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 1

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. 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, (2000).

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

10. 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

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. 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

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

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

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

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

20. 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

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.