  In the framework of the study of the Galactic metallicity gradient and its
time evolution, we present new high-resolution spectroscopic observations
obtained with FLAMES and the fiber link to UVES at VLT of three open clusters
(OCs) located within $\sim$7~kpc from the Galactic Center (GC): NGC~6192,
NGC~6404, NGC~6583. We also present new orbit determination for all OCs with
Galactocentric distances (R$_{\rm{GC}}) \leq$8~kpc and metallicity from
high-resolution spectroscopy. We aim to investigate the slope of the inner disk
metallicity gradient as traced by OCs and at discussing its implication on the
chemical evolution of our Galaxy. We have derived memberships of a group of
evolved stars for each clusters, obtaining a sample of 4, 4, and 2 member stars
in NGC~6192, NGC~6404, and NGC~6583, respectively. Using standard LTE analysis
we derived stellar parameters and abundance ratios for the iron-peak elements
Fe, Ni, Cr, and for the $\alpha$-elements Al, Mg, Si, Ti, Ca. We calculated the
orbits of the OCs currently located within 8~kpc from the GC, and discuss their
implication on the present-time radial location. {The average metallicities of
the three clusters are all oversolar: [Fe/H]= $+0.12\pm0.04$ (NGC~6192),
$+0.11\pm0.04$ (NGC 6404), $+0.37\pm0.03$ (NGC 6583). They are in qualitative
agreement with their Galactocentric distances, being all internal OCs, and thus
expected to be metal richer than the solar neighborhood. The abundance ratios
of the other elements over iron [X/Fe] are consistent with solar values. The
clusters we have analysed, together with other OC and Cepheid data, confirm a
steep gradient in the inner disk, a signature of an evolutionary rate different
than in the outer disk.
