  We investigate the effect of an additional modulation parameter $\delta$ on
the mobility properties of quasiperiodic lattices described by a generalized
Ganeshan-Pixley-Das Sarma model with two on site modulation parameters. For the
case with bounded quasiperiodic potential, we unveil the existence of
self-duality relation, independent of $\delta$. By applying Avila's global
theory, we analytically derive Lyapunov exponents in the whole parameter space,
which enables us to determine mobility edges or anomalous mobility edges
exactly. Our analytical results indicate that the mobility edge equation is
described by two curves and their intersection with the spectrum gives the true
mobility edge. Tuning the strength parameter $\delta$ can change the spectrum
of the quasiperiodic lattice, and thus engineers the mobility of quasi-periodic
systems, giving rise to completely extended, partially localized, and
completely localized regions. For the case with unbounded quasiperiodic
potential, we also obtain the analytical expression of the anomalous mobility
edge, which separates localized states from critical states. By increasing the
strength parameter $\delta$, we find that the critical states can be destroyed
gradually and finally vanishes.
