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Optimal controlled variable selection for individual process units

Optimal controlled variable selection for individual process units. Ramprasad Yelchuru Sigurd Skogestad. Outline. Problem formulation, c = Hy Convex formulation (full H) CVs for Individual unit control (Structured H) MIQP formulations Distillation Case study Conclusions.

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Optimal controlled variable selection for individual process units

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  1. Optimal controlled variable selection for individual process units Ramprasad Yelchuru Sigurd Skogestad

  2. Outline • Problem formulation, c = Hy • Convex formulation (full H) • CVs for Individual unit control (Structured H) • MIQP formulations • Distillation Case study • Conclusions CV – Controlled Variables MIQP - Mixed Integer Quadratic Programming

  3. J cs = constant + u + + y Loss K - + d + c H u Controlled variables, Assumptions: (1) Active constraints are controlled (2) Quadratic nature of J around uopt(d) (3) Active constraints remain same throughout the analysis 1. Problem Formulation Optimal steady-state operation Loss is due to (i) Varying disturbances (ii) Implementation error in controlling c at set point cs Ref: Halvorsen et al. I&ECR, 2003 Kariwala et al. I&ECR, 2008

  4. 2. 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

  5. Vectorization subject to Problem is convex QP in decision vector

  6. qF Tray temperatures T1, T2, T3,…, T41 Full H c=Hy Top section T21, T22, T23,…, T41 Bottom section T1, T2, T3,…, T20 Binary distillation column

  7. qF Tray temperatures T1, T2, T3,…, T41 Need for structural constraints (Structured H) Top section T21, T22, T23,…, T41 Bottom section T1, T2, T3,…, T20 Transient response for 5% step change in boil up (V) *Compositions are indirectly controlled by controlling the tray temperatures Binary distillation column

  8. qF Tray temperatures T1, T2, T3,…, T41 Need for structural constraints (Structured H) Individual Unit control Top section T21, T22, T23,…, T41 Bottom section T1, T2, T3,…, T20 Transient response for 5% step change in boil up (V) Structured H is required for better dynamics and controllability Binary distillation column

  9. So we can use D to match certain elements of to 3. CVs for Individual Unit control (Structured H) D : any non-singular matrix For individual unit control HIU only block diagonal D preserve the structure in H and

  10. CVs for Individual Unit control (Structured H) Example 2 : Example 1 : This results in convex upper bound

  11. Optimization problem : Minimize the average loss by selecting H and CVs as (i) best individual measurements (ii) best combinations of all measurements (iii) best combinations with few measurements Minimize the average loss by selecting H and CVs as (i) best individual measurements of disjoint measurement sets (ii) best combinations of disjoint measurement sets of all measurements (iii) best combinations of disjoint measurement sets with few measurements st. Controlled variable selection Individual unit control

  12. 4. MIQP Formulation (full H) Big M approach We solve this MIQP for n = nu to ny

  13. MIQP Formulation (Structured H) Matching elements Big M approach Selecting measurements Structured H We solve this MIQP for n = nu to ny

  14. qF Tray temperatures T1, T2, T3,…, T41 5. Case Study : Distillation Column Binary Distillation Column LV configuration (methanol & n-propanol) 41 Trays Level loops closed with D,B 2 MVs – L,V 41 Measurements – T1,T2,T3,…,T41 3 DVs – F, ZF, qF *Compositions are indirectly controlled by controlling the tray temperatures

  15. qF Tray temperatures T1, T2, T3,…, T41 Case Study : Individual section control Top section T21, T22, T23,…, T41 Bottom section T1, T2, T3,…, T20

  16. Case Study : Distillation Column Data Results

  17. Case Study : Distillation Column • The proposed methods are not exact (Loss should be same for H full, H disjoint with individual measurements) • Proposed method provide tight upper bounds

  18. 6. Conclusions Using steady state economics of the total plant, the optimal controlled variables selection as • optimal individual measurements from disjoint/(individual unit) measurement sets • combinations of optimal fewer measurements from disjoint/(individual unit) measurement sets is solved using MIQP based formulations. The proposed methods are not exact, but provide upper bounds to Loss to find CVs as combinations of measurements from individual units.

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