Transfer Function of DC motor in s domain

Objective
To do the derivation for the DC motor transfer function.

Activity
Find the derivation for the transfer function of DC motor in s domain.

Analysis
The derivation of the DC motor transfer function can be seen below:

DC motor model

The transfer function for the DC motor is:

Gv(s)=(θ(s))/V(s) =K/([(R+Ls)(Js+b)+K^2])

We assume the physical parameter of the motor is:

* moment of inertia of the rotor (J) = 0.01 kg.m^2/s^2
* damping ratio of the mechanical system (b) = 0.1 Nms
* electromotive force constant (K=Ke=Kt) = 0.01 Nm/Amp
* electric resistance (R) = 1 ohm
* electric inductance (L) = 0.5 H
* input (V): Source Voltage
* output (theta): position of shaft
* The rotor and shaft are assumed to be rigid