New Perspectives in Control System Design: Pseudo-Constrained to Market Responsive Control

Transcription

1 New Perspectves n Control System Desgn: Pseudo-Constraned to Market Responsve Control Donald J. Chmelewsk Department of Chemcal & Bologcal Engneerng x Illnos Insttute of Technology PRODUCTS SEPARATR * EDOR s due to dfferent controller tunngs BOP wth less proft FLUE-GAS STRP-STM RISER REGEN-TR u BOP wth more proft * * OSSOP AIR REG-CATY STEAM FEED-OIL

2 Outlne Motvatng Example Pseudo-Constraned Control Proft Control Market Responsve Control Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

3 Motvatng Example (Non-sothermal Reactor) F C A, T F V V r A dca F( CAn CA) VrA dt dt F( Tn T ) ( VH / C dt k( T) C A p ) r A Increase F Increased producton rate Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

4 Motvatng Example (Non-sothermal Reactor) F C A, T F V V r A dca F( CAn CA) VrA dt dt F( Tn T ) ( VH / C dt k( T) C A p ) r A Increase F Decrease F Increased producton rate Increase T Increase reacton rate Increase producton Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

5 Lmted Operatng Regon Process Lmtatons: T( t) T F( t) F (max) (max) - Catalyst protecton or onset of sde reactons - Pump lmt or lmt on downstream unt Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

6 Lmted Operatng Regon Process Lmtatons: T( t) T F( t) F F K c (max) ( T (max) Possble Controller: T ( sp) - Catalyst protecton or onset of sde reactons - Pump lmt or lmt on downstream unt ) F ( sp) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

7 Performance n Tme Seres F T (sp) T(t) T (max) C A, T F F(t) tme F (max) F (sp) tme Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

8 Performance n Phase Plane T(t) * F(t) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

9 Dynamc Operatng Regon T(t) * F(t) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

10 Expected Dynamc Operatng Regon T(t) * F(t) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

11 Steady-State Relaton Controller: F K c ( T T ( sp) ) F ( sp) Steady-State Relaton: F ( sp) ( sp) f ( T ) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

12 Dynamc Operatng Regon T(t) * F(t) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

13 Steady-State Operatng Lne T(t) * F(t) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

14 Optmal Operatng Pont T(t) * Decrease F Increase T Increase converson Increase producton F(t) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

15 Optmal Operatng Pont: T(t) Another Possblty * Increase F Increased producton rate F(t) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

16 Optmal Operatng Pont: Another Possblty T(t) Increase F Increased producton rate * F(t) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

17 Requres Dfferent Controller Tunng T(t) * F(t) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

18 Less Aggressve Tunng T(t) T (sp) T(t) T (max) * F(t) F (sp) F(t) tme F (max) tme Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

19 Need for Automated Tunng T(t) * * F(t) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

20 Outlne Motvatng Example Pseudo-Constraned Control Proft Control Market Responsve Control Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

21 Mass-Sprng-Damper Example r s the mass poston Mass r r max v f s the velocty s thenput force (MV)and f w r mn w s the dsturbance force Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

22 Mass-Sprng-Damper Example r s the mass poston Mass r r max v f s the velocty s thenput force (MV)and f w r mn w s the dsturbance force System Model: r v r v 1 f 1 w Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

23 Mass-Sprng-Damper Example r s the mass poston Mass r r max v f s the velocty s thenput force (MV)and f w r mn w s the dsturbance force System Model: r 1 v 2 3 r v 1 f 1 w System Constrants: 1 r 1 and f 16 Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

24 Department of Chemcal and Bologcal Engneerng Illnos Insttute of Technology Mass-Sprng-Damper Example 16 and 1 1 f r System Model: w f v r v r System Constrants: z n z t z z 1 ) ( w D D u D x z Gw Bu Ax x w u x w f v r z z

25 Process Model: Covarance Analyss (Open-Loop Case) Steady State Covarance: A x z T T x x A G wg z w(t) A x D x G w D T w (t) z(t) Plant Dx Gaussan whte nose wth covarance w Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

26 Expected Dynamc Operatng Regon (EDOR) z 1 EDOR defned by: 11 * z Illnos Insttute of Technology z 2 Department of Chemcal and Bologcal Engneerng

27 Closed-Loop Covarance Analyss (Full State Informaton Case) Process Model: x Ax Bu G w z u( t) Lx( t) T T ( A BL) ( A BL) G G ( D D L) ( D D L) z D x x Controller: x D u x u u D x x w Steady-State Covarance: w x u w(t) u(t) T w D w w D Plant T w L z(t) x(t) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

