884 XXXI International Mineral Processing Congress 2024 Proceedings/Washington, DC/Sep 29–Oct 3
the roll length, which is a key feature in HPGR operations.
The power profile is then given as:
sina
Pjl
Pl
P U 2F 2 k m
ip
j
N
k
1
B
la
=
=
/
k (15)
where Pl
k is calculated on the basis of the Fourier Transform
and allows describing profiles that vary from the common
parabolic to the trapezoidal shape profile (Campos et al.,
2021):
cos sin Pl nr e nry 4
2n
1
k
n
n
k
1
100 2 2
r =-r
=
-n /^h (16)
where n is a fitting parameter,
y
y y
2 k
k k 1 =
+
-and y N
k
k
b
=.
A breakage efficiency term (W ),which is a function
of the overall specific energy consumption, is also incorpo-
rated in Eq. (13) as is given by (Campos et al., 2021):
/Q
exp El
P
W =-c
K
m F (17)
where El is the energy densification parameter and K is a
fitting parameter.
MATERIALS AND METHODS
Industrial HPGR
The HPGR from one of the pelletizing plants from
Complexo de Tubarão from Vale S.A. (Vitória, Brazil) was
selected for investigation in the present work. The machine
has a roll diameter of 2.25 m and roll length of 1.55 m
and operates in the regrinding prior to pellet formation,
in which ball milling and classification stages are upstream
(Campos et al., 2023b). Given its large roll dimensions,
the machine faces a particular challenge by operating below
the designed capacity since the feed hopper does not allow
to keep the HPGR operating in choke fed condition,
thus driving the machine to operate with roll peripheral
velocities below the recommended value. Maximum roll
peripheral velocities for the machine investigated are set
to 1.2 m/s, which forces the machine to operate with the
minimum level allowed in the HPGR column feed as 35%.
Table 1 presents the nominal capacity and installed power
of the HPGR, as well as the operational limits for both
operating pressure and roll peripheral velocity. As briefly
discussed in the introductory section, the HPGR investi-
gated in the present work is controlled by torque regulation
with a fuzzy logic algorithm to manipulate pressure in order
to achieve the desired product Blaine specific surface area
(BSA). Further details on the machine investigated in the
present work can be found elsewhere (Campos et al., 2021
Campos et al., 2023b).
Model Implementation
The Modified Torres and Casali model (Section “Modeling
background”) was selected and implemented in Matlab ®
(version R2021a, Mathworks Inc.) for all simulations. To
investigate the application of a non–linear model predic-
tive control (NMPC) for pressing iron ore concentrates in
industrial–scale, the present work assumes that the plant
operation will be described by the Modified Torres and
Casali model. This assumption is valid given its extensive
validation on an industrial scale as a predictive tool for
pressing iron ore concentrate in both steady–state (Campos
et al., 2021) and pseudo–dynamic (Campos et al., 2023b)
operation.
Based on the model equations presented in the
“Modeling background” section, there is a key require-
ment of using the complete feed size distribution as input
to the model. A previous work by the authors (Campos et
al., 2023b) proposed and demonstrated feasibility of using
the Rosin–Rammler distribution to predict the HPGR feed
size distribution based on the BSA as:
*exp:-a W x
x
1
i
i =-
a k D (18)
where x
i is particle size, a is a fitting parameter given by
0,97 and *x is the 62.3% passing size parametrized as
(Campos et al., 2023b):
*=x BSA 126.5 0.0412
Alim #-(19)
where *x is given in µm and BSA
lim A is the Blaine spe-
cific surface area (cm2/g) of the HPGR feed.
Non-Linear Model Predictive Control Structure
Analysis of the mathematical formulation presented in the
“Modeling background” section ensures that the entire
model is a function of only two independent variables,
which are the degrees of freedom, namely operating pres-
sure (pm) and roll peripheral velocity (U). The variables that
introduce disturbances into the process and will constantly
change are, in this case, the Blaine surface area (BSA) of the
Table 1. Summary of the range of the main operating
conditions and performance variable of the HPGR
Operational Variable Value Unit
Operating pressure 40–120 bar
Roll peripheral velocity 0.8–1.2 m/s
Throughput 400–1200 t/h
Power consumption 500–3600 kW
the roll length, which is a key feature in HPGR operations.
