I'm working on a Ball & Beam project. As I'm doing it for an engineering project, I'm supposed to model the system mathematically, calculate the PID parameters, etc. to center the ball in the middle of the beam. I'm using Arduino for this project and a servo motor to rotate the beam. A step of modelling the system is to find the input voltage of the servo, in order to find the transfer function of the system. I've come across many research papers using this equation to find it:
This is a general motor equation, with I being the armature current, Ra being the armature resistance, Km as the motor torque constant, etc. My question is: Is there a way, if they exist, to find thsese values for a servo motor? The other question is, does a servo motor even have varying voltage input to begin with, or is its input a constant one, i.e. the rated one in its datasheet?