EPR verses N1
On modern turbofan engines, thrust is more accurately controlled by setting fan speeds, particularly engines with large fans (GE90, etc.). This is because all of the airflow is pumped by the fan rotor. The core rotor (compressor) only handles a portion of the airflow, a lesser amount of the total, as the fan size increases in diameter. That said, as the fan speed and core speeds are coupled, thrust can be accurately modulated by scheduling core speed as a function of PLA (Power Lever Angle). A speed curve can be generated. This is a curve of corrected fan speed verses corected core speed, or corrected core speed verses thrust.
Earlier turbofan engines used core speed control exclusively. In other words, the pilot set EPR including fan speed with the throttle. Speed is affected by various parameters like engine component efficiencies and stackups (relationship of one component to another), altitude, mach number, schedule tolerances and deteriorations. Therefore, core speed is not an optimum manipulated variable to set fan speed. Override controls have been established to allow for direct scheduling of fan speed in a limited PLA range, usually in the takeoff or max climb PLA regions. Fan speed is typically controlled as a function of T2 (engine inlet temperature) which results in corrected fan speed.
Obviously, this may be debatable as historic practices differ from one engine manufacturer to another and even differences in basic engine design, two spool verses three spool.