The power profile is then given as:
sina
Pjl
Pl
P U 2F 2 k m
ip
j
N
k
1
B
la
=
=
/
k (15)
where Pl
k is calculated on the basis of the Fourier Transform
and allows describing profiles that vary from the common
parabolic to the trapezoidal shape profile (Campos et al.,
2021):
cos sin Pl nr e nry 4
2n
1
k
n
n
k
1
100 2 2
r =-r
=
-n /^h (16)
where n is a fitting parameter,
y
y y
2 k
k k 1 =
+
-and y N
k
k
b
=.
A breakage efficiency term (W ),which is a function
of the overall specific energy consumption, is also incorpo-
rated in Eq. (13) as is given by (Campos et al., 2021):
/Q
exp El
P
W =-c
K
m F (17)
where El is the energy densification parameter and K is a
fitting parameter.
MATERIALS AND METHODS
Industrial HPGR
The HPGR from one of the pelletizing plants from
Complexo de Tubarão from Vale S.A. (Vitória, Brazil) was
selected for investigation in the present work. The machine
has a roll diameter of 2.25 m and roll length of 1.55 m
and operates in the regrinding prior to pellet formation,
in which ball milling and classification stages are upstream
(Campos et al., 2023b). Given its large roll dimensions,
the machine faces a particular challenge by operating below
the designed capacity since the feed hopper does not allow
to keep the HPGR operating in choke fed condition,
thus driving the machine to operate with roll peripheral
velocities below the recommended value. Maximum roll
peripheral velocities for the machine investigated are set
to 1.2 m/s, which forces the machine to operate with the
minimum level allowed in the HPGR column feed as 35%.
Table 1 presents the nominal capacity and installed power
of the HPGR, as well as the operational limits for both
operating pressure and roll peripheral velocity. As briefly
discussed in the introductory section, the HPGR investi-
gated in the present work is controlled by torque regulation
with a fuzzy logic algorithm to manipulate pressure in order
to achieve the desired product Blaine specific surface area
(BSA). Further details on the machine investigated in the
present work can be found elsewhere (Campos et al., 2021
Campos et al., 2023b).
Model Implementation
The Modified Torres and Casali model (Section “Modeling
background”) was selected and implemented in Matlab ®
(version R2021a, Mathworks Inc.) for all simulations. To
investigate the application of a non–linear model predic-
tive control (NMPC) for pressing iron ore concentrates in
industrial–scale, the present work assumes that the plant
operation will be described by the Modified Torres and
Casali model. This assumption is valid given its extensive
validation on an industrial scale as a predictive tool for
pressing iron ore concentrate in both steady–state (Campos
et al., 2021) and pseudo–dynamic (Campos et al., 2023b)
operation.
Based on the model equations presented in the
“Modeling background” section, there is a key require-
ment of using the complete feed size distribution as input
to the model. A previous work by the authors (Campos et
al., 2023b) proposed and demonstrated feasibility of using
the Rosin–Rammler distribution to predict the HPGR feed
size distribution based on the BSA as:
*exp:-a W x
x
1
i
i =-
a k D (18)
where x
i is particle size, a is a fitting parameter given by
0,97 and *x is the 62.3% passing size parametrized as
(Campos et al., 2023b):
*=x BSA 126.5 0.0412
Alim #-(19)
where *x is given in µm and BSA
lim A is the Blaine spe-
cific surface area (cm2/g) of the HPGR feed.
Non-Linear Model Predictive Control Structure
Analysis of the mathematical formulation presented in the
“Modeling background” section ensures that the entire
model is a function of only two independent variables,
which are the degrees of freedom, namely operating pres-
sure (pm) and roll peripheral velocity (U). The variables that
introduce disturbances into the process and will constantly
change are, in this case, the Blaine surface area (BSA) of the
Table 1. Summary of the range of the main operating
conditions and performance variable of the HPGR
Operational Variable Value Unit
Operating pressure 40–120 bar
Roll peripheral velocity 0.8–1.2 m/s
Throughput 400–1200 t/h
Power consumption 500–3600 kW