1. CIMExcel Software Inc. Slide 1 Flotation Cell Levels – Nonlinear Model Reference Modal Control

2. CIMExcel Software Inc. Slide 2 Flotation Cell Levels - Nonlinear Model Reference Modal Control Q air 1 Q in S in L1L1 V1V1 U1U1 Q air i LiLi ViVi UiUi Q air n ρnρn LnLn VnVn UnUn z1z1 zizi ρiρi ρ1ρ1 note, hysteresis (backlash) is included V i = valve position U i = valve positioner

3. CIMExcel Software Inc. Slide 3 Flotation Cell Levels - Nonlinear Model Reference Modal Control Q slurry in ÷ f i -1 () Hysteresis Compensator valve position V j Feedforward Dynamic Observer PI actuator positioner U j Level Setpoints Operator Fixed Feed Dependent Startup/Shutdown Level i Q air i Solids in Level i Q air i LiLi + - + +

4. Flotation Cell Levels - Nonlinear Model Reference Modal Control operator cell level setpoint changes CIMExcel Software Inc. Slide 4 time scale: 10 minutes per division, 100 minutes

5. Flotation Cell Levels - Nonlinear Model Reference Modal Control feed flow dependent cell level setpoint mode CIMExcel Software Inc. Slide 5 time scale: 10 minutes per division, 100 minutes

6. Flotation Cell Levels - Nonlinear Model Reference Modal Control froth pushup mode CIMExcel Software Inc. Slide 6 time scale: 10 minutes per division, 100 minutes

7. Flotation Cell Levels - Nonlinear Model Reference Modal Control shutdown – startup mode CIMExcel Software Inc. Slide 7 time scale: 10 minutes per division, 100 minutes

8. Flotation Cell Levels - Nonlinear Model Reference Modal Control excellent cell level control during variable feed flow, solids, and air flow CIMExcel Software Inc. Slide 8 time scale: 10 minutes per division, 100 minutes

9. CIMExcel Software Inc. Slide 9 Flotation Cell Level Dynamics d/dt V 1 = A 1 d/dt L 1 = d/dt V a1 + d/dt V p1 A 1 d/dt L 1 = d/dt V a1 + Q in - Q 1out = d/dt V a1 + Q in - α 1 f 1 (V 1 )(ρ 1 L 1 + ρ 1 z 1 - ρ 2 L 2 ) 0.5 A i d/dt L i = d/dt V ai + Q i-1out - Q iout = d/dt V ai + α i-1 f i-1 (V i-1 )(ρ i-1 L i-1 + ρ i-1 z i-1 - ρ i L i ) 0.5 - α i f i (V i )(ρ i L i + ρ i z i - ρ i+1 L i+1 ) 0.5 A n d/dt L n = d/dt V an + Q n-1out - Q nout = d/dt V an + α n-1 f n-1 (V n-1 )(ρ n-1 L n-1 + ρ n-1 z n-1 - ρ n L n ) 0.5 - α n f n (V n )(ρ n L n ) 0.5 α 1, α i, α n constants. L 1, L i, L n from bottom of tank. z 1 = tank 1 – tank 2 elevations. z i = tank i - tank i+1 elevations. z n = 0. Q 1out = Q in + d/dt V a1 - A 1 d/dt L 1 = α 1 f 1 (V 1 )(ρ 1 L 1 + ρ 1 z 1 - ρ 2 L 2 ) 0.5 Q 2out = Q 1out + d/dt V a2 - A 2 d/dt L 2 = Q in + d/dt V a1 + d/dt V a2 - A 1 d/dt L 1 - A 2 d/dt L 2 Q iout = Q in + ∑ j=1 i (d/dt V aj - A j d/dt L j ) = α i f i (V i )(ρ i L i + ρ i z i - ρ i+1 L i+1 ) 0.5 Q nout = Q in + ∑ j=1 n (d/dt V aj - A j d/dt L j ) = α n f n (V n )(ρ n L n ) 0.5

10. CIMExcel Software Inc. Slide 10 Flotation Cell Level Dynamics solids: τ s1 d/dt S 1 = S in - S 1 τ si d/dt S i = S i-1 - S i τ sn d/dt S n = S n-1 - S n solids time constant: τ s1 = ρ 1 V 1 / ρ in Q in τ si = ρ i V i / ρ s i-1 Q i-1 τ sn = ρ n V n / ρ s n-1 Q n-1 slurry density from solids: ρ s1 = ρ ore / ( S 1 + (ρ ore /ρ water )(1 - S 1 ) ) Ρ s i = ρ ore / ( S i + (ρ ore /ρ water )(1 - S i ) ) ρ sn = ρ ore / ( S n + (ρ ore /ρ water )(1 - S n ) ) cell density: ρ 1 = ρ s1 (1 - f 1 ) ρ i = ρ si (1 - f i ) ρ n = ρ sn (1 - f n )

11. CIMExcel Software Inc. Slide 11 Flotation Cell Level Dynamics cell air: f = void fraction τ ar i = cell average rise time (s) a ffi = cell averaged void fraction - air flow factor 0.5 τ ar 1 d/dt f 1 = a ff1 Q ain1 - f 1 0.5 τ ar i d/dt f i = a ffi Q ain i - f i 0.5 τ ar n d/dt f n = a ffn Q ain n - f n V ai = V i f i = A i L i f i d/dt V a1 = 2 A 1 L 1 (a ff1 Q ain1 - f 1 ) / τ ar 1 d/dt V ai = 2 A i L i (a ffi Q aini - f i ) / τ ar i d/dt V an = 2 A n L n (a ffn Q ainn - f n ) / τ ar n

12. Flotation Cell Level Dynamics – Identification Mode valve perturbations CIMExcel Software Inc. Slide 12 time scale: 1 minute per division, 10 minutes

13. Flotation Cell Level Dynamics – Identification Mode air valve perturbations CIMExcel Software Inc. Slide 13 time scale: 1 minute per division, 10 minutes

14. Flotation Cell Level Dynamics – Identification Mode long term feed flow perturbations CIMExcel Software Inc. Slide 14 time scale: 10 minutes per division, 100 minutes

15. Flotation Cell Level Dynamics – Identification Mode feed flow perturbations CIMExcel Software Inc. Slide 15 time scale: 10 minutes per division, 100 minutes

16. Flotation Cell Level Dynamics – Identification Mode air flow perturbations CIMExcel Software Inc. Slide 16 time scale: 10 minutes per division, 100 minutes

17. Flotation Cell Level Dynamics - Identification Mode feed solids perturbations CIMExcel Software Inc. Slide 17 time scale: 10 minutes per division, 100 minutes