# Ramprasad Yelchuru, Optimal controlled variable selection for Individual process units, 1 Optimal controlled variable selection for individual process.

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

Ramprasad Yelchuru, Optimal controlled variable selection for Individual process units, 2 Outline 1.Problem formulation, c = Hy 2.Convex formulation (full H) 3.CVs for Individual unit control (Structured H) 4.MIQP formulations 5.Distillation Case study 6.Conclusions CV – Controlled Variables MIQP - Mixed Integer Quadratic Programming

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

Ramprasad Yelchuru, Optimal controlled variable selection for Individual process units, 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 subject to Full H Convex optimization problem Global solution Problem is convex in decision matrix H

Ramprasad Yelchuru, Optimal controlled variable selection for Individual process units, 5 Vectorization subject to Problem is convex QP in decision vector

Ramprasad Yelchuru, Optimal controlled variable selection for Individual process units, 6 Full H T 1, T 2, T 3, …, T 41 Tray temperatures qF Top section T 21, T 22, T 23,…, T 41 Bottom section T 1, T 2, T 3,…, T 20 c = Hyc = Hy Binary distillation column

Ramprasad Yelchuru, Optimal controlled variable selection for Individual process units, 7 Need for structural constraints (Structured H) Binary distillation column T 1, T 2, T 3, …, T 41 Tray temperatures qF Transient response for 5% step change in boil up (V) Top section T 21, T 22, T 23,…, T 41 Bottom section T 1, T 2, T 3,…, T 20 *Compositions are indirectly controlled by controlling the tray temperatures

Ramprasad Yelchuru, Optimal controlled variable selection for Individual process units, 8 Need for structural constraints (Structured H) T 1, T 2, T 3, …, T 41 Tray temperatures qF Top section T 21, T 22, T 23,…, T 41 Bottom section T 1, T 2, T 3,…, T 20 Individual Unit control Transient response for 5% step change in boil up (V) Binary distillation column Structured H is required for better dynamics and controllability

Ramprasad Yelchuru, Optimal controlled variable selection for Individual process units, 9 3. CVs for Individual Unit control (Structured H) D : any non-singular matrix So we can use D to match certain elements of to For individual unit control H IU only block diagonal D preserve the structure in H and

Ramprasad Yelchuru, Optimal controlled variable selection for Individual process units, 10 CVs for Individual Unit control (Structured H) Example 1 : Example 2 : This results in convex upper bound

Ramprasad Yelchuru, Optimal controlled variable selection for Individual process units, 11 Controlled variable selection 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. Individual unit control

Ramprasad Yelchuru, Optimal controlled variable selection for Individual process units, 12 4. MIQP Formulation (full H) We solve this MIQP for n = nu to ny Big M approach

Ramprasad Yelchuru, Optimal controlled variable selection for Individual process units, 13 MIQP Formulation (Structured H) We solve this MIQP for n = n u to n y Big M approach Matching elements Selecting measurements Structured H

Ramprasad Yelchuru, Optimal controlled variable selection for Individual process units, 14 5. Case Study : Distillation Column T 1, T 2, T 3, …, T 41 Tray temperatures qF Binary Distillation Column LV configuration (methanol & n-propanol) 41 Trays Level loops closed with D,B 2 MVs – L,V 41 Measurements – T 1,T 2,T 3,…,T 41 3 DVs – F, ZF, qF *Compositions are indirectly controlled by controlling the tray temperatures

Ramprasad Yelchuru, Optimal controlled variable selection for Individual process units, 15 Case Study : Individual section control T 1, T 2, T 3, …, T 41 Tray temperatures qF Top section T 21, T 22, T 23,…, T 41 Bottom section T 1, T 2, T 3,…, T 20

Ramprasad Yelchuru, Optimal controlled variable selection for Individual process units, 16 Case Study : Distillation Column Results Data

Ramprasad Yelchuru, Optimal controlled variable selection for Individual process units, 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

Ramprasad Yelchuru, Optimal controlled variable selection for Individual process units, 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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