From Feud’s perspective Macbeth represents the Id, Macduff represents the Ego, and Lady Macbeth represents the Super-ego.
Lady Macbeth is often considered to represent the Super-ego. The Super-ego is Freud’s term for wanting to satisfy your own narcissistic tendencies. She seems to think that she should be queen, and therefore her husband should kill Duncan to get her what she wants—but she does not want to do it herself.
Had he not resembled
My father as he slept, I had done't. (Act 2, Scene 2, enotes etext p. 29)
Lady Macbeth giddily talks about cracking her baby’s head open after nursing it, but she can’t kill Duncan. She sets everything up, but then makes him do it!
Macbeth represents the Id from Feud’s perspective. The Id is the pleasure center of our consciousness, according to Feud. Macbeth always acts on impulse. He wants to be king because the witches told him he would be king, and his wife is egging him on. Macbeth is impressed with his wife’s ruthlessness.
Bring forth men-children only,
For thy undaunted mettle should compose
Nothing but males. (Act 1, Scene 7, p. 24)
Between the two forces of encouragement, Macbeth can’t say no. He does kill Duncan to get the throne, and then finds himself in an endless cycle of killing in order to keep it.
At stark contrast to Macbeth and his wife, Macduff represents the Ego. The Ego represents reality, and Macduff is always rooted in reality. He is honest and loyal, and while he is sensitive and compassionate he is also intelligent. When Macbeth drives Malcolm out, Macduff works hard to help him gather an army to retake the throne, even after Macbeth kills his entire family.
But, gentle heavens,
Cut short all intermission; front to front
Bring thou this fiend of Scotland and myself;(270)
Within my sword's length set him; if he 'scape,
Heaven forgive him too! (Act 4, Scene 3, p. 74)
Even though his family is dead and he wants to grieve, he realizes that he has to keep going. The only way to end Macbeth’s tyranny is to help Malcolm retake the throne.