Best way is to start with each individual process and explain how each process should work. For example if you have an influent pump station, that would be on process area. Explain how you want the pump station to work.

Thank you for your feedback, I am more interested in the documentation, For example, I would apparently need a document called Operating and control philosophy and another one called Cause & Effect Matrix.

I do not have any knowledge on how to elaborate them, this is a first for me,

I am improvising, so, any recommendation will be helpful at this stage.

If written what you are calling for is call a functional description. It is just a narrative describing how you, the engineer wishes to have the system operate. For example from a recent specification:

"In the DO Setpoint Mode the operator shall enter a dissolved oxygen setpoint for each oxic zone. Upon receiving DO setpoints from the HMI, PLC-B will execute a PLC PID loop to compare each oxic zone DO measurement with the DO setpoint. PLC-B will then modulate the air control valve to each oxic zone in order to match the DO setpoint using most open valve logic. The re-aeration zone (Oxic Zone 11 / OX-11) will be controlled to maintain an operator adjustable constant airflow. PLC-B shall compare the airflow entering OX-11 and modulate the zone 11 control valve accordingly to meet the setpoint."