PFC Predictive Functional Control

Transcription

1 PFC Prdiciv Funcional Conrol Prof. Car d Prada D. of Sm Enginring and Auomaic Conrol Univri of Valladolid, Sain rada@auom.uva.

2 Oulin A iml a oibl Moivaion PFC main ida An inroducor xaml

3 Moivaion Prdiciv conrol i a widl ud conrol chniqu in h roc indur combind wih an oimizaion lar Mo of h imlmnaion u inrnal linar modl ( ron) and LP oimizr

4 DMC DMC no conrain LP, conomic oimizr MV, OP a u() Comu MV fuur S oin S oimal MV S arg im SP CV, PV Oou rdicion 2... imo

5 Moivaion Whn a ignifican non-linar roc i facd, a nonlinar conrollr bad on a non-linar lan modl i rquird. Currn aroach bad on fir-rincil modl,, volrra ri, c. lad o a non-linar oimizaion roblm ha mu b olvd on-lin hi i a hav burdn, boh from h imlmnaion and comuaional load

6 on-linar Prdiciv Conrol w Oimizr u v Proc (j) Prdicor u 2 [ ŷ( j) w( j) ] [ β u( j) ] 2 min u J j j 0 x f (x(), u()) () g(x(), u()) ( j) u u( j) u 2

7 Solving h dnamic LP roblm Oimizr u() Proc () u J w Simulaion from o 2 for comuing J(u,x()) Sa conrain Gradin

8 Aim h aim of Paramric Prdiciv Conrol (PPC) i o facilia h imlmnaion of h conrollr whil raining h main non-linar characriic in i inrnal modl Good comromi bwn d of xcuion, a of imlmnaion and rformanc arg: Embddd conrollr in a DCS

9 PPC Main ida Combin fir rincil modl wih MPC ida and gnra a imlifid oluion ha i udad vr amling im. Paramric Prdiciv Conrol (PPC) (J. Richal, 996) wa dvlod for, and uccfull alid o, mraur conrol of bach racor. A. Aandri, A. Ruda, PhD udn hr : Baic ida rnd in h linar ca Exndd o h non-linar ca wih a chmical racor CSR Indurial alicaion o h boom mraur conrol of a diillaion column had wih a furnac-rboilr.

10 Baic conc aado Conigna Proc Proco Modlo m SP rn w Pa Fuur fuuro Ed m m Aim: Dcra h rror in h fuur unil a crain rcnag of h currn rror w () hi imli o chang h roc ouu b U h modl o comu h conrol u() ha rovid a chang in h modl ouu m (u) K dign quaion: m (u)

11 Baic conc h fuur rror a mu b a fracion of h currn rror w- () SP Conigna w Ed E d λ (w ()) 0 < λ < Proc Proco ( - λ )(w ()) Examl: Fir ordr modl Modlo m m m d() d () k u() aado rn Pa Fuur fuuro

12 Baic conc (Monorg) Examl: Fir ordr modl d() d () Auming ha u() i k conan along h rdicion horizon, ha i u, and wih iniial condiion (): amling im rdicion (o coincidnc) horizon k u() m ( u() ) () k u() () k u() m im

13 Dign quaion SP Conigna Proc Proco w Ed ( - λ )(w ()) Modlo m m m m () k u() aado rn Pa Fuur fuuro dign quaion: m (u) Exlici oluion for h conrol ignal u() () K ( λ )[ w() ()]

14 uning aramr A dicr fir ordr m wih ol λ will giv a fr ron a h on dird a λq x u() () K ( λ )[ w() ()] rdicion horizon (numbr of amling riod rquird o dcra h currn rror b λ ) λ Rducion facor (0,..,)

15 Examl. Idal ca IME Proc ouu and SP hour w Modl Proc G() Conrol ignal u K 5 min IME 20 λ 0.8

16 Exnion o u > Examl: Fir ordr modl d() d () k u() m ( ) u 2 Prdicion ar mor comlx m m ( ) ( ) () () k u() m ( ) k u( u() ) u( ) wo unknow: u(), u( ), hn wo coincidnc oin ar rquird () im

17 Robun Proc ouu and SP IME Conrol ignal IME hour w u 0% chang in h aramr Modl Proc Modl: G() λ 0.8 A bi lowr

18 Robun Sad a rror IME Conrol ignal IME hour w u Modl Proc Modl: G() 20 λ Soluion: rror modl or xlici ingraor addd

19 Incororaing rror Modl: d() d () k u() v v diurbanc Auming alo ha v do no chang along h rdicion horizon: u() ( ) () K u() v m () K u() v im

20 Dign quaion SP Conigna Proc Proco w Ed ( - λ )(w ()) Modlo m m m m () K u() v aado rn Pa Fuur fuuro dign quaion: m (u) Conrollr quaion. v i no known and nd o b imad vr amling im u() ( ) ( () v λ )[ w(k) ()] K

21 Eimaing v - - u(-) (- ) () v ) K u( ) ( () ) K u( ) ( () vˆ v i imad from h roc modl in ordr o cancl h diffrnc bwn h maurd roc ouu a and h rdicion mad wih valu a -

22 Examl h rror imaion comna h modlling rror w Modl Proc IME hour Modl: Conrol ignal u G() IME Eimad diurbanc 20 λ v IME

23 Adding an ingraor )) ( ) (w( ) i( ) ( ) i( () i i i ( )[ ] ( ) ( ) i i K () w() () u() λ PPC i d k i ( ) ) ( u() w ()

24 o ud morar la imagn n momno. Examl Modl Proc hour Modl: 0.9 G() 5.5 Conrol ignal 20 λ 0.8 i 0. min 20 c.

25 Fir ordr dla Modl: d() d () v diurbanc k u( d) v Proc Modl d d dla m m d D ( D λ )[ w() ()] u() im

26 Fir ordr dla ( ) D D m ) (m m v u() K D) u(m K () ( )[ ] () w() D λ ( ) ( )[ ] λ D m ) (m D D v D) u(m K () () w() K u() > D

27 Eimaing v u(-(d) ) (- ) - () v i imad from h roc modl in ordr o cancl h diffrnc bwn h maurd roc ouu a and h rdicion mad wih valu a - (D) D D vˆ () moohing filr ( ) K u( (D ) )

28 Examl. Idal ca IME Proc ouu and SP hour w Modl Proc G() K Conrol ignal IME u 5 min. d 0 min. 40 λ 0.8 min.

29 Robun h modlling rror IME h rror imaion comna hour w Modl Proc Modl: Conrol ignal u G() IME λ IME Eimad diurbanc v