Model Predictive Control of Distributed and Hierarchical Systems

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

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. MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 1

General Objective Drive the manufacturing process to its economical optimum anytime ! market process uncertainties & disturbances constraints • equipment, safety, environment • capacity, quality, reproducability decision making on process operations time-varying profiles manipulated variables MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 observed variables 2

Real-Time Business Decision Making Real-time business decision making (RT-BDM) corporate planning • the set of activities performed by humans and assisting process operation support technology planning & scheduling • to manage a manufacturing process • for profibability and agility site, enterprise plant, packaged unit set-point optimization advanced control field instrumentation and base layer control unit, group of units field increasing degree of automation MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 3

process plant A Systems View on Manufacturing operations support system decision maker (Schuler, 1992, Backx et al. , 1998) 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 MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 split of work ? towards higher levels of automation ! 4

RT-BDM – An Integrated Approach • optimal output feedback decision maker structure decision maker optimizing feedback control system dynamic optimal optimizing feedback data reconcontrol ciliation control system process including base control process including base layer control • solution of optimal control reconciliation problems at controller sampling frequency • computationally demanding, operation limited by model complexity support system • lack of transparency, redundancy and reliability (Terwiesch et al. , 1994; plant Helbig et al. , 1998; Wisnewski & Doyle, 1996; process Biegler & Sentoni, 2000 Diehl et al. , 2002, van Hessem, 2004) MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 5

Horizontal (Functional) Decomposition decision maker optimizing feedback control system • decentralization typically oriented at functional constituents of the plant coordinator • coordination strategies enable approximation of ”true” optimum optimizing feedback controller 1 optimizing feedback controller 2 subprocess 1 • not adequately covered in optimization-based control and operations yet subprocess 2 • (Mesarovic et al. , 1970; Findeisen et al. , 1980; Morari et al. , 1980; Lu, 2000; Venkat et al. , 2006) MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 see technical presentation ! 6

Vertical (Time-Scale) Decomposition decision maker optimizing feedback control system long time scale dynamic data reconciliation optimal trajectory design time scale separator short time scale dynamic data reconciliation tracking controller process including base control MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 • generalizes steady-state real-time optimization and constrained predictive control • generalizes cascaded feedback control structure • requires (multiple) timescale 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) 7

Dynamic Real-time Optimization decision maker optimizing feedback control system long time scale dynamic data reconciliation optimal trajectory design time scale separator short time scale dynamic data reconciliation • dynamic optimization a versatile means for problem formulation • economical objectives and constraints tracking controller • still a challenge for numerical methods process including base control MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 8

Mathematical Problem Formulation objective function (e. g. economics) DAE system (process model) path constraints (e. g. temp. bound) endpoint constraints (e. g. specs. ) decision variables: u(t) p tf time-variant control variables time-invariant parameters final time MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 9

Sequential Solution Strategy Control vector parameterization ui(t) parameterization functions ci, k(t) parameters t Reformulation as nonlinear programming problem (NLP) s. t. DAE system solved by underlying numerical State and sensitivity integration dominate computational effort! Gradients for NLP solver typically obtained by integration of sensitivity systems MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 10

Improved Algorithms – Sequential Approach Sensitivity integration is expensive Improve efficiency of sensitivity integration New methods for first and second-order sensitivity integration Schlegel et al. , 2003 Hannemann & M. , 2007 State integration is expensive Reduce number of sensitivity parameters Control grid adaptation strategy Schlegel & M. , 2004, …, Hartwich & M. , 2006 MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 Reduce model complexity Methods for model reduction Schlegel et al. , 2001, Romijn et al. , 2007 11

Optimization under uncertainty (CNLD) Optimization under parametric uncertainty • e. g. reaction kinetics, drifting catalyst activity … Problem Optimum may be unstable, constraints may be violated because of uncertainty. k a, k k r F a Process properties defined by critical manifolds in the parameter space Constructive nonlinear dynamics (CNLD) Tasks addressed with 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 • robust stability • robust performance • robust process constraints • robust optimal control (cf. technical presentation) MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 12

