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M. Spinola et al.
Fig. 8 Obtained process parameters u G (a) and u in (b) during optimization with d(u G ) = d(u in )
of discretization points together with the optimal ones illustrated in red, respectively. Generated
PSDs q(t f , ·) at the final time for d(u G ) = d(u in ) together with the monomodal target q d (c) and
the surface plot of the resulting optimal solution (d)
in [51–55], the transformation of monomodal PSDs into bimodal distributions is a
technically relevant issue. Since only the target PSD changes whereas the rest of the
setting remains untouched, the here presented gradient-based optimization scheme
can be used to obtain optimal process conditions despite the fact that there is a distinct
difference in the shape of the inflow PSD q in and the target PSD q d .
Figure 9 shows, analogously to Fig. 8, the optimal process conditions, the final
PSDs together with the target PSD q d for different (d(u G ), d(u in )) and the surface
plot of optimal PSD q. Also here time-varying optimization parameters and thus
M. Spinola et al.
Fig. 8 Obtained process parameters u G (a) and u in (b) during optimization with d(u G ) = d(u in )
of discretization points together with the optimal ones illustrated in red, respectively. Generated
PSDs q(t f , ·) at the final time for d(u G ) = d(u in ) together with the monomodal target q d (c) and
the surface plot of the resulting optimal solution (d)
in [51–55], the transformation of monomodal PSDs into bimodal distributions is a
technically relevant issue. Since only the target PSD changes whereas the rest of the
setting remains untouched, the here presented gradient-based optimization scheme
can be used to obtain optimal process conditions despite the fact that there is a distinct
difference in the shape of the inflow PSD q in and the target PSD q d .
Figure 9 shows, analogously to Fig. 8, the optimal process conditions, the final
PSDs together with the target PSD q d for different (d(u G ), d(u in )) and the surface
plot of optimal PSD q. Also here time-varying optimization parameters and thus