How is prosperous present in act 4 and the play as a whol

Prospero changes through the play so it is difficult to give you a detailed account on this short-answer forum. In act 4, Prospero wrestles with the idea of punishment. Prospero tries to dismiss his tyrannical demands for Ferdinand's service as "trials of thy love" but also makes mention in this first scene that he has "punished" Ferdinand, which implies a need for retribution for a wrongdoing He uses the love of his daughter and Ferdinand to satisfy his own need for vengeance.