28 Closed-Loop EDOR z 1 EDOR s from dfferent controllers * u L x 1 u L2 x z 2 Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

29 Constraned Closed-Loop EDOR z 1 Constrants ( z z ) * z 2 Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

30 Constraned Closed-Loop EDOR z 1 Constrants ( z z ) * z 2 Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

31 Department of Chemcal and Bologcal Engneerng Illnos Insttute of Technology Does there exst L such that: 1 column th Constraned Controller Exstence T w w w T u x x u x z D D D L D D L D ) ( ) ( ) ( ) ( T w T x x G G BL A BL A z T z n z 1 2

32 Department of Chemcal and Bologcal Engneerng Illnos Insttute of Technology If and only f there exst X> and Y such that: 1 Constraned Controller Exstence (Convex Condton) ) ( ) ( X D Y X D D Y X D D D T T u x u x T T w w w ) ( ) ( T w T G G BY AX BY AX z n z L YX And controller s constructed as: u Lx

33 Regon of Unconstraned Controller Exstence 1 Achevable Performance Levels Unachevable 2 Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

34 Regon of Constraned Controller Exstence 1 1 <z <z Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

35 Constraned Controller Exstence <z * 1 T(t) * * 2 <z F(t) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

36 Department of Chemcal and Bologcal Engneerng Illnos Insttute of Technology such that: Pseudo-Constraned Control Y X d mn,, ) ( ) ( X D Y X D D Y X D D D T T u x u x T T w w w ) ( ) ( T w T G G BY AX BY AX z n z 1 2

37 Pareto Fronter Interpretaton 1 All Pseudo-Constraned Controllers are on the Pareto Fronter Unachevable Regon Achevable Regon 2 Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

38 MPC Equvalence Theorem 1 (Chmelewsk & Manthanwar, 24): All controllers generated by Pseudo- Constraned Control (PCC) are concdent wth a controller generated by some Unconstraned Model Predctve Controller. Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

39 Outlne Model Predctve Controller Tunng Pseudo-Constraned Control Proft Control Market Responsve Control Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

40 Constraned Operatng Regon CV s Steady-State Operatng Pont Constrants EDOR * MV s Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

41 Real-Tme Optmzaton Orgnal Nonlnear Process Model: s f ( s, m, p) q h( s, m, p) (s,m,p,q) ~ (state, mv, dst, performance) ~ (x,u,w,z) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

42 Department of Chemcal and Bologcal Engneerng Illnos Insttute of Technology Real-Tme Optmzaton ),, ( ),, ( p m s h q p m s f s Orgnal Nonlnear Process Model: max mn,, ),, ( ),, ( s.t. ) ( mn m q s q q q p m s h q p m s f q g Real-Tme Optmzaton (mnmze proft loss): (s,m,p,q) ~ (state, mv, dst, performance) ~ (x,u,w,z) RTO soluton denoted as (s ossop,m ossop,p ossop,q ossop )

43 Real-Tme Optmzaton Steady-State Operatng Pont CV s Constrants EDOR * Optmal Steady-State Operatng Pont (OSSOP) * MV s Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

44 Backed-off Operatng Pont (BOP) CV s Backed-off Operatng Pont (BOP) EDOR * * * MV s Optmal Steady-State Operatng Pont (OSSOP) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

45 mn Steady-State BOP Selecton (Bahr, Bandon & Romagnol, 1996) Solve the followng Sem-nfnte Programmng Problem g( q) s.t. s.t. max s, m, q mn max p[ p, p ] Extensons: - Dynamc verson n Bahr, et al, (1995) max { q q ( s, m, h( s, m, - Lnearzed verson n Contreras-Dordelly & Marln (2) q f q q } p) p) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

46 Natural Varables Nonlnear g( q q mn bop ) s f ( s, m, p) q h( s, m, p) q q max Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

47 Devaton Varables Nonlnear g( q q mn bop ) s f ( s, m, p) q h( s, m, p) q q max Lnear wrt OSSOP g( q s ' As' Bm' Gp' q' q' mn ossop q' D s' D m' D x q' ) g u q q' max w p' Devaton Varables w.r.t. OSSOP: s = s bop s ossop m = m bop - m ossop p = p bop - p ossop q = q bop - q ossop Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

