Using Dynamic Flexibility Analysis to Integrate Design and Control under Uncertainty

1. Using Dynamic Flexibility Analysis to Integrate Design and Control under Uncertainty AIChE 2005 Annual Meeting Cincinnati, OH October 30-November 4 Paper 496b Session 10C10: Design & Operation under Uncertainty Andrés Malcolm, Libin Zhang and Andreas A. Linninger 11/03/2005 Laboratory for Product and Process Design, Department of Chemical Engineering, University of Illinois, Chicago, IL 60607, U.S.A.

2. Arbitrary overdesign Flexible process? Model Optimize Control Integrated Design & Control Simultaneous Design and control optimization Model Exact Metrics of Flexibility Classical Design Approach • MODEL: • Make Steady State Model of the Process • DESIGN OPTIMIZATION: • Nominal operating conditions and specifications • Optimization and validation • DESIGN FLEXIBILITY • Empirical overdesign to accommodate uncertainty • DYNAMICS and OPERABILITY • Controller design to accommodate disturbances and uncertainty Arbitrary overdesign Flexible process? Model Optimize Control

3. Trade-off between design and control Total Cost (Capital + Operating) Design Decisions Control Complexity Optimal minimum cost integrated design and control

4. Overview Obtain a minimum expected cost design (d) Ensure Flexibility • Level 1- Dynamic Modeling, Flexibility Concepts and Structural Decisions • Level 2- Design Optimization

5. 1)Initiation 2)Propagation 3)Termination Integrated Design and Control of a Polymerization Reactor • Polymerization Reactor (Ogunnaike, AIChE J. 1999) Relationship of product quality and total annualized cost under varying and uncertain process conditions

6. Level-1: Identification of Structural Decisions • Product Quality target: D1/D0 • Change on target  change on set-point • Change on set-point  change on operating conditions • Need to change design variables to accommodate production needs • NEED to integrate design and control • Design variables, controls, and uncertainty sources • Design: Reactor Volume , Monomer Concentration, Control Parameters • Control: Coolant Flow and Initiator Flow • Uncertainty Sources: Coolant Inlet Temperature, Heat Transfer Coef. (U) • Kinetic Parameters (k, E)

7. Level-2: Integrated Design and Control Design Initial d, c Sample Uncertain Space θNEW, ξNEW(t) θ, ξ(t) Min Expected Cost Optimal Design d, c Min Cost Design Not Flexible Rigorous Dynamic Flexibility Test Update Critical Scenarios Min Cost Flexible Design Flexible Optimal d, c

8. Dynamic uncertainty Tcool time P() Time-Invariant uncertainty U q2 time q1 Level-2: Uncertainty Modeling Scenario sampling: by LHS techniques Simple method to compute expected performance

9. Minimize Total Expected Cost Conservational Laws Control Algorithm Process and Product Constraints Level-2: Optimal Expected Design and Control • Stochastic dynamic optimization • Defined over the finite sample set • Optimizes design and control decisions for minimum expected cost

10. Minimize Total Expected Cost Conservational Laws Control Algorithm Process and Product Constraints Level-2: Optimal Expected Design and Control Minimum Expected Cost Design V=0.23 m3 Cmi=4.52 mol/l Kc=0.0042 Tsp=295.2 K Psp=24,950

11. Level-2: Integrated Design and Control Design

12. UUCL quality UCL SP LCL LLCL Time Integrated Design and Control Results Optimal Design V=0.28 m3 Cmi=5.02 mol/l Kc=0.0052 Tsp=296 K Psp=24,950 • The optimal design proposes a small reactor • Smaller reactors are more sensitive to input uncertainty • Smaller resident time leads to a faster control • Bigger overshoots but for shorter times

13. Exploring the Control Dimension: MIMO sys. MIMO System P+I Control IMC Control Total Cost (Capital + Operating) RTDA Control DMC Control NMPC Control Design Decision (Reactor Volume) 0.05 m3 0.1 m3 .15 m3 • Trade-off between design and control decisions • MIMO systems with high value product complex control schemes are identified to be optimal • Why not always use the most sophisticated control scheme?

14. Exploring the Control Dimension: SISO sys. SISO System NMPC Control DMC Control Total Cost (Capital + Operating) P+I Control IMC Control RTDA Control Design Decision (Condenser Area) 30 m2 40 m2 50 m2 • SISO systems with low value product: simpler control schemes are identified to be optimal • Complex control scheme capital investment not justified • Each system has it optimal combination of design and control

15. Conclusions • The NMPC and a small batch reactor rendered the optimally integrated design solution under dynamic uncertainty and disturbance scenarios • Simultaneous design and control identifies best trade off between design and control options • Tradeoff between D&C decisions for an industrial batch polymerization process were quantified. • Systematic decision hierarchy for integrated D&C was applied successfully to process of industrial complexity

16. Open Questions - Future Work • Recent advancement in robust large scale stochastic dynamic optimization algorithms are expected to enhance the benefits of integrated design and control (e.g MIDO embedded in g-proms)

17. Acknowledgements • Environmental Manufacturing Management (EvMM) fellowship from the UIC Institute for Environmental Science and Policy. • National Science Foundation Grant DMI-0328134.