Was it obligatory for him to pray tahajjud

Those from the salaf and the khalaf disagreed as to if it was obligatory or not for the Messenger of Allaah (sallallaahu alayhi wa sallam) to pray the tahajjud prayer.

Both groups derive evidence for their position from the following Qur'aanic Verse:

And from [part of] the night, pray with it as additional [worship] for you; it is expected that your Lord will resurrect you to a praised station.

[Qur'aan 17:79 - Sahih International Translation]

The word translated above as "additional [worship]" is naafilah.

The group that argues it was not obligatory for the Messenger of Allaah (sallallaahu alayhi wa sallam) says that the word naafilah is explicit evidence that it was not obligatory for him as the very word means optional. 

The second group says that it was obligatory and argues that the word naafilah is not used here in its meaning which is the opposite of obligatory. Rather, it is used in the meaning of ziyaadah [extra]. 

Allaah ordered him to pray the prayer, and the naafilah means that it will raise his (sallallaahu alayhi wa sallam) ranks. It does not mean that it is optional for him (sallallaahu alayhi wa sallam).  

Reference(s):

tamaam al-minnah

Volume 1 Page 382