On Adaptive Control of Simulated Moving Bed Plants. Plants Using Comsol s Simulink Interface. Speaker: Marco Fütterer

Transcription

1 daptve Smulated Movng ed Plants Usng Comsol s Smulnk Interfae Speaker: Maro Fütterer Insttut für utomatserungstehnk Otto-von-Guerke Unverstät Unverstätsplatz, D Magdeburg Germany e-mal: maro.fuetterer@ovgu.de On daptve Smulated Movng ed Plants

2 Contents daptve Smulated Movng ed Plants Usng Comsol s Smulnk Interfae On daptve Smulated Movng ed Plants

3 to hromatography How we an separate a mxture of two omponents? + + One way s to make use of dfferent adsorpton affntes of omponents On daptve Smulated Movng ed Plants

4 to hromatography Consder a smple ppe On daptve Smulated Movng ed Plants

5 to hromatography Consder a smple ppe whh s flled up wth adsorpton materals On daptve Smulated Movng ed Plants

6 to hromatography Now, a buket wth a mxture of two omponents dssolved n an eluent s pumped through ths adsorpton olumn. On daptve Smulated Movng ed Plants

7 to hromatography The more retaned omponent takes more tme to travel through the olumn as the less retaned omponent. On daptve Smulated Movng ed Plants

8 to hromatography Therefore, hromatography provdes a smple method to separate omponents. On daptve Smulated Movng ed Plants

9 to smulated movng bed How one an aheve a ontnuous separaton? Several hromatograph olumns are arranged n a rle, where the feedngs and drans are shfted ylally. I El U I IV, Ex Ex, U Ex Ex II Portshftng III, Ra Ra, U Ra Ra,, Soure: D.. roughton, G. Gerhold, US Patent, (1961) + + U On daptve Smulated Movng ed Plants

10 to smulated movng bed The four zones may be arranged n a plane to plot the assoated onentraton profle n ylsteady-state above the olumns. El I U I IV Ex,, Ex U Ex Ex II Portshftng III Ra,, Ra U Ra Ra I II III IV P, + + U,, P, El v I II III IV Ex v v, s Ra v, s z The spatal oordnate s hosen so that ths always begns wth the frst zone + + On daptve Smulated Movng ed Plants

11 to smulated movng bed The four zones may be arranged n a plane to plot the assoated onentraton profle n ylsteady-state above the olumns. Ex, Ex, U Ex Ex I II + + El U I Portshftng U IV III,, Ra, Ra, U Ra Ra On daptve Smulated Movng ed Plants

12 Modelng a hromatograph olumn G. Guohon,. n, Modelng for Preparatve Chromatography, adem Press, San Dego ( 003) ( fast adsorpton) adsorpton behavor left boundary: (, ) Dε t z n, () t = ( t,0) V z rght boundary: ( t, z) (, ) q + F = v + D t t z z l (, ) q + F = v + D t t z z l z z= = 0 z= 0 ntal: 0 z =, =, ( 0, z) = ( z) =,,,,0 1 ε F = ε V vl = ε q ε D q = q flud onentraton adsorbed onentraton volumetr flow rate vod fraton ross seton area dffuson (, ) On daptve Smulated Movng ed Plants =,

13 Modelng Comsol Implementaton Comsol Multyphyss Users Gude, Comsol, Sweden, ( 005) Comsol s pde equaton n general form: u d a + Γ = F t boundary ondton n general form: R n Γ = G + μ, u R = 0 T G G T ( ), u = q q 1+ F F =, q q F 1+ F V V Γ = D D ε z ε z d a F = T ( 0 0 ). ε ε V V = ε ε T V V = 0 n, n,, z= z= T, T, R z = z= ( ) T = M. Fütterer, Pro. of the European COMSO Conf On daptve Smulated Movng ed Plants

14 Modelng Couplng of olumns El U I I IV Ex,, Ex U Ex Ex II Portshftng III Ra,, Ra U Ra Ra External flow- rates: 0 = El + Ex V Ra Eluent feed: Extrat- dran: V = V + V I IV El II I Ex V = V =, ni,, I outiv,, IV V = V V,, =,, =, nii outi Ex U,, =, ed: V = V + V III II V = V + V, n, III III, out, II II, Raffnate- dran: V = V V IV III Ra = =, Ra, n, IV, out, III =, On daptve Smulated Movng ed Plants

