1. Model Predictive Control of Distributed and Hierarchical Systems Leuven, February 15, 2007 Process Systems Engineering RWTH Aachen University Johannes Gerhard, Jan Busch

2. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.20071 The Current Business Climate From growing market volume and limited competition to market saturation and global competition in the 21 st century: internet and e-commerce facilitate complete market transparency, transportation cost continue to decrease, engineering and manufacturing skills are available globally. Economic success requires to quickly transform new ideas into marketable products: product innovation to open-up new market opportunities, process design for best-in-class plants to maximize lifecycle profits, efficient, robust, and agile manufacturing to make best use of existing assets.

3. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.20072 General Objective Drive the manufacturing process to its economical optimum anytime ! decision making on process operations market process uncertainties & disturbances constraints equipment, safety, environment capacity, quality, reproducability time-varying profiles manipulated variables observed variables

4. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.20073 Real-Time Business Decision Making Real-time business decision making (RT-BDM) the set of activities performed by humans and assisting process operation support technology to manage a manufacturing process for profibability and agility increasing degree of automation cor- porate planning set-point optimization field instrumentation and base layer control advanced control planning & scheduling site, enterprise plant, packaged unit unit, group of units field

5. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.20074 A Systems View on Manufacturing processing subsystem the process plant – materials processing entities operating subsystem the „control system“ – monitoring, controlling and automated decision making managing subsystem the „plant operators“ – all humans participating in decision making and execution towards higher levels of automation ! split of work ? process plant operations support system decision maker (Schuler, 1992, Backx et al., 1998)

6. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.20075 RT-BDM – An Integrated Approach dynamic data recon- ciliation decision maker optimal control process including base control optimizing feedback control system optimizing feedback control system process including base layer control optimal output feedback structure solution of optimal control reconciliation problems at controller sampling frequency computationally demanding, limited by model complexity lack of transparency, redundancy and reliability (Terwiesch et al., 1994; Helbig et al., 1998; Wisnewski & Doyle, 1996; Biegler & Sentoni, 2000 Diehl et al., 2002, van Hessem, 2004) plant operation support system process decision maker

7. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.20076 Horizontal (Functional) Decomposition decentralization typically oriented at functional constituents of the plant coordination strategies enable approximation of ”true” optimum not adequately covered in optimization-based control and operations yet (Mesarovic et al., 1970; Findeisen et al., 1980; Morari et al., 1980; Lu, 2000; Venkat et al., 2006) decision maker subprocess 2 subprocess 1 coordinator optimizing feedback controller 2 optimizing feedback controller 1 optimizing feedback control system subprocess 2subprocess 1 see technical presentation !

8. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.20077 Vertical (Time-Scale) Decomposition generalizes steady-state real-time optimization and constrained predictive control generalizes cascaded feedback control structure requires (multiple) time- scale separation, e.g. d(t) = d 0 (t) +  d(t) with trend d 0 (t) and zero mean fluctuation  d(t) (Helbig et al., 2000, Kadam et al., 2003) decision maker tracking controller optimal trajectory design long time scale dynamic data reconciliation short time scale dynamic data reconciliation time scale separator optimizing feedback control system process including base control

9. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.20078 decision maker tracking controller optimal trajectory design long time scale dynamic data reconciliation short time scale dynamic data reconciliation time scale separator Dynamic Real-time Optimization dynamic optimization - a versatile means for problem formulation economical objectives and constraints still a challenge for numerical methods optimizing feedback control system process including base control

10. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.20079 decision variables: u(t) time-variant control variables p time-invariant parameters t f final time Mathematical Problem Formulation objective function (e.g. economics) endpoint constraints (e.g. specs.) DAE system (process model) path constraints (e.g. temp. bound)

11. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.200710 Sequential Solution Strategy Control vector parameterization parameterization functions parameters t ui(t)ui(t)  i,k (t) c i,k Reformulation as nonlinear programming problem (NLP) s.t. DAE system solved by underlying numerical integration Gradients for NLP solver typically obtained by integration of sensitivity systems State and sensitivity integration dominate computational effort!

12. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.200711 Improved Algorithms – Sequential Approach Sensitivity integration is expensive Reduce number of sensitivity parameters Improve efficiency of sensitivity integration Reduce model complexity State integration is expensive Control grid adaptation strategy New methods for first and second-order sensitivity integration Methods for model reduction Schlegel et al., 2003 Hannemann & M., 2007 Schlegel et al., 2001, Romijn et al., 2007 Schlegel & M., 2004,…, Hartwich & M., 2006

13. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.200712 Optimization under uncertainty (CNLD) Optimization under parametric uncertainty e.g. reaction kinetics, drifting catalyst activity … Constructive nonlinear dynamics (CNLD) Normal vector constraints guarantee minimal distance to critical manifolds Optimum is robust w.r.t. to uncertain parameters General concept of critical manifolds allows different problem formulations close relationship to semi-infinite programming a k Problem Optimum may be unstable, constraints may be violated because of uncertainty. a,k Process properties defined by critical manifolds in the parameter space r  F F kk Tasks addressed with CNLD robust stability robust performance robust process constraints robust optimal control (cf. technical presentation)

14. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.200713 decision maker tracking controller process including base control optimal trajectory design long time scale dynamic data reconciliation short time scale dynamic data reconciliation time scale separator Integration of Control and Optimization type of controller? control problem formulations: models, constraints, algorithms, …? how to reconcile control and optimization levels? how to account for process and model uncertainty?... optimizing feedback control system

15. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.200714 Trajectory Tracking Predictive Control dynamic real-time optimization (D-RTO) on slow time-scale model predictive control (MPC) on fast time-scale –time-variant linear model from linearization and linear model reduction –some constraints (which?) –control performance monitoring works well in (simulated) Bayer polymerization process (Dünnebier et al., 2004) D-RTO MPC updated

16. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.200715 MPC Tight Integration of Control and Optimization updated fast trajectory updates reoptimization with refinement of control discretization reoptimization with coarse control discretization linear time-varying MPC in delta-mode for trajectory tracking, dynamic real-time optimization (D-RTO), trajectory updates when necessary D-RTO linear time-varying controller neighboring extremal update, when possible Kadam et al. (2003) Kadam & M. (2004) sensitivity analysis with changing active set

17. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.200716 A Radically Different Approach Do you solve optimal control problems when you drive a car? Join in my driver‘s contest!

18. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.200717 Solution Model FinishStart Slope of street uncertain MAX MIN PATH acceleration a time [second] velocity v distance x time [second]

19. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.200718 velocity v distance x 11 22 NCO Tracking assume non-changing switching structure due to uncertainty: parametric but no structural changes in the solution model parameterize nominal optimal control profiles (sequence & type of arcs): the solution model implement a (linear) multi-variable (decentralized switching) control system with solution model as setpoint: track the NCO (Bonvin, Srinivasan et al., 2003) automatically detect switching structure by numerical optimization: facilitate solution model generation (Schlegel & Marquardt, 2004, Hartwich & M., 2006) tracking active constraint adjust switching time close to optimal performance without on-line optimization

20. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.200719 decision maker tracking controller process including base control optimal trajectory design long time scale dynamic data reconciliation short time scale dynamic data reconciliation time scale separator Integration with Planning and Scheduling models, formulations, algorithms,... integrated or decomposed problem formulations how to account for process performance and uncertainty on the planning level... optimizing feedback control system

21. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.200720 Scenario-based Decision Making Situated action: adjust operational strategy to context ! scenario (market, suppliers, demand, state of plant...) strategy 1 strategy 2... stra.... tftf t0t0 strategy 2 stra.... strategy 1 tftf t0t0 strategy 2strat. 3strategy 1 optimal changeover & automatic sequencing... Min cost Max flexibility different objectives …... product A product B different products …

22. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.200721 Disjunctive Programming Formulation Dynamic model: Constraints: Initial conditions: Stage transition conditions: Objective: Propositional logic: (MLDO) Disjunctions: Raman, Grossmann (1994), Oldenburg et al. (2003) Dynamic optimization / MLDO implemented in DyOS

23. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.200722 decision maker tracking controller process including base control optimal transitions med. time scale dynamic data reconciliation short time scale dynamic data reconciliation time scale separator Real-time Business Decision Making optimizing feedback control system on different time-scales planning & scheduling long time scale dynamic data reconciliation implementation requires … process systems methods and tools technology platforms for product packaging and implementation business platforms for market penetration

24. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.200723 Technology Platform Prerequisites Computing power –hardware: processor –networks: bus systems –software high computing performant computing: no saturation yet communication networks: field bus systems, LAN, WAN etc. are in place software platform: management execution systems link ERP and manufacturing levels

25. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.200724 INCA Software Platform IPCOS OPC Server Matlab – State Estimation gPROMS – process simulation 2 PLS DyOS – Real Time Optimization Matlab - MPC gPROMS – process simulation 1 INCOOP, PROMATCH EU-projects modular design easy plant / simulator replacement

26. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.200725 Research Interests sub- system 1 2 coordination coordination – from the linear to the nonlinear case robustness – NLD for distributed (linear) controllers open issues technical presentations

27. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.200726 Research Interests sub- system 1 2 coordination – from the linear to the nonlinear case robustness – NLD for distributed (linear) controllers use of overall process models? open issues D-RTO scheduling

28. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.200727 Research Interests coordination coordination – from the linear to the nonlinear case robustness – NLD for distributed (linear) controllers use of overall process models? hierarchy in subsystems coordination in 2-dim space open issues coordination

29. MPC of Distributed and Hierarchical Systems – Leuven, 15.2.200728 Research Interests coordination coordination – from the linear to the nonlinear case robustness – NLD for distributed (linear) controllers use of overall process models? hierarchy in subsystems? coordination in 2-dim space? NCO tracking – a promising alternative for subsystem optimization? open issues coordination NCO tracking