Integration of Control and Optimization decision maker • type of controller? optimizing feedback control system long time scale dynamic data reconciliation optimal trajectory design time scale separator short time scale dynamic data reconciliation tracking controller process including base control MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 • control problem formulations: models, constraints, algorithms, …? • how to reconcile control and optimization levels? • how to account for process and model uncertainty? • . . . 13

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 D-RTO updated MPC • works well in (simulated) Bayer polymerization process (Dünnebier et al. , 2004) MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 14

Tight Integration of Control and Optimization D-RTO dynamic real-time optimization (D-RTO), trajectory updates when necessary neighboring extremal update, when possible linear time-varying MPC in delta-mode for trajectory tracking, reoptimization with refinement of control discretization reoptimization with coarse control discretization fast trajectory updates updated linear time-varying controller MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 sensitivity analysis with changing active set Kadam et al. (2003) Kadam & M. (2004) 15

A Radically Different Approach Do you solve optimal control problems when you drive a car? Join in my driver‘s contest! MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 16

Solution Model MAX acceleration a velocity v PATH distance x MIN time [second] Finish Start Slope of street uncertain MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 17

NCO Tracking (Bonvin, Srinivasan et al. , 2003) (Schlegel & Marquardt, 2004, Hartwich & M. , 2006) • automatically detect switching structure by numerical optimization: facilitate solution model generation e nc a • assume non-changing switching form tion structure due to uncertainty: per iza 1 al parametric but no structural optim m p i ine changes in the solutiont model o to on-l e os out velocity v cl th • parameterize nominal i w optimal control profiles (sequence & type of arcs): the solution model tracking active constraint 2 adjust switching time distance x • implement a (linear) multi-variable (decentralized switching) control system with solution model as setpoint: track the NCO MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 18

Integration with Planning and Scheduling decision maker optimizing feedback control system long time scale dynamic data reconciliation optimal trajectory design short time scale dynamic data reconciliation tracking controller time scale separator • models, formulations, algorithms, . . . • integrated or decomposed problem formulations • how to account for process performance and uncertainty on the planning level • . . . process including base control MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 19

Scenario-based Decision Making Situated action: adjust operational strategy to context ! different. . . products objectives strategy 1 product A Min cost strategy 2 product B Max flexibility . . . scenario (market, suppliers, demand, state of plant. . . ) … … strategy 2 optimal changeover & automatic sequencing stra. . . . strategy 1 t 0 tf t 0 MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 strat. 3 strategy 2 tf 20

Disjunctive Programming Formulation Raman, Grossmann (1994), Oldenburg et al. (2003) • Objective: (MLDO) DO ML • Constraints: n / OS tio Dy • Initial conditions: iza in tim ted • Stage transition conditions: op en ic m m na mple Dy i • Dynamic model: • Disjunctions: • Propositional logic: MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 21

Real-time Business Decision Making optimizing feedback control system on different time-scales long time scale dynamic data reconciliation time scale separator med. time scale dynamic data reconciliation planning & scheduling optimal transitions decision maker implementation requires … • process systems methods and tools short time scale dynamic data reconciliation tracking controller process including base control MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 • technology platforms for product packaging and implementation • business platforms for market penetration 22

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 MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 23

INCA Software Platform Dy. OS – Real Time Optimization PLS IPCOS OPC Server g. PROMS – process simulation 1 g. PROMS – process simulation 2 Matlab - MPC Matlab – State Estimation • INCOOP, PROMATCH EU-projects • modular design • easy plant / simulator replacement MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 24

Research Interests open issues • coordination – from the linear to the nonlinear case • robustness – NLD for distributed (linear) controllers technical presentations coordination subsystem MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 1 subsystem 2 25

Research Interests open issues scheduling • coordination – from the linear to the nonlinear case • robustness – NLD for distributed (linear) controllers D-RTO • use of overall process models? subsystem MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 1 subsystem 2 26

Research Interests open issues 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 coordination MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 27

Research Interests open issues coordination • coordination – from the linear to the nonlinear case • robustness – NLD for distributed (linear) controllers NCO tracking • use of overall process models? • hierarchy in subsystems? • coordination in 2 -dim space? • NCO tracking – a promising alternative for subsystem optimization? coordination MPC of Distributed and Hierarchical Systems – Leuven, 15. 2. 2007 28