in act 4 why does Prospero punish Ferdinand by forcing him to carry logs?

In Act I, 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 (IV.i.6). The word "punished" that he uses recalls the fabricated charges Prospero raises against Ferdinand in the first act, of Ferdinand being a spy or a potential usurper; and the irony is that Prospero heaps his suspicion on Ferdinand, who has no such designs, while forgetting the very real plots of Caliban and his brothers.