XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 89
CONCLUDING REMARKS
This work discusses an E-MPC strategy for flotation using
a novel dynamic model that considers froth physics. The
strategy is validated in a laboratory-scale flotation cell. The
results of the experiments reveal that the E-MPC approach
leads to higher metallurgical recoveries while it also has
potential to handle feed flowrate disturbances efficiently.
The results are encouraging for further research to be car-
ried out to validate the E-MPC strategy in a laboratory-
scale flotation bank, and then at industrial-scale.
REFERENCES
Andersson, J. A. E., Gillis, J., Horn, G., Rawlings, J. B.,
&Diehl, M. (2019). CasADi: a software framework
for nonlinear optimization and optimal control.
Mathematical Programming Computation, 11, 1–36.
doi: 10.1007/s12532-018-0139-4.
Ellis, M., Durand, H., &Christofides, P. D. (2014). A
tutorial review of economic model predictive control
methods. Journal of Process Control, 24(8), 1156–1178.
doi: 10.1016/j.jprocont.2014.03.010.
Ferreira, J. P., &Loveday, B. K. (2000). An improved
model for simulation of flotation circuits. Minerals
Engineering, 13(14–15), 1441–1453. doi: 10.1016
/S0892-6875(00)00129-1.
Maldonado, M., Sbarbaro, D., &Lizama, E. (2007).
Optimal control of a rougher flotation pro-
cess based on dynamic programming. Minerals
Engineering, 20(3), 221–232. doi: 10.1016/j.mineng
.2006.08.015.
Oosthuizen, D. J., le Roux, J. D., &Craig, I. K.
(2021). A dynamic flotation model to infer pro-
cess characteristics from online measurements.
Minerals Engineering, 167, 106878. doi: 10.1016
/j.mineng.2021.106878.
Perez-Correa, R., Gonzalez, G., Casali, A., Cipriano, A.,
Barrera, R., &Zavala, E. (1998). Dynamic modelling
and advanced multivariable control of conventional flota-
tion circuits. 11(4), 333–346.
Putz, E., &Cipriano, A. (2015). Hybrid model pre-
dictive control for flotation plants. Minerals
Engineering, 70, 26–35. doi: 10.1016
/j.mineng.2014.08.013.
30
32
34
36
38
40
0 2 4 6 8 10 12 14 16 18 20
Time [min]
0
20
40
60
80
Figure 4. Level control using tail flowrates (Q
tails ).Red lines are set points from E-MPC optimisation, and blue lines are
filtered pulp height (hp) in process
h p
[cm]
Q
tails
[lpm]
CONCLUDING REMARKS
This work discusses an E-MPC strategy for flotation using
a novel dynamic model that considers froth physics. The
strategy is validated in a laboratory-scale flotation cell. The
results of the experiments reveal that the E-MPC approach
leads to higher metallurgical recoveries while it also has
potential to handle feed flowrate disturbances efficiently.
The results are encouraging for further research to be car-
ried out to validate the E-MPC strategy in a laboratory-
scale flotation bank, and then at industrial-scale.
REFERENCES
Andersson, J. A. E., Gillis, J., Horn, G., Rawlings, J. B.,
&Diehl, M. (2019). CasADi: a software framework
for nonlinear optimization and optimal control.
Mathematical Programming Computation, 11, 1–36.
doi: 10.1007/s12532-018-0139-4.
Ellis, M., Durand, H., &Christofides, P. D. (2014). A
tutorial review of economic model predictive control
methods. Journal of Process Control, 24(8), 1156–1178.
doi: 10.1016/j.jprocont.2014.03.010.
Ferreira, J. P., &Loveday, B. K. (2000). An improved
model for simulation of flotation circuits. Minerals
Engineering, 13(14–15), 1441–1453. doi: 10.1016
/S0892-6875(00)00129-1.
Maldonado, M., Sbarbaro, D., &Lizama, E. (2007).
Optimal control of a rougher flotation pro-
cess based on dynamic programming. Minerals
Engineering, 20(3), 221–232. doi: 10.1016/j.mineng
.2006.08.015.
Oosthuizen, D. J., le Roux, J. D., &Craig, I. K.
(2021). A dynamic flotation model to infer pro-
cess characteristics from online measurements.
Minerals Engineering, 167, 106878. doi: 10.1016
/j.mineng.2021.106878.
Perez-Correa, R., Gonzalez, G., Casali, A., Cipriano, A.,
Barrera, R., &Zavala, E. (1998). Dynamic modelling
and advanced multivariable control of conventional flota-
tion circuits. 11(4), 333–346.
Putz, E., &Cipriano, A. (2015). Hybrid model pre-
dictive control for flotation plants. Minerals
Engineering, 70, 26–35. doi: 10.1016
/j.mineng.2014.08.013.
30
32
34
36
38
40
0 2 4 6 8 10 12 14 16 18 20
Time [min]
0
20
40
60
80
Figure 4. Level control using tail flowrates (Q
tails ).Red lines are set points from E-MPC optimisation, and blue lines are
filtered pulp height (hp) in process
h p
[cm]
Q
tails
[lpm]