Dynamic Real-Time Optimization

Transcription

1 Dynamc Real-Tme Omzaon Wolfgang Marquard Holger Scheu AVT Process Sysems Engneerng RWTH Aachen Unversy HD-MPC Indusral Worksho June 24 2 Leuven Belgum

2 Two Omsaon Sraeges Smulaon Wha s he bes feed rae B? Feed B Omsaon Sraegy : Deermne omal and feasble feed rae by ral and error Sudy varous rajecores by dynamc smulaon scenaros Unsysemac aroach hgh human effor Feed B Sraegy 2: Deermne omal and feasble feed rae by means of dynamc omsaon Dynamc omser sysemacally searches for he bes rajecory Sysemac and effcen aroach Exac soluon Srnvasan e al. 23) HD-MPC Indusral Worksho Leuven 2 2

3 Two Omsaon Sraeges Smulaon Wha s he bes feed rae B? Feed B Omsaon Sraegy : Deermne omal and feasble feed rae by ral and error Sudy varous rajecores by dynamc smulaon scenaros Unsysemac aroach hgh human effor Feed B Sraegy 2: Deermne omal and feasble feed rae by means of dynamc omsaon Relace human effor by numercal algorhms! Solve he nverse roblem drecly! Dynamc omser sysemacally searches for he bes rajecory Sysemac and effcen aroach Exac soluon Srnvasan e al. 23) HD-MPC Indusral Worksho Leuven 2 3

4 Oulne Problem formulaon for economcally omal conrol roblems Effcen soluon mehods for omal conrol roblems adave grd refnemen srucure deecon sofware realzaon Omal conrol onlne Dynamc Real-Tme Omzaon DRTO) herarchcal MPC me-scale decomoson subomal NMPC Neghborng Exremal Udaes sofware realzaon Dsrbued MPC a new aroach for DRTO HD-MPC Indusral Worksho Leuven 2 4

5 Oulne Problem formulaon for economcally omal conrol roblems Effcen soluon mehods for omal conrol roblems adave grd refnemen srucure deecon sofware realzaon Omal conrol onlne Dynamc Real-Tme Omzaon DRTO) herarchcal MPC me-scale decomoson subomal NMPC Neghborng Exremal Udaes sofware realzaon Dsrbued MPC a new aroach for DRTO HD-MPC Indusral Worksho Leuven 2 5

6 Some Samle Problems Large-scale ndusral rocess Shell): How fas can an nermedae chemcals lan be moved from oerang on A o B? Olefne olymerzaon rocess Novolen): Can we decde on a roducon schedule and omze grade ransons smulaneously? Membrane boreacor for wase waer reamen Koch Membrane Sysems): Can we mnmze energy demand and reduce membrane sress n real me? Syrene-buylacrylae co-olymerzaon BASF): Is real-me omzaon ready for use n he chemcal ndusres o ncrease roducvy and mrove rocess oerably? HD-MPC Indusral Worksho Leuven 2 6

7 Mahemacal Problem Formulaon mn ) Φ x f u f )) objecve funcon e.g. economcs) M x& = = F x u ) x P x u ) E x ) x f )) [ [ f f ] ] DAE sysem rocess model) ah consrans e.g. em. bound) endon consrans e.g. secs.) decson varables: u) me-varan conrol varables f me-nvaran arameers fnal me HD-MPC Indusral Worksho Leuven 2 7

8 Sequenal Soluon Sraegy Conrol vecor arameerzaon u ) ) c k φ k k Λ u ) c k φ k ) φ ) k c k arameerzaon funcons arameers Reformulaon as nonlnear rogrammng roblem NLP) s.. mn Φ x c f c f E x )) )) P x c ) f Τ DAE sysem solved by underlyng numercal negraon Gradens for NLP solver ycally obaned by negraon of sensvy sysems How o kee number of sensvy negraons low? HD-MPC Indusral Worksho Leuven 2 8

9 Oulne Problem formulaon for economcally omal conrol roblems Effcen soluon mehods for omal conrol roblems adave grd refnemen srucure deecon sofware realzaon Omal conrol onlne Dynamc Real-Tme Omzaon DRTO) herarchcal MPC me-scale decomoson subomal NMPC Neghborng Exremal Udaes sofware realzaon Dsrbued MPC a new aroach for DRTO HD-MPC Indusral Worksho Leuven 2 9

