 2005 Local Disturbance Rejection u 2 Stabilized System u 1 d y2y2 z - r - + n + + With y 2 controlled:

18. 18 Sequential Approach u z Primary CVs Economically self-optimizing System1. Kariwala, Forbes and Meadows, Automatica, 2005 (Integrity) z Stabilized System Pairing selection Integrity, Interactions u1u1 y 2,set 3. y 2,set y2y2 Secondary CVs and pairing with MVs Stabilization, Disturbance rejection System z u1u1 u2u2 2. K

19. 19 Control Structure Design Challenges Tools (partial solutions) Case Studies Future Directions

20. 20 Applications Traditional: Chemical plants Aerospace and mechanical systems Emerging: Fuel cells Bioreactors Systems biology

21. 21 Example: Binary Distillation Column 1. Primary CVs (self-optimizing) z: Top and Bottom compositions 2a. Stabilization y 2: Holdups u 2 : External flows

22. 22 Example: Binary Distillation Column 2b. Disturbance rejection y 2: Temperature on Tray 15 u 2 : Vapor Boilup 3. Pairings x D – Reflux x B – Temperature setpoint

23. 23 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

24. 24 Extra Manipulated Variables Air Blow-Off Air Bypass Fuel Bypass Disturbance sensitivity – Fresh fuel, Air Bypass

25. 25 Performance Evalution Inputs are also within bounds

26. 26 Control Structure Design Challenges Tools (partial solutions) Case Studies Future Directions

27. 27 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

28. 28 Computational Aspects Millions of Alternatives Problem size Alternatives How to avoid combinatorial issues? – Integer variables, Non-convexity, Multi-objective – NP-hardness (Integrity problem) Cao and Saha, Chem. Eng. Sci., 2005

29. 29 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

30. Control Structure Design: New Developments and Future Directions Vinay Kariwala and Sigurd Skogestad Department of Chemical Engineering NTNU, Trondheim, Norway skoge@chemeng.ntnu.no