st 1 HYCON PhD School on Hybrid Systems www.ist-hycon.org www.unisi.it Hybrid Systems in Industrial Process Control Olaf Stursberg University of Dortmund, Germany o.stursberg@ct.uni-dortmund.de scimanyd suounitnoc enibmoc smetsys dirbyH lacipyt (snoitauqe ecnereffid ro laitnereffid) scimanyd etercsid dna stnalp lacisyhp fo fo lacipyt (snoitidnoc lacigol dna atamotua) fo senilpicsid gninibmoc yB .cigol lortnoc ,yroeht lortnoc dna smetsys dna ecneics retupmoc dilos a edivorp smetsys dirbyh no hcraeser ,sisylana eht rof sloot lanoitatupmoc dna yroeht fo ngised lortnoc dna ,noitacifirev ,noitalumis egral a ni desu era dna ,''smetsys deddebme`` ria ,smetsys evitomotua) snoitacilppa fo yteirav ssecorp ,smetsys lacigoloib ,tnemeganam ciffart .(srehto ynam dna ,seirtsudni HYSCOM IEEE CSS Technical Committee on Hybrid Systems 17 Siena, July 1 9-22, 2005 - Rectorate of the University of Siena
� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � First HYCON PhD School on Hybrid Systems - Siena, July 2005 Outline Hybrid Systems in Control Architecture of Production Systems Industrial Process Control Design Tasks Modeling with Hybrid Automata Optimal Control of Transition Procedures Olaf Stursberg Synthesis of Supervisory Controllers Process Control Laboratory Controller Verification using Reachability Analysis University of Dortmund, Germany Conclusions and Open Problems Hybrid Systems in Industrial Process Control - Olaf Stursberg 2 Control Structure of Production Systems Example: Polymer Production Plant Type of Dynamics: Layers: Functions: Enterprise Control Layer Controller Functions: discrete event Weighting logistics, supply planning (1) Coordination control: time and algebraic scheduling Production Control Layer - follow recipes constraints quality control - assign task to resources Higher functions: [mostly DCS, operator] Process Control Layer advanced continuous control continuous Mixing recipe control, discrete event Operator Station, (2) Group control: alarm handling, visualization ... mixed (PC, WS) supervise the sequence of Basic functions: control actions in one unit continuous Process Stations, basic feedback control [PLC + Industrial PC] discrete event ( + time ) Programmable Logic Controllers sequence control Reaction safety trips, interlocks discrete event (3) Basic Control: supervise / control one Field Layer local manual operating mixed Storage local displays (or a few) dependent ... sensing, actuating process quantities Process Layer hybrid: [mostly PLC, hard-wired; continuous dynamics ... feedback loops] Module 1 Module 2 Module n with autonomous events, continuous and discrete inputs Hybrid Systems in Industrial Process Control - Olaf Stursberg Hybrid Systems in Industrial Process Control - Olaf Stursberg 3 4 Design Task Modeling with Hybrid Automata – Syntax Hybrid automaton: HA X , U , V , Z , inv , , g , r , f Control design for production plants ... n ... is challenging: � heterogeneity: the various control functions require different continuous states: x X R x models and design techniques u U [ u , u ] [ u , u ] continuous inputs: 1 1 n � interdependency: functions on different layers affect each other; n u u how to guarantee consistency? n finite set of discrete inputs: v V { 1 � v , ,v } , v R v n j d � complexity: � due to dynamic type (nonlinearity, non-convexity) Z { 1 z , , z } finite set of locations: n � due to size (large number of state variables, z manipulated variables, operating modes, etc.) X invariants: , polyhedral for all z inv : Z 2 � hardware requirements ( z , z ) Z Z transitions: � modularity: suitable communication paradigms? 1 2 X guards: , polyhedral g : 2 ... includes the following tasks: � optimization of transition procedures � optimal control resets: r : X X � algorithmic generation of supervisory controllers � synthesis n flow functions: x � a-posteriori analysis of the control design � verification f : Z X U V R s.t. defines a continuous vector field x f z , x , u , v What can hybrid systems contribute? [for simplicity: no synchronization] Hybrid Systems in Industrial Process Control - Olaf Stursberg Hybrid Systems in Industrial Process Control - Olaf Stursberg 5 6
� � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � Modeling with Hybrid Automata – Semantics Modeling with Hybrid Automata – Example Reactor with liquid-phase chemical reaction: u ( t 1 ), v ( t 1 ) inv (z 1 ) Set of event times: T = { t 0 , t 1 , t 2 , ...} F 1 M F 2 x 2 Variables: � discrete inputs: F 1 , F 2 , s H x ( t 0 ) Input trajectories: � u = ( u 0 , u 1 , ...) � � u , � ( t ) � continuous inputs: F C , F 3 V , T , c A , c B g (( z 1 , z 2 )) � v = ( v 0 , v 1 , ...) � � v � state variables: V , T , c A , c B s H with u k , v k constant for t � [ t k , t k +1 [ ( z 1 ,z 2 ) F C r (( z 1 , z 2 ), x ) Discrete dynamics: V � 0.8 low high (no resets) level level Hybrid state: � k � ( z k , x k ) � � with V � 0.8 F 3 x k = x ( t k ), z k = z ( t k ) dV Continuous inv (z 2 ) F F F 1 2 3 Feasible run of HA for given � 0 , � u and � v : dynamics: dt x 1 � � = ( � 0 , � 1 , � 2 , ...) with � k from: dT F k T F k T 1 1 2 2 F k k T f k f s k k T f c 3 4 v , 1 5 r h 6 7 v , 2 (i) continuous evolution: and is the unique solution of the flow 0 x t dt V k dc F k c F c function for t � [0, � ]; � ( t ) � inv ( z k ) but � ( t ) � g (( z k , � )) A 1 8 A 2 A k f only for “high level” 9 r for t < � dt V dc F k c F c B 1 10 B 2 B (ii) transition: ( z k , z k +1 ) � � , � ( � ) � g (( z k , z k +1 )), and k f 11 r dt V x k +1 = r (( z k , z k +1 ), � ( � )) � inv ( z k +1 ) k k k 2 13 15 16 with : f k , f k , f c c exp � � v , 1 12 v , 2 14 r A B V V T Hybrid Systems in Industrial Process Control - Olaf Stursberg Hybrid Systems in Industrial Process Control - Olaf Stursberg 7 8 Task 1: Optimal Control of Transition Procedures Problem Statement given: � hybrid automaton Target region: ( z tar , x tar ) � � tar � � , with one z tar � Z , x tar � inv ( z tar ) � specifications: � transfer from initial state to goal set � safety restriction (exclusion of unsafe states) Forbidden sets: F { 1 F , F } with F j � � , polyhedral continuous sets n j � maximized performance / minimized costs Assume: time set T = { t 0 , t 1 , ..., t f } is finite [industrial relevance: start-up, shut-down, or change-over of processing systems] unsafe location Optimal control task: set * , v * * z 2 determine such that is the solution to: u � Objective: reset min t , , , f u v z 3 Determine input trajectories , u u v v such that the specs are met! z 1 subject to: (set of feasible runs) goal x ( t ) � � � � � x 2 � 0 = ( z 0 , x 0 ), � f � � tar , � � F initialization x 1 Chosen cost function � : t f in combination with weighted distances of � k to � tar Literature: different approaches suggested; most based on piecewise affine approximations Hybrid Systems in Industrial Process Control - Olaf Stursberg Hybrid Systems in Industrial Process Control - Olaf Stursberg 9 10 Decomposition Approach Results for the Example (1) Principle : Objectives : � reach nominal reaction (target) from an initially empty reactor � separate the optimization of continuous and discrete degrees of freedom: � time optimality (i) high level: search tree encoding the discrete DOF � v ( t ) � avoid overflow and critical temperatures (ii) low level: embedded NLP for the continuous DOF � u ( t ) � branch&bound and heuristics to prune the search tree efficiently Configurations : � cost function evaluated by hybrid simulation � best-first search (throughout) � pruning based on an adjacency criterion (chooses a locally best v k ) � prediction horizon: p = 2 Hybrid Automaton HA Specification: � 0 , � , � Results : � termination after 959 nodes, � u , � v , � � Neighborhood info Graph Search Algorithm � 721 nodes fathomed due to adjacency, the remainder due to costs node n, v k ˆ ˆ ˆ u , x , t , , , k k 1 p u v [theoretical number of nodes for the encountered path length: 3 � 10 14 ] Embedded Nonlinear Programming Prediction horizon p � computation time: 484 CPU-sec (P4-1.5 GHz) ˆ ˆ ˆ x , , k u v Hybrid Simulation relaxed discrete inputs Hybrid Systems in Industrial Process Control - Olaf Stursberg Hybrid Systems in Industrial Process Control - Olaf Stursberg 11 12
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