Woyzeck is psychologically real, and in my view Georg Büchner was ahead of his time in creating such a character in the early nineteenth century, when dramatists were beginning to explore themes not dealt with previously on the stage.
Woyzeck is a working-class man who is a victim of forces around him which he cannot control or understand. The Captain treats him almost as a non-person and is befuddled by Woyzeck's attempt to explain that it's difficult for a person who has no money to be "moral" in the way the Captain requires. This comes after the Captain has criticized Woyzeck for the child he has had with Marie "without the blessing of the church." The Captain, despite (or conversely, because of) his holier-than-thou attitude, is also mystified by the text Woyzeck quotes from the New Testament in which Jesus blesses the children.
The Doctor is another member of the establishment who ridicules and abuses Woyzeck, experimenting on him by a restricting his diet to peas and then congratulating himself that Woyzeck is feeling the adverse effects of it. Finally, Marie, the one person Woyzeck believes loves him, cheats on him with the Drum Major. Driven mad by the abuse and deprivation of his life, he takes it out on Marie and murders her, thus destroying his own life, bleak as it was to being with.
Woyzeck is a man suffering from trauma, and in this sense especially, he is one of the most psychologically realistic characters in drama. Arguably, it was not until the modernist period, nearly a century after Büchner's time, that authors as diverse as Bertolt Brecht and Arthur Miller would similarly deal with the "little man" in socially relevant drama.