  We study periodically driven closed quantum systems where two parameters of
the system Hamiltonian are driven with frequencies $\omega_1$ and $\omega_2=r
\omega_1$. We show that such drives may be used to tune towards dynamics
induced freezing where the wavefunction of the state of the system after a
drive cycle at time $T= 2\pi/\omega_1$ has almost perfect overlap with the
initial state. We locate regions in the $(\omega_1 ,r)$ plane where the
freezing is near exact for a class of integrable and a specific non-integrable
model. The integrable models that we study encompass Ising and XY models in
$d=1$, Kitaev model in $d=2$, and Dirac fermions in graphene and atop a
topological insulator surface whereas the non-integrable model studied involves
the experimentally realized one-dimensional (1D) tilted Bose-Hubbard model in
an optical lattice. In addition, we compute the relevant correlation functions
of such driven systems and describe their characteristics in the region of
$(\omega_1,r)$ plane where the freezing is near-exact. We supplement our
numerical analysis with semi-analytic results for integrable driven systems
within adiabatic-impulse approximation and discuss experiments which may test
our theory.
