Stepper overheating in closed loop control

Hi everyone,
Hope you are all doing well. I've a problem regarding overheating of a stepper motor.In particular, the machine is a three-axis printer with the addition of a fourth axis as an extruder. The extruder axis has a closed-loop signal to monitor the position through an optical encoder (mounted directly on the stepper motor for the axis). The loop is closed through a PID control, you can find both the hal and ini files attached.The motor tends to get extremely hot (cannot touch it) while the driver does not heat up. I've already set the current to the minimum value for the stepper driver (DM542T) and enabled half-current setting.   The printer is controlled through a MESA 7i80db board interfaced with a 7i76 which both controls the motors and reads the encoder.Do you have any suggestions on how to solve this issue?

Thanks

What current is the motor rated for?
What is the minimum current set on the drive?
Not a software issue.
Extruder is always on during print working at relatively slow speeds, so heating is normal as long as you can keep the hand on the motors or up to 80C.
80C seems like very very hot to human hands, but it can not burn the skin for short periods of time.
Another way to check is smell the motor back side where the shaft hole is, if it does not stink as burning enamel, it is OK.

The motor is rated for 1.2 A per phase @ 4V (model sy42sth47-1206b), while the current limit for the driver is 0.71 A RMS (1 A peak). The driver outputs 24 V. No smell coming out the motor but the motor is still too hot to keep hands on it.

I would not worry to much ...

The reason why I asked in the first place is that without the closed looped the motor does not heat as much. Do you think there could be something to be improved in the configuration? Maybe in the PID parameters? Thanks.

Not an expert, but my initial thought is that the drive is programmed to switch to half-current if there is no input command for some time value (.5ms or so).  When running open loop the drive drops the current - and motor heating - whenever it can.

With the external PID loop, the drive is constantly getting corrections - possibly a bit of a mismatch between encoder counts, step distance, and following error tolerance in the control.  This causes the half-current motor cooling drive feature to never kick in.

Check if the half-current feature is turned on in the drive - if so, that might partly confirm my guess.  This may be one of those times where closing the loop at the drive (i.e. an OEM closed loop) rather than back to LCNC is preferred.

Once you figure it out you can then decide if you even care - the motor may be hot but not TOO hot.