  We investigate the evolution of the galaxy Star Formation Rate Function
(SFRF) and Cosmic Star Formation Rate Density (CSFRD) of $z\sim 1-4 $ galaxies,
using cosmological Smoothed Particle Hydrodynamic (SPH) simulations and a
compilation of UV, IR and H$\alpha$ observations. These tracers represent
different populations of galaxies with the IR light being a probe of objects
with high star formation rates and dust contents, while UV and H$\alpha$
observations provide a census of low star formation galaxies where mild
obscuration occurs. We compare the above SFRFs with the results of SPH
simulations run with the code {\small{P-GADGET3(XXL)}}. We focus on the role of
feedback from Active Galactic Nuclei (AGN) and supernovae in form of galactic
winds. The AGN feedback prescription that we use decreases the simulated CSFRD
at $z < 3$ but is not sufficient to reproduce the observed evolution at higher
redshifts. We explore different wind models and find that the key factor for
reproducing the evolution of the observed SFRF and CSFRD at $z \sim1-4$ is the
presence of a feedback prescription that is prominent at high redshifts ($z \ge
4$) and becomes less efficient with time. We show that variable galactic winds
which are efficient at decreasing the SFRs of low mass objects are quite
successful in reproducing the observables.