15 Determnng Operatng ponts V I, V Ex, V, V? Ra, TS El U I,0 1 H H = K H H + H H H = K H H H K H H P, >,,0 H H = ( H H) ( 1+ K, ) + 4 H ( H + H) K K,, ( H H) ( 1 K, ) K ( H ( H + H) K, + ( H H) ) ( H + H) K, ( H H) ( + ), + ( ) P, ( H H ) F ( H H ( 1 τi) ) + + τ V = K V, I, I, F τ I, ( H H) ( H + H) V = K V V Gven: ( H H ) Ex, τ I,, Ra = τ IV, P, T S,, V ( H H ), F = 1+ F V H + H K ( ) τ, M. Fütterer, Chem. Eng. Teh., 009, I IV, 0 τ 1, Ex Ex, q El v U Ex Ex I II III IV v I II III IV Ex, P I II P, Portshftng v, s T S On daptve Smulated Movng ed Plants U Ra,, adsorpton behavor v, s IV III H = 1 + K z, Ra Ra, U Ra Ra

16 SM Plants Why ontrol? 1. robust operaton n presene of dsturbanes. mnmze runnng osts e.g. redung eluent onsumpton On daptve Smulated Movng ed Plants

17 SM Plants for omplete separaton Model the essental dynam UV- sensor mounted between two olumns of one zone keep all ontrols fxed durng one swthng tme model only the foot pont movement. tz (, ) t ( + T, z) S Ex, Ex, U Ex Ex El zone I U I zone IV UV 1 UV UV 4 5 UV 3 zone II zone III U,, 6 7 SM wth 8 olumns Ra, Ra, U Ra Ra v( k ) v( k) Δ z ( k) Δz ( k) ( t, zuv ) ( k 1) Δ z + R UV- sensor t τ T S T S M. Fütterer, Chem. Eng. Teh., 008, 31 ( 10), ( ) ( ) τ( ) S ( ) τ [ 01] ( ) ( )( 1 ( )) S ( ) Δ z k = v k k T k,, Δ z k = v k τ k T k R ( 1) ( ) Δ z k+ = Δz k ( + 1) τ( + 1) ( + 1) = ( ) 1 τ( ) S R ( ) S ( ) v k k T k v k k T k τ ( k 1) ( ) ( ) ( ) 1 τ ( ) S ( + 1) ( + 1) v k k T k + = v k T k S On daptve Smulated Movng ed Plants

18 SM Plants for omplete separaton Rename the varables to make t ne for ontrol peoples. model equatons: ( ) = ( ) = 134,,, u5 ( k) = TS ( k) ( ) = ( ) 5 ( ) y( k) = τ ( k 1) θ u( k 1) ( 1 y( k) ) ( k+ 1) = u ( k) u k V k u k u k u k y v( k) = ( k ) θ * * * = u = V TS θ = 134,,, Use a P- ontroller wth deal open loop ontrol: u k = y y k ˆ θ (, ) ( ) ˆ θ 0.5 ( ) ref = 134,,, Use a parameter estmator for model parameters: ˆ θ ˆ ˆ ( ) ( k) = θ ( k 1) + ( 1 a ) u ( k 1) y ( k) y ( k) θ a θ < 1 = 134,,, M. Fütterer, Chem. Eng. Teh., 008, 31 ( 10), On daptve Smulated Movng ed Plants

19 SM Plants for omplete separaton Smulaton Results ( ) q H = 1 + K =, feed, / [ mol/ m 3 ] ,, ( t) ( t) a ounter step dsturbane ˆ, ˆ, t step,, = ˆ = 0,5 ˆ,, t, / [ mol/ m 3 ] extrat raffnate z / [m] El 1 UV UV 3 UV UV zone I zone II zone III zone IV Ex Ra 1 El 1 UV UV 3 UV UV zone I zone II zone III zone IV Ex Ra θ 1, θ, θ 3, θ 4 / [ m 3 ] 11 x t / [ mn] t step τ I, τ II, τ III, τ IV ,, ( t) ( t) ˆ, ˆ, = ˆ,, t / [ mn] t step M. Fütterer, Pro. of the European COMSO Conf t step = 0.5 ˆ,, t T S / [ s] t / [ mn] t step On daptve Smulated Movng ed Plants

20 SM Plants for omplete separaton Control onept wth mnor a-pror knowledge. referenes More knowledge s not neessary than for operaton n open loop! ˆ I ontroller parameter ˆEx ˆV ˆRa T ˆS ˆ, ˆ, Plug and Play soluton dsturbane,, τ 1,Ref τ,ref τ 3,Ref τ 4,Ref postons of foot ponts adaptve ontroller I Ex Ra TS SM proess Ex, Ex, Ra, Ra, On daptve Smulated Movng ed Plants

21 n adaptve ontrol onept of was suessfully mplemented and tested usng Comsol Multphyss and Matlab Smulnk. Comsol s a powerful tool to model omplex dynam systems desrbed by partal dfferental equatons. Comsol s nterfae to Matlab Smulnk provdes ontrol desgners a smple way to desgn and test ontrol loop s n famlar Smulnk envronment. On daptve Smulated Movng ed Plants

22 End of Presentaton Detals an be found at Comsol s onferene CD. The full smulaton example wll be made publ for everyone. Thank You On daptve Smulated Movng ed Plants