How does Prospero have control over Caliban?

Prospero has clearly got some control over Caliban.
However the extent of control is substantially lower than you would have thought.  In
act 1 scene 2, Miranda and Prospero visit Caliban. Miranda obviously doesn’t care about
control over him, “I do not love to look on,” all she wants is too stay away from him.
This is not her only vain moment in the play. Prospero however makes a great show of how
much power he has, how he can punish Caliban, yet Caliban is completely used to this
form of abusive behaviour that he replies with a non-sequitur. He is obviously immune to
his punishments by now.  That shows that he just ignores Prospero most of the time, and
doesn’t see him as a threat. However Prospero can control some aspects of Calibans life.
He controls where Caliban lives, what Caliban does, and where he is allowed to go.
Prospero cannot control what Caliban says to him. Prospero taught him their language, so
Caliban must have heard it from Prospero first.  In conclusion, Prospero controls
Caliban in the only way he knows how, with magic.