Answer:
While changing into passive voice, the tense will never be changed.
Also, Inter-conversion of subject and object:
I have done nothing to displease him
I is Subject, nothing is object and the underlined words are a prepositional clause the position of which will remain the same in passive voice.
Passive Voice:
Nothing has been done by me to displease him. (Tense i.e. Present perfect tense hasn't been changed)