48 More Devaton Varables Nonlnear Lnear wrt OSSOP Lnear wrt BOP g( q q mn bop ) s f ( s, m, p) q h( s, m, p) q q max g( q q' q' mn ossop q' D s' D m' D x q' ) g u q s ' As' Bm' Gp' x Ax Bu Gw q' max w p' z D z mn x x z D u z u max D w w Devaton Varables w.r.t. OSSOP: s = s bop s ossop m = m bop - m ossop p = p bop - p ossop q = q bop - q ossop Devaton Varables w.r.t. BOP: x = s s bop u = m - m bop w = p - p bop z = q - q bop Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

49 Stochastc BOP Selecton (Loeblen & Perkns, 1999) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

50 Department of Chemcal and Bologcal Engneerng Illnos Insttute of Technology Assume controller L s gven and calculate : T w w w T u x x u x z D D D L D D L D ) ( ) ( ) ( ) ( T w T x x G G BL A BL A z T z n 1 Stochastc BOP Selecton (Loeblen & Perkns, 1999)

51 Assume controller L s gven and calculate : T T ( A BL) ( A BL) G G ( D D L) ( D D L) z Stochastc BOP Selecton (Loeblen & Perkns, 1999) x z T x u x x x 1n u T D Solve the followng Lnear Program: z w w w D T w mn s', m', q' g q q' s.t. As' Bm' q ' ( D s' D m') 1/ 2 q' x max q' u q mn 1/ 2 q' q' q q' max mn Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

52 Fxed Controller BOP Selecton Loeblen and Perkns (1999): x * EDOR * * u OSSOP Controller s fxed EDOR has fxed sze and shape Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

53 Varable Controller BOP Selecton Peng et al. (25): x EDOR Varable Controller * OSSOP * * u EDOR has varable sze and shape Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

54 Proft Control (Smultaneous BOP and Controller Selecton) EDOR s due to dfferent controller tunngs BOP wth less proft BOP wth more proft * * Max Proft Illnos Insttute of Technology Peng et al. (25) Department of Chemcal and Bologcal Engneerng

55 Assume controller L s gven and calculate : T T ( A BL) ( A BL) G G ( D D L) ( D D L) z Stochastc BOP Selecton (Loeblen & Perkns, 1999) x z T x u x x x 1n u T D Solve the followng Lnear Program: z w w w D T w mn s', m', q' g q q' s.t. As' Bm' q ' ( D s' D m') 1/ 2 q' x max q' u q mn 1/ 2 q' q' q q' max mn Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

56 Department of Chemcal and Bologcal Engneerng Illnos Insttute of Technology mn 2 1/ max 2 1/ max mn,, ' ', ', ' ' ' ' ' ') ' ( ' ' ' s.t. ' mn u x q Y X q m s q q q q q q q D m D s q Bm As q g ) ( ) ( X D Y X D D Y X D D D T T u x u x T T w w w ) ( ) ( T w T G G BY AX BY AX Proft Control (Smultaneous BOP and Controller Selecton) Peng et al. (25)

57 Department of Chemcal and Bologcal Engneerng Illnos Insttute of Technology mn 2 1/ max 2 1/ max mn,, ' ', ', ' ' ' ' ' ') ' ( ' ' ' s.t. ' mn u x q Y X q m s q q q q q q q D m D s q Bm As q g ) ( ) ( X D Y X D D Y X D D D T T u x u x T T w w w ) ( ) ( T w T G G BL AX BY AX Peng et al. (25) Computatonal Aspects of Proft Control

58 Reverse-Convex Constrants 1 1 (z ss, +d max mn, ) 2 2 (z ss, +d max, ) 2 mn 2 1 ( q' 1 q' 1 ) 1 ( q' 1q' 1 ) z ss, q' 1 Feasble Regon Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

59 Global Soluton Based on Branch and Bound algorthm Regon 2 Regon 3 Regon Regon 1 Regon q' 1 z ss, Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

60 Proft Control Applcatons Mechancal Systems Chemcal and Reacton Systems Hybrd Vehcle Desgn Inventory Control Electrc Power System Desgn Buldng HVAC Water Resource Management Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

61 Proft Control Applcatons Mechancal Systems Chemcal and Reacton Systems Hybrd Vehcle Desgn Inventory Control Electrc Power System Desgn Buldng HVAC Water Resource Management Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

62 Fludzed Catalytc Cracker Regenerator and Separator (dynamc): Rser (pseudo steady state): Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng (adapted from Loeblen & Perkns, 1999)

63 FCC Constrants and Economcs Process Constrants: Proft Functon: F gs F gl and F ugo are product flows (gasolne, lght gas and unconverted ol). Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng (adapted from Loeblen & Perkns, 1999)

