Averaging Level Control of Multiple Tanks: A Passivity Based Approach
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1 Avergng Level Control of Mltple Tnks: A Pssvty Bse Approch Dnel Sbrbro Deprtment of Electrcl Engneerng, Unvers e Concepcón, Concepcón,, Chle. In collborton wth Romeo Orteg Lbortore es Sgn et Systèmes mes, SUPELEC, Gf-sr sr-yvette, rnce. UTSM-8
2 Otlne The vergng level control problem Controller esgn sng IDA-PBC Sngle tnk Csce of tnks Some smlton reslts nl remrks
3 The vergng level control problem LT o mn m The problem: n smooth otlet flow so tht the neqltes ssocte to the level re stsfe. I ths wy, the ownstrem effect of the nlet flow strbnces s mnmze.
4 The vergng level control problem Trtonl pproches: Controllers wth proportonl n ntegrl moes or smple nttvely bse nonlner controllers. Moel prectve controller, where the objectve s qntfe by the mmm rte of chnge of otlet fow for gven nlet flow strbnce sbject to level constrnts These works conser only one tnk processes, n the close-loop stblty nlyss s not consere.
5 The vergng level control problem
6 Controller esgn sng IDA-PBC The open-loop system The esre close-loop loop ( J (, R (, g ( ( J (, R (, ( ( ( ( Key mtchng eqton ( J (, R (, g ( ( T R(,
7 Controller esgn sng IDA-PBC Tght control Avergng control X* The e: To shpe the totl mss fnctons ssocte to ech tnk. or smooth otlet flow flt energy fncton ron nomnl level, wll be reqre. owever, to keep tght control ron the set pont,, energy penlzng bg errors shol be esgne.
8 Controller esgn sng IDA-PBC ( J (, R(, g( Bt s n estmte of n nknown ( J (, R (, ~ g ~
9 Controller esgn sng IDA-PBC Etene Lypnov fncton cnte W (, ~ ( ln γ ( ( τ τ ~ γ ( ( T ( ( g W T ( ( R (, (
10 kh ( f Ah t o o t o,,, ( ( ( ( m mn * φ kh ( f φ Sngle tnk Sngle tnk
11 ln(, ( * * φ kh ( f * ( * * Sngle tnk Sngle tnk ( ( ( t φ γ
12 Sngle tnk
13 Sngle tnk Splt rnge vergng level controller T t kc e e T T e < eb T e > eb τ
14 Csce of tnks LT LT LT K v K v Kv v t A h o o o f ( K v o f f ( K ( K v v h h h h h
15 Csce of tnks Csce of tnks K v v K v v K v v LT LT LT LT LT LT A K A A K A A K v v v
16 Csce of tnks Csce of tnks,,, ( ( ( ( m mn * φ ln(, ( * * φ ( ( * * *, ( α φ Tght Tght control control Avergng Avergng control control
17 Csce of tnks Csce of tnks Key mtchng eqton Key mtchng eqton ( ( ( φ γ
18 Csce of tnks Sme energy fncton for ll cells Level level smples step responses smples peroc strbnce
19 Some smlton reslts rst tnk wth vergng level strtegy n sme energy fncton for cells n Level.5 Level smples smples step responses peroc strbnce
20 Some smlton reslts Control sgnls peroc strbnce smples smples Sme energy fncton for ll cells rst tnk wth vergng level energy fncton
21 Three PI controllers. Some smlton reslts level smples smples
22 nl remrks We hve propose new pproch bse on shpng the totl mss fncton to eten the systemtc esgn of vergng controller to mlt-tnks systems. A smple emple, conserng three tnks flotton crct, hs llstrte the mn fetres of the propose pproch. tre work wll conser the nonlner chrcterstcs of the cttor, the effect of ng ecoplng n mpng to the controllers, s well s the presence of nonconstnt strbnces.
23 D. Sbrbro n R. Orteg, Avergng level control: An pproch bse on mss blnce, Jornl of Process Control, olme 7, Isse 7, Agst 7, Pges 6-69.
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