The five books of Psalms follow the pattern of the Torah, which in turn follows the five-fold pattern of all the biblical Covenants:
Transcendence (God's authority - who's the boss?)
...Hierarchy (Delegated authority - who's in charge?)
......Ethics (What are the rules - what do I do?)
...Sanctions (What do we get - blessings and curses)
Succession (The future - what's next?)
(In history, this five fold pattern opens into a sevenfold pattern, because the Ethics are triune:
So if the five books of Psalms follow the five books of Moses, the subject matter of each section would generally correspond. Ray Sutton has an analysis of the Psalms as an appendix (page 225) in his book on this Covenant structure (That You May Prosper; Dominion By Covenant [PDF]).
In my book on the Covenant structure (Bible Matrix II: The Covenant Key), I include many other examples which follow the pattern, including some of the Psalms, and the parable of the Good Samaritan.
Perhaps the most interesting is the book of Revelation, which is a Covenant lawsuit against the first century Covenant breakers, just as Ezekiel's revelation was in his day:
Transcendence: Vision of Jesus (7 attributes - Sabbath)
Hierarchy: The Churches (7 lamps - Passover)
The New Covenant Scroll given (7 eyes and horns - Firstfruits-Nearbringing)
The New Covenant opened ( 7 seals - Pentecost - Gospel as four horsemen)
The New Covenant received (7 Trumpets - Trumpets - final apostolic warnings)
Sanctions: (Seven Bowls of Judgment - seven sprinklings/Atonement- Coverings - tribulation as first goat, Jewish war as second goat)
Succession: A New World (Booths/Ingathering - Satan bound from gathering the nations)
What is really cool is that this Covenant pattern (a five with a triune three at the centre, making it a seven) is found throughout the Bible at every level:
and told the people
Ethics 1 (Law given - Presentation)
all the words of the Lord
Ethics 2 (Law opened - Purification)
and all the rules.
Ethics 3 (Law received - Transformation)
And all the people
Sanctions (Oath - Vindication)
answered with one voice and said,
Succession (Future - Representation)
“All the words (ethics1)
that the Lord has spoken (ethics2)
we will do.” (ethics3)
Check out Sutton's book. I don't agree with everything (I have a different take on the Ten Words, based on the Jewish division) but it's a great intro.