ANAIS (Annual modulation with NaI Scintillators) is a dark matter direct
detection experiment consisting of 112.5 kg of NaI(Tl) detectors in operation
at the Canfranc Underground Laboratory (LSC), in Spain, since August 2017.
ANAIS' goal is to confirm or refute in a model independent way the DAMA/LIBRA
positive result: an annual modulation in the low-energy detection rate having
all the features expected for the signal induced by dark matter particles in a
standard galactic halo. This modulation, observed for about 20 years, is in
strong tension with the negative results of other very sensitive experiments,
but a model-independent comparison is still lacking. By using the same target
material, NaI(Tl), such comparison is more direct and almost independent on
dark matter particle and halo models. Here, we present the annual modulation
analysis corresponding to three years of ANAIS data (for an effective exposure
of 313.95 kg$\times$y), applying a blind procedure which updates that developed
for the 1.5 years analysis, and later applied to 2 years. The analysis also
improves the background modelling in the fitting of the region of interest
rates. We obtain for the best fit in the [1-6] keV ([2-6] keV) energy region a
modulation amplitude of -0.0034$\pm$0.0042 cpd/kg/keV (0.0003$\pm$0.0037
cpd/kg/keV), supporting the absence of modulation in our data, and incompatible
with DAMA/LIBRA result at 3.3 (2.6) $σ$, for a sensitivity of 2.5 (2.7)
$σ$. Moreover, we include two complementary analyses: a phase-free annual
modulation search and the exploration of the possible presence of a periodic
signal at other frequencies. Finally, we carry out several consistency checks
of our result, and we update the ANAIS-112 projected sensitivity for the
scheduled 5 years of operation.