We investigate the evolution of the galaxy star formation rate function (SFRF) and cosmic star formation rate density (CSFRD) of z similar to 1-4 galaxies, using cosmological smoothed particle hydrodynamic (SPH) simulations and a compilation of ultraviolet (UV), infrared (IR) and Ha 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 Ha 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 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 similar to 1-4 is the presence of a feedback prescription that is prominent at high redshifts (z >= 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.