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 1

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

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

Optimal operation : Solution methods Optimal Feedforward y

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

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

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

Self optimizing control Controller Process d u(d) c = Hy cs e - + n cm Acceptable loss 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. Reference: S. Skogestad, “Plantwide control: The search for the self-optimizing control structure'', Journal of Process Control, 10, 487-507 (2000).

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

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

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

Problem Formulation: Vectorization & MIQP formulation Big M approach

Controlled variable selection 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. IBM ILOG Optimizer’s CPLEX solver

Summary Data to be supplied:

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

Kaibel Column Kaibel column T21 – T30 T31 – T40 T1 – T10 T61 – T70

Kaibel Column c = Hy Find H that minimizes Kaibel column T21 – T30

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

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

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

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

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

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.