10 Adave Refnemen of Conrol Parameerzaon Mesh analyss wavele analyss elmnae refne Conces from sgnal analyss Grd on elmnaon Grd on nseron coarse nal mesh re-solve omzaon refne re-solve omzaon Schlegel and Marquard 25) unl song creron me. HD-MPC Indusral Worksho Leuven 2

11 A ycal nu rajecory x -3 x ecewse consan sol..4.2 ecewse lnear sol Obvous oen ssues how o caure swchng ons? how o avod over-arameerzaon? analycal sol. Srnvasan e al. 23) Is here a way o deec swchng srucure from numercal soluon? HD-MPC Indusral Worksho Leuven 2 2

12 Swchng Srucure Deecon 8 arameers. Solve coarsely dscrezed snglesage roblem SSP) u max u sens 2. Deermne he swchng srucure from NCO of NLP u max u mn u sens MSP black): 6 arameers! Convenonal SSP blue): 25 arameers! u mn 3. Reformulae as a mul-sage roblem MSP) accordng o swchng srucure Schlegel and Marquard 26) HD-MPC Indusral Worksho Leuven 2 3

13 Does Work? Le s Try Connuous Polymerzaon Process Bayer AG Dünneber e al. 24) comlex reacon mechansm large-scale model ~ 2 equaons) 3 nu varables 6 ah consrans rocess oeraon asks: omal load change omal grade change MV 3: recycle monomer [kg/h] coolng waer buffer ank MV : fresh monomer [kg/h] reacor TC monomer caalys MV 2: caalys [kg/h] Q LC CV : converson [%] searaon Q CV 2: vscosy os rocessng Polymer HD-MPC Indusral Worksho Leuven 2 4

14 Illusraon of Adaaon Sraegy MV : monomer feed MV 2: caalys feed MV 3: recycle flowrae / ref / ref / ref -.5 Ieraon HD-MPC Indusral Worksho Leuven 2 5

15 Illusraon of Adaaon Sraegy MV : monomer feed MV 2: caalys feed MV 3: recycle flowrae / ref / ref / ref -.5 Ieraon 3 HD-MPC Indusral Worksho Leuven 2 6

16 Illusraon of Adaaon Sraegy MV : monomer feed MV 2: caalys feed MV 3: recycle flowrae / ref / ref / ref -.5 Ieraon 6 HD-MPC Indusral Worksho Leuven 2 7

17 Non-adave Algorhm u.5 MV : fresh monomer u 3.5 MV 3: recycle flowrae / ref / ref y.5 consran : reacor oule y 2.75 consran 2: buffer ank volume / ref / ref HD-MPC Indusral Worksho Leuven 2 8

18 Adave Algorhm wh Srucure Deecon u.5 MV : fresh monomer u max u ah u ah u ah u mn u 3.5 MV 3: recycle flowrae u ah u mn u ah u ah / ref u ah / ref y.5 consran : reacor oule y 2.75 consran 2: buffer ank volume / ref / ref HD-MPC Indusral Worksho Leuven 2 9

19 DyOS Dynamc Omzaon Sysem gproms PSE Ld.) rocess model ESO SeVarables GeResduals model server e.g. gproms) ESO u ) nal rajecory CAPE-OPEN comlan sofware nerface u ) NLP solver DAE negraor ESO CORBA Objec Bus grd refnemen u ) DyOS no u ) song creron yes omal rajecory DyOS AC-SAMMM jon work wh Uwe Naumann RWTH Aachen): Srucured Auomac Manulaon of Mahemacal Models Poser Sesson) Modelca: Oen source objec-orened modelng language ESO Modelca-model Modelca-model DLL Modelca-model Modelca-model C-+ Modelca-model Modelca-model Modelca DCC Transl. h://wk.sce.rwh-aachen.de/bn/vew/projecs/ers/webhome HD-MPC Indusral Worksho Leuven 2 2

20 Oulne Problem formulaon for economcally omal conrol roblems Effcen soluon mehods for omal conrol roblems adave grd refnemen srucure deecon sofware realzaon Omal conrol onlne Dynamc Real-Tme Omzaon DRTO) herarchcal MPC me-scale decomoson subomal NMPC Neghborng Exremal Udaes sofware realzaon Dsrbued MPC a new aroach for DRTO HD-MPC Indusral Worksho Leuven 2 25

21 Dynamc Real-Tme Omzaon decson maker measuremens saes omzng feedback conrol sysem Φh manulaed varables dynamc daa reconclaon d r ) x r c ) omal conrol reconclaon conrol redcon me δ c economcal objecves & consrans δ c u c ) ) omal ouu feedback η ) rocess ncludng base conrol d soluon of omzaon roblems a samlng frequency rocess ncludng base layer conrol comuaonally demandng lmed by model comlexy HD-MPC Indusral Worksho Leuven 2 26

