Ramprasad Yelchuru (PhD Candidiate) Professor Sigurd Skogestad

1. Optimal measurement selection for controlled variables in Kaibel Distillation Column: A MIQP formulation Ramprasad Yelchuru (PhD Candidiate) Professor Sigurd Skogestad Deeptanshu Dwivedi* (PhD Candidiate) Department of Chemical Engineering, Norwegian University of Science and Technolgy, Trondheim, Norway 20th Oct 2011, AIChE Annual Meeting, Minneapolis

2. Outline • Plantwide control • Self Optimizing Control • Problem formulation, c = Hy • Case study: 4- product Kaibel Column • Results • Conclusions

3. Plantwide control: Hierarchical decomposition Process control OBJECTIVE RTO min J (economics); MV=y1s Optimal operation y1s MPC y2s PID u (valves)

4. Optimal operation : Solution methods Optimal Feedforward y

5. Optimal operation : Solution methods Optimizing feedback control Optimal Feedforward y Self optimizing control

6. Optimal operation : Solution methods Optimal Feedforward Self optimizing control Optimizing feedback control y H What should we control ?? y

7. Outline • Plantwide control • Self Optimizing Control • Problem formulation, c = Hy • Kaibel Column Case study • Results • Conclusions

8. e + cs Controller - cm + u(d) n c = Hy d Process Self optimizing control Self-optimizing control is said to occur when we can achieve an acceptable loss (in comparison with truly optimal operation) with constant setpoint values for the controlled variables without the need to reoptimize when disturbances occur. Acceptable loss self-optimizing control Reference: S. Skogestad, “Plantwide control: The search for the self-optimizing control structure'', Journal of Process Control, 10, 487-507 (2000).

9. Outline • Plantwide control • Self Optimizing Control • Problem formulation, c = Hy • Kaibel Column Case study • Results • Conclusions

10. J(u,d) cs = constant + u + + K - + + c H H Controlled variables, Loss (=J(u,d) -Jopt) with constant setpoint for c: Ref: Halvorsen et al. I&ECR, 2003 Kariwala et al. I&ECR, 2008 Problem Formulation y

11. Problem Formulation: Convex Formulation (Full H) Seemingly Non-convex optimization problem D : any non-singular matrix Objective function unaffected by D. So can choose freely. We made H unique by adding a constraint as Full H Convex optimization problem Global solution subject to Problem is convex in decision matrix H Alstad et al. JPC 2009, Yelchuru et al., DYCOPS 2010

12. Problem Formulation: Vectorization & MIQP formulation Big M approach

13. Optimization problem : Minimize the average loss by selecting H and CVs as Optimal individual/combinations of ’n’ measurements Measurements selection from different section, structural constraint Inclusion of additional measurement st. Controlled variable selection • IBM ILOG Optimizer’s CPLEX solver

14. Summary Data to be supplied:

15. Outline • Plantwide control • Self Optimizing Control • Problem formulation, c = Hy • Case study: 4-Product Kaibel Column • Results • Conclusions

16. L T21 – T30 T31 – T40 T1 – T10 T61 – T70 T11 – T20 T41 – T50 T51 – T60 T71 Kaibel Column Kaibel column

17. L T21 – T30 T31 – T40 T1 – T10 T61 – T70 T11 – T20 T41 – T50 T51 – T60 T71 Kaibel Column c=Hy Find H that minimizes Kaibel column

18. L T21 – T30 T31 – T40 T1 – T10 T61 – T70 T11 – T20 T41 – T50 T51 – T60 T71 Problem 1: Choose ’n’ measurements without constraints Kaibel column

19. L T21 – T30 T31 – T40 T1 – T10 T61 – T70 T11 – T20 T41 – T50 T51 – T60 T71 Problem 2: Choose measurements with constraints Kaibel column

20. L T21 – T30 T31 – T40 T1 – T10 T61 – T70 T11 – T20 T41 – T50 T51 – T60 T71 Problem 3 : Including extra measurements Including extra measurements to given non-optimal measurement set Given non-optimal set =[T12 T25 T45 T62] where n = 5,6,7 Kaibel column

21. Outline • Plantwide control • Self Optimizing Control • Problem formulation, c = Hy • Kaibel Column Case study • Results • Conclusions

22. Kaibel Column : Results *Single measurement from each section Ɨ given non-optimal measurement set ** Including additonal measurements to given non-optimal measurement set

23. Conclusions Using steady state economics of the plant, the optimal controlled variables are obtained as • optimal individual/combinations of measurements • Measurements selection from different sections • Loss minimization with the inclusion of additional measurement to a given measurement set using MIQP based formulations. The computational time required for CVs as combinations of measurements from different sections is less as the alternatives are lesser.