What is the output of a PID controller (or any controller in general)?
The same as with any math equation representing reality, you have to keep track of your units. The output of a PID will be in whatever set of units you design it to be. 

However, although this is often ignored, PIDs represent continuous systems and Nyquist theorem still applies. Discrete-time, quantized, or saturated-variables PIDs introduce other considerations that will affect behavior. Some times for the better other times for the worse. 

Any discontinuous or quantized element, such as an IGBT, requires this behavior to be modeled and, very likely, designed-around so that the PID can remain (mostly) continuous and common design heuristics can still apply.