# Servo Motor Input Voltage Equation

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?

• To me the word "servo" in the context of motors covers a very large range of equipment. Could you be a bit more specific on the model/type?
– NMech
Sep 13, 2021 at 18:04
• @NMech I'm using an ES9258 Sep 13, 2021 at 18:20
• K_m looks like the back-EMF constant? Anyway as an approximation you can measure most of them. For the back EMF, rotate it at a constant RPM from an external source, and observe voltage on an oscilloscope. This lets you measure both RPM and voltage amplitude. For Ra, measure it while immobilized by putting a known current into it. For L you can run sinusoidal current through it, although I don't think it will be all that that constant vs either frequency nor RPM. All this is just so that you can control the current (unless you have a light load). Sep 13, 2021 at 21:54
• "servo" may itself be just a dc motor, a potentiometer, and a circuit providing negative feedback to drive the potentiometer to a position. model away, don't forget to take measurements as you go to validate pieces of your model, and tweak the model if it is too simple to match truth
– Abel
Sep 14, 2021 at 1:42