Caliban himself explains how it is that Prospero came to have control over him. We know that Caliban is at least partly animalistic, perhaps more animal than human; he is described as having been "litter'd" like a puppy, the offspring of Sycorax the witch and the Devil.
Like an animal, then, he responds to affection and empathy—in act 1, scene 2, Caliban says (speaking to Prospero) that when Prospero first arrived, "thou strok'st me and made much of me," like a man trying to gain the favour of a cat. This worked—Caliban was then happy to show Prospero all the "fruits" of the island, in return for what seems to be Prospero teaching Caliban language: "how to name the bigger light and how the less/That burned by day and night."
After this, Caliban says, he loved Prospero; before Prospero, we can infer, nobody had ever showed Caliban kindness or attention,...
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