how to simulate the pid on PC, without actual devices

[MiKiJT]

how to simulate the pid on PC, without actual devices

[drf5n]

You would need to simulate the missing devices to make the system provide the feedback from the PI/D Output into the PID Input. Otherwise it is open-loop, and the PID will not produce sensible results.

[TuxLeon]

The dependencies to the HW and Arduino are very little.
I don't see any dependency to HW.
There is only one dependency to Arduino.h. This ist the function millies() in the line
unsigned long now = millis();

So if you provide a Arduino Stub with the implementation of this function you should be fine to compile PID_V1.cpp on your PC.
To get some output you should
-instantiate PID
-periodically call PID::Compute() and increment the the milli seconds in the Millies() stub
-Inputs and Outputs of the PID are provided by pointers. So should be quite easy. The example folder should help you.