22 Tme-Scale Decomoson omzng feedback conrol sysem me scale searaor η ) δ Δη) δ c long me scale dynamc daa reconclaon shor me scale dynamc daa reconclaon u x c d ) x ) c Δd) x ) c decson maker Φh ) y ) u ) c ) = u ) + Δu ) c omal rajecory desgn δ rackng conroller δ c c c me-scale? Fas Udaes rocess ncludng base conrol Ψ d) slow me-scale changng envronmen rocess varaons mos economcal rajecory sasfyng safey or equmen consrans! fas me-scale measuremen and rocess nose rajecory rackng sasfyng conrol bounds and qualy consrans! How can we acheve economc omaly on he faser HD-MPC Indusral Worksho Leuven 2 27

23 HD-MPC Indusral Worksho Leuven 2 29 Fas Neghborng Exremal Udaes θ arameerze uncerany exlo sensvy nformaon of revously solved omzaon roblem o generae an aroxmaon of he omal udae = ) ) ) ) ) θ θ θ θ λ g L g g L T a T a ) : ) ) : ) ) : = = Δ Δ = = Δ Δ = = Δ na na na a a a a λ θ λ λ θ θ λ λ θ λ λ θ θ θ θ θ Sensvy sysem Facco 983) nvaran acve se L: Lagrange funcon f: objecve funcon g: consrans : dscrezed conrols : unceran aram. ref ref ref ref T ref T ref T z g g g f L L + Δ Δ Δ + Δ + Δ Δ Δ Δ θ θ θ θ s...5 mn Changng acve se Ganesh & Begler 987) comue frs- and secondorder dervaves solve QP for fas udae re-erae f necessary Kadam & Marquard 24; Würh e al. 29) θ g θ g f L L

24 Effcen Comuaon of 2 nd order Sensves fne dfferences and 2 nd order forward sensves Vasslads e al. 999) scale On 2 ) adjon sensvy analyss for roblems whou ah consrans Cao e al Özyur e al. 25) 8. 2 nd order adjon sensvy analyss for ah-consraned roblems Hannemann & M. 27 2) NIXE Sueroson rncle for he lnear adjon sysem: only one 2 nd order adjon sysem Cu s) Wllams-Oo benchmark roblem Number of arameers n Jacoban Hessan Hessan evaluaon scales! HD-MPC Indusral Worksho Leuven 2 3

25 Sofware Realzaon DRTO Toolbox ) Use lan smulaor for develomen of advanced MPC conrol mehods Tes communcaon daa exchange and aler managemen offlne DRTO Module sandalone OPC Server MPC module lan smulaon Develo algorhms n Malab gproms C++... Sae Esmaor... OPC Clens OPC daa access HD-MPC Indusral Worksho Leuven 2 3

26 Sofware Realzaon DRTO Toolbox 2) Connec he conrol mehods o he real conrol rocess hrough he lan s conrol sysem Plan Process conrol sysem sandalone negraed OPC Server DRTO Module MPC module lan smulaon Sae Esmaor... Daa srucure n lan smulaon should be he same as n PCS) OPC Clens OPC daa access HD-MPC Indusral Worksho Leuven 2 32

27 Sofware Realzaon DRTO Toolbox 3) HD-MPC Indusral Name der Worksho Präsenaon Leuven

28 Case Sudy Connuous Polymerzaon Process ) Large-scale ndusral rocess Bayer AG Dünneber e al. 24) ~ 2 dynamc) sae varables ~ 2 algebrac varables 3 manulaed varables Task: Se on change from olymer A o B Dsurbance: Rao of monomer and monomer 2 d HD-MPC Indusral Worksho Leuven 2 34

29 Case Sudy Connuous Polymerzaon Process 2) Reference conrol sraegy Objecve value:.59 Consran volaons:.6 Delayed Sngle-Layer DRTO Objecve value:.8 Consran volaons: 6.2 Sngle Layer: Negborng Exremal Udaes NEU) Objecve value:.74 Consran volaons: 2. Two-Layer DRTO and NEU) Objecve value:.6 Consran volaons: 2. Würh e al. 2) HD-MPC Indusral Worksho Leuven 2 35

