In particular, say I have a dynamic model of the inverted pendulum / cart as described here. Instead of using the error difference in force to input into my controller, I want to take into consideration a motor driver (voltage input) to a DC motor for the force. Would the best method then to analytically describe the force relationship to the voltage input? If so, then would I need to include a voltage state variable so that I can build a controller based on that signal?
My motivation for asking is that I feel I have a fundamental disconnect with controls engineering. In my studies I've gone over classical and modern theory without the benefit of actually applying theory to application. Most of what I participate in deal with electromechanical systems, but most books, articles, etc I come across don't really delve into the physical interpretation of the plant input. I would appreciate any feedback on the matter.