XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3 885
HPGR feed and the breakage behavior of the blend feeding
the process (Campos et al., 2023b). Considering the goal
of the study to reduce the variability of the HPGR product
BSA based on the variabilities (disturbances) imposed by its
feed, while still maintaining product quality and machine
throughput, the NMPC structure was adopted and imple-
mented following the block diagram in Matlab/Simulink as
shown in Figure 1. The main structure followed a nonlin-
ear model predictive control (NMPC) framework, which
calculates optimal control moves over the prediction hori-
zon using a nonlinear prediction model and a nonlinear
cost (objective) function. This approach was chosen in the
present study to avoid the use of linear model predictive
control (MPC), given the highly nonlinear nature of the
process. Figure 1 presents the red box as the setpoint of ref-
erence, while light green boxes are the controlled variables,
orange boxes the manipulated variables and dark green
boxes the process states that are not controlled. The HPGR
icon represents the plant operation, while the controller is
represented by the purple box. The red square on the bot-
tom right shows the HPGR feed BSA as the disturbance of
the process.
The NMPC then relies on two predicted states, which
are also the two controlled variables, given by the HPGR
product BSA and throughput. Operating pressure (pm)
and roller peripheral velocity (U) are the manipulated
variables, while the measured disturbance is the BSA of
the feed (BSAAlim). Operating gap, as demonstrated in
Section “Modeling background” should be considered as
model response (Eq. (9)). The present work then considers
the model sampling time (Ts) of 1 s, while the control and
prediction horizons are defined according to the HPGR
dynamics in Section “Results and discussions.” Sampling
time of 1s, even though small when compared to the real
sampling of the feed BSA (Campos et al., 2023a), was
selected to ensure a proper response based on the control
actions. In the context of this work, given the steady-state
nature of the Modified Torres and Casali model (Campos
et al., 2021 Campos et al., 2023b), it is assumed that the
mathematical model updates at discrete time intervals, in
which all simulations were performed considering a dis-
crete-time model.
The NMPC structure as presented requires a cost
(objective) function to define the optimal trajectory that
will be achieved based on the plant conditions and model
prediction. The present work proposes a customized cost
function (objective) as presented in Eq. (20). The function
uses the reference values that must be achieved (setpoints)
for the product BSA (BSARef) and for the throughput
(QRef), thus using the least squares method to find the opti-
mal set of operating conditions that will allow absorbing
the disturbances in the feed (HPGR feed BSA). Given the
differences in magnitude between the values of both vari-
ables used in Eq. (20), normalization to the reference value
Figure 1. Schematic diagram of the NMPC structure implemented in Matlab/Simulink
HPGR feed and the breakage behavior of the blend feeding
the process (Campos et al., 2023b). Considering the goal
of the study to reduce the variability of the HPGR product
BSA based on the variabilities (disturbances) imposed by its
feed, while still maintaining product quality and machine
throughput, the NMPC structure was adopted and imple-
mented following the block diagram in Matlab/Simulink as
shown in Figure 1. The main structure followed a nonlin-
ear model predictive control (NMPC) framework, which
calculates optimal control moves over the prediction hori-
zon using a nonlinear prediction model and a nonlinear
cost (objective) function. This approach was chosen in the
present study to avoid the use of linear model predictive
control (MPC), given the highly nonlinear nature of the
process. Figure 1 presents the red box as the setpoint of ref-
erence, while light green boxes are the controlled variables,
orange boxes the manipulated variables and dark green
boxes the process states that are not controlled. The HPGR
icon represents the plant operation, while the controller is
represented by the purple box. The red square on the bot-
tom right shows the HPGR feed BSA as the disturbance of
the process.
The NMPC then relies on two predicted states, which
are also the two controlled variables, given by the HPGR
product BSA and throughput. Operating pressure (pm)
and roller peripheral velocity (U) are the manipulated
variables, while the measured disturbance is the BSA of
the feed (BSAAlim). Operating gap, as demonstrated in
Section “Modeling background” should be considered as
model response (Eq. (9)). The present work then considers
the model sampling time (Ts) of 1 s, while the control and
prediction horizons are defined according to the HPGR
dynamics in Section “Results and discussions.” Sampling
time of 1s, even though small when compared to the real
sampling of the feed BSA (Campos et al., 2023a), was
selected to ensure a proper response based on the control
actions. In the context of this work, given the steady-state
nature of the Modified Torres and Casali model (Campos
et al., 2021 Campos et al., 2023b), it is assumed that the
mathematical model updates at discrete time intervals, in
which all simulations were performed considering a dis-
crete-time model.
The NMPC structure as presented requires a cost
(objective) function to define the optimal trajectory that
will be achieved based on the plant conditions and model
prediction. The present work proposes a customized cost
function (objective) as presented in Eq. (20). The function
uses the reference values that must be achieved (setpoints)
for the product BSA (BSARef) and for the throughput
(QRef), thus using the least squares method to find the opti-
mal set of operating conditions that will allow absorbing
the disturbances in the feed (HPGR feed BSA). Given the
differences in magnitude between the values of both vari-
ables used in Eq. (20), normalization to the reference value
Figure 1. Schematic diagram of the NMPC structure implemented in Matlab/Simulink