I'm looking for a "bogo process" transfer function for a PID loop plant. That is to say something that's not real hardware but just so I can calibrate the software/ensure that the loop is generating sane values prior to connecting it to a real plant and working on tuning.
The "bogo loop" would just be say PID core -> PWM output/DAC -> analog filter -> back into uP via ADC -> digital filter representing the transfer function of some idealized plant and sensor -> "virtual" ADC -> control value/input summer/error amp -> PID core
Again this isn't to derive any kind of tuning parameters representative of the real world, just to sanity-check the software implementation by e.g. transmitting real-time values at various nodes in the loop over serial to a PC and logging them.
Like maybe a "generic" heater + temperature sensor model or something that generates a vaguely realistic lag for some parameters of thermal time constant, max power output, and Vout/degree for the sensor