My doubts are:

- what's the difference between "Input" and "Input_PER"? When should I use the first one, when the second one? What should I do with the unused input? Leaving it floating or putting some dummy value? (zero?)

- similar question about "Output" and "Output_PER".

Hello salrandazzo;
Let's see if we can answer some of your questions.
By the way, I must admit I have never used the PID instruction with a S7-1200, these answersare based on my experience with S7-300 and S7-400 PLCs; the algorithm seems to bethe same implementation, basically.
The information in the attached document is extracted from the following source:
SIMATIC S7 S7-1200 Programmable controller

1- As you can see in the attachment, Input is a REAL variable, which means a floating-point value that has been scaled to give you enginnering units; 0.0 - 100.0%, 10.0 - 250.0 gpm... Input_PER is a word value, expressed in binary (_PER means "periphery", or analog channel). The value expected here is the address of the analog input channel (PIWxxx) where the process value will be read by the CPU; you do not scale this value. In you case, your signal being 4-20 mA will be digitized in a 0-27648 by the analog input card A/D circuit, and the PID loop will use this value directly in its calculations.

2- Same thing for the outputs. "Output" should be sent to an unscaling block before it can be used by the analog output channel to control your valve, or motor... Whereas Output_PER is already expecting the analog channel address as a parameter(PQWxxx), where the D/A circuit of the module will output the correct voltage (in your case).

3. A PWM output is generally used to control heating solenoids, in resistance coil applications.

4. Correct.The value of ManualValue will be sent to both Output and Output_PER (notice that they can be both active inparallel, so you can send the controller output value to the controller (directly to the analog output channel)and to the HMI (in Engineering units) in parallel if you want to

5. As you can see in the attachment, the value"w - x" is recurrent in all three sections of the PID equation. This is the "error", calculated internally at every cycle of the PID loop, and the calculation of the controller output is an amalgam of Proposrtional, Integral and Derivative terms appliedto this error.

Hope this helps,
Daniel Chartier

Edit: You might be interested in the following link provided by Siemens. It presents a series of tutorials on the programming of the S7-1200 PLC.
Chapter M06 introduces closed-loop control (PID) and should help you clarify some of your issues.
http://www.automation.siemens.com/mcms/sce/en/advanced_training/training_material/download_training_material/m_series_simatic_s7_1200_sps/pages/default.aspx?HTTPS=REDIR
D.C.