30 On-Se and Sofware Imlemenaon Sae esmaon Malab) Samlng rae s Measuremens Conrols Saes Measuremens Inca OPC-Server IPCOS) Saes Conrols Conrols Saes Process conrol sysem/ Process How can we overcome lmaons n he sze of he rocess consdered? Dsrbued MPC Dynamc omzaon DyOS Malab) Samlng rae 2 s MPC-Conroller Malab) Samlng rae s HD-MPC Indusral Worksho Leuven 2 39

31 Oulne Problem formulaon for economcally omal conrol roblems Effcen soluon mehods for omal conrol roblems adave grd refnemen srucure deecon sofware realzaon Omal conrol onlne Dynamc Real-Tme Omzaon DRTO) herarchcal MPC me-scale decomoson subomal NMPC Neghborng Exremal Udaes sofware realzaon Dsrbued MPC a new aroach for DRTO HD-MPC Indusral Worksho Leuven 2 4

32 Parellzaon va Problem Decomoson Alcaons can usually naurally be decomosed no subsysems conneced va nerconnecng varables local nus P 2 local ouus P P 3 P 4 P 5 P u u 2 u 3 u 4 u 5 P P 2 P 3 P 4 P 5 y y 2 y 3 y 4 y 5 HD-MPC Indusral Worksho Leuven 2 4

33 HD-MPC Indusral Worksho Leuven 2 42 Decomoson of Omzaon Problem searable objecve funcon = Φ = Φ N f f u x x ) )) )) mn searable endon consrans searable DAE sysem searable ah consrans ) ] [ ) ) ] [ ) f f f E u x P x x u x F x M = = & addonal nonsearable neracons here eq. consr.) T T T u x H m ] [ = } 2... { N

34 HD-MPC Indusral Worksho Leuven 2 43 Soluon Sraeges for Decomosed Problems ) Reformulaon as se of NLPs s.. DAE sysem solved by underlyng ndeenden numercal negraon )) mn c m c x Φ } 2... { N ) )) ) T m c x h x E T c x P k N k f k k = = nonsearable neracons Prmal decomoson Slverman 972) s.. ) T m c x h k k = γ M )) mn c m c x Φ resource allocaon s.. = = N γ Dual decomoson Lasdon 97) s.. )) mn λ m c m c x L...)...) )) T h m c x L λ λ + = Φ M rce coordnaon s.. = = N h

35 Soluon Sraeges for Decomosed Problems 2) Sensvy-Drven Dsrbued Model-Predcve Conrol S-DMPC) Scheu Marquard 2) Alcaon of he lnearzed aral goal-neracon oeraor Mesarovc e al.97) Cos funcon of he dsrbued conrollers lnearzed nformaon of nonlocal objecve funcons coy of he local objecve funcon HD-MPC Indusral Worksho Leuven 2 44

36 Alkylaon of Benzene Process J. Lu e al. 2) Subsysems Inus HD-MPC Indusral Worksho Leuven 2 45

37 Mahemacal model For each subsysem: Mass balances for each seces and energy balance For CSTRs: reacon knecs For flash searaor: hase equlbrum descrons Medum scale DAE sysem: - 25 dfferenal equaons - ~ algebrac equaons HD-MPC Indusral Worksho Leuven 2 46

38 Resuls Scheu and Marquard 2) S-DMPC rovdes he same conroller erformance as a cenralzed MPC Solve 5 small QP n arallel nsead of large QP faser comuaon ossble HD-MPC Indusral Worksho Leuven 2 48

39 Conclusons & Fuure Persecves Algorhms for dynamc omzaon are connuously maurng bass for DRTO reduce comung me sll many challenges ahead e.g. dsconnuous and mxed neger roblems Herarchcal and dsrbued MPC are enablng echnologes for real-me alcaons Herarchcal MPC Mehods already successfully aled o largescale ndusral rocesses smulaon and exermens) Dsrbued MPC s a key echnology o aly DRTO o even larger lans mehods are maurng have o be negraed no DRTO oolbox HD-MPC Indusral Worksho Leuven 2 49

40 Acknowledgemens PhD sudens Jan Busch Bayer Technology Servces Ralf Hannemann AVT.PT Arnd Harwch Bayer Technology Servces Jendra Kadam Exxon Chemcals Jan Oldenburg BASF Adran Praa Bayer Technology Servces Marn Schlegel BASF Lynn Würh Bayer Technology Servces Fundng BASF Shell Global Soluons German Research Foundaon Euroean Unon HD-MPC Indusral Worksho Leuven 2 5