570
M. Spinola et al.
Fig. 13 Graphical
illustration of the grade
efficiency function of screen
1 and screen 2
Where μ in and μ out , respectively, denote the mean particle size of the input and output
stream of the crusher and ˙
m is the incoming mass flow. In the definition of μ out it
is ensured that it cannot reach arbitrary small values which is equivalent to set an
appropriate upper bound on the milling power depending on the incoming mass flow
and incoming mean particle size. By assuming a uniform crushing of the particles
and considering the conservation of mass, q crush,3 can be obtained as follows:
∞
x min
q crush,3 (P(t), t, x) dx = 0.1
∞
x min
1 (x)q 3 (t, x) dx
Such that it leads to the subsequent representation of q crush :
q crush (P(t), t, x) = 0.1
μ in (t)
μ out (t)
1
x
μ in (t)
μ out (t)
q
t, x
μ in (t)
μ out (t)
.
Eventually, together with the introduced terms this leads to the following representation of the optimization problem considered in this example:
M. Spinola et al.
Fig. 13 Graphical
illustration of the grade
efficiency function of screen
1 and screen 2
Where μ in and μ out , respectively, denote the mean particle size of the input and output
stream of the crusher and ˙
m is the incoming mass flow. In the definition of μ out it
is ensured that it cannot reach arbitrary small values which is equivalent to set an
appropriate upper bound on the milling power depending on the incoming mass flow
and incoming mean particle size. By assuming a uniform crushing of the particles
and considering the conservation of mass, q crush,3 can be obtained as follows:
∞
x min
q crush,3 (P(t), t, x) dx = 0.1
∞
x min
1 (x)q 3 (t, x) dx
Such that it leads to the subsequent representation of q crush :
q crush (P(t), t, x) = 0.1
μ in (t)
μ out (t)
1
x
μ in (t)
μ out (t)
q
t, x
μ in (t)
μ out (t)
.
Eventually, together with the introduced terms this leads to the following representation of the optimization problem considered in this example: