  We present a suite of galaxy formation simulations that directly model star
cluster formation and disruption. Starting from a model previously developed by
our group, here we introduce several improvements to the prescriptions for
cluster formation and feedback, then test these updates using a large suite of
cosmological simulations of Milky Way mass galaxies. We perform a differential
analysis with the goal of understanding how each of the updates affects star
cluster populations. Two key parameters are the momentum boost of supernova
feedback $f_{\mathrm{boost}}$ and star formation efficiency per freefall time
$\epsilon_{\mathrm{ff}}$. We find that $f_{\mathrm{boost}}$ has a strong
influence on the galactic star formation rate, with higher values leading to
less star formation. The efficiency $\epsilon_{\mathrm{ff}}$ does not have a
significant impact on the global star formation rate, but dramatically changes
cluster properties, with increasing $\epsilon_{\mathrm{ff}}$ leading to a
higher maximum cluster mass, shorter age spread of stars within clusters, and
higher integrated star formation efficiencies. We also explore the redshift
evolution of the observable cluster mass function, finding that most massive
clusters have formed at high redshift $z>4$. Extrapolation of cluster
disruption to $z=0$ produces good agreement with both the Galactic globular
cluster mass function and age-metallicity relation. Our results emphasize the
importance of using small-scale properties of galaxies to calibrate subgrid
models of star cluster formation and feedback.
