  In this contribution, a novel Reduced Order Model (ROM) formulation of the
grey-box model proposed in Elkhashap et al. (2020a) for the pharmaceutical
continuous vibrated fluid bed dryer (VFBD) is presented. The ROM exploits the
$\mathcal{H}_2$-norm projection-based model order reduction method after a
special solution formulation of the model's infinite-dimensional part. This is
mainly by introducing a vector field mapping between the model parts casting
the semi-discretized PDE into a bilinear form. The ROM produced is then
integrated into an nonlinear Kalman Filtering-based observer design also
handling the estimation of the model's algebraic variables. Evaluations of the
FOM, ROM, ROM-based observer variants, and the FOM-based observer are performed
using Monte-Carlo simulations as well as simulations based on experimental data
of the real system. It is shown that the ROM could reproduce the FOM states
accurately with a relative mean square error below $0.3\,\%$ for the
experimental data simulation. This is while reaching a computational-time
reduction up to a factor of $40$. The ROM-based observer with algebraic states
correction is shown (using Monte-Carlo simulations) to be able to converge to
the true values for all cases regardless of initialization. Moreover, it is
also shown that the performance degradation of the observer due to reduction is
practically insignificant. This is while the computational speedup of the
observer due to reduction reached a factor of more than third order of
magnitude.
