Post on 11-Jan-2016
description
CIMExcel Software Inc. Slide 1
Flotation Cell Levels – Nonlinear Model Reference Modal Control
CIMExcel Software Inc. Slide 2
Flotation Cell Levels - Nonlinear Model Reference Modal Control
Qair 1
Qin
Sin
L1
V1
U1
Qair i
Li
Vi
Ui
Qair n
ρn
Ln
Vn
Un
z1
zi
ρi
ρ1
note, hysteresis (backlash) is included
Vi = valve position
Ui = valve positioner
CIMExcel Software Inc. Slide 3
Flotation Cell Levels - Nonlinear Model Reference Modal Control
Qslurry in
÷ fi-1()
HysteresisCompensator
valve position
Vj
Feedforward
Dynamic Observer
PI
actuator positioner
Uj
Level Setpoints
• Operator Fixed• Feed Dependent• Startup/Shutdown
Leveli
Qair i
Solidsin
Leveli
Qair i
Li
+
-
++
Flotation Cell Levels - Nonlinear Model Reference Modal Controloperator cell level setpoint changes
CIMExcel Software Inc. Slide 4
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 5
time scale: 10 minutes per division, 100 minutes
Flotation Cell Levels - Nonlinear Model Reference Modal Controlfroth pushup mode
CIMExcel Software Inc. Slide 6
time scale: 10 minutes per division, 100 minutes
Flotation Cell Levels - Nonlinear Model Reference Modal Controlshutdown – startup mode
CIMExcel Software Inc. Slide 7
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 8
time scale: 10 minutes per division, 100 minutes
CIMExcel Software Inc. Slide 9
Flotation Cell Level Dynamicsd/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 - α1 f1(V1)(ρ1L1 + ρ1z1 - ρ2L2 )0.5
Ai d/dt Li = d/dt Vai + Qi-1out - Qiout = d/dt Vai + αi-1 fi-1(Vi-1)(ρi-1Li-1 + ρi-1zi-1 - ρiLi )0.5 - αi fi(Vi)(ρiLi + ρizi - ρi+1Li+1 )0.5
An d/dt Ln = d/dt Van + Qn-1out - Qnout = d/dt Van + αn-1 fn-1(Vn-1)(ρn-1Ln-1 + ρn-1zn-1 - ρnLn )0.5 - αn fn(Vn)(ρnLn )0.5
α1 , αi , αn 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
= α1 f1(V1)(ρ1L1 + ρ1z1 - ρ2L2 )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)
= αi fi(Vi)(ρiLi + ρizi - ρi+1Li+1 )0.5
Qnout = Qin + ∑j=1n (d/dt Vaj - Aj d/dt Lj)
= αn fn(Vn)(ρnLn )0.5
CIMExcel Software Inc. Slide 10
Flotation Cell Level Dynamicssolids:τs1 d/dt S1 = Sin - S1
τsi d/dt Si = Si-1 - Si
τsn d/dt Sn = Sn-1 - Sn
solids time constant:τs1 = ρ1 V1 / ρin Qin
τsi = ρi Vi / ρs i-1 Qi-1
τsn = ρn Vn / ρs n-1 Qn-1
slurry density from solids:
ρs1 = ρore / ( S1 + (ρore/ρwater)(1 - S1) )Ρs i = ρore / ( Si + (ρore/ρwater)(1 - Si) )ρsn = ρore / ( Sn + (ρore/ρwater)(1 - Sn) )
cell density:
ρ1 = ρs1 (1 - f1 ) ρi = ρsi (1 - fi ) ρn = ρsn (1 - fn )
CIMExcel Software Inc. Slide 11
Flotation Cell Level Dynamicscell air:
f = void fraction
τar i = cell average rise time (s)affi = cell averaged void fraction - air flow factor
0.5 τar 1 d/dt f1 = aff1 Qain1 - f1
0.5 τar i d/dt fi = affi Qain i - fi
0.5 τar n d/dt fn = affn Qain n - fn
Vai = Vi fi = Ai Li fi
d/dt Va1 = 2 A1 L1 (aff1Qain1 - f1) / τar 1
d/dt Vai = 2 Ai Li (affiQaini - fi) / τar i
d/dt Van = 2 An Ln (affnQainn - fn) / τar n
Flotation Cell Level Dynamics – Identification Mode valve perturbations
CIMExcel Software Inc. Slide 12
time scale: 1 minute per division, 10 minutes
Flotation Cell Level Dynamics – Identification Mode air valve perturbations
CIMExcel Software Inc. Slide 13
time scale: 1 minute per division, 10 minutes
Flotation Cell Level Dynamics – Identification Mode long term feed flow perturbations
CIMExcel Software Inc. Slide 14
time scale: 10 minutes per division, 100 minutes
Flotation Cell Level Dynamics – Identification Mode feed flow perturbations
CIMExcel Software Inc. Slide 15
time scale: 10 minutes per division, 100 minutes
Flotation Cell Level Dynamics – Identification Mode air flow perturbations
CIMExcel Software Inc. Slide 16
time scale: 10 minutes per division, 100 minutes
Flotation Cell Level Dynamics - Identification Mode feed solids perturbations
CIMExcel Software Inc. Slide 17
time scale: 10 minutes per division, 100 minutes