64 Catalyst Flow (kg/s) Inlet Ar (kg/s) Regenerator Temp (K) Cyclone Temperature (K) Proft Control vs. Fxed Controller Back-off Fxed Controller Free Controller Coke Fracton n Separator Separator Temperature (K) Fracton of Coke n Regenerator x Oxygen Mass Fracton x 1-4 Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

65 FCC Proft Gross Proft ($/day) Dff from OSSOP ($/day) OSSOP $36,95 $. Fxed Control $34,631 - $2,274 Proft Control $35,416 - $1,489 Improves proft by 2% Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

66 Hybrd Vehcle Desgn Power Bus arm fc bat scap R arm Fuel Cell E fc R bat E bat R scap E scap E arm L arm w arm Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

67 DC-DC Converters Power Bus arm fc afc bat abat scap ascap R arm Fuel Cell E fc DC-DC Converter R bat E bat DC-DC Converter R scap E scap DC-DC Converter E arm L arm w arm k fc k bat k scap Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

68 Servo-Loops wth PI Controllers PI (sp) P fc + - PI (sp) P bat + - PI (sp) P scap + - k fc P fc k bat P bat k scap P scap Vehcle Power System Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

69 Supervsory Control Hgh Level Controller (sp) P mot PI (sp) P fc + - PI (sp) P bat + - PI (sp) P scap + - k fc P fc k bat P bat k scap P scap Vehcle Power System Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

70 Power to Motor (kw) Speed (mph) Drve Cycle Data and Modelng tme (sec) tme (sec) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

71 Hgh Level Battery Model E bat P bat P (loss) bat Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

72 Hgh Level Battery Model E bat P bat P (loss) bat E mn bat E mn E bat bat E max bat E max bat eˆ bat m bat Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

73 Hgh Level Battery Model E bat P bat P (loss) bat E mn bat E mn E bat bat E max bat E max bat eˆ bat m bat P P P mn bat mn bat P mn bat P max bat bat rate d Cˆ, bat eˆ batmbat ˆ rate, c bat eˆ batmbat C Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

74 Power and Energy Constrants of the Battery E bat P C E max rate,c max bat bat bat E eˆ m max bat bat bat E mn bat P bat Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng P C E mn rate,d max bat bat bat

75 Constrants a Functon of the Mass E bat P C E max rate,c max bat bat bat E eˆ m max bat bat bat P bat Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

76 Aspect Rato a Functon of C-Rate E bat P C E max rate,c max bat bat bat E eˆ m max bat bat bat P bat Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

77 Hgh Level Battery Model E bat P bat P (loss) bat E mn bat E mn E bat bat E max bat E max bat eˆ bat m bat P ( loss) bat lˆ P bat 2 bat m bat P P P mn bat mn bat P mn bat P max bat bat rate d Cˆ, bat eˆ batmbat ˆ rate, c bat eˆ batmbat C Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

78 Operatng Regon wth Power Losses E bat P bat Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

79 Hgh Level Super Cap Model E sc P sc P (loss) sc E mn sc E mn E sc sc E max sc E max sc eˆ sc m sc P ( loss) sc 2 Psc lˆ m sc sc P P P mn sc mn sc mn sc P P max sc sc rate d Cˆ, sc eˆ scmsc ˆ rate, c sc eˆ scmsc C Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

80 Fuel Cell Model Anode Sold Materal Current Collector In Cathode (H 2, H 2 O) H Ar n 2 O 2 H + H + H 2 O H + H + H + N 2 Anode Exhaust H + H + H + H 2 O Cathode Exhaust MEA Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

81 Hgh Level Fuel Cell Model P P fc fc P mn fc P P mn fc P max pˆ fc fc fc m P fc max fc P P P mn fc mn fc max fc P fc C C P rate, d bat rate, c bat pˆ max fc pˆ fc fc m m fc fc Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

82 Power Losses Increases Average Fuel Cell Power P fc E bat ` Δ P fc P bat Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

83 Desgn Problem Formulaton mn{ cˆ m cˆ m cˆ m } st.. fc fc bat bat sc sc P P P P fc o bat sc m m m m m v o fc bat sc Pbat bat Pbat bat lbatmbat Pbat lbatm bat P P sc sc sc l m sc sc sc sc sc sc P l m T AX BY AX BY Go mvg 1 1 Go mvg1 w x u T T x u D X D X D Y X D Y P E E 2 max fc max bat max sc P P P max fc max bat max sc P fc E E bat sc P 1 2 E 3 4 P 5 6 fc E bat sc P P P P bat sc fc bat P sc P fc mn fc E E mn bat mn sc P P P mn bat mn sc mn fc Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

