CIMExcel Software Inc. Slide 1

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Flotation Cell Levels – Nonlinear Model Reference Modal Control. CIMExcel Software Inc. Slide 1. Flotation Cell Levels - Nonlinear Model Reference Modal Control. Q air 1. L 1. Q air i. ρ 1. U 1. L i. Q air n. Q in. V 1. ρ i. S in. U i. z 1. L n. V i. ρ n. U n. z i. V n. - PowerPoint PPT Presentation

Transcript of CIMExcel Software Inc. Slide 1

  • CIMExcel Software Inc. Slide *Flotation Cell Levels Nonlinear Model Reference Modal Control

  • CIMExcel Software Inc. Slide *Flotation Cell Levels - Nonlinear Model Reference Modal ControlQair 1 QinSinL1V1U1Qair i LiViUiQair n nLnVnUnz1zii1note, hysteresis (backlash) is included

    Vi = valve position

    Ui = valve positioner

  • CIMExcel Software Inc. Slide *Flotation Cell Levels - Nonlinear Model Reference Modal ControlQslurry in fi-1() HysteresisCompensator valve positionVjFeedforwardDynamic ObserverPI actuator positionerUjLevel Setpoints Operator Fixed Feed Dependent Startup/Shutdown LeveliQair i SolidsinLeveliQair i Li+-++

  • Flotation Cell Levels - Nonlinear Model Reference Modal Controloperator cell level setpoint changes CIMExcel Software Inc. Slide *time scale: 10 minutes per division, 100 minutes

  • Flotation Cell Levels - Nonlinear Model Reference Modal Controlfeed flow dependent cell level setpoint mode CIMExcel Software Inc. Slide *time scale: 10 minutes per division, 100 minutes

  • Flotation Cell Levels - Nonlinear Model Reference Modal Controlfroth pushup mode CIMExcel Software Inc. Slide *time scale: 10 minutes per division, 100 minutes

  • Flotation Cell Levels - Nonlinear Model Reference Modal Controlshutdown startup mode CIMExcel Software Inc. Slide *time scale: 10 minutes per division, 100 minutes

  • Flotation Cell Levels - Nonlinear Model Reference Modal Controlexcellent cell level control during variable feed flow, solids, and air flow CIMExcel Software Inc. Slide *time scale: 10 minutes per division, 100 minutes

  • CIMExcel Software Inc. Slide *Flotation Cell Level Dynamics

    d/dt V1 = A1 d/dt L1 = d/dt Va1 + d/dt Vp1

    A1 d/dt L1 = d/dt Va1 + Qin - Q1out = d/dt Va1 + Qin - 1 f1(V1)(1L1 + 1z1 - 2L2 )0.5 Ai d/dt Li = d/dt Vai + Qi-1out - Qiout = d/dt Vai + i-1 fi-1(Vi-1)(i-1Li-1 + i-1zi-1 - iLi )0.5 - i fi(Vi)(iLi + izi - i+1Li+1 )0.5

    An d/dt Ln = d/dt Van + Qn-1out - Qnout = d/dt Van + n-1 fn-1(Vn-1)(n-1Ln-1 + n-1zn-1 - nLn )0.5 - n fn(Vn)(nLn )0.5

    1 , i , n constants. L1 , Li , Ln from bottom of tank. z1 = tank 1 tank 2 elevations. zi = tank i - tank i+1 elevations. zn = 0.

    Q1out = Qin + d/dt Va1 - A1 d/dt L1 = 1 f1(V1)(1L1 + 1z1 - 2L2 )0.5

    Q2out = Q1out + d/dt Va2 - A2 d/dt L2 = Qin + d/dt Va1 + d/dt Va2 - A1 d/dt L1 - A2 d/dt L2

    Qiout = Qin + j=1i (d/dt Vaj - Aj d/dt Lj) = i fi(Vi)(iLi + izi - i+1Li+1 )0.5

    Qnout = Qin + j=1n (d/dt Vaj - Aj d/dt Lj) = n fn(Vn)(nLn )0.5

  • CIMExcel Software Inc. Slide *Flotation Cell Level Dynamicssolids:s1 d/dt S1 = Sin - S1si d/dt Si = Si-1 - Sisn d/dt Sn = Sn-1 - Sn

    solids time constant:s1 = 1 V1 / in Qinsi = i Vi / s i-1 Qi-1sn = n Vn / s n-1 Qn-1

    slurry density from solids:

    s1 = ore / ( S1 + (ore/water)(1 - S1) )s i = ore / ( Si + (ore/water)(1 - Si) )sn = ore / ( Sn + (ore/water)(1 - Sn) )

    cell density:

    1 = s1 (1 - f1 ) i = si (1 - fi ) n = sn (1 - fn )

  • CIMExcel Software Inc. Slide *Flotation Cell Level Dynamicscell air:

    f = void fractionar i = cell average rise time (s)affi = cell averaged void fraction - air flow factor

    0.5 ar 1 d/dt f1 = aff1 Qain1 - f10.5 ar i d/dt fi = affi Qain i - fi0.5 ar n d/dt fn = affn Qain n - fn

    Vai = Vi fi = Ai Li fi

    d/dt Va1 = 2 A1 L1 (aff1Qain1 - f1) / ar 1d/dt Vai = 2 Ai Li (affiQaini - fi) / ar id/dt Van = 2 An Ln (affnQainn - fn) / ar n

  • Flotation Cell Level Dynamics Identification Mode valve perturbations CIMExcel Software Inc. Slide *time scale: 1 minute per division, 10 minutes

  • Flotation Cell Level Dynamics Identification Mode air valve perturbations CIMExcel Software Inc. Slide *time scale: 1 minute per division, 10 minutes

  • Flotation Cell Level Dynamics Identification Mode long term feed flow perturbations CIMExcel Software Inc. Slide *time scale: 10 minutes per division, 100 minutes

  • Flotation Cell Level Dynamics Identification Mode feed flow perturbations CIMExcel Software Inc. Slide *time scale: 10 minutes per division, 100 minutes

  • Flotation Cell Level Dynamics Identification Mode air flow perturbations CIMExcel Software Inc. Slide *time scale: 10 minutes per division, 100 minutes

  • Flotation Cell Level Dynamics - Identification Mode feed solids perturbations CIMExcel Software Inc. Slide *time scale: 10 minutes per division, 100 minutes

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