DC Motor Velocity

A common problem for Mechanical Engineers is the control of an armature$-$controlled

DC motor. In this problem we will control the velocity of the motor.

The following model, values and equations describe the behavior of the motor:

Rotor moment of inertia $(J)=0\mathrm{.}05kg\frac{m^2}{s^2}$

Mechanical damping $($b$)=0\mathrm{.}1Nms$

Electromotive Force $(K)=0\mathrm{.}01N\frac{m}{a}mp$

Electrical resistance $(R)=1$ ohm

Electrical inductance $(L)=1H$

$V=$ input voltage

$=$ output position of shaft

$w=$ output velocity of shaft

Motor Torque $(T)=K$ i $($where i is the current in the armature circuit$)$

Back emf $(e)=$ K w

a$.$ Using what you know about the mechanics of a rotating shaft, an R$-$L circuit and the

above equations and constants, derive the differential equations that describe the system.