84 Case Study Data Technology Lthum Battery Super- Capactor PEM Fuel Cell Cost $59/kg $93/kg $3/kg C-Rate.5 hr hr -1 1 hr -1 Power Densty 1 W/kg 11, W/kg 1 W/kg Appetecch & Prosn (25) Portet, Taberna, Smon, Flahaut, & Laberty-Robert (25) Murphy, Csar & Clarke (1998) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

85 Case Study Soluton Technology Lthum Battery Super- Capactor PEM Fuel Cell Mass 3 kg 2.8 kg 3.5 kg Nomnal Power.1 kw 1.5 kw 1.8 kw Total Captal Cost Cost $177 $26 $15 $3,8 Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

86 P fc (kw) Optmal Fuel Cell Sze and Operatng Regon 3.5 Fuel Cell 2.1 Fuel Cell Power(kW) P fc (kw/s) x tme(hr) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

87 E sc (kj) Optmal Super Cap Sze and Operatng Regon 7 Super Capactor 15 SuperCap Power, kw P sc (kw) tme(hr) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

88 E bat (kj) Optmal Battery Sze and Operatng Regon 1 8 Battery Battery Power, kw P bat (kw) tme(hr) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

89 Buldng HVAC Heat Leakage (T outsde measured) Volume of Ar (the Room) Sold Materal T sold T room, C room Contamnant Source: S c F rcy, T room, C room F rcy, T cool, C room F fresh, T room, C room F fresh, T cool, C fresh Ar Processng Unt (T cool = 2 o C) Energy Usage F fresh, T room, C room F fresh, T outsde, C fresh (C fresh = ) Control Varables: T room and C room Manpulated Varables: F rcy and F fresh Dsturbances: T outsde and S c Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

90 F fresh (m 3 /s) F ryc (m 3 /s) HVAC Control C (ppm) room T ( o C) room Energy Usage of Tradtonal Controller: 3.16 kw Energy Usage of Energy Effcent Controller: 2.55 kw (a reducton of almost 2%). Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

91 Outlne Model Predctve Controller Tunng Pseudo-Constraned Control Back-off and Proft Control Market Responsve Control Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

92 Thermal Energy Storage (TES) Heat Leakage T outsde Volume of Ar (the Room) T room Heat from Room Heat to Cooler Heat to TES Unt Coolng Unt TES Unt Energy Usage In HVAC systems TES s used for Load Levelng and to shft usage to Off-Peak Hours Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

93 Cents per k hr Temperature ( C) Energy Prces and Weather 4 Electrcty Prce Outsde Temperature Tme (days) Cyclcal pattern wth a phase shft of about 3 hours. Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

94 Cents per k hr Temperature ( C) Operaton of the TES Heat Leakage T outsde Volume of Ar (the Room) T room Heat from Room Heat to Cooler Heat to TES Unt Coolng Unt TES Unt Energy Usage 4 Electrcty Prce Outsde Temperature Tme (days) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

95 Response to Market Changes EDOR s due to dfferent controller tunngs BOP wth less proft BOP wth more proft * * OSSOP Illnos Insttute of Technology Peng et al. (25) Department of Chemcal and Bologcal Engneerng

96 Electrc Prce Model Whte Nose Input Shapng Flter Sequence wth Electrcty Prce Characterstcs Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

97 Electrc Prce Model Whte Nose Input Shapng Flter Sequence wth Electrcty Prce Characterstcs Measured Electrcty Prce State Estmator and/or Predctor Predcton of Electrcty Prce Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

98 Model Predctve Control T mn pe( t)* vu ( t) dt v u ( t) where pe( t) ~ the predcted prce (or value) vu ( t) ~ the velocty of usage and S(t) ~ amount n storage Constrants nclude : v u ( t) v max u and S( t) S max Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

99 Model Predctve Control T mn pe( t)* vu ( t) dt E[ pe * vu ] Ce v u ( t) where pe( t) ~ the predcted prce (or value) vu ( t) ~ the velocty of usage and S(t) ~ amount n storage Constrants nclude : v u ( t) v max u and S( t) S max Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

100 System Desgn mn vu ( t) T pe( t)* vu ( t) dt E * p e vu Ce ( v u ( t) max v max u and max How does v and S mpact C u e S( t) S max )? Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

