Advanced phase- and amplitude control of a coriolis mass flow meter (CMFM)

Transcription

1 Advanced phase- and ampliude conrol of a coriolis mass flow meer (CMFM) H. öck and F. Koschmieder nsiue for Auomaion and Conrol Engineering Kaisersr., D-443 Kiel, Germany hr@f.uni-kiel.de Absrac The operaion of a Coriolis Mass Flow Meer (CMFM) is dependen upon he proper oscillaion of he flow ube conrolled by drive signals generaed by a ransmier. Commonly used echniques for conrolling Coriolis meers are analogue posiive feedback which has proved adequae in convenional applicaions. n difficul siuaions however as baching o/from empy, wo phase flow or when changes in se poin are injeced o gaher diagnosic informaion [-8], more elaborae conrol sraegies are necessary o preven he meer from salling. The approach presened in he paper uses a ime varian phasor represenaion of a nd order oscillaion sysem, allowing for simulaneously conrolling ampliude and phase wihou he necessiy o chronologically separae boh of hese conrol asks. Keywords: Coriolis mass flow meer, phasor conrol. nroducion Commonly used echniques for conrolling Coriolis meers are analogue posiive feedback which has proved adequae in convenional applicaions. n difficul siuaions however [] more elaborae conrol sraegies are necessary o preven he meer from salling. n Fig. he Coriolis Mass Flow Meer CMFM and he associaed mahemaical model in erms of lumped parameers are shown. Fig.. Coriolis Mass Flow Meer CMFM and associaed mahemaical model. n wha follows, only he simulaion of he CMFM in is s eigenmode (ransfer funcion G ) is invesigaed, corresponding o a common mode simulaion via he acuaors F a and F b. The corresponding velociy signals can be measured via he sensors S and S. is well known, ha he mass flow is proporional o he phase-shif or more precisely he ime-shif beween hese harmonic velociy signals. -3

2 Conroller and Acuaor Sae and parameer Esimaor G k s s s d s Phase measuremen Fig.. Schemaic of he conrol sysem for he s eigenmode. imaginary par ( ) ( ) j ( ) m{ } () e{ } real par Fig. 3. Phasor represenaion of he oupu y ()=m{ () e jφ() }. n order o assure proper oscillaion of he CMFM in difficul siuaions when rapid changes in eigenfrequency and ampliude occur, he following conrol objecives have o be me: () on-line esimaion of he parameers d, ω, k (Fig. ) () harmonic simulaion of he oscillaion sysem in is eigenmode ω by phase/frequency conrol (3) ampliude conrol of he oupu. Phasor approach for ampliude conrol The inpu u () and he oupu y () are boh modeled as harmonic signals ha can be derived from a phasor represenaion as harmonic signals wih ime varying ampliude and phase. From he phasor represenaion we ge: y j e j () ( ) m (a) j( ) j( ) y ( ) m ( ) e j( ) e (b) y ( ) m ( ) e j( ) e (c) j ( ) j( ) sing he phasor represenaion u j e j () ( ) m () for he sysem inpu, we can ransform he differenial equaion of he oscillaion sysem y ( ) d y y ( ) k u ( ) (3) ino an equivalen phasor represenaion given by d ( d ) k d d A A Now i is easy o conrol he phasor ampliude wih a predescribed dynamics (rajecory conrol) W Trajecory Generaor M A M A M kw + s Trajecory () + Oscillaion wih Conroller Sysem W W W (6) Fig. 4. DOF rajecory conrol of he CMFM. (4) -4

3 represening he reference for he real- and imaginary par of he phasor oupu. The implemenaion is done using a DOF-Srucure [7]. As A and A are depending on and, he conrol is ime varian. 3. Phase and frequency conrol To mee he conrol objecive, i.e. simulaion of he oscillaion sysem in is eigenfrequency we have o measure he phase shif beween inpu and oupu imaginary and se up a conrol law for he momenary frequency par. sing a simple P- Conroller, we ge: real par Kp () d T (7a) par Fig.. Phase shif beween he phasor signal and where () represens a normalized phase-shif. As he phase-shif is only defined in seady sae and no during ransiens, we have o derive an equivalen measuremen (cf. ). The oscillaion sysem is operaed in is eigenfrequency, when. For we ge he relaion (8) sing normalized signals ; ; ; ; we define he normalized phase shif () as follows () (9) 4. Kalman-filer The DOF conrol can only be implemened if esimaes of he real- and imaginary pars of he phasors ogeher wih heir derivaes are provided. sing an exended Kalman-Filer for he nd order ime varying sysem G (s) X X X X X d d X X d d X ogeher wih he measuremen equaion y M ( ) sin cos X X X X we can esimae boh he saes i.e. he real- and imaginary pars of he phasors and heir derivaives as well as he model parameers k, d,. () -