101 System Desgn mn vu ( t) T pe( t)* vu ( t) dt E * p e vu Ce ( v u ( t) max v max u and max How does v and S mpact C u e S( t) S max )? MPCcannot answer ths queston! Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

102 Expected Cost of Electrcty Whte Nose Input Shapng Flter p e (t) E[p e* v u ] Manpulated Varables (Controller s u=lx) Process Model v u (t) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

103 Re-Scalng of Prce a w(t) Shapng Flter p' e (t) ( p' e a pe) E[p' e* v u ] Manpulated Varables Process Model v u (t) (Controller s u=lx) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

104 Correlatng Prce and Usage If E 2 ( ' ) p e v u and p' e a p e then v u ( t) a p e ( t) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

105 Department of Chemcal and Bologcal Engneerng Illnos Insttute of Technology Correlatng Prce and Usage ) ( ) ( then t p t v e u a ) ' ( If 2 p e v u E e e p p a ' and ] [ ] [ 2 ] [ u u e e v E v p E p E a a ] [ ] [ ] [ u u e e v E v p E p E a a e u e e C v p E p E ] [ ] [ 2 a

106 Mnmum Cost of Electrcty L, a C e mn c R a 2 R p e ( c E[ ]) E E E 2 ( ' ) p e v u 2 max 2 v u v ) ( u 2 max 2 S (S ) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

107 kw hr / day Thermal Energy Storage (Small Storage Unt) Heat Leakage T outsde Volume of Ar (the Room) T room Heat from Room Heat to Cooler Heat to TES Unt Coolng Unt TES Unt Energy Usage 25 2 Heat from Room Heat to Cooler Heat to TES Unt Tme (days) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

108 kw hr / day Thermal Energy Storage (Medum Storage Unt) Heat Leakage T outsde Volume of Ar (the Room) T room Heat from Room Heat to Cooler Heat to TES Unt Coolng Unt TES Unt Energy Usage Heat from Room Heat to Cooler Heat to TES Unt Tme (days) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

109 kw hr / day Thermal Energy Storage (Large Storage Unt) Heat Leakage T outsde Volume of Ar (the Room) T room Heat from Room Heat to Cooler Heat to TES Unt Coolng Unt TES Unt Energy Usage 3 2 Heat from Room Heat to Cooler Heat to TES Unt Tme (days) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

110 kw hr / day kw hr / day kw hr / day Thermal Energy Storage (Comparson of Storage Cases) 25 2 Heat from Room Heat to Cooler Heat to TES Unt Tme (days) Heat from Room Heat to Cooler Heat to TES Unt 3 2 Heat from Room Heat to Cooler Heat to TES Unt Tme (days) Tme (days) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

111 $ / kw hr Electrcty Costs ($ / day) Thermal Energy Storage (Cost Comparsons) 3 2 One Ton TES Unt Fve Tons TES Unt Ten Tons TES Unt 1 Electrcty Prce Tme (days) Average Coolng Costs: One ton: $8 per day Fve tons: $7 per day (14% savngs) Ten tons: $6 per day (25% savngs) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

112 Mnmum Levelzed Cost L, a, v mn max u, S max c R a c L,1 v max u c L,2 S max E E E 2 ( ' ) p e v u 2 max 2 v u v ) ( u 2 max 2 S (S ) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

113 Mnmum Levelzed Cost L, a, v mn max u, S max E c R a c L,1 v max u 2 ( ' ) p e v u c L,2 S max E E 2 max 2 v u v ) ( u 2 max 2 S (S ) Non-Convex Problem (but global soluton from branch and bound) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

114 Integrated Gasfcaton Combned Cycle (IGCC) Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

115 Acknowledgements Current Students: Ben Omell Mng-We Yang Former Students and Collaborators: Amt Manthanwar Davd Mendoza-Serrano Syed Amed Dr. Ju-Kun Peng (ANL) Professor Ralph Muehleson (CAEE, IIT) Professor Demetros Moschandreas (CAEE, IIT) Fundng: Natonal Scence Foundaton (CBET 96796) Graduate and Armour Colleges, IIT Chemcal & Bologcal Engneerng Department, IIT Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng

116 Conclusons Relatonshp between control system performance and plant proft quantfed. Enables proft guded control system desgn. Broad set of applcatons from a varety of dscplnes. Lnear controller can be desgned for market responsveness. Non-convex, but global methods can be used to sze and/or select equpment. Illnos Insttute of Technology Department of Chemcal and Bologcal Engneerng