4 drive ampliude [V] drive ampliude [V] oupu ampliude [V] oupu ampliude [V] normalized phasor error frequency conrol normalized drive ampliude normalized signal imaginary par normalized oupu ampliude normalized drive ampliude. Simulaion To show he performance of he proposed conrol scheme, a nd order oscillaion sysem (Fig. ) is simulaed (nominal parameers ω =., d = -, k = ). A sar-up here is a difference of abou % in he acual parameers compared o he nominal parameers. Figs. 7 - y () u () () () Fig. 7. Sar-up and sep change in ampliude. Fig. 8. Phasor descripion of y ().. -. () () B Fig. 9. Adjusing he drive frequency from sar-up.. ω B drive frequency ωb [rad/s] pure Waer wo phase flow ca. 4% (GVF) pure Waer resonan frequency ωb [rad/s] 9 air waer Fig.. Oupu wih/wihou 4% gas void fracion (GVF) Fig.. Two phase flow (Bach experimen empy o full). -6

5 and 8 show he performance of ampliude conrol in erms of ime signals as well as phasor signals. As he oscillaion sysem has o be operaed in is eigenfrequency ω, i.e. =, he frequency of he harmonic drive signalb has o be adjused o he a priori unknown frequency ω. Figure 9 shows he performance of phase/frequency conrol. The conrol of a real CMFM according o he proposed conrol scheme is given in Figs. and. As commercial meers ofen sall in siuaions wih wo phase flow, he ransiion from waer o wo phase flow is invesigaed. Due o he increased damping during wo phase flow, he drive ampliude shows dramaic changes in ampliude, whereas he ampliude of he oupu is consan if we neglec he small seady sae error ha will disappear if inegral acion is provided. The adjusmen of he drive frequency B o he eigenfrequency in case of wo phase flow is also very fas. n a furher bach experimen he ransiion from empy o full is invesigaed. During he ransiion he damping increases rapidly if flow eners he empy ube and decreases if he ube is filled up. As he driver oupu is bounded he ampliude of oscillaion decreases as well, bu reaches is se-poin again when he meer is filled up. Furher invesigaions, regarding he accuracy of he meer wih he proposed conrol scheme in siuaions wih wo phase flow have o be carried ou. eferences. M. Henry, M. Tombs, and H. eung. Coriolis Meer in Two Phase Flow. h nernaional Conference on Muliphase Producion Technology, Barcelona.... Sorm, K. Kolahi and H. öck. Model Based Correcion of Coriolis Mass Flow Meers. 8 h EEE nsrumenaion and Measuremen Technology Conference, Budapes, Hungary. -3 May, vol., pp. 3-36; and EEE nsrumenaion and Measuremen. Augus, vol., No. 4, pp K. Kolahi,. Sorm and H. öck. Deecion of Zero Shif in Coriolis Mass Flow Meers. Proc. of he XV MEKO World Congress. Ausria. -8 Sepember, vol. V, pp T. Schröder. Modellgesüze Online-Selbsdiagnose bei einem Coriolis- Massendurchflussmesser mi einem einzigen geraden Messrohr (Model Based Online Self- Diagnosis of a Coriolis Mass Flow Meer wih a Single Sraigh Pipe). Disseraion, nsiue for Auomaion and Conrol Engineering, Chrisian-Albrechs-niversiy of Kiel. February 6 (in German).. K. Kolahi and H. öck. Densiy and Pressure Measuremen wih Coriolis Mass Flow meers. nernaional Conference on nsrumenaion, Communicaion and nformaion Technology (CC), ndonesia. 3- Augus. 6. T. Schröder, K. Kolahi and H. öck. Modellgesüze egelung eines Coriolis- Massendurchflussmessers. GMA/ TG Fachagung Sensoren und Messsyseme 4, Tagungsband (VD-Beriche), Ludwigsburg. -6 March 4, pp. 6-7 (in German). 7. H. öck, T. Schröder, K. Kolahi and F. Koschmieder. Flaness-Based Conrol of a Coriolis Mass Flow Meer. Proc. SMT 7, Sendai, Japan F. Koschmieder and H. öck. Besimmung charakerisischer Größen eines CMD im laufenden Berieb durch Anwendung der Zeigerregelung. GMA/ TG Fachagung Sensoren und Messsyseme 8, Tagungsband (VD-Beriche) Ludwigsburg. - March 8, pp. 